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Ch-31 Page 19 Monday, January 22, 2001 2:05 PM

FIGURE 31.7 Example application—“stress shielding.” An analysis of intramedulary fixation using the site-dependent strain energy density equations. (a) The simplified two-dimensional configuration showing a cortical shell with the displacement boundary conditions, an intramedullary rod, and the applied bending moment. (b) Shows the loss of bone that was simulated with the use of the most flexible stem design. (c) Much more severe bone loss is shown as a consequence of using the net remodeling simulation with the stiffest design, shown in (c). (From Huiskes, R. et al., J. Biomech., 20(11–12), 1135, 1987. With permission.) Ch-31 Page 20 Monday, January 22, 2001 2:05 PM

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FIGURE 31.8 Simulation of the gradual straightening of a femur that is broken and heals with a malposition. The simulation, not explicitly time-dependent, shows the implementation of the “CAO” program that seeks a shape that minimizes notch stress. (From Mattheck, C., Design in Nature, Springer-Verlag, Berlin, 1998. With permission.)

31.4.6 Strength Optimization: Fatigue Damage and Repair A more mechanistic method—that stops short of directly addressing the biological processes of adaptation—has been developed based on the hypothesis that “bone adapts to attain an optimal strength by regulating the damage generated in its microstructural elements.”59 Prendergast and Taylor59 hypothesized that there is some damage at RE (remodeling equilibrium), and that the rate of repair is associated with the damage rate. Ch-31 Page 21 Monday, January 22, 2001 2:05 PM

Bone Modeling and Remodeling: Theories and Computation 31-21

Mathematically, at RE, ˙ eff 0 and ˙ RE, where eff is the effective damage, ˙ is the current rate of damage production, and RE is the rate of damage production at RE. Then,59,60

t dX () ------C eff C ˙ ˙ RE dt, (31.26) dt t0

where X measures the extent of the remodeling process. This expression can be implemented as a site- speciﬁc theory by variation of either the constant, C, based upon location, or by including an initial variation in the remodeling equilibrium damage. Interestingly, it has been shown that the use of the damage stimulus is equivalent to using the strain energy density,61 although the damage stimulus may be easier to investigate experimentally.

31.4.6.1 Example Application: Ulnar Osteotomy The same ulnar osteotomy experiment by Lanyon et al.62 that was simulated using the theory of adaptive elasticity by Cowin et al.45 has also been simulated using the strength optimization method.60 A three- dimensional finite-element model of the sheep radius and ulna was developed using eight-noded linear isoparametric elements, shown in Fig. 31.9a. A finite-element analysis of the intact forelimb provided the distribution of damage at the remodeling equilibrium, calculated with a load simulating static stance. Then, following the removal of a portion of the ulna, and using a uniform constant, C, they generated a plot of the stress differences and damage distribution near the endocortical and periosteal surfaces, shown in Fig. 31.9b. Although the analysis shows the distribution of the adaptation stimulus rather than incrementally changing the shape, the strength optimization analysis needed only one remodeling rate constant, C. This is in contrast to three different remodeling rate constants needed to produce the simulation results shown in Figs. 31.4 and 31.5. “In particular the low strains on the endosteal surface, though they generate an appreciable strain and corresponding stress difference, do not generate a significant remodelling stimulus with this approach … this suggests that a damage variable may contain more of the nonlinearity of the remodelling process than does a strain variable.”60

31.5 Theoretical Models and Simulations: Trabecular Bone

This section provides a review of many of the theoretical models that have been developed and used to simulate trabecular bone adaptation, and closely follows a recent review of ﬁnite-element modeling for trabecular bone.30 Although continuum-level characterizations of the mechanical properties for trabecular bone depend primarily upon the solid volume fraction (i.e., the volume of pores is discounted), they also depend on the predominant orientation of the trabeculae. Thus, adaptation models intended to describe changes in continuum material properties have been developed to describe density changes with and without changes in anisotropy. In contrast, tissue-level descriptions are dependent only upon descriptions of trabecular shape—their size and orientation changes are manifested as volume fraction and orientation changes at the continuum level.

31.5.1 Adaptive Elasticity The theory of adaptive elasticity discussed previously for cortical bone adaptation has been supplemented to also simulate trabecular bone adaptation at the continuum level. In addition to a description for changing material properties, Eq. 31.5, by changing the volume fraction of material, Eq. 31.10, the changing anisotropy of material is also now described. Ch-31 Page 22 Monday, January 22, 2001 2:05 PM

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FIGURE 31.9 Another ﬁnite-element study of the adaptation to the ulnar osteotomy shown in Fig. 31.4. (a) Finite- element model of the intact sheep radius and ulna was developed using eight-noded linear isoparametric elements and analyzed to provide the distribution of damage at the remodeling equilibrium, corresponding to a load to simulate a static stance. (b) Approximate visualization of the stress difference for the intact and osteotomized conditions, and the corresponding damage-rate distribution calculated using the strength optimization equation. The dashed lines represent the stress; the crosshatched area represents the calculated damage distribution. (From McNamara, B. P. et al., J. Biomed. Eng., 14(3), 209, 1992. With permission.) Ch-31 Page 23 Monday, January 22, 2001 2:05 PM

Bone Modeling and Remodeling: Theories and Computation 31-23

Cowin defined a mathematical expression of Wolff’s trajectorial theory,41 and the mathematics also have an appealing intuitive description.63 The basis of the mathematical expression is the use of a second- rank tensor, called the fabric tensor,64 defined by stereological measures of predominant trabecular orientation.65,66 (Chapter 13 has a discussion of these measures.) Mathematically, Cowin points out that at remodeling equilibrium—defined in this case as the alignment of the trabecular orientations with the principal stresses—the product of any two of the second-rank tensors that define stress, T, strain, E, and the fabric tensor, H, must be commutative. Then, using the notation of X0 to represent the equilibrium value of X (where X can be T, E, or H) Wolff’s trajectorial theory can be expressed as

T 0E0 E0T 0, T 0H 0 H 0T0, H 0E0 E0H 0. (31.27) The intuitive description comes from using an ellipsoid to represent a second-rank tensor geometrically (strain, stress, or fabric) with the normalized length of the axes of the ellipsoid proportional to the value of the eigenvalues of the tensor, and the orientation representing the principal directions.41,63 Then, Fig. 31.10a can be used to represent an initial situation in remodeling equilibrium, indicated by the common alignment of the three ellipsoids used to represent the stress, strain, and the fabric. A perturbation in the stress is represented in Fig. 30.10b as a new alignment of the stress ellipsoid. The strain, which responds instantaneously to the changed stress, also has a new alignment, but is not yet aligned with the stress. The trabecular bone fabric, unable to change instantaneously, retains the original alignment. After some time during which the trabecular bone has time to adapt to the new stress imposed in Fig. 31.10b, a new remodeling equilibrium is achieved, as seen in Fig. 31.10c, where the ellipsoids are once again in alignment with each other, but in the new direction dictated by the new stress imposed in Fig. 31.10b.30 If only the relative degree of anisotropy is of interest, then the fabric tensor H can be normalized by making the trace equal to one, i.e., trH 1, and it becomes easier to manipulate mathematically.44

FIGURE 31.10 Intuitive description of Cowin’s ideas for trabecular realignment. (Top) Representation of an initial situation in remodeling equilibrium, indicated by the common alignment of the three ellipsoids used to represent the stress, strain, and the fabric. A perturbation in the stress is shown (middle) with a new alignment of the stress ellipsoid. The strain, which responds instantaneously to the changed stress also has a new alignment, but is not yet aligned with the stress. The fabric, unable to change instantaneously, retains the original alignment. After some time during which the trabecular bone has time to adapt to the new imposed stress, a new remodeling equilibrium is achieved (bottom). The ellipsoids are once again in alignment with each other, but in a new direction. (From Hart, R. T. and Fritton, S. P., Forma, 12, 277, 1997. With permission.) Ch-31 Page 24 Monday, January 22, 2001 2:05 PM

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Then, the deviatoric part of the normalized fabric tensor is a measure of the relative degree of anisotropy denoted by K, and is deﬁned as44

KH ()13 I. (31.28)

The stress–strain relationship can then be written as

TDK (), e E, (31.29) where e 0 is a measure of the change in solid volume fraction, , from a reference solid volume fraction, 0. This shows that the mechanical properties that express Hooke’s law are explicitly expected to be functions of both the amount of material present, as measured by the solid volume fraction, , and the orientation of the material, as quantiﬁed by a measure of the fabric, K. If it is assumed that the objective of the remodeling process is to reestablish the remodeling equilibrium

strain, then a speciﬁc bone location is in RE when the eigenvalues of the strain tensor, E1, E2, E3, are equal 0 to (or within an acceptable range of) the eigenvalues of the remodeling equilibrium strain tensor, E1 . 0 0 44 E2 , E3. Then two general rate equations can be written to describe the mechanically adaptive process of trabecular bone. One equation describes how the fabric changes with time,

dK dKK(), E, e ------ ------, (31.30) dt dt

and a second equation describes how the solid volume fraction changes with time,

de de()K, E, e ----- ------. (31.31) dt dt

The process of porosity and fabric changes would continue until the material was entirely void, entirely solid, or at remodeling equilibrium. To specialize and implement the ideas in Eqs. 31.30 and 31.31, Cowin et al.44 wrote them in polynomial form. Then, if higher-order terms are neglected, and if it is assumed that (1) the rate of change of the fabric depends only upon the fabric and the deviatoric strain (which measures distortion), and (2) that the rate of change of the bulk density depends only upon the bulk density and upon the dilatational strain (which measures change in volume), then Eqs. 31.29 through 31.31 can be approximated as

() ()() () ()()() () T g1 g2e trE I g3 g4e E g5 KE EK g6 I tr KE trE K , (31.32)

dK 0 0 3 0 0 ------ h ()Eˆ Eˆ h I()trK ()Eˆ Eˆ -- ()KE()ˆ Eˆ ()Eˆ Eˆ K , (31.33) dt 1 2 2

de 0 ----- ()f f e ()trE trE , (31.34) dt 1 2

where the circumﬂex indicates the deviatoric part of the indicated tensor, and g1 to g6, h1, h2, f1, and f2 represent constants. Cowin et al.44 calls this set of equations the “approximate noninteracting microstructure theory.” 31.5.1.1 Example Application: Fabric Reorientation The RFEM3D program, described previously for simulations of cortical bone adaptation, has been enhanced with the implementation of Eqs. 31.32 through 31.34.67 Several changes were made to the program to allow for evolution of trabecular porosity and orientation in the element stiffness matrices for trabecular bone elements.67,68 To test the implementation of the trabecular remodeling theory, an idealized ﬁnite-element Ch-31 Page 25 Monday, January 22, 2001 2:05 PM

Bone Modeling and Remodeling: Theories and Computation 31-25

FIGURE 31.11 RFEM3D simulation of idealized trabecular bone reorientation. (Top row) The initial remodeling equilibrium stress, strain, and fabric tensors. (Middle row) The new fabric tensor applied, with altered stress and strain tensors shown. (Bottom row) The new remodeling equilibrium stress, strain, and fabric tensors. (From Hart, R. T. and Fritton, S. P., Forma, 12, 277, 1997. With permission.)

model of a section of trabecular bone was constructed, representing a small column (10 10 20 mm) of trabecular bone (see Fig. 31.11). To ensure accurate results, a convergence test was conducted and an appropriate model (16 elements and 141 nodes) was chosen. Each element in the model measured 5 5 5 mm, the approximate minimum-length scale for valid fabric tensor measurement.69 For equilibrium conditions, the fabric was aligned with the global axes. Prescribed displacements in the axial direction were applied to the model, with the bottom surface constrained in the axial direction, along with the middle bottom node constrained in all three directions to prevent rigid-body motion. The initial equilibrium strains and stresses were calculated, and are shown along with the initial fabric tensors in the top row of Fig. 31.11. The tensors are illustrated with the principal components emanating from an icon placed at the centroid of each element. To perform an idealized example of trabecular bone adaptation, the stress and strain ﬁelds were altered by changing the principal fabric directions to an off-axis angle of 30 (Fig. 31.11, middle row). RFEM3D was then run using the trabecular remodeling routines incorporating Eqs. 31.32 through 31.34 to simulate the changes in the fabric tensor and solid volume fraction for the column. The remodeling rate constants were the same as in Cowin et al.,44 and were chosen so the net remodeling process takes approximately Ch-31 Page 26 Monday, January 22, 2001 2:05 PM

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160 days. After the simulated 160 days of net remodeling, results show that the stress, strain, and fabric tensor principal directions coincided once again (Fig. 31.11, bottom row). These results indicate that this computational implementation of the trabecular remodeling theory is able to simulate trabecular reorientation in response to altered stress and strain fields. The example was chosen as a convenient way to change the stress and strain fields in the bone, and the program was shown to reorient the bone correctly back to its equilibrium orientation similarly to the intuitive description of the alignment of the tensors shown in Fig. 31.10. 31.5.1.2 Trabecular Density and Orientation Models for Skeletal Morphogenesis Using a fundamentally different approach from adaptive elasticity, Fyhrie and Carter11 developed a theory to predict both the apparent density (or volume fraction) of bone and the trabecular orientation for a continuum description of trabecular bone material. First, they assumed that bone is an anisotropic material that tends to optimize its structural integrity while minimizing the amount of bone present. For trabecular adaptation simulations, they introduced the notion of an objective function of the form Q(,, T), which is dependent upon the apparent density (or volume fraction), , the orientation, , and the stress, T. Then, two special cases were examined: the case where the net bone remodeling objective is based upon the strain energy and the case where the objective is based upon the failure stress.11 An extension of this work to a comprehensive theory for relating local tissue stress history to skeletal biology was developed by Carter et al.12 The theory goes beyond the usual ideas for modeling functional adaptation by relating “tissue mechanical stresses to many features of skeletal morphogenesis, growth, regeneration, maintenance, and degeneration.”12 They make a case for the consistency of the theory with many of the features of skeletal biology, and argue that the role of mechanical influence upon the biological processes is more important than has previously been recognized. This assertion brings to focus the lack of verification for the ideas about the relative importance of genetics and environment in the development, growth, and maintenance of structural tissues. In an effort to use mechanical input as a regulator of the trabecular architecture in the proximal end of a femur, Carter et al.70 used finite-element models with multiple loads, noting that a single loading condition cannot reasonably be expected to be the stimulus for the full trabecular architecture. The time rate of the process was not accounted for, but rather it was assumed that there was a relationship between element density and an “effective stress” written as

()12M c K  M , (31.35) ni i i1

where c is the number of discrete loading conditions, K and M are constants, and n is the number of 11,12 loading cycles at the “energy stress,” defined as energy 2EavgU. As described subsequently, the objective of the study was to examine the influence of mechanical factors upon the trabecular architecture, and of note is the use of a non-site-specific rule (i.e., the remodeling objective is the same for all points in the bone). Beaupré et al.71 modified and extended the ideas to develop a time-dependent modeling/remodeling theory. The model is based upon using a daily “stress stimulus” with a continuum level measure, , defined as

1m  m ni i , (31.36) day

where ni is the number of cycles of load type i, i is the continuum level “stress” as above, and m is an empirical constant. Then, a piecewise linear approximation to an assumed bone deposition rate vs. tissue Ch-31 Page 27 Monday, January 22, 2001 2:05 PM

Bone Modeling and Remodeling: Theories and Computation 31-27

stress stimulus is proposed that could be used for “modeling,” i.e., net changes in external bone shape similar to Eq. 31.23:

c () ()c c w ; () w  1 b bAS 1 2 1 b bAS 1 () () c2 b bAS ; w1 b bAS 0 r˙  (31.37) () () c3 b bAS ; 0 b bAS w2  () () () c4 b bAS c3 c4 w2; b bAS w2 ,

where bAS is the attractor state stress stimulus (for remodeling equilibrium), b is the actual stress

stimulus, c1, c2, c3, and c4 are empirical rate constants, and w1 and w2 deﬁne the width of the normal activity region.71 The normal activity region allows for a “window” of values for the stress stimulus in which there would be no signal for net remodeling responses.29 In addition, by using Eq. 31.37 with histomorphometric relations and the data of Martin72 for descriptions of bone apparent density and surface area density, Beaupré et al.71 write a consistent equation for the rate of change of density (net internal remodeling):

˙ r˙Sv t, (31.38)

where ˙ is the time rate of change of the apparent density, r˙ is the linear rate of bone apposition, Sv is the bone surface area density, and t is the “true density” of the bone tissue, assumed to be the density of fully mineralized tissue. Thus, an error between the remodeling equilibrium state (called here the attractor state) and the present mechanical state drives the signals for bone formation or resorption. More recently, Jacobs et al.73 have proposed a different method for simulation of net trabecular remodeling that can account for both changes in the volume fraction of material present and in the alignment of the material. Their approach does not explicitly divide the realignment and the volume fraction changes as done by Cowin et al.44 Rather, Jacobs has chosen to operate directly upon the anisotropic stiffness tensor (with up to 21 independent constants, depending on the degree of anisotropy) that relates the stress and the strain. In that fashion, no a priori assumptions are needed for describing the elastic symmetry of the continuum approximation of trabecular bone behavior. This is significant because, although trabecular bone may be well characterized at the continuum level using orthotropic material properties (9 of the 21 constants are independent), there is reason to believe that during active realignment, a more general degree of anisotropy may be needed. Unfortunately, finding the 21 needed constants may not be practical, and the problem is now to assemble the structural stiffness matrix in its entirety. Thus, the advantage of separating out the measurable material properties (the bone matrix material properties) and the measurable structural properties (such as the fabric tensor) from the structural stiffness is lost. With the general approach of adding evolution equations to the general anisotropic stiffness tensor, two special cases have been studied.73 One approach was to assume that the stiffness changes in the stiffness tensor occur to maximize mechanical efficiency. The second case, more consistent with Wolff’s ideas, was for stiffness changes to occur in the principal stress directions. For this second case, the time rate of change of the stiffness tensor is written as the sum of the changes in the isotropic and anisotropic portions of the tensor. If the stress, T, is given by the product of the stiffness tensor, C, and the strain tensor, E, then the rate equation is written as the following:73

˙ ˙ ˙ C Ciso Caniso. (31.39)

The isotropic rate equation is the same as has been used previously, Eq. 31.37 by Beaupré et al.71,74 For the anisotropic portion, the magnitude of each principal stress is compared to the average magnitude of the principal stresses. If a principal stress component is larger (smaller) than the average, then the Ch-31 Page 28 Monday, January 22, 2001 2:05 PM

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magnitude of the stiffness corresponding to the component in question is increased (decreased). Thus, stiffening of the material property tensor occurs in the direction of overloading, whereas softening occurs in the direction of underloading.73 31.5.1.3 Example Applications: Trabecular Bone in the Femoral Head A 1989 paper by Carter et al.70 is one in a series based on the use of a two-dimensional finite-element model of the proximal human femur as the basis for the application of skeletal morphogenesis theories. The basic idea is to begin with a model in which the elements all have a uniform density distribution, to then apply loads and iterate the density of each finite element based on a remodeling rule, and compare the calculated density pattern to in vivo patterns. Using Eq. 31.35 with multiple loads, Carter et al.70 calculated density distributions shown in Fig. 31.12, which are similar to those seen in the proximal femur. However, the best correspondence was observed after the third iteration of the computational implementation and in subsequent iterations, the density distribution progressed to nonphysiological distributions. (Note that because time was not specifically incorporated into the model, the iteration number has significance only within the context of the implementation the

FIGURE 31.12 Examination of the distribution of trabecular bone density in the femoral head. (Top) The two- dimensional ﬁnite-element mesh. (Bottom) The predicted density distributions from Eq. 31.35 using multiple loads and a linear relationship between the density and the “effective stress.” The density distribution in the third iteration is closer to the in vivo distribution than that found in subsequent iterations (the seventh iteration is also shown). (From Carter, D. R. et al., J. Biomech., 22(3), 231, 1989. With permission.) Ch-31 Page 29 Monday, January 22, 2001 2:05 PM

Bone Modeling and Remodeling: Theories and Computation 31-29

FIGURE 31.13 Another examination of the distribution of trabecular bone in the femoral head. Density distributions were calculated based upon time-dependent density equations (Eqs. 31.36 through 31.38) with a similar two- dimensional ﬁnite-element model of the proximal human femur, shown in Fig. 31.12. The results are shown for an implementation using a “lazy zone” for 330 days, left, and 412.5 days, right. In contrast to the simulation shown in Fig. 31.12, this solution was convergent with calculated density distributions remarkably similar to physiological distributions. (From Beaupré, G. S. et al., J. Orthrop. Res., 8(5), 662, 1990. With permission.)

authors describe.) The authors believe that ignoring other biological influences prevented the mechanical model from converging to an equilibrium solution.70 Interestingly, as a consequence of the use of multiple loadings to determine the trabecular architecture, the trabecular orientations are no longer always perpendicular. This finding is at odds with Wolff’s firmly held presumption, and his consequently flawed observation, that the trabeculae can only intersect at right angles.75 In reality, the angles are not always at right angles (see Chapter 29). In 1990, Beaupré et al.74 used the time-dependent bone density equations (Eqs. 31.36 through 31.38) with a similar two-dimensional finite-element model of the proximal human femur, shown in Fig. 31.13. The implementation also used multiple load cases, but in contrast to the results obtained by Carter et al.70 the solution was convergent with calculated density distributions remarkably similar to physiological distributions. The results are “consistent with the hypothesis that similar stress-related phenomena are responsible for both normal morphogenesis and functional adaptation in response to changes in the bone loading.”74 They also note, however, that the response to changed mechanical loading may not be unique, consistent with Weinans et al.76 Jacobs et al.73 have used Eq. 31.39, which operates directly upon the full stiffness matrix with no a priori assumptions about the degree of anisotropy of the trabecular bone, to simulate the density distribution using a two-dimensional finite-element model of the proximal femur. The results were very similar to those obtained using an isotropic rule for density evolution,74 and are thus also remarkably similar to physiological distributions.

31.5.2 Trabecular Density: Strain Energy Dependence Huiskes et al.8 presented a theory for the density distribution of bone, as well as a computational implementation and preliminary applications in prosthesis design as discussed previously. In addition to the Eq. 31.23 for shape changes, Huiskes et al.8 proposed the following description of modulus changes:

C ()U ()1 s U ; U ()1 s U  e n n dE () () ------0; 1 s Un U 1 s Un (31.40) dt  () () () Ce U 1 s Un ; U 1 s Un, Ch-31 Page 30 Monday, January 22, 2001 2:05 PM

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where E is the elastic modulus for the point considered, U is the current strain energy density, Un is the

homeostatic value of strain energy density, Ce is a remodeling rate constant, and 2s is the width of the “lazy zone” representing a range of strain energy density values near the homeostatic value in which there is no net remodeling response. With no lazy zone, i.e., s 0, the equation can be rewritten as

dE ------ C ()UU . (31.41) dt e n

In 1992, Weinans et al.77 expanded upon computational work to simulate adaptive bone remodeling that was ﬁrst presented in 198978 and 1990.79 They used a time-dependent rule for regulation of density as follows:

d Ua ------ B ------ k , 0 , (31.42) dt  cb

where the apparent density is represented by (x, y, z), cb is the maximum density of cortical bone,

B and k are constants, and Ua represents the sum of the apparent strain energy density for the number of loading configurations being considered. To calculate the isotropic stiffness, the apparent density was used with the power law relation between density and Young’s modulus.80 31.5.2.1 Example Applications: Discrete Structures In 1992, Weinans et al.76 used Eq. 31.42 in a series of example applications using finite-element models. Rather than explicitly incorporate a new set of equations to account for the changing orientation of the trabeculae, they chose to use dense meshes of finite elements and apply Eq. 31.42 to each element. Each element in the mesh was originally given the same density and during the simulations could then reach ≈ ≈ one of three outcomes: become completely resorbed ( 0); become cortical ( cb); or remain cancellous with intermediate densities (0 cb). The simulations were performed for two-dimensional models of a proximal femur and a simple two-dimensional plate model with a linear loading distribution. The simple plate models, shown in Fig. 31.14, allowed for an investigation of the stability and uniqueness of the net remodeling equation (Eq. 31.42) and gave some surprising results. In particular, the plate model could be manipulated (by choice of the remodeling rate constants and the loading) to develop the appearance of a discrete structure, with some elements at “full” or intermediate densities, and other elements essentially “turned-off” with zero densities. In addition to creating “trabecular-like” structures, the simulations also sometimes produced “checkerboard” patterns of elements with full and zero densities.76 For these simulations, the solution—in terms of the discrete structures produced—was shown to be dependent upon the methods of postprocessing (averaging results gave the appearance of continuum solutions) and upon mesh refinement. The solutions prompted studies 81–83 to examine in more detail the stability and uniqueness of these solutions that give discrete structures, even though the methodology was initially dependent upon a continuum assumption. Interestingly, the checkerboard and mesh-dependent anomalies have been observed while computationally designing microstructures for new materials.84,85 In these cases, the checkerboarding was attributed to “poor numerical modeling of the stiffness of check- erboards by lower-order finite elements” and the mesh-dependency problem—nonconvergence of the solutions—was eliminated using ideas borrowed from image processing.85 The image-processing technique essentially allows for systematic averaging of results by “blurring” the results. The use of higher- order finite elements as an alternate means to eliminate the checkerboarding pattern has been suggested by Jacobs et al.86 and has also been suggested in the material design literature.84 Another computational remedy that prevents the checkerboarding was suggested by Jacobs et al.83 with the use of a “nodal approach” (density calculated at each node) as opposed to an “element approach” (density calculated at the element centroid). Beyond the computational remedies, Mullender et al.87 justify a “biological averaging” technique based on a spatial influence function, described next. This technique eliminates the checkerboarding by Ch-31 Page 31 Monday, January 22, 2001 2:05 PM

Bone Modeling and Remodeling: Theories and Computation 31-31

FIGURE 31.14 Analysis of the stability and uniqueness of adaptation solutions via density changes for a simple plate model. (a) Shows the plate with four-noded linear elements (5 5) and with additional mesh densities, including 10 10 and 20 20. The linear surface traction and boundary conditions are also shown. (b) The resultant density distributions are shown as a result of dependence of density upon strain energy density, as expressed in Eq. 31.42. The continuous structure has developed into a discrete structure with some elements at “full” or intermediate densities, and other elements essentially “turned-off” with zero densities. (Redrawn from Weinans, H. et al., J. Biomech., 25(12), 1425, 1992. With permission.)

distinguishing the sensor grid (the spatial arrangement of the osteocytes) from the actor cells (the osteoblasts and osteoclasts) and the ﬁnite-element mesh.87 Thus, the results of Weinans et al.76 have focused attention on some of the underlying difﬁculties in converting theories to computer implementations. Now it is widely recognized that the checkerboarding is simply a numerical artifact. However, the evolution of “trabecularization” in continuous structures is Ch-31 Page 32 Monday, January 22, 2001 2:05 PM

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a topic of continuing interest. Further research into the optimality, uniqueness, and stability of the proposed discrete structures is needed.

31.5.3 Trabecular Density and Orientation: Spatial Influence Function Recently, a mechanistic model has been proposed for the functional adaptation of trabecular bone by Mullender and co-workers.87,88 The basis of the model is the hypothesis that “osteocytes located within the bone sense mechanical signals and that these cells mediate osteoclasts and osteoblasts in their vicinity 88 to adapt bone mass.” Each osteocyte i measures its local mechanical signal, Si(t), assumed to be the strain energy density, and influences all other “actor” cells (osteoclasts and osteoblasts) with decreasing influence based on the distance from the osteocyte. Mathematically, this is achieved by the use of a “spatial influence function” written using an exponential form as

()() () di x D fi x e , (31.43)

where di(x) is the distance between osteocyte and location x, D is the distance from an osteocyte at which its effect is e 1, so that the inﬂuence of an individual osteocyte, i, decreases exponentially with distance

from the cell. The use of the inﬂuence function to modify the stimulus amplitude, Si(t), summed from each osteocyte results in the stimulus value, F(x,t):

N () ()()() F x,t fi x Si t k , (31.44) i1

where k is the reference strain energy density. Then the regulation of the relative density, m(x,t), is

dm()x,t ------ F()x,t for 0 m()x,t 1, (31.45) dt

where is a rate constant, and the elastic modulus at location x, given by

E()x,t Cm()x,t , (31.46)

where C and are constants. As described subsequently, this model has been used to investigate the “trabecularization” of bone in response to mechanical loading. 31.5.3.1 Example Applications: Tissue-Level Adaptations The two-dimensional computational examples give striking results. First, the spatial influence function solves the computational checkerboarding artifact that had been observed with some other finite- element approaches.87,88 Further, by using a tissue-level approach they show that initial idealized geometries with both uniform density distributions and lattice structures can give very similar “trabecularized” geometries during the computational simulations if they are loaded in the same fashion, as seen in Fig. 31.15. This computational test is a first step in showing the conditions needed for uniqueness of solutions. They also show that changing the direction of loading for the “trabecularized” geometries results in realignment of the trabeculae, and that severing a strut in the structure leads to its resorption and complete removal, as seen in Fig. 31.16. These computer simulations do a remarkably good job in mimicking a variety of the physiological behaviors of trabecular bone, and hold the real promise of providing a computational vehicle for simulation and study of the adaptive behavior of trabecular bone at the microstructural level. Ch-31 Page 33 Monday, January 22, 2001 2:05 PM

Bone Modeling and Remodeling: Theories and Computation 31-33

FIGURE 31.15 Trabecular bone density and orientation simulations from use of the spatial inﬂuence function. Trabecular-like patterns are formed from initial idealized goemetries with both uniform density distributions and lattice structures. The ﬁnal equilibrium directions of the trabeculae match the principal stress orientation from the applied loading. (From Mullender, M. G. and Huiskes, R., J. Orthrop. Res., 13(4), 503, 1995. With permission.)

FIGURE 31.16 Simulation of the trabecular bone response due to a severed trabecular spicule. The unloaded trabecular portion is resorbed, and surrounding spicules are thickened and realigned. (From Mullender, M. G. and Huiskes, R., J. Orthrop. Res., 13(4), 503, 1995. With permission.) Ch-31 Page 34 Monday, January 22, 2001 2:05 PM

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The notion of a spatial influence function has also been used by Smith et al.89 with models in which the trabecular surface bone is added and removed based on the osteocytic signals. These models explore the consequences of assuming that the “set point” is located exclusively in the bone-lining cells to compare with the assumption used by Mullender and co-workers 87,88 in which the “set point” is located in the osteocytes. The simulations show trabecular reorientations similar to those in Fig. 31.15. However, an interesting consequence of having the set point located in the bone-lining cells is that—even in the equilibrium configurations—the strain energy density varies throughout the structure. This is a result of having the strain energy in the bone-lining cell dependent upon the influence function summation, and thus upon the local configuration of the trabecular architecture. The surprising consequence is that the trabecular structure shows “implicit site dependence even though each cell has the same explicit set point.”89

31.5.4 Boundary-Element Implementation Rather than use finite elements, Luo et al.90 and Sadegh et al.10 have used two-dimensional boundary elements to model idealized trabecular adaptation at the tissue level. The advantage of the boundary- element method is that due to an extra integration step in derivation of the computational implementation of the method, the dimensional order can be reduced by one. Thus, two-dimensional problems can be solved with one-dimensional elements only on the periphery of the area, and three-dimensional problems can be solved with two-dimensional elements only on the surface of the volume. There is an additional advantage for the boundary-element method when used to model free-boundary problems because boundary elements sidestep many difficulties faced when finite-element mesh distortion leads to poor numerical performance or disappearing elements.17 Sadegh et al.10 demonstrate the implementation and feasibility of incorporating the phenomenological surface remodeling rate equation (Eq. 31.9) into a boundary- element method. 31.5.4.1 Example Applications: Mergers and Separations; Strain and Strain Rate For simulation of trabecular adaptation, the use of boundary-element methods is especially promising with microscale models. Sadegh et al.10 used a series of idealized trabecular models to show that the method can be used to simulate two adjacent trabeculae that join together in a single column or the separation of one into two separate columns, as shown in Fig. 31.17. Luo et al.90 used similar idealized boundary-element models to compare the computed differences in shape change when using dilatational strain and dilatational strain rate as the stimuli for the net remodeling response. First, they analytically demonstrated the equivalence of the stimuli in all cases except when the cyclic strain is always tensile. Consequently, in the cases when the stimuli are the same, the state of remodeling equilibrium is independent of the choice of dilatational strain or strain rate as the net remodeling stimulus. Luo et al.90 then used models of three idealized trabecular bone patterns (cruciform, square diamond, and “brick-wall pattern”) subjected to biaxial loads, and computationally demonstrated the analytical results. The computational examples (Fig. 31.18) showed that although the final shape was the same (for the cases where the two stimuli were shown to be equivalent), the two stimuli gave remarkably different evolutionary paths. The results seem to indicate this model does not suffer from some of the limitations in terms of uniqueness and stability that were observed with computational implementations of continuum-based models.

31.6 Discussion

The review provided in this chapter has described the fundamental concepts and assumptions inherent in development of models to describe the mechanical adaptation of bone. While not comprehensive, a number of adaptation models have been introduced, and example applications provided. As described recently by Currey 91 and seen in this review, many adaptation simulations have been developed and produce solutions that are qualitatively reasonable, and may ﬁt with experimentally reported results. However, Currey points out a major problem with the approach of developing theoretical models and observing their qualitative response. Does any one particular simulation produce a better solution than Ch-31 Page 35 Monday, January 22, 2001 2:05 PM

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FIGURE 31.17 Boundary-element implementation of adaptation used with microscaled trabecular models. Ideal- ized changes show that an original cruciform structure could either separate into two parallel struts (top) or join into a wide strut. (From Sadegh, A. M. et al., J. Biomech., 26(2), 167, 1993. With permission.)

another approach that has already been developed? The dilemma raised by this question is evident with the examples presented in this chapter. The six models describing cortical bone adaptation illustrate examples of optimization, phenomenological, and mechanistic models. The model applications represent the consequences of osteotomy, malalignment, and intramedullary implants. For trabecular adaptation, five models have been presented, again illustrating the three model types. The applications for trabecular adaptation represent a wide range of examples and use continuum-level and tissue-level models. Although there are a variety of implementation differences—time-dependent and time-independent simulations, site-dependent and site-independent remodeling rate constants, and a variety of different strain and stress stimuli—all the applications show qualitative agreement with some experimentally observed cortical and trabecular bone changes. Currey91 writes, “This is a fundamental difficulty if progress is to be made, because the literature becomes full of algorithms that predict real-life outcomes to some extent, but they are not matched against each other, there is no saying which is better than the others, so everybody can happily think that their own algorithm is satisfactory.” Certainly, a conclusion from the numerous theories and applications described in this chapter is that, at least for the simulations shown, bone models certainly seem to adapt to mechanical usage but seem not to be very picky about the specific mechanical stimuli used. It seems that any description of the mechanical situation can be successfully used to drive a satisfactory adaptation response. This apparently promiscuous response of bone to mechanical stimuli may be due to the choices used for parameters to monitor. For example, for axially loaded structures the areas of high axial strains also correlate to areas of high strain energy and to von Mises stresses. A study of 50 different mechanical parameters (six local strain components, six local stress components, three principal strains, three principal stresses, three strain invariants, three stress invariants, maximum shear strain, maximum shear stress, strain energy Ch-31 Page 36 Monday, January 22, 2001 2:05 PM

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FIGURE 31.18 Boundary-element implementation of idealized periodic elements to approximate trabecular geometries. In this case, models are used to compare the computed differences in shape change when using dilatational strain and dilatational strain rate as the stimuli for net remodeling response. This example shows that although the ﬁnal shape was the same when using dilatational strain (left) and dilatatational strain rate (right), the two stimuli gave remarkably different evolutionary paths. (From Luo, G. et al., J. Biomech. Eng., 117(3), 329, 1995. With permission.)

density, 21 spatial strain gradients of the six strain gradients and dilatation in the three local directions, the mechanical intensity scalar, Eˆ , and a signed strain energy density) shows that many of these parameters that have been used in adaptation simulations are highly correlated to one another.92 This correlation of mechanical parameters helps mask the true regulators of the adaptation process so that distinct starting Ch-31 Page 37 Monday, January 22, 2001 2:05 PM

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assumptions about the nature of the mechanical parameters can result in similar simulation solutions. To be more useful, the modeling assumptions should be more tightly coupled to biological parameters that can be histologically measured and manipulated.93 Currey points out that a second major problem is based on the tendency for simulations to be used with a single remodeling situation, with no indication that the method is appropriate for any other one.91 Again, which methods are best? He suggests that an algorithm be chosen as the “null hypothesis algorithm” that can satisfactorily solve a combination of idealized problems, and mirror experimental results as well. New algorithms should only be introduced to the literature if they prove superior to the “null hypothesis algorithm.”91 A response is offered by Huiskes.94 He points out the merit in using phenomenological models for predicting bone response even if the process is not yet well understood. He argues that the process of learning from each other as new ideas are tried and results published may be confusing, but is necessary while ideas and methods are incrementally refined and improved. Most important, he describes a specific example of how computational simulations may help in guiding experiments that can explore the mechanisms for adaptation. The specific testable hypothesis that arises from the spatial influence function87,88 is that osteocyte density may be related to trabecular architecture. This is an exciting insight, and could be quantitatively explored.94 As mentioned at the outset, the merit from adaptation simulations depends upon recognizing that the different approaches have different objectives and outcomes. Optimization studies help to further understanding of bone as a mechanical structure, but do not provide useful information about the physiological process of adaptation. Phenomenological models may be useful in framing experimental questions, testing the consequences of different starting assumptions, and for the predictions of outcomes. They may even be useful for preliminary stages of implant design. However, as the focus shifts toward introducing mechanisms into the phenomenological models, the real benefits of developing and imple- menting a variety of different theories for bone adaptation studies begin to emerge. The models can help focus in vivo experiments on quantification of assumed parameters. Specifically, further advances in simulating bone adaptation will come from addressing a number of key steps, concepts, and questions: the transducers involved in converting mechanical usage into cellular responses; the degree of and physiological mechanisms for site specificity in adaptive responses; the time dependence of mechanical stimuli and physiological mechanisms responsible; and the question of a remodeling equilibrium state, how it may be initially set, and how it might be reset over time. As inspired by Currey’s91 comments, the use of a “test suite” of example problems would prove useful as theories are developed and refined. A suite of problems could be solved using a variety of algorithms and assumptions—especially including cases that fail to produce reasonable solutions— and would help to improve these methods incrementally. Specific examples for the test suite may include the gradual straightening of a long bone (shown in Figs. 31.3 and 31.8). In fact, the use of strain energy density, which is always positive, did not allow the coordinated addition and removal of bone in a case where axial strains did produce the correct tendencies.47 Similar difficulties would be expected with use of the strength optimization methods that incorporate damage as the stimulus. A test case for skeletal morphogenesis simulations might be first to determine the influence of various assumptions that are required for producing reasonable trabecular density and orientation outcomes. A test would be then to use the same values for a different region, e.g., the distal femur or proximal tibia to see the predicted patterns. Increasingly, the simulations should be cast in terms of physiological parameters that can be measured and manipulated, allowing tests of their validity as important players in functional adaptation processes. A final suggestion is the use of a “fully quantified” osteotomy experiment that includes measures of the temporal and spatial strains on the intact radius and ulna, followed by those same measures immediately following an ulnar osteotomy, and during use for several months thereafter. This level of quantification of the mechanical environment will allow a host of simulations similar to those already presented (Figs. 31.2, 31.4, 31.5, 31.6, and 31.9) but allow many more of the components of the strain history to be included as the primary stimuli. Ch-31 Page 38 Monday, January 22, 2001 2:05 PM

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Clearly, continued progress in the study of the functional adaptation of bone will depend upon interdisciplinary studies, and require increasingly sophisticated in vivo, mechanical, chemical, and cellular methods. The continuing fascination with bone—a unique and complex living structural material—will eventually yield quantitative models that allow for prediction of bone responses and for testing the consequences of therapeutic interventions.

Acknowledgments

This work was supported, in part, with a Whitaker Special Opportunity Award for Computational Tissue Engineering. The author appreciates the comments and suggestions made by M. D. Roberts, J. C. Coleman, R. B. Martin, R. Huiskes, and S. C. Cowin on an earlier draft of this chapter.

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Patrick J. Prendergast 32.1 Introduction...... 32-1 Trinity College Dublin 32.2 Fracture Healing...... 32-1 32.3 Mechanobiological Models ...... 32-4 Marjolein C. H. van der Pauwels’ Theory • Interfragmentary Strain Meulen Theory • Deformation/Pressure Models Cornell University • Models Including Fluid Flow 32.4 Future Directions...... 32-10

32.1 Introduction

Bone has the capability to regenerate, forming new osseous tissue at locations that are damaged or missing. Although this capability extends to regeneration of whole limbs in some animals,1 in humans regeneration is on a more limited scale and occurs during defect healing, e.g., after the removal of bone screws; fracture healing; distraction osteogenesis (during limb lengthening); and integration of orthopedic implants with the host bone. During the regenerative process, bone tissue can form directly or indirectly. During indirect bone formation, also called endochondral ossification, cartilage is formed, calcified, and replaced by bone tissue. During direct bone formation, or intramembranous ossification, bone tissue forms without the intermediate cartilage stage. The importance of the mechanical environment on tissue regeneration is evident in several ways. For example, during defect healing, when the regenerating bone is shielded from load, intramembranous, not endochondral, bone formation occurs.2 Excessive motion during long bone fracture healing inhibits bone formation. Instead of bone, a layer of cartilage forms at the fracture ends, creating a pseudoarthrosis (‘‘fake joint’’).3 Similarly, if an implant moves excessively relative to the surrounding bone, bone formation is inhibited and a persistent fibrous tissue layer forms at the bone–implant interface.4 The complex nature of bone regeneration has mostly been studied during fracture healing of long bones. For this reason, experiments designed to understand long bone fracture healing will be described in Section 32.2. In Section 32.3, different theories to describe the influence of mechanics on bone regeneration will be reviewed.

32.2 Fracture Healing

Bone fracture repair occurs either by:

1. Primary (direct, osteonal) fracture healing, where the fracture gap ossiﬁes via intramembranous bone formation without external callus, or

32-1

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32-2 Bone Mechanics

2. Secondary (indirect, spontaneous) fracture healing, where a multistage process of tissue regeneration stabilizes the bone with an external callus and repairs the fracture via endochondral ossiﬁcation.

During primary fracture healing, the fractured cortices repair directly by osteonal remodeling across the cortex. This process is less common than secondary fracture healing because the fracture must be extremely stable and well reduced for direct healing to occur. Clinically this process is observed when fractures are stabilized by rigid fixation such as compression plating. Secondary fracture healing occurs in a sequence of three biological phases: the inflammatory, reparative, and remodeling phases.5 These phases involve the coordinated activity of different cell populations that proliferate, differentiate, and synthesize extracellular matrix components. This cellular activity is spatially and temporally coordinated by a variety of growth factors and other regulatory molecules, including insulin-like growth factors (IGFs), fibroblast growth factors (FGFs), platelet- derived growth factors (PDGFs), transforming growth factors (TGFs), and bone morphogenetic proteins (BMPs).6–8 During the inflammatory phase, the periosteum of the bone lifts, and a hematoma forms between the bone ends due to the rupture of blood vessels. This hematoma releases a large number of signaling molecules, including inflammatory cytokines such as interleukin-1 (IL-1) and interleukin-6 (IL-6), and growth factors such as PDGF and transforming growth factor- (TGF-).7 These factors appear to regulate the initiation of fracture healing and the associated cellular response. For example, TGF- has been shown to accelerate fracture healing.9 The first cells present are pluripotent progenitor cells called mesenchymal stem cells: they originate from several possible sources (the inner cambial layer of the periosteum, the endosteum, the bone marrow, or the vascular endothelium10–13). These stem cells then differentiate into chondrocytes and osteocytes, which proliferate and generate the reparative callus. This differentiation of the mesenchymal cells appears to be activated by BMPs.14 During the reparative phase an external (periosteal) callus and an internal (medullary) callus are formed (Fig. 32.1). Intramembranous and endochondral bone formation occur simultaneously in different regions of the fracture calluses. Intramembranous ossification occurs only at the callus periphery, beneath the damaged periosteum but somewhat removed from the fracture site, and appears to be regulated by TGF-.8 This rapidly formed woven bone creates a mineralized hard callus. Endochondral ossification occurs adjacent to the fracture site and initiates with cartilage. This soft callus bridges across the fracture. The rapid cartilage formation of the early callus is accomplished primarily by the differentiation of mesenchymal cells into chondrocytes, and less by proliferation of existing chondrocytes.15 TGF- may regulate this cartilage matrix synthesis. Injection of BMP-2 into fractured rabbit tibiae increases the rate of healing, but not the size of the fracture callus.16 Mineralization of the cartilage involves a mechanism similar to long bone growth at the growth plate11 and requires reestablishment of the vascular and nutrient supply. Chondrocytes hypertrophy, the extracellular matrix calcifies and blood vessels penetrate the matrix. Then the calcified cartilage tissue is resorbed and replaced by woven bone formed by osteoblasts. In the final healing phase, osteonal remodeling of the newly formed bone tissue and of the fracture ends restores the original shape and lamellar structure of the bone. White et al.17 defined four biomechanical stages of fracture repair. At this final healing stage, the failure of a healed bone when loaded is not related to the original fracture site, while at the early stages, failure occurs through the weaker fracture. In the reparative phase, the formation of a callus with a large cross-sectional area increases the rigidity of the bone and stabilizes the fracture ends. As ossification proceeds, the fracture becomes stiffer and the motion of the fracture fragments decreases further. Therefore, fracture stiffness may indicate successful, or unsuccessful, healing. Marsh18 measured callus size and bending stiffness during healing of human tibiae and found no correlation between callus index (ratio of the maximum width of the callus to the diameter of the original shaft) and bending stiffness. However, a bending stiffness of less than 7 Nm/° at 20 weeks indicated a delayed union or a non-union. Similarly, Richardson et al.19 found that patients whose tibial fractures had reached a bending stiffness of 15 Nm/° did not refracture after external fixation. This stiffness was proposed to define successful union of these fractures.

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Mechanics of Bone Regeneration 32-3

FIGURE 32.1 Histological section of a mouse fracture callus 5 days postfracture. The femur was pinned and then fractured, so no endosteal callus is present. Intramembranous bone formation is evident under the periosteum at the callus periphery; ﬁbrous and cartilaginous callus is present adjacent to the fracture. OB original bone, NB new membranous bone, FC ﬁbrous callus, CC cartilage callus, MC medullary canal, MU muscle. Trichrome staining.

The importance of the mechanical environment on fracture repair has been demonstrated experimentally and can be examined during each stage of the repair process. The type of fixation device* and the nature of the musculoskeletal loading will determine the mechanical environment within the regenerating tissue. This environment, in turn, will influence callus size, ossification rate, and healed bone strength. Based on a series of sheep experiments, Goodship et al.20 concluded, More flexible fixation may lead to excessive interfragmentary motion … whereas more rigid fixation may impair callus formation contributing to … non-union. The rates of healing, tissue ossification, and stiffness are enhanced by cyclic mechanical loading.21–23 In sheep, Goodship and Kenwright21 found that cyclic axial motion compared to rigid fixation induced earlier ossification and more rapid healing, based on increased whole-bone stiffness (Fig. 32.2). Gardner et al.24 investigated the effect of reducing the displacement across a fracture during healing; they found more rapid healing if the displacement was reduced as healing progressed. Comparing static and cyclic compression of healing fractures, Panjabi and co-workers22 observed a greater rate of strength increase at the middle and later healing stages in bones with cyclic loading. Delaying mechanical stimulation until after the initiation of ossification eliminates the beneficial influence of cyclic loads.25 In the study by Goodship et al.,20 the importance of strain rate was also demonstrated. Fractures stimulated at a moderate strain rate (40 mm/s) increased bone mineral content and stiffness faster than those stimulated at slow (2 mm/s) and fast (400 mm/s) rates. Finally, the size of the fracture gap is critical to healing. Augat et al.26 used external fixation of metatarsus of sheep to compare healing with 1, 2, and 6 mm osteotomies, and two amounts of interfragmentary strain (7 or 31%). They showed that increasing the gap size reduced the bone stiffness and tensile strength. Because the lower interfragmentary strain adequately stimulated the callus, gap size was the more dominant of the two factors in the fracture-healing process.

*See Chapter 35 for a description of fracture ﬁxation devices.

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FIGURE 32.2 Mean in vivo increase in fracture stiffness in two groups of sheep with experimental tibial fractures. Axial movement at the fracture site different in the two groups. The difference between the two groups was signiﬁcant at the 8 to 10 week period. (From Goodship, A.E. and Kenwright, J., J. Bone Joint Surg., 67B, 650, 1985. With permission.)

Particularly interesting questions arise from the interaction of growth factors involved in the normal healing cascade and mechanical loading during fracture healing.27 Growth factor expression may be regulated by mechanical stimuli, but is difficult to study in fracture healing. Distraction osteogenesis induces a bone formation response similar to fracture healing and has a better-defined spatial gradient of bone formation. Increased mechanical stimulus during distraction osteogenesis increases expression of BMP-2 and BMP-4, which may be responsible for enhanced ossification.28 During distraction osteogenesis, BMP-4 is found at sites of proliferation and differentiation of mesenchymal cells suggesting a regulatory role in the early fracture callus.29 The development of rodent fracture models will lead to a better understanding of these interactions.30,31 In particular, knockout mice and other genetic manipulations offer exciting possibilities32 and will greatly improve knowledge of fracture healing.

32.3 Mechanobiological Models

According to Carter et al.,33 mechanobiology is the study of how mechanical or physical conditions regulate biological processes. During bone regeneration, physical forces contribute to the differentiation of the cell populations that arise over the healing period. For musculoskeletal tissues, Caplan and Boyan34 have hypothesized that mesenchymal stem cells differentiate into one of several musculoskeletal tissues (Fig. 32.3). The mechanics of bone regeneration involves understanding how the osteogenic pathway shown in Fig. 32.3 is regulated by mechanical forces within the tissue.

32.3.1 Pauwels’ Theory Much of present-day understanding of the regulative effect of mechanical forces on tissue differentiation comes from Friedrich Pauwels. Pauwels recognized that physical factors cause stress and deformation of the mesenchymal cells, and that these stimuli could determine the cell differentiation pathway. Using simple experimental models of a fracture callus,35 he demonstrated how shearing results in a change of shape of a

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Mechanics of Bone Regeneration 32-5

Mesenchymal Stem Cell (MSC)

Proliferation MSC Proliferation

Tendogenesis/ Osteogenesis Chondrogenesis Ligamentagenesis Myogenesis Marrow Stroma Other Commitment Bone Marrow / Periosteum Bone Marrow Transitory Transitory Transitory Transitory Osteoblast Chondrocyte Fibroblast Myoblast Stromal Cell Lineage Progression Chondrocyte Osteoblast Myoblast Fusion Differentiation Unique Micro-niche

Maturation Adipocytes, Mesenchymal Tissue Mesenchymal Osteocyte Hypertroph T/L Myotube Stromal Dermal and Chondrocyte Fibroblast Cells Other Cells TENDON/ CONNECTIVE BONE CARTILAGE LIGAMENT MUSCLE MARROW TISSUE

FIGURE 32.3 Mesenchymal stem cells have the potential to differentiate into a variety of tissues, such as bone, cartilage, tendon, muscle, fat, and dermis. Commitment to a particular pathway, as well as progression through the lineage, is dependent not just on speciﬁc growth factors and/or cytokines but also on biophysical stimuli acting on the cells. Continuous differentiation from the mesenchymal cell pool ensures that changing biophysical stimuli will elicit changing tissues. (From Caplan, A.I. and Boyan, B.D., in Mechanism of Bone Development and Growth, B. K. Hall, Ed., CRC Press, Boca Raton, FL, 1994. With permission.)

FIGURE 32.4 A direct compressive force (denoted D) “deforms the elementary particles of a cube of elastic material” into ellipsoids, as does a tensile force (denoted Z) and a shear force (denoted S). (Adapted from Pauwels, F., in Biomechanics of the Locomotor Apparatus, translated by Maquet, P. and Furlong, R., Springer, Berlin, 1980, 375–407.) piece of tissue (Fig. 32.4) whereas hydrostatic pressure results in a change in volume. Using this concept, he proposed a quantitative hypothesis for the influence of mechanical factors on tissue differentiation as follows: 1. Shear, which causes a change in cell shape, stimulates mesenchymal cell differentiation into fibroblasts, and 2. Hydrostatic compression, which causes a change in volume without a change in shape, stimulates mesenchymal cell differentiation into chondrocytes. By decomposing mechanical stimuli into shear and hydrostatic compression, Pauwels also predicted that a combination of shear and hydrostatic pressure would stimulate differentiation of fibrocartilage, such as occurs in the menisci of the knee or in the intervertebral disk.36

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FIGURE 32.5 Pauwels’ concept of tissue differentiation. Bone regeneration occurs only after stabilization of the mechanical environment by the formation of soft tissue. (From Weinans, H. and Prendergast, P.J., Bone, 19, 143, 1996. With permission.)

Pauwels’ theory, as illustrated in Fig. 32.5, also predicted the following: 1. Primary bone formation requires a stable mechanical environment so endochondral bone formation will proceed only if the soft tissues create this low strain environment. 2. Ligamentous tissue ossifies by the process of desmoid ossification. 3. Both ossified tissues remodel and are replaced by secondary lamellar bone (indicated by arrows). Pauwels’ concept that tissue differentiation is evoked by mechanical factors drew on the ideas of earlier German biologists such as Roux and Krompecher; see Prichard.37 Roux proposed that cells compete for a functional stimulus within the tissue.38 Interpreting this in the context of the Pauwels theory, the functional stimulus favoring fibroblast differentiation from the mesenchymal cell pool is high shear. Endochondral bone formation, on the other hand, occurs in low strain/high compression environments.

32.3.2 Interfragmentary Strain Theory When a fractured bone is loaded, the fracture fragments displace relative to each other. The strain produced in the fracture gap was named the ‘‘interfragmentary strain (IFS)’’ by Perren.39 If the width of the fracture gap is given by L and the change in the fracture gap after loading is given by L, then the strain in the longitudinal direction (IFS) is

L IFS ------. (32.1) L

Perren’s interfragmentary strain theory proposes that the fracture gap can be ﬁlled only with a tissue capable of sustaining the IFS without rupture.40 The strain tolerance is greatest for granulation tissue, intermediate for cartilage, and least for bone (Fig. 32.6). If the IFS is high, only granulation tissue can form according to the interfragmentary strain theory. If granulation tissue does form, the callus will

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Mechanics of Bone Regeneration 32-7

FIGURE 32.6 Strain tolerance of repair tissues. A tissue cannot exist in an environment where the interfragmentary strain exceeds the strain tolerance of the extracellular matrix of the tissue. (From Perren, S.M. and Cordey, J., in Current Concepts of Internal Fixation of Fractures, Springer, Berlin, 1980, 65. With permission.)

reduce the IFS. This reduction in the motion of the fracture fragments generates the environment where chondrocytes can sustain the IFS and proliferate. In this way, endochondral bone formation proceeds as the IFS is ‘‘gently and progressively limited.’’40 Whether or not the presence of soft tissue will actually reduce the IFS depends on many factors, including the nature of the musculoskeletal loading on the bone, and the structural behavior of the fracture fixation device.41 Although the interfragmentary strain theory is useful for understanding the relationship between motion and bone healing, the theory is not a general theory of bone regeneration because 1. The strain field in the fracture gap is multiaxial,42 2. Mechanical stimuli vary spatially in the fracture callus.43,44 Furthermore, if the displacement is not very small relative to the gap size, the longitudinal strain in a fracture gap cannot be accurately calculated using Eq. 32.1 because of geometric and material nonlinearity.45 It is noteworthy that Claes et al.,46 who were able to determine the IFS with a telemeterized external fixation system, concluded that the IFS did not significantly influence the success of fracture healing, although inferior tissue properties were observed histologically for larger IFS.

32.3.3 Deformation/Pressure Models Investigating the mechanics of endochondral ossiﬁcation, Carter and colleagues47,48 proposed that intermittent or cyclic mechanical loading occurring over a period of time (load history) stimulates tissue differentiation. The loading history was decomposed into discrete loading conditions, denoted c. Using the concepts proposed by Pauwels,35 the stress acting on the regenerating tissue was described as a combination of two scalar quantities:

1. Hydrostatic stress (related to the dilatational strain) denoted Di and

2. Octahedral shear stress also called the deviatoric stress (related to the distortional strain) denoted Si, where the subscript denotes the ith load case, and i 1, 2, 3, …. c.

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32-8 Bone Mechanics

There are six independent stresses in a material* written as x, y, z, xy , yz, and xz, where x, y, z is an orthogonal axis. The hydrostatic stress is given by

1 D -- () (32.2) 3 x y z

and the octahedral shear stress is given by

1 2 2 2 2 2 2 S -- () () () 6() . (32.3) 3 x y x z y z xy yz xz

The hydrostatic and octahedral shear stresses are invariants of the stress—i.e., they will have the same numeric value no matter what coordinate system is used. Carter and colleagues proposed that cyclic octahedral shear stress encourages cartilage ossiﬁcation whereas the action of a cyclic hydrostatic stress inhibits ossiﬁcation. The driving force for bone formation may be described by a linear combination of the stress invariants. This is termed the osteogenic index (OI), given as

c () OI ni Si kDi , (32.4) i1

where ni is the number of loading cycles for the ith load case. The value of k, the empirical constant, is determined by parametric variation in computer models of fracture healing,48,49 joint formation,50 and endochondral ossification of the sternum.51 High values of OI are caused by high shear stress or by tensile hydrostatic stresses—therefore, according to the osteogenic index theory, these stimuli favor endochondral bone formation. Bone formation is inhibited in the presence of large compressive hydrostatic stresses. In a finite-element analysis of the mechanical stimuli on ossifying surfaces during fracture healing, Claes and colleagues52,53 hypothesized that magnitudes of hydrostatic pressure and strain regulate the selection of either intramembranous or endochondral bone formation processes. By quantitative analysis of a real callus geometry, they found that if the compressive hydrostatic pressure (negative) exceeded 0.15 MPa at the regenerating bone surface then endochondral bone formation (i.e., prior formation of cartilage) occurred, whereas if the hydrostatic pressure was below this threshold then intramembranous bone formation proceeded (Fig. 32.7a). While the osteogenic index theory refers specifically to ossification within cartilage, the concept of a stimulus combined from hydrostatic stress and shearing due to tension may be applied more generally to tissue differentiation. Tissue formation in tendons,54 at implant interfaces,55 and during distraction osteogenesis56 has been analyzed using a relationship between mechanical stimuli and tissue differentiation shown in Fig. 32.7b. Stress and strain are combined on these diagrams even though these are not, in general, decoupled.57

32.3.4 Models Including Fluid Flow Although models of tissues as solid elastic materials may give adequate macroscopic load/deformation responses, the cells respond to cell level deformations and fluid flows (see Chapter 27). Since tissues are composed of a solid phase (collagen, with hydroxyapatite in the case of bone) and a significant amount of fluid (mostly water), they may be analyzed as mixtures of solid and fluid constituents. When bone58 or cartilage59 is loaded, the fluid component may flow and cause complex mechanical stimuli within tissues at the cellular level. Several in vitro cell studies have demonstrated the potential regulatory role of mechanical stimulation of bone cells,60 in the form of both fluid flow (osteocytes61 and osteoblasts62) and

*See Chapter 6 for an introduction to mechanics of materials. ch-32 Page 9 Monday, January 22, 2001 2:07 PM

Mechanics of Bone Regeneration 32-9

FIGURE 32.7 (a) Relationship between mechanical stimuli and bone formation. (Adapted from Claes, L.E. and Heigele, C.A., J. Biomech., 32, 255, 1999.) (b) Relationship between loading history and tissue phenotype. (Adapted from Carter, D.R. et al., Trans. Orthop. Res. Soc., 234, 1998.)

FIGURE 32.8 (a) A mechanoregulation diagram for bone formation and resorption based on mechanical strain and ﬂuid ﬂow; (b) application to simulation of fracture healing. (Courtesy of Damien Lacroix.)

substrate strain (osteocytes63 and osteoblasts64). Owan et al.65 have found that the responsiveness to fluid flow may dominate that of mechanical strain in bone cells. The biomechanical stress acting on cells will be high if the fluid flow is high: therefore, deformation and fluid flow must be taken together to define the mechanical milieu on the cell.66,67 Following Pauwels and the interfragmentary strain theory, high strains may be hypothesized to create the mechanical environment for fibroblast differentiation from the mesenchymal cell pool and the subsequent emergence of a fibrous connective tissue phenotype. Similarly, intermediate strains will allow cartilage formation and low strains will allow bone formation. The influence of fluid flow is to increase the deformation of the cells further. Therefore, the presence of high fluid flow will increase the biomechanical stress and thus decrease the potential for tissue differentiation in the case of each tissue phenotype. If the strain or fluid flow becomes low, then the lack of mechanical stimulation to the cells may initiate a resorptive process, as indicated by the resorption field on Fig. 32.8a. ch-32 Page 10 Monday, January 22, 2001 2:07 PM

32-10 Bone Mechanics

This regulatory scheme can simulate the time course of bone regeneration around implants using a poroelastic biphasic theory to calculate the stress in the ﬂuid and solid phases of a tissue.68,69 For a biphasic material, the solid stress, denoted s, and ﬂuid stresses, denoted f, are given by

s s s s pI e I 2 , (32.5)

f f pI, (32.6)

where e and denote the dilatational strain and the total strain in the solid phase, p is the apparent pressure in the ﬂuid, with denoting the volume fraction, and and being the Lamé constants. This model has been used to simulate the time-course of fracture healing70 where the inﬂuence of loading on bone regeneration in the callus can be predicted, see Fig. 32.8b.

32.4 Future Directions

This chapter has introduced the biology of bone healing and reviewed the theories that describe the regulation of bone regeneration by mechanical forces. Fracture repair is increasingly well understood from the point of view of the molecular biologist; the inﬂuence of the mechanical factors and the interaction between biophysical and biochemical regulatory pathways have yet to be fully elucidated. Further development of models is needed to relate continuum stress to subcontinuum stimuli at the cellular level. With such models, mechanical stimuli determined from in vitro cell culture experiments could be used to compute how cells react within regenerating bone. These models have exciting potential not only for understanding fracture healing and tissue formation but also for designing bioreactors used to grow tissue-engineered constructs.71

Acknowledgments

The authors acknowledge ﬁnancial support from the Wellcome Trust for a Biomedical Research Collab- oration Grant between Trinity College and Cornell University. We thank Alicia Bailon-Plaza and Damien Lacroix for their contributions to this chapter.

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8. Barnes, G.L, Kostneuik, P.J., Gerstenfeld, L.C., and Einhorn, T.A., Perspective: growth factor regulation of fracture repair, J. Bone Miner. Res., 14, 1805, 1999. 9. Joyce, M.E., Terek, R.M., Jingushi, S., and Bolander, M.E., Role of transforming growth factor—in fracture repair, Ann. N.Y. Acad. Sci., 593, 107, 1990. 10. McKibbin, B., The biology of fracture healing in long bones, J. Bone Joint Surg., 60B, 150, 1978. 11. Einhorn, T.A., The cell and molecular biology of fracture healing, Clin. Orthop., 355S, 7, 1998. 12. Yoo, J.U. and Johnstone, B., The role of osteochondral progenitor cells in fracture repair, Clin. Orthop., 355, 73, 1998. 13. Brighton, C.T. and Hunt, R.M., Early histological and ultrastructural changes in the medullary fracture callus, J. Bone Joint Surg., 73A, 832, 1991. 14. Bostrom, M.P.G., Expression of bone morphogenetic proteins in fracture healing, Clin. Orthop., 355S, S116, 1998. 15. Sandberg, M., Aro, H., Multimäka, P., Aho, H., and Vuorio, E., In situ localization of collagen production by chondrocytes and osteoblasts in fracture callus, J. Bone Joint Surg., 71A, 69, 1989. 16. Bax, B.E., Wozney, J.M., and Ashurst, D.E., Bone morphogenetic protein-2 increases the rate of callus formation after fracture of rabbit tibiae, Calcif. Tissue Int., 65, 83, 1999. 17. White, A.A., Panjabi, M.M., and Southwick, W.O., The four biomechanical stages of fracture repair, J. Bone Joint Surg., 59A, 188, 1977. 18. Marsh, D., Concepts of fracture union, delayed union, and nonunion, Clin. Orthop., 355S, 22, 1998. 19. Richardson, J.B., Cunningham, J.L., Goodship, A. E., O’Connor, B.T., and Kenwright, J., Measuring stiffness can define healing of tibial fractures, J. Bone Joint Surg., 76B, 389, 1994. 20. Goodship, A.E., Watkins, P.E., Rigby, H.S., and Kenwright, J., The role of fixator frame stiffness in the control of fracture healing. An experimental study, J. Biomech., 26, 1027, 1993. 21. Goodship, A.E. and Kenwright, J., The influence of induced micromovement upon the healing of tibial fractures, J. Bone Joint Surg., 67B, 650, 1985. 22. Wolfe, S.W., Lorenze, M.D., Austin, G., Swigart, C.R., and Panjabi, M.M., Load-displacement behaviour in a distal radial fracture model—the effect of simulated healing on motion, J. Bone Joint Surg., 81A, 53, 1999. 23. Probst, A., Janson, H., Ladas, A., and Spiegel, H.U., Callus formation and fixation rigidity: a fracture model in rats, J. Orthop. Res., 17, 256, 1999. 24. Gardner, T.N., Evans, M., and Simpson, H., Temporal variation of applied inter fragmentary displacement at a bone fracture in harmony with maturation of the fracture callus, Med. Eng. Phys., 20, 480, 1998. 25. Goodship, A.E., Cunningham, J.L., and Kenwright, J., Strain rate and timing of stimulation and mechanical modulation of fracture healing, Clin. Orthop., 355S, S105, 1998. 26. Augat, P., Margevicius, K., Simon, J., Wolf, S., Suger, G., and Claes, L., Local tissue properties in bone healing: Influence of size and stability of the osteotomy gap, J. Orthop. Res., 16, 475, 1998. 27. Cornell, C.N. and Lane, J.M., Newest factors in fracture healing, Clin. Orthop., 277, 297, 1992. 28. Sato, M., Ochi, T., Nakase, T., Hirota, S., Kitamura, Y., Nomura, S., and Jasui, N., Mechanical tension-stress induces expression of bone morphogenetic protein (BMP)-2 and BMP-4, but not BMP-6, BMP-7, and GDF-5 mRNA, during distraction osteogenesis, J. Bone Miner. Res., 14, 1084, 1999. 29. Li, G., Berven, S., Simpson, H., and Triffitt, J.T., Expression of BMP-4 mRNA during distraction osteogenesis in rabbits, Acta Orthop. Scand., 69, 420, 1998. 30. Bonnarens, F. and Einhorn, T.A., Production of a standard closed fracture in laboratory animal bone, J. Orthop. Res., 2, 97, 1984. 31. Aro, H., Eerola, E., and Aho, A.J., Determination of callus quantity in 4-week-old fractures of the rat tibia, J. Orthop. Res., 3, 101, 1985. 32. van der Meulen, M.C., Bailón-Plaza, A., and Hunter, W.L., Long bone fracture healing in bone morphogenetic protein-5-deficient mice, J. Bone Miner. Res., 13, S352, 1998. ch-32 Page 12 Monday, January 22, 2001 2:07 PM

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33. Carter, D.R., Beaupré, G.S., Giori, N.J., and Helms, J.A., Mechanobiology of skeletal regeneration, Clin. Orthop. Relat. Res., 355S, 41, 1998. 34. Caplan, A.I. and Boyan, B.D., Endochondral bone formation: the lineage cascade, in Mechanism of Bone Development and Growth. B. K. Hall, Ed., CRC Press, Boca Raton, FL, 1994. 35. Pauwels, F., Eine neue Theorie über den einfluss mechanischer Reize auf die Differenzierung der Stützgewebe, Z. Anat. Entwickl., 121, 478, 1960. (Translated by Maquet, P., Furlong, R. as A new theory concerning the influence of mechanical stimuli in the differentiation of supporting tissues, in Biomechanics of the Locomotor Apparatus, Springer, Berlin, 1980, 375–407. 36. Pauwels, F., Atlas zur Biomechanik der Gesunden und Kranken Hüfte, Springer, Berlin, 1973. 37. Prichard, J.J., Bone, in Tissue Repair, McMinn, R.M.H., Ed., Academic Press, London, 1969, chap. 4. 38. Weinans, H. and Prendergast, P.J., Tissue adaptation as a dynamical process far from equilibrium, Bone, 19, 143, 1996. 39. Perren, S.M., Physical and biological aspects of fracture healing with special reference to internal fixation, Clin. Orthop., 138, 175, 1979. 40. Perren, S.M. and Cordey, J., The concept of interfragmentary strain, in Current Concepts of Internal Fixation of Fractures, H. K. Uhthoff, Ed., Springer, Berlin, 1980, 63–77. 41. Tencer, A.F. and Johnson, D., Biomechanics in Orthopaedic Trauma, Martin Dunitz, London, 1994. 42. DiGioia III, A.M., Cheal, E.J., and Hayes, W.C., Three-dimensional strain fields in a uniform osteotomy gap, J. Biomech. Eng., 108, 273, 1986. 43. Biegler, F.R. and Hart, R.T., Finite element modelling of long bone fracture healing, in Computer Methods in Biomechanics and Biomedical Engineering, Books and Journals International, Swansea, J. Middleton, G.N. Pande, K.R. Williams, Eds., 1992, 30–39. 44. Gardner, T.N., Stoll, T., Marks, L., and Knote-Tate, M., Mathematical modelling of stress and strain in bone fracture repair tissue, in Computer Methods in Biomechanics and Biomedical Engineering II, Gordon and Breach, Amsterdam, 1998, 247. 45. Meroi, E.A. and Natali, A.N., A numerical approach to the biomechanical analysis of fracture healing, J. Biomed. Eng., 11, 390, 1989. 46. Claes, L., Augat, P., Suger, G., and Wilke, H.-J., Influence of size and stability of the osteotomy gap on the success of fracture healing, J. Orthop. Res., 15, 577, 1997. 47. Carter, D.R., Mechanical loading history and skeletal biology, J. Biomech., 20, 1095, 1987. 48. Carter, D.R., Blenman, P.R., and Beaupré, G.S., Correlations between mechanical stress history and tissue differentiation in initial fracture healing, J. Orthop. Res., 6, 736, 1988. 49. Blenman, P.R., Carter, D.R., and Beaupré, G.S., Role of mechanical loading in the progressive ossification of a fracture callus, J. Orthop. Res., 7, 398, 1989. 50. Carter, D.R. and Wong, M., The role of mechanical loading histories in the development of diarthrodial joints, J. Orthop. Res., 6, 804, 1988. 51. Wong, M. and Carter, D.R., Mechanical stress and morphogenetic endochondral ossification of the sternum, J. Bone Joint Surg., 70A, 992, 1988. 52. Claes, L.E., Heigele, C.A., Neidlinger-Wilke, C., Kaspar, D., Seidl, W., Margevicius, K.J., and Augat, P., Effects of mechanical factors on the fracture healing process, Clin. Orthop., 355S, S132, 1998. 53. Claes, L.E. and Heigele, C.A., Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing, J. Biomech., 32, 255, 1999. 54. Giori, N.J., Beaupré, G. S., and Carter, D.R., Cellular shape and pressure may medicate mechanical control of tissue composition in tendons, J. Orthop. Res., 11, 581, 1993. 55. Giori, N.J. Ryd, L., and Carter, D.R., Mechanical influences of tissue differentiation at bone–cement interfaces, J. Arthroplasty, 10, 514, 1995. 56. Carter, D.R., Helms, J.A., Tay, B.K., and Braupré, G. S., Stress and strain distributions predict tissue differentiation patterns in distraction osteogenesis, Trans. Orthop. Res. Soc., 44, 234, 1998. 57. Cowin, S.C., Deviatoric and hydrostatic mode interaction in hard and soft tissue, J. Biomech., 23, 11, 1990. 58. Cowin, S.C., Bone poroelasticity, J. Biomech., 32, 217, 1999. ch-32 Page 13 Monday, January 22, 2001 2:07 PM

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59. Mow, V.C., Ratcliffe, A., and Poole, A.R., Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures, Biomaterials, 13, 67, 1992. 60. Brown, T.D., Techniques for mechanical stimulation of cells in vitro: a review, J. Biomech., 33,3, 2000. 61. Klein-Nulend, J., van der Plas, A., Seimens, C.M., Ajubi, N.E., Frangos, J.A., Nejweide, P.J., and Burger, E.H., Sensititivity of osteocytes to biomechanical stress in vitro, FASEB J., 9, 441, 1995. 62. Jacobs, C.R., Yellowley, C.E., Davis, B.R., Zhou, Z., Cimbala, J.M., and Donahue, H.J., Differential effect of steady versus oscillating flow on bone cells, J. Biomech., 31, 969, 1998. 63. Pitsillides, A.A., Mechanical strain-induced NO production by bone cells: a possible role in adaptive bone (re)modelling, FASEB J., 9, 1614, 1995. 64. El Haj, A.J., Mitner, S.L., Rawlinson, S.C.F., Suswillo, R., and Lanyon, L.E., Cellular responses to mechanical loading in vitro, J. Bone Miner. Res., 5, 923, 1990. 65. Owan, I., Burr, D.B., Turner, C.H., Qui, J., Tu, Y., Onya, J.E., and Duncan, R.L., Mechanotrans- duction in bone: osteoblasts are more responsive to fluid flow than mechanical strain, Am. J. Physiol., 273, C810, 1997. 66. Prendergast, P.J. and Huiskes, R., Finite element analysis of fibrous tissue morphogenesis—a study of the osteogenic index using a biphasic approach, Mech. Composite Mater. (Riga), 32, 209, 1996. 67. Prendergast, P.J., Huiskes, R., and Søballe, K., Biophysical stimuli on cells during tissue differentiation at implant interfaces, J. Biomech., 30, 539, 1997. 68. van Driel, W.D., Huiskes, R., and Prendergast, P.J., A regulatory model for tissue differentiation using poroelastic theory, in Poromechanics: A Tribute to Maurice A. Biot, J.-F. Thimus, Y. Abousleiman, A.H.-D. Cheng, O. Coussy, and E. Detournay, Eds., A.A. Balkema, Rotterdam, 1998, 409–413. 69. Huiskes, R., van Driel, W.D., Prendergast, P.J., and Søballe, K., A biomechanical regulatory model for peri-prosthetic tissue formation, J. Mater. Sci. Mater. Med., 8, 785, 1997. 70. Lacroix, D. and Prendergast, P.J., A model to simulate the regenerative and resporption phases of long bone fracture healing, Trans. Orthop. Res. Soc., 25, 869, 2000. 71. Patrick, C.W., Mikos, A.G., and McIntire, L.V., Frontiers in Tissue Engineering, Pergamon, Oxford, 1998.

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Section-VI Page 1 Monday, January 22, 2001 2:24 PM VI Clinically Related Issues

33 Applications of Bone Mechanics Marta L. Villarraga and Catherine M. Ford ...... 33-1 Introduction • Parameters Related to Applied Loads • Ex Vivo Behavior and Imaging Parameters • In Vivo Fracture Risk and Imaging Parameters • Development of Models of Skeletal Structures 34 Noninvasive Measurement of Bone Integrity Jonathan J. Kaufman and Robert S. Siffert ...... 34-1 Introduction • X-Ray Densitometry • Ultrasonic Techniques • Alternative Techniques • Summary 35 Bone Prostheses and Implants Patrick J. Prendergast ...... 35-1 Introduction • Biomaterials • Design of Bone Prostheses • Analysis and Assessment of Implants • Future Directions 36 Design and Manufacture of Bone Replacement Scaffolds Scott J. Hollister, Tien-Min Chu, John W. Halloran, and Stephen E. Feinberg ...... 36-1 Introduction • Designing Bone Scaffolds • Fabricating Bone Scaffolds • Bone Scaffolds: An Example from Design to Testing • Conclusion

VI-1

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CH-33 Page 1 Monday, January 22, 2001 2:13 PM 33 Applications of Bone Mechanics

Marta L. Villarraga 33.1 Introduction...... 33-1 Exponent Failure Analysis 33.2 Parameters Related to Applied Loads...... 33-2 Associates Proximal Femur • Spine Catherine M. Ford 33.3 Ex Vivo Behavior and Imaging Parameters...... 33-9 Proximal Femur • Spine Exponent Failure Analysis Associates 33.4 In Vivo Fracture Risk and Imaging Parameters...... 33-16 Proximal Femur • Spine 33.5 Development of Models of Skeletal Structures ...... 33-18 Proximal Femur • Spine • Future Trends in Modeling Skeletal Structures

33.1 Introduction

From youth to old age, the human skeleton is routinely exposed to mechanical environments that challenge its structural integrity. Among younger individuals, bone fractures typically occur only when the applied loads substantially exceed those associated with routine daily activities. Common events that produce fractures among younger individuals include motor vehicle accidents, falls from heights, sports-related injuries, and occupational trauma.1 Efforts to reduce fractures associated with these types of activities often focus on designing environments and protective equipment that limit the applied loads to a level below the tolerance of the bone. In contrast, fractures among older individuals often result from events whose associated energies are substantially lower, including falls from standing height or lifting activities. In these cases, questions arise about the contribution of age-related reductions in bone strength in determining whether fracture will occur. Efforts to reduce these fractures focus on affecting the intrinsic strength of skeletal structures, for example, through pharmacological or dietary interventions, as well as on protective systems such as hip padding and energy-absorbing floors. This is in contrast to the strictly environment-oriented intervention efforts associated with higher-energy fractures in younger people. Any intervention effort to prevent bone fracture, whether aimed at the mechanical environment, bone strength, or both, must be based on a sound understanding of how the bone responds to in vivo mechanical loads. Failure of skeletal structures can be described in terms of the factor of risk,2 which is the ratio of the force applied to a bone during a specific activity to the force at which the bone will fracture. A factor of risk greater than 1 indicates that the bone will be overloaded and will most likely fail, whereas a factor of risk lower than 1 indicates that fracture is less likely to occur. This is the inverse of the factor of safety, traditionally used in engineering to characterize the safety of a structure. From an engineering mechanics perspective, material properties, geometry, and loading and boundary conditions are the key pieces of information needed for the design of a safe structure. All of these factors contribute to the stress distribution within the bone, and therefore influence the likelihood of bone failure (Fig. 33.1).

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33-2 Bone Mechanics

FIGURE 33.1 Characteristics of the spine that determine its capacity to carry load: material properties, structural design, and loading conditions. (From Myers, E.R. and Wilson, S.E., Spine, 22(24 Suppl.), 25S–31S, 1997. With permission.) Investigators have used multiple approaches to examine the relative contributions of material properties, geometry, and loading conditions to the mechanical behavior of skeletal structures. For example, substantial knowledge has been derived from examining relationships between empirically determined structural properties of whole bones ex vivo and densitometric, geometric, and architectural measurements. This has been facilitated by the evolution of bone imaging technologies that allow investigators to examine the intricate details of the microstructure and material of bone. Clinical studies of factors related to in vivo fracture risk have complemented the understanding of whole-bone mechanics gained by examining ex vivo structural behavior. Issues that have emerged as important from both ex vivo and in vivo work include the relative contributions of cortical and trabecular bone, loading conditions, geometry, and age-related density variations. A parallel approach to understanding the mechanical behavior of skeletal structures utilizes engineering models based on fundamental principles of mechanics. These models utilize the bone material properties and geometry to predict stresses under a variety of loading conditions, which is advantageous since stress cannot be directly measured in bone. Models have evolved, with ever-increasing complexity, from two-dimensional idealizations with closed-form solutions into three-dimensional, patient-specific finite-element models. While shortcomings related to these models currently limit their use in accurate prediction of whole-bone failure, such models have contributed substantially to the understanding of the factors that govern whole-bone behavior. The aim of this chapter is to review and synthesize the research that has led to the current state of the art in the understanding of whole-bone mechanics, in particular as it relates to whole-bone fracture. Specific approaches used to study whole-bone mechanics (including experimental, clinical, and modeling work) are emphasized, using research involving the proximal femur and spine to illustrate these approaches (Fig. 33.2). The chapter begins with a review of the in vivo loads associated with fracture, followed by a discussion of how parameters related to applied loads affect mechanical behavior of the femur and spine. Work that has been performed to relate ex vivo structural properties and in vivo fracture risk to imaging parameters is then reviewed, followed by a discussion of the development of mathematical models of the proximal femur and spine. 33.2 Parameters Related to Applied Loads

33.2.1 Proximal Femur The ability to predict the stress distribution within a skeletal structure is of little practical value unless the relevant in vivo loading conditions are known. In the same way, studies of ex vivo behavior are most valuable when the loading conditions employed reﬂect approximate in vivo loading conditions. Early efforts to deﬁne loads acting on the proximal femur involved the use of mathematical models and reaction

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Applications of Bone Mechanics 33-3

FIGURE 33.2 Femur and vertebra whole bones. (Illustration © Paul Chang. With permission.)

force measurements to estimate forces across the hip joint during stance and gait. A thorough review of the earliest work in this area is contained in Rydell.3 Williams and Lissner4 calculated a resultant force on the femoral head of 2.4 times body weight during single-leg stance. McLeish and Charnley5 predicted values of 1.8 to 2.7 times body weight with the pelvis in a normal walking attitude, and found that the pelvis angle and the position of the trunk and limbs had a considerable effect on femoral forces. These predicted forces are in general agreement with those reported by Rydell,3 whose first attempt at direct measurement of hip joint forces using an instrumented hip prosthesis yielded force magnitudes of 2.3 to 2.9 times body weight for single-leg stance and 1.6 to 3.3 times body weight for level walking. Later measurements for single-leg stance and gait using telemetered hip prostheses were generally consistent with those of Rydell for loads associated with stance and walking.6–9 Davy et al.7 noted that measured values for gait were often lower than previous predictions using optimization routines,10–13 which could be explained in part by gait differences between normal subjects and those with prostheses. The results from mathematical models and early instrumented hips have provided a fundamental understanding of the magnitude and direction of loads applied to the femur during routine (and typically noninjurious) activities of daily living. Although these data are applicable to determining stress distributions under physiological loads, the loads under which many femur fractures occur are substantially different from simple stance and gait configurations in magnitude and direction. Evidence from both clinical and experimental studies suggest that loads associated with muscular contraction can be sufficient to result in femur fracture among elderly people.14–18 Studies using optimization methods as well as instrumented hip prostheses have demonstrated the importance of muscle forces as determinants of load transmission across the joint and therefore the stress distribution within the bone.9,19,20 Recent investigations using instrumented hip prostheses have shown that although patients in the early postoperative

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33-4 Bone Mechanics

period can execute planned activities of daily living with relatively low joint contact forces, unexpected events such as stumbling or periods of instability during single-leg stance can generate resultant forces in excess of eight times body weight as a result of muscular contraction.8,21 Forces that are within the capacity of the muscles crossing the hip joint have been shown to produce clinically realistic fracture patterns in ex vivo experiments,18 consistent with retrospective clinical studies in which femur fractures were attributed to turning, stumbling, rising from a seated position, or climbing.16,17,22 These data suggest that femur fracture can occur as a result of muscular contraction in individuals with reduced bone strength. However, attempts to rule out impact from a fall as a cause of proximal femur fracture based on either primitive stress analyses23 or ex vivo fracture studies18 should be interpreted with caution. Despite compelling evidence that the majority of femur fractures are associated with falls,24–27 surpris- ingly little is known about the magnitude and direction of loads applied to the femur during a fall. Robinovitch and colleagues28 combined pelvis release experiments with a lumped parameter model of the body to predict peak impact forces up to approximately 8000 N or more, depending on fall height and trochanteric soft tissue thickness. By comparing their predictions to measurements of the forces required to fracture the femur under fall loading conditions, these investigators concluded that any fall from standing height with direct impact to the greater trochanter has the potential to fracture the elderly femur. van den Kroonenberg and co-workers29 used dynamic link models of the body to predict hip impact velocities, effective mass, and peak femur impact forces during falls from standing height. Using their most-sophisticated model, which reflected experimentally determined values for impact configuration and impact velocity,30 they predicted peak forces on the greater trochanter of 2.9 and 4.3 kN for females of 5th and 95th percentile height and weight, respectively. The stress distribution within the femur, and therefore the likelihood of fracture, depends on the direction of the applied loads as well as their magnitude. Despite its potential importance, however, few studies have directly addressed the configuration of loads applied to the femur during a fall, and how changes in this configuration influence failure load. Courtney and co-workers31 derived a loading configuration (Fig. 33.3) based on body positions at impact during a fall,30 which produced clinically relevant fracture patterns. Pinilla and colleagues32 extended this work by using cadaveric femurs to examine the

FIGURE 33.3 Diagram of the mechanical testing setup for failure tests of the proximal femur. The femoral shaft is aligned 10° from horizontal and femoral neck is internally rotated 15° relative to vertical. The femoral shaft is ﬁxed distally but remains free to slide and rotate. (From Bouxsein, M.L. et al., Calcif. Tissue Int., 56(2), 99–103, 1995. With permission.)

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Applications of Bone Mechanics 33-5

effect of subtle variations in impact direction from a fall. They found a significant reduction in failure load with a 30° change in the angle between the line of action of the applied force and the angle of the femoral neck, as viewed from the superior aspect of the femoral head. This reduction in failure load was noted to be comparable in magnitude to approximately 25 years of age-related bone loss after age 65. These experimental results have been confirmed by parametric finite-element analyses.33 Loading rate is an additional variable related to applied load that must be considered in determining the stress distribution in the femur and the likelihood of fracture. Weber et al.34 found that, under loading conditions approximating a fall, the force required to fracture the femur increased with increasing loading rate. This general information regarding the influence of loading rate was refined by Courtney and co-workers,31 who used a predicted loading rate based on time to peak force during a fall.28 These authors reported that fracture forces for both younger adult and older adult femurs increase by about 20% with a 50-fold increase in applied displacement rate. Differences in both loading configuration and loading rate may partly explain why investigators have reported mean structural capacities of the proximal femur under both stance and fall loading conditions that vary by as much as a factor of four to five (Table 33.1). The wide range in failure loads reported in these ex vivo studies shows that failure load can be dramatically influenced by several variables; however, substantial future work is necessary to characterize precisely the contributions of these variables.

33.2.2 Spine Every routine activity, including sitting, standing, walking, or lifting a light or heavy object, creates loads on the spine. Knowledge of relevant in vivo loading conditions on the spine is necessary to predict adequately the stress distribution in this structure, in both in vivo and ex vivo studies. Schultz et al.64 predicted in vivo lumbar spine compressive loads ranging from 440 N (relaxed standing position) to 2350 N (forward bending with the trunk at 30° and holding an 8-kg weight at arm’s length) using a combination of electromyography (EMG) and intradiscal pressure measurements on volunteers and mathematical modeling. In a later study using volunteers, Hansson et al.65 estimated that the compressive loads on L3 during squat lifting and lifting while bent at the waist range from 5000 to 11,000 N. Using a biomechanical analysis, validated against EMG and intradiscal pressure measurements, they estimated that the compressive load on L3 during these types of exercises was about eight times greater than the shear load. Actual magnitudes of loads on an individual’s lumbar vertebrae depend on the anatomy and weight of the individual, as well as on muscle forces. Characterizing activities as speciﬁc events leading to spine fractures is the subject of current research. Complications arise in part from the fact that osteoporotic compression fractures of the spine are usually associated with minimal trauma and with loads no greater than those encountered during normal activities of daily living.66 Another contributing factor is fatigue, which may in part explain vertebral fractures that are reported as spontaneous or are detected incidentally.67 Loading of the spine during falls is currently under investigation, with particular emphasis on the transmission of impact forces along the spine.67 To understand how loads are distributed in the spine, it is important to consider the structures that form the spine and how each of these components contributes to load transmission. The majority of the compressive forces in the spine are transmitted from the intervertebral disks to the vertebral end plates, and are then distributed between the trabecular bone and cortical shell that make up the vertebral bodies. The exact percentage of contribution of the cortical shell to load sharing is still not well established and is currently under investigation. A portion of the compressive loads can also be transmitted along a parallel path, through the posterior elements and facet joints. The overall contribution of the posterior elements to vertebral body strength is currently under investigation with the help of mathematical models.68 In evaluations of the effects of compressive loads on vertebrae, stress levels associated with end plate failure are of special concern, since the end plate has been shown to fail ﬁrst under high compressive loads.65,69 Also of concern are stress levels that exceed the strength of trabecular bone, because most of the axial compressive load on a vertebral body is carried by the trabecular bone.67,70

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33-6 Bone Mechanics q g q 0.05 — — — 0.001 Value 0.0001 p (continued) 2(c) r —— 0.60 0.071 0.64 0.005 0.66 0.55 Max Max b osity s ’ ximal cular density, cular density, nsity, Ward nsity, intertrochanteric triangle neck diaphysis Correlated Parameter Correlated a ———— ———— ———— ———— ———— ———— ———— ———— ———— ———— ———— XRS BMC 0.79 DPA BMC NS DESPR density index Neck 0.29 Imaging Method e 59 102 7850 475 624 5950 9720 BMD, 7850 4940 DPA neck BMD, 0.89 18,700 15,000 10,700 10,000 X-ray12,600 De CS19,500 Trabe DPA pro BMD, 12,800 13,300 X-ray Average area por 11,900 – – – – – – – – – – – – – – – – – – ————— ————— 4310 2670 2270 3830 1600 5100 1600 3070 1280 m14 Failure Load Failure —— —— — — 3830 980 4900 2940 3860 29 N Mean (N)Mean Range (N) — — —— — — — 0.25 0.33 50 3040 ImpactImpact 371 J Impact 415 J 170 49 J 233 24 (mm/s) Load Rate f guration ﬁ Loading h h compression, compression, torsion contraction compression Con StanceFall bendingAnterior Gradual Gradual 9470 Gradual 4000 8230 Stance Stance 37 N/sStance 6200 0.03 11,000 d d d d d d j d 6 4000 6020 3110 6 shear Bending, Gradual 3410 4 14 3510 2190 n 21 20 22 26 13 13 17 Bending, shear, shear, 17 Bending, 3314 Stance Muscle 39 Stance613219 Fall 0.08 10 Stance 0.20 Stance 10 Fall Fall 0.08 6100 0.7 2930 1770 28 Bending, shear, shear, 28 Bending, 22 Torsion — 20 10 35 Reported Failure Properties of the Proximal Femur and Correlations with Femur Imaging Parameters of Properties Failure the Proximal Reported 41 37 42 44 39 43 36 34 14 40 18 38 Leichter (1982) Leichter (1989) Delaere Hirsch (1960) Hirsch Mizrahi (1984) (1963) Vose (1988) Werner TABLE 33.1 TABLE (year) Author (1953) Smith Phillips (1975) Backman (1957) Sartoris (1985) Dalen (1976) (1992) Weber Yang (1996) Yang

CH-33 Page 7 Friday, February 2, 2001 2:42 PM

Applications of Bone Mechanics 33-7 — — — — — — — — — — — 0.001 0.001 0.001 0.001 0.001 0.001 0.0001 0.0001 0.0001 0.001 0.001 0.001 0.01 0.66 0.93 0.93 0.84 0.68 0.71 0.89 0.82 0.83 0.47 min min FNAL FNAL CSA, CSA, CSA, neckCSA, midshaftCSA, midshaftCSA, headCSA, 0.50 0.62 0.50 CSA, 0.71 head intertrochanteric (trabecular) (trabecular) CSA CSA intertrochanteric CSA, neckCSA, 0.79 BMD FE ModelFE model 0.75 0.90 BMD, neckBMD, 0.72 CA, trochanter CA, calcaneus BUA, US calcaneus BUA, 0.51 0.002 QCT HU QCT QCT BMD Trochanter QCT HU QCT subcapital BMD, QCT 0.61 FE model 0.0001 0.82 QCT BMD Neck QCT HU QCT subcapital HU, 0.64 0.02 DXA neck BMD, DXA total BMD, DXA 0.92 trochanter BMD, 0.68 0.88 DXA neck CSA, 0.77 US 6730 DXA neck BMD, 0.79 4040 QCT HU 16,100 QCT superomedial BMD, – – — — — — — — — — — – 2750–9610 QCT HU 4940 k — —— —— —— —— 3820 3060 /min 74.6(Nm) —— — —— — —— — /min ° ° 0.21 5 15 100 4050 m l l ° ° n ° Fall, 15 Fall, 30 Rotation 8 Stance 0.88 13 Fall 26 9200 365026 Stance12 Rotation Stance22 Fall13 — Compression Stance 0.08 5490 18 0.70 6100 Stance 2110 0.5 25 778 19 Stance17 Fall16 Fall33 Fall 0.21 0 Fall, 100 9920 2 2 5430 3680 1730 18 Fall — 56 31 57 32 48 54 52 55 50 53 45–47 47 49 51 58,59 Nicholson (1997) Lang (1997) Bouxsein (1995) Alho (1988) (1989) Husby Alho (1989) Esses (1989) (1992) Smith (1999) Cody Courntey (1994) Cheng (1997), 64 Fall 14 3980 Pinilla (1996) Keyak (1998) Keyak Courtney (1995) Alho (1988) Lotz (1990) CH-33 Page 8 Monday, January 22, 2001 2:13 PM

33-8 Bone Mechanics — value 0.001 0.0001 0.0001 0.001 p quantitative quantitative nite element; element; nite ﬁ

2(c) r 0.45 0.52 q p Correlated Correlated Parameterb Max femoral FE neck axis length; neck dual-photon absorptiometry; dual-photon QCT DXA load Failure 0.83 US calcaneus BUA, 0.70 Imaging Methoda 7000 US calcaneus SOS/BUA, 7000 DXA and trochanter BMD, – – cross-sectional area; FNAL FNAL area; cross-sectional Failure Load Failure — eld units; CSA eld units; Mean (N)Mean Range (N) fi sultrasound. speed of sound. Houns dual-energy scanned projection radiography; DPA dual-energy radiography; scanned projection DPA (mm/s) Load Rate guration fi Stance 1.0 3150 933 Stance 60 3200 933 Loading Con bone mineral density; HU Compton scattering; DESPR scattering; Compton dual-energy absorptiometry; X-ray US d d n 2225 Fall Fall 0.5 100 2640 DXA trochanter BMD, 0.92 58 45 broadband ultrasound attenuation; SOS ultrasound broadband attenuation; cant. fi 61 63 62 Reported Failure Properties of the Proximal Femur and Correlations with (Continued) Femur Imaging Parameters of Properties Failure the Proximal Reported bone mineral content; BMD bone mineral content; 60 X-ray spectophotometry; X-ray CS cortical area; BUA BUA cortical area; not signi value calculated from raw data. raw from value calculated p Compression applied approximately along femoral neck axis. applied approximately Compression computed tomography; DXA computed CA Angle between femoral neck axis and applied load, as viewed from superior as viewed from aspectAngle femoral between neck axis and applied load, of femoral head. Femur embedded up to neck; force applied perpendicular shaft. to force neck; embedded up to Femur Embalmed specimens. curved beam model. using a DXA-based load calculated Failure BMC Composite value of Composite SOS and BUA. Median value. Median

XRS Seven specimens dislocated from pelvis specimens from without dislocated Seven fracture. NS Simulated gluteus medius and iliopsoas contraction. Simulated Dried specimens. and defatted Femoral head cemented in polyurethane blocks and rotated about femoral neck axis. blocks and rotated in polyurethane head cemented Femoral a b c d e f g h j k l m n p q Bouxsein (1999) Lochmuller (1999) Lochmuller (1998) TABLE 33.1 TABLE (year) Author Beck (1998) CH-33 Page 9 Monday, January 22, 2001 2:13 PM

Applications of Bone Mechanics 33-9

Although much of the loading imposed on the spine during daily activities involves compression, many lifting activities also involve bending, which introduces a flexion component as well. Flexion has been shown to produce greater peak compressive stresses on vertebral bodies than pure compresssion.64 To determine the effects of flexion, Granhed et al.69 examined whether the compressive strength of thoracolumbar vertebrae varied with the direction of the applied load by comparing compressive loads applied axially to those applied in different degrees of flexion. In their study, the first components to fail were the end plates and the underlying trabecular bone. These results were similar to those of previous studies in which vertebral bodies with 3 mm of adjacent disks covering each end plate were loaded strictly axially.71 The intervertebral disks play an important role in the transfer of loads to the vertebral body. To examine the influence of the presence of disk material (annulus and nucleus pulposus) on load transfer and the consequent effects on the strength and stiffness of lumbar vertebral bodies, Keller et al.72 examined the mechanical properties of trabecular bone samples from different locations with respect to the annulus or nucleus pulposus. They found regional variations in compressive properties of trabecular bone samples as a function of location with respect to the disk, with posterocentral samples having greater stiffness and strength than peripheral samples. This heterogeneous distribution of compressive mechanical properties in segments with normal disks was different from the more homogeneous distribution in segments with degenerated disks. In addition to load magnitude and direction, loading rates and the resulting differences in strain rates must be considered when evaluating the effects of prescribed loading conditions on the spine (Table 33.2). This is of particular significance since it has been hypothesized that elderly individuals could be subjected to loads at relatively low strain rates.73 Furthermore, strain rate has been found to increase as a result of muscular fatigue at other skeletal sites, suggesting a causal relationship with stress fractures.74,75 Occasional overloads may increase the risk of vertebral fracture by substantially degrading the mechanical properties of trabecular bone.73 Examples include non-fracture-producing falls that could potentially have a deleterious effect on the mechanical competence of vertebral bodies. Keaveny et al.73 quantified the percentage reductions in modulus and strength and the development of residual strains due to overloading. Reductions in modulus of up to 85% and reductions in strength of up to 50% occurred with overloads of as much as 3% of the total applied strain, and residual strains developed depended mainly on the magnitude of the applied strains. Work that has been performed to characterize the magnitude and direction of loads applied to the proximal femur and spine during both daily activities and falls provides an important foundation for ex vivo experimental work. However, further research is necessary to characterize the loads leading to femur and spine fractures. Further consideration of boundary conditions is also warranted, including, for example, the effects of irregular end plates and compliant disks in the spine, as well as the effects of constraints at the knee joint and acetabulum on the behavior of the femur.

33.3 Ex Vivo Behavior and Imaging Parameters

33.3.1 Proximal Femur Investigations of the mechanical behavior of the proximal femur ex vivo and the relationship to imaging parameters have provided insight into factors that are important in determining the stress distribution in the bone and resultant failure properties. Early ex vivo investigations of the proximal femur were primarily oriented toward determining the tolerance of the femur under different loading conditions, as well as examining the associated fracture patterns.14,35,36,91 The results of these early investigations suggested the importance of the complex interplay between loading conﬁguration, variations in local strength, and variations in geometry in determining the tolerance of the femur as well as the resulting fracture pattern, despite a lack of sophisticated imaging techniques. CH-33 Page 10 Monday, January 22, 2001 2:13 PM

33-10 Bone Mechanics 0.001 0.001 0.001 0.001 0.001 0.01 0.0001 0.001 0.001 0.001 Value 0.001 0.05 <0.01 p

, g fg g g f g f f f f f 2(e) 0.48 0.59 0.49 0.002 r Max Max d 0.48 0.22 0.55 0.24 T T B B (L1) 0.38 0.007 (L1) 0.50 0.002 in compression) in compression) Correlated Correlated Parameter TBV (%) TBV trabecular (L3) pattern (L1) TbTh (L1)Vtr 0.52 0.001 Radiographic BMC BMC BMC CTh (L1)Vm 0.56 0.001 c DPA BMC Imaging Method 11,000 DPA BMC 0.74 0.01 7.8 Age 0.66 10090 DPA BMC positive 4.95 0.48 0.01 8600 0.35 9860 BV/TV (%) 9860 BV/TV 7.04 Iliac crest 7.04 Iliac – – – – – – – Range 1.5 Loads(N), Loads(N), 2.00 Stress (MPa) Stress 2400 75 yrs) 75yrs) 75 yrs) 75 yrs) – – – 50 yrs) (females) Age 0.69 5 yrs) 75 yrs) 75 yrs) 50 yrs) (males) Age 0.61 – 75 yrs) 50 yrs.)50 yrs) (females) Age 0.66 (females) Age 0.71 2.27 1.02 3850 1520 3850 5430 810 6940 ( 1.95 ( 4590 (50 3110 ( 2.96 (50 3260 (50 2800 ( 2.62 (50 2.29 ( 8260 ( 5.83 ( 5.70 ( Mean Loads (N), Loads (N), Mean (MPa) Stress b 6290 3940 6290 max max max max max max max max max max max max max max max max F F F F F F F F Parameter Mechanical Mechanical h (mm/min) Loading Rate a Type Sample n 43 L5 52 FSU-NE 12 – L4 109L4 VB-D 46 VB-NE 5 4.5 L2 46 VB-NE 4.5 L2 22L2 VB-NE 15 VB-NE 4.5 L2 4.5 14 VB-NE 4.5 L2 T5 43 VB-NE 4.5 T7 – – Level Spine L1 T12 L2 70 76 77 79 69 71 Correlations of Mechanical Parameters with Noninvasive Parameters for Spine Segments or Vertebral Bodies (all was done testing Vertebral for Spine Segments or Parameters with Noninvasive of Parameters Correlations Mechanical 78 80 Granhed (1989) Ortoft (1993) TABLE 33.2 TABLE Author(year) (1986) Mosekilde Vesterby (1991) Vesterby Korstjens (1996) Korstjens Mosekilde (1988) Mosekilde Mosekilde (1990) Mosekilde Hansson (1980) Hansson CH-33 Page 11 Monday, January 22, 2001 2:13 PM

Applications of Bone Mechanics 33-11 ) — — — — — — — 0.0001 0.0001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.061 0.001 0.001 0.001 continued (

j j k k 0.41 0.82 0.78 CSA 0.88 CSA 0.45 CSA 0.61 EPA 0.64 EPA EPA 0.76 SA 0.55 0.23 T T region) density BMD 0.46 BMD BMD Apparent QCT HU by 0.52 DPADPA BMD 0.41 BMC 0.64 QCT BMD 0.51 QCT HUQCTQCT HU 0.30 QCT BMD 0.47 rBMD (central QCTQCT HUQCT HU HU 0.23 0.51 9000 QCT BMD – 19) QCT rBMD 0.65 0.002 20)17)20)20) 0.89 0.74 0.74 0.001 0.51 0.001 0.001 0.004 17) QCT rBMD 0.43 0.035 19)15)19)18) 0.75 0.65 0.35 0.001 0.69 0.005 0.029 0.001 n n n n n n n n n n 4.22 DXA BMD 0.44 4.22 DXA BMD 5300 2100 5770 DXA BMD 0.64 1460 ( 1720 ( max max max max max max max max max max max max max max (kN/m) QCT BMD QCT BMD 0.44 QCT QCT BMD BMD F rBMD F F F F F F F 12 16 2100 ( 12 13 1910 ( L1 20 2 FSU-NE 12.5 10 18 1690 ( 8 16 Stiffness 10 17 2000 ( 8 17 VB-D 25.4 – – – L24 18 18 1890 ( 2070 ( 4 15 1650 ( L4 73 FV-D 5 – – – – – – – – T9 T11 L1 L3 T7 T9 T11 L1-L2L3 18 1760 ( L1 L1,L3 16TH,L VB-DL2 36TH,L FSU-NET11 30 6 98 1kN/s VB-NET7 FSU-NE 4.5 1kN/s L3 62 VB-D 480 85 87 82 84 83 81 88 86

Cheng (1997) Mosekilde (1989) Mosekilde Cody (1991) Cody Biggeman (1988) Biggeman Brinckmann (1989) Eriksson (1989) McBroom (1985) McBroom (1995) McCubbrey CH-33 Page 12 Monday, January 22, 2001 2:13 PM

33-12 Bone Mechanics 0.05 0.01 0.01 0.001 0.001 Value p

cross- ); TbTh ); 3 BMC

2(e) B r 0.45 0.71 0.38 0.74 0.88 0.69 0.001 0.36 0.67 (Continued) (Continued) Max Max d regional BMD; CSA regional BMD; in compression) Correlated Correlated Parameter (lateral) (AP) BMD(L2), functional spinal unit (two vertebra functional vertebra spinal unit (two marrow space star volume (mm star volume space marrow c

Imaging Method m); Vm m); DXA(AP) BMD (L2) 0.52 QCT VCDDXA BMD 0.50 0.71

rBMD area; endplate full with vertebra discs at both ends. BMC whole BMC vertebrae (w/posterior elements); (MPa)

T (N), Stress Stress (N), Range Loads surface area; EPA area; surface 2080 DXA BMD (L2) 2080 DXA BMD 2620 DXA(lateral) BMD (L2) 0.79 vertebral body with body vertebral FSU discs at both ends; mean thickness of cortical ring ( Stress (MPa) Stress eld units; SA eld units; Mean Loads (N), Loads (N), Mean dual energy absorptiometry. x-ray ﬁ bone mineral content; BMC bone mineral content; b Houns full FV-D (w/posterior vertebra elements); max max max max F F F F ); BMC ); 3 Parameter Mechanical Mechanical 6 6 — (mm/min) Loading Rate Loading Rate 15 degrees). dual photon absorptiometry;dual photon DXA l l fractional volume offractional volume trabecular CTh bone; NE – maximum load. exion ( exion Typea ﬂ Sample trabecular of star volume L1(mm max corrected for frontal area of area for frontal HU vertebrae; corrected functional spinal unit w/o endplates; FV functional spinal unit w/o endplates; T n BMC m); Vtr m);

T T4 T12 T12 T8 T8 T4 16 VB L5 L5 L2 11 2 FSU vertebral cancellous density. cancellous vertebral T11 11 2 FSU – – – – – – – – Level Spine T1 L1 L1 T9 T9 T5 T5 T1 90 Correlations of Mechanical Parameters with Noninvasive Parameters for Spine Segments or Vertebral Bodies (all was done testing Vertebral for Spine Segments or Parameters with Noninvasive of Parameters Correlations Mechanical vertebral body without endplates at both ends and sawed plano-parallel ends; VB-D plano-parallel without ends; body vertebral at both ends and sawed endplates 89 quantitative computed tomography; DPA tomography; computed quantitative trabecular bone volume; BV/TV(%) trabecular bone volume; maximum compressive stress; F stress; maximum compressive max mean trabecular thickness ( vertebral body only; body vertebral BMD Not reported. Not and intervertebral FSU-NE disc); sectional area; VCD sectional area; Also loaded in compression combined with combined Also loaded in compression Multiple-regression model. Multiple-regression TBV

Vertebral bodies above and below embedded in PMMA and below bodies above Vertebral As reported in Figure 1. in Figure reported As VB-NE Other correlations may have been reported. have may Other correlations QCT Negative relationship. Negative Log-log relationship. — a b c d e f g h j k l TABLE 33.2 TABLE (year) Author (1995) Moro Edmonston (1997) Edmonston CH-33 Page 13 Monday, January 22, 2001 2:13 PM

Applications of Bone Mechanics 33-13

Imaging modalities that have been used to characterize the mechanical behavior of the proximal femur include radiography, single photon absorptiometry, dual photon absorptiometry, dual energy X-ray absorptiometry, computed tomography, and ultrasound. These techniques are discussed in Chapter 34. Correlations between femoral failure load and various measurements using these techniques are presented in Table 33.1. Initial attempts to correlate mechanical behavior of the proximal femur with densitometric measures utilized simple radiographs.38,39 Vose and Mack38 found significant correlations between density measures at the Ward’s triangle region and yield load of the femur; however, the loading conditions used did not reproduce clinically relevant fracture patterns. Phillips et al.39 utilized radiographic measurements as inputs to a two-dimensional beam-bending model of the femur, achieving reasonable agreement between measured and predicted failure loads. Although this study was essentially two dimensional and limited to loading in the frontal plane, the authors did note the importance of overall neck depth, cortical thickness, neck length, neck angle, and age in predicting femoral failure load. The difficulties associated with assessing bone mineral content via radiographs led to the use of more- sophisticated imaging techniques for this application, including X-ray spectophotometry40 and Compton scattering.37,41,92 Bone mineral content at the femoral neck and associated variables measured using these techniques were found to be correlated with femoral failure load,37,40,41 as was density of the trabecular bone of the greater trochanter.92 Correlations between densitometric measures and femoral strength have also been established using dual-energy projection radiography42,93 and dual photon absorptiometry (DPA).43,44 Although these investigations established a correlation between densitometric measures and failure load, the loading conditions studied were limited to the frontal plane and in some instances were highly nonphysiological. This limits extrapolation of these results to predicting in vivo loads likely to be associated with many hip fractures. The relationships between densitometric parameters measured via quantitative computed tomography (QCT) and femoral structural capacity have also been widely investigated (see Table 33.1). Alho and colleagues45–49 established correlations between QCT densities of both cortical and trabecular bone regions and femoral strength under bending and rotational loading conditions. Under the loading conditions examined, these investigators found that mass-related measurements (estimated by considering QCT density as well as cross-sectional area measurements) generally performed better than QCT density measurements alone in predicting femoral failure load. The results of these studies showed that, under axial loading conditions, trabecular parameters were better correlated with mechanical behavior than cortical parameters.45,49 By contrast, under rotational loading conditions, cortical parameters were better correlated with failure load.48 Esses et al.50 also investigated QCT measurements as predictors of femoral strength ex vivo. These authors found that the average QCT density of trabecular bone at the subcapital region was the best predictor of strength under loads representing simplified single-leg stance. Similarly, Smith and co-workers52 also found that trabecular QCT parameters were correlated with the compressive force required to produce impacted subcapital fractures. The importance of considering geometric factors in the mechanical behavior was reflected in the work of Cordey et al.,94 who found that apparent femoral stiffness under stance loading conditions was better correlated with geometric than densitometric parameters measured by QCT. The work of Lotz and Hayes51 was the first to examine relationships between QCT parameters and femoral strength under loads associated with falls on the greater trochanter. These investigators found that the product of the average trabecular QCT number and the total cross-sectional area of the bone at the intertrochanteric region was the best predictor of failure load under fall loading conditions. Lang et al.53 measured trabecular and integral bone mineral density (BMD) using an automated QCT technique. Their results were consistent with those of Lotz and Hayes in that trochanteric trabecular BMD was strongly correlated with femoral strength under fall loading conditions.51 However, in contrast to the results of Lotz and Hayes51 and Lang et al.,53 Cheng and colleagues58 found that trochanteric cortical area was best correlated with femoral strength under loads simulating a fall on the greater trochanter. The authors of these studies emphasized the advantages of QCT in predicting femoral failure load in that QCT allows examination of the separate contributions of cortical and trabecular bone, and also allows CH-33 Page 14 Monday, January 22, 2001 2:13 PM

33-14 Bone Mechanics

for separate consideration of bone cross-sectional area. A consistent conclusion that can be drawn from this work is that incorporation of cross-sectional geometry improved predictions of femoral structural capacity, thereby demonstrating the independent contribution of geometry in determining the stress distribution within the bone. By contrast to QCT, dual energy X-ray absorptiometry (DXA) provides a two-dimensional array of intensity proﬁles that are an integrated measure of bone density and geometry. Numerous investigators have reported relationships between regional BMD values measured using DXA and ex vivo femoral strength under both stance54,86,95 and fall31,32,54,56–61 loading conditions (see Table 33.1). The incorporation of DXA-based structural geometry into beam bending models of the proximal femur has resulted in improved predictions of femoral strength over DXA-based density parameters alone.60 Courtney et al.56 noted that once either the densitometric or geometric data were accounted for, age was not an independent predictor of fracture load. In general, DXA-based density parameters have been found to predict femoral failure load nearly as well as ﬁnite-element models.54,55

33.3.2 Spine Understanding the mechanical behavior of the spine ex vivo and the relationship between mechanical behavior and imaging parameters has provided insight into important factors that can be useful in predicting the stress distribution and strength properties of this skeletal structure. The introduction of dual-photon absorptiometry (DPA) for in vivo assessment of bone mineral content (BMC) has led to its use in applications simulating in vivo measurements and their relationship to mechanical parameters in the spine.69,71,72,80,96 Different specimen types have been used to determine the mechanical competence of vertebral bodies (see Table 33.2). Hansson et al.71 noted a gender difference in vertebral strength; however, they did not note any difference between the levels tested (L1–L4) when the specimens from both sexes were combined. The studies presented in Table 33.2 suggest that density measures from DPA could be used to predict accurately the compressive properties of spinal bone.69,71,72,80,96 The direction in which DPA measurements are performed in the spine has also been considered for its potential effect on the correlations with mechanical strength parameters. Ortoft et al.80 found that BMC measurements from DPA performed in a lateral direction gave better correlations with vertebral compressive loads, compared with BMC measurements obtained in the anteroposterior (AP) direction. These authors noted that measurements done in the AP direction include densitometric data from the posterior elements, which do not necessarily contribute as signiﬁcantly as the vertebral body to the weight-bearing capabilities of the vertebrae. In addition, this study found that using BMC measures

corrected for vertebral height (BMDT) gave a slightly improved correlation with vertebral body compressive strength. Bone densitometric measurements in the spine determined from QCT have also been utilized to predict the mechanical properties of vertebral bone (see Table 33.2).2,82–87,97 These studies provided positive indications of the value of using QCT as a noninvasive tool to evaluate the mechanical properties of vertebral trabecular bone. Hayes et al.2 provided a comprehensive review up to 1991 of the efforts to relate QCT measures with directly measured density and vertebral bone strength. One of the advantages of using QCT is that this imaging modality can provide geometric dimensions in addition to density measurements. Another advantage is that densitometric data can be obtained for both cortical and cancellous bone from a single measurement. McBroom et al.82 conducted one of the earliest studies supporting the idea that QCT could be used as a predictor of vertebral fracture risk; they also evaluated the contribution of the cortical shell to the mechanical competence of lumbar vertebral bodies by comparing the compressive strength of vertebral bodies with and without the cortex. These investigators showed that the removal of the cortex was associated with approximately a 10% reduction in vertebral load to failure. Efforts to relate combined QCT-derived density and geometric measurements to mechanical parameters of vertebral bone strength have also been reported (see Table 33.2).81,83,85,86,90 Biggemann et al.83 and Brinckman et al.85 have pointed out that combining bone density measurements with end plate CH-33 Page 15 Monday, January 22, 2001 2:13 PM

Applications of Bone Mechanics 33-15

FIGURE 33.4 Methodologies used to derive input data for determining the relationship between vertebral density, geometry, and strength: (A) mechanical testing; (B) morphometric measurements; (C) QCT; (D) DXA. (From Edmondston, S.J. et al., Osteoporosis Int., 7(2), 142–148, 1997. With permission.)

cross-sectional area measurements, as determined from QCT, provide a more significant correlation with thoracolumbar vertebral body compressive strength than QCT bone density measurements alone. The importance of considering the end plate cross-sectional area cannot be overlooked since cross- sectional area is inversely proportional to failure stress. Brinckmann et al. obtained a specific prediction formula for in vivo determination of compressive strength based on both density and end plate area with an error limit of 1 kN.85 Cody et al.86 combined QCT-derived regional bone density measurements (rBMD) with measurements of the minimum cross-sectional area of vertebral bodies to predict thoracolumbar vertebral fracture strength. Considering density measures from multiple regions (superior to inferior, and anterior to posterior) of the cancellous bone of the vertebral bodies is important because there are specific vertebral body locations that are more commonly selected as locations for measurement of in vivo BMD. In addition, McCubbrey et al.87 showed that the distribution of cancellous BMD measures had different effects on the predictive models of static failure properties compared with models of fatigue-based failure properties. In their study, anterior density regions were more often included in the static predictive models, while posterior regions were more predictive of fatigue properties. These models indicate that different failure mechanisms may be involved in the two different mechanical test types, and, as such, care should be used when interpreting the findings from ex vivo testing when test protocols and loading conditions differ among studies (see Table 33.2). Edmonston et al.90 combined morphometric measurements from QCT scans with BMD measurements from DXA to assess the relative contributions of bone densitometry and vertebral morphometry in the prediction of thoracolumbar vertebral body strength (Fig. 33.4). Contrary to previous studies, they suggested that vertebral deformity and size (as assessed by vertebral morphometry) made only a minor additional contribution to the prediction of vertebral strength compared with that provided by bone densitometry alone. Other studies have evaluated the feasibility of using QCT to characterize the cortical shell thickness and end plate, and the dependence of these measurements on age, gender, and anatomical region within the vertebral body.98 These geometric measurements could lead, indirectly, to a better understanding of the role of these components in vertebral mechanical properties and their relative importance in fracture etiology. The evaluation of changes in thickness of these components and the effect of such changes on overall vertebral mechanical properties are perhaps better suited for evaluation using computational models, as presented later in this chapter. In contrast to QCT, BMD measurements obtained from DXA have been utilized much less in ex vivo studies for prediction of mechanical properties of vertebral bone. Investigators have used BMD measurements from DXA to predict failure properties for both thoracic and lumbar vertebrae.67,88–100 Myers et al.99 showed that supine lateral BMD measurements provided a better assessment than anteroposterior BMD of the fracture properties of lumbar vertebral bodies. This was in agreement with the study of Ortoft et al.,80 which showed the effects of the presence of the posterior elements in the BMD measurements taken in the CH-33 Page 16 Monday, January 22, 2001 2:13 PM

33-16 Bone Mechanics

AP direction. In a follow-up study, Moro et al.89 used BMD measurements of cadaveric lumbar vertebrae obtained using DXA in both the lateral and AP directions and found that these provided a valid assessment for predicting compressive strength of both lumbar and thoracic vertebral bodies. The importance of this approach was that it evaluated the feasibility of using lumbar BMD to assess the mechanical competence of thoracic vertebrae, since BMD measurements at thoracic levels are limited due to shadowing of the ribs. Since BMD measured by DXA is the BMC of a region of interest divided by the projected area in the view of the DXA scan, both apparent density and geometric bone properties can influence DXA measurements.67 The relative structural contributions of the cortical shell, end plates, vertebral body and end plate cross-sectional area, and the trabecular bone microstructure are important in the prediction of vertebral bone strength. Consideration of these variables will allow increased understanding of how loads are distributed among different regions of the vertebrae, thereby providing better indicators of the strength of vertebral bodies. All of these factors are potentially functions of age, and can have a composite effect on the load-bearing capacity of the vertebra. The role of the cortical ring thickness and its effects on vertebral bone strength have been evaluated.78,101 Vesterby et al.78 showed that the cortical ring thickness may play an important role in predicting the compressive strength of vertebral bodies. Mosekilde et al.101 found that the thickness of the cortical ring changes with age, noting that this and changes in other aspects (internal architecture, dimensions, size) all contribute to the overall strength of vertebral bone. In a separate cadaveric lumbar vertebrae study, Mosekilde et al.76 reported that male vertebrae had significantly greater cross-sectional area and a significant increase in vertebral body size with aging. The authors speculated that this could compensate for the un- avoidable loss of vertebral bone density and ultimate strength with age. This was in contrast to females, where no age-related increases in cross-sectional area of vertebrae have been demonstrated. A number of investigators have examined the mechanical properties of vertebral bodies and their components (primarily trabecular bone) by evaluating the effects of applied loads on ex vivo specimens. Testing parameters, sample types, number of samples, and loading rates are summarized in Table 33.2. Anisotropy in thoracic and lumbar vertebral trabecular bone has been characterized by Mosekilde and Viidik.102 Even though the relationships between whole vertebral body strength and age and trabecular bone strength and age were very similar, at any age, the maximum compressive strength for whole vertebral bodies was about 1.6 MPa higher than that of the trabecular bone specimens. In addition, in a separate study, Mosekilde et al.70 showed that the compressive properties of whole vertebral bodies depended mainly on the compressive strength of their trabecular bone, and that there was an increase in diameter of vertebral bodies with age (4 to 5 mm from age 20 to 80 years), attributable to periosteal growth. This increase in diameter led to a significant increase in cross-sectional area, and therefore an age-related reduction in the maximum compressive stress. Trabecular bone microstructure has long been considered for its role in vertebral bone strength and as a contributory factor to fracture risk.77,79,103–105 In two separate studies, Mosekilde77 and Moseklide and Danielsen103 concluded that the strength of vertebral trabecular bone depends not only on bone mass, but also on the continuity of the trabecular bone. Furthermore, vertebral trabecular bone strength was inversely correlated with age when trabecular bone volume changes were taken into account. Both trabecular bone continuity and trabecular bone volume were an indication of the status of trabecular bone microstructure. Specific changes in trabecular morphology observed with decreasing bone density, such as number and thickness of trabeculae and intertrabecular spacing, posed a direct threat to the strength of vertebral trabecular bone.104

33.4 In Vivo Fracture Risk and Imaging Parameters

33.4.1 Proximal Femur Studies centered on evaluating in vivo fracture risk and its relationship to imaging parameters have conﬁrmed and extended what has been learned about skeletal mechanics from ex vivo studies. The clinically observed increases in proximal femur fracture risk with reductions in bone density106,107 are consistent CH-33 Page 17 Monday, January 22, 2001 2:13 PM

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with ex vivo studies that have demonstrated strong correlations between bone density and fracture load (see Table 33.1). However, there is a substantial amount of overlap in bone density values between patients with femur fracture and controls without fractures.108,109 Parameters associated with the mechanics of falling have been shown to be strong independent predictors of proximal femur fracture,110–112 consistent with experimental and modeling studies that have demonstrated reductions in femoral strength associated with impact direction.32,33 Clinical studies have provided substantial (albeit indirect) insight into the contributions of geometric parameters to femoral strength. Using femoral radiographs, Horsman and colleagues113 found that femoral cortical area, lateral cortical width, and calcar width were significantly lower in fracture cases compared with controls.113 Beck et al.114,115 evaluated changes in cross-sectional moment of inertia (CSMI) with age in men and women, noting that although the data for men suggested compensatory increases in CSMI with age, CSMI decreased with age in postmenopausal women. Using a simple beam-bending model of the femur, these authors predicted a 4 to 12% per decade increase in femoral neck stresses in women due to an apparent lack of geometric restructuring. Significant differences in hip axis length measured using DXA have been demonstrated between patients with femur fracture and controls, and differences of only a few millimeters were found to be associated with substantial differences in femoral fracture risk.116 Despite lower bone mass, Japanese women have a lower risk of femur fracture, which could be related to the fact that they have shorter femoral necks and/or smaller neck–shaft angles.117 It may be that femoral neck axis length and loading angle combine to determine the moment arm and the bending moment acting on the femoral neck, and therefore the likelihood of fracture.32 Gluer et al.118 studied pelvic radiographs, and found that reduced thickness of the femoral shaft cortex and femoral neck cortex, as well as a wider trochanteric region, were all significant and independent predictors of proximal femur fracture. Furthermore, a combination of these parameters predicted femur fracture at least as strongly as femoral neck BMD, thus emphasizing the importance of geometric parameters in femoral fracture risk. The material and geometric properties of a bone, combined with the applied loads, determine both the load at which the bone will fracture and the resulting fracture pattern. Studies that have examined fracture patterns in the femur provide indirect but useful information with regard to stress distributions and mechanical behavior. Several investigators have found differences between populations of patients who suffer cervical vs. trochanteric femur fractures.119–123 A consistent result from studies that have evaluated fracture patterns is that patients who suffer trochanteric fractures tend to be older,120,123,124 and the ratio of trochanteric to cervical fractures increases with age.123,125 Regional differences in femoral BMD may also play a role in determining whether a fracture is cervical or trochanteric. Eriksson and Widhce120 found that, although both trochanteric and femoral neck BMD were lower in patients with trochanteric fracture, patients who suffered femoral neck fractures had lower femoral neck BMD than trochanteric BMD. Greenspan et al.122 noted that trochanteric BMD was lower in patients with trochanteric fracture than in those with femoral neck fracture; furthermore, they found that both a decrease in trochanteric BMD and an increase in femoral neck BMD were independently associated with trochanteric fracture. These investigators also evaluated the effects of factors related to fall mechanics, but found that these parameters did not distinguish between the two types of fractures. This is consistent with the results of ex vivo fracture experiments, in which variations in fall loading direction did not have a statistically significant effect on fracture pattern.32 These findings, combined with the result that differences in regional BMD predict femur fracture type, suggest that intrinsic factors (such as density distribution) may contribute more strongly to fracture pattern than differences in loading conditions. This hypothesis is further supported by the fact that most subsequent contralateral proximal femur fractures are of the same type as the first fracture.126–128 Intrinsic factors related to geometry may also contribute to type of proximal femur fracture. For example, Ferris and colleagues121 found that patients with trochanteric fractures had significantly shorter femoral neck lengths than patients with subcapital fractures. Further work is necessary to elucidate fully the relative contributions of density variations and loading configuration to type of femur fracture. CH-33 Page 18 Monday, January 22, 2001 2:13 PM

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33.4.2 Spine Prediction of vertebral bone strength in vivo is required to assess the risk of fracture or to explore potential causes of injury by relating vertebral strength to calculated spinal loads under speciﬁc circumstances. Noninvasive in vivo measurements of the spine have been used to predict fracture risk and to monitor the effects of interventional regimens for osteoporosis. Biggeman et al.129 utilized QCT-based parameters, such as trabecular bone density and end plate area, to determine vertebral compressive strength in vivo using the relationship previously proposed by Brinckmann et al.85 This methodology had been previously validated ex vivo with a standard error of less than 0.95 kN.83 A limiting vertebral strength value of 3 kN was suggested as the minimum value below which there would be an extremely high risk of insufﬁciency fractures, which typically result from excessive loading of normal spines or routine loading of osteoporotic spines.129 The use of BMD measurements at multiple sites and their relationship to a spine deformity index (SDI) have been investigated by Sogaard et al.130 in a group of women with osteoporosis. This SDI measure was introduced as a standardized method for detecting vertebral fractures by comparing individual vertebral body heights to their original heights as predicted from measurements of T4. After performing peripheral density measurements at the distal forearm (SPA) and iliac crest (ash density), and comparing these with direct density measurements at the lumbar spine (DPA), it was concluded that lumbar BMC was the best parameter for predicting vertebral fracture risk. It was also noted that the loading history as related to microfractures, the rate of repair, and resulting changes in bone architecture must play a role in SDI as well. Gordon et al.105 also used measurable density parameters from different noninvasive modalities to assess vertebral fracture risk in vivo. The use of high-resolution QCT images to assess trabecular microstructure in conjunction with BMD measurements from DXA enhanced the ability to evaluate vertebral fracture risk in a group of women, which included some who had sustained vertebral fractures. This study showed the importance of including parameters other than bone mineral density to assess vertebral fracture risk. The trends for future assessment of in vivo vertebral fracture risk lie in the potential to combine measurements from noninvasive modalities with mathematical models to localize potential vertebral fracture sites and to quantify the load levels that can induce them and the resulting stresses at the tissue level. Eventually, it may be possible to monitor and quantify the effects of therapeutic interventions that are aimed at preventing osteoporosis at the microstructural level.

33.5 Development of Models of Skeletal Structures

33.5.1 Proximal Femur Although studies of ex vivo mechanical behavior and in vivo fracture risk provide important empirical information about skeletal behavior, many questions remain regarding the contributions of various factors to whole-bone mechanics. The development of techniques for analytical modeling of skeletal structures provides a complementary approach that can aid in answering questions about bone behavior that are difficult or impossible to address experimentally or clinically. Mathematical models are particularly powerful in that they provide estimates for quantities that cannot be directly measured experimentally, such as internal stresses in whole bones. These models are intimately connected with ex vivo studies, in that experimental data are used as inputs to models and for validation purposes. The earliest structural models of the proximal femur took the form of analytical expressions describing the stress distribution within the bone, derived using simple beam theory.35,131–134 Early calculations of the principal stress distributions under loads simulating stance or gait were noted to reflect trabecular architecture within the proximal portion of the femur.132,133 Much of the early theoretical work served to establish the fact that fundamental principles of mechanics could be used to estimate the stress distribution within a complex skeletal structure such as the femur. Backman35 was among the first to utilize an analytical model of the femur to address an issue in clinical orthopedics, specifically, fracture of the proximal femur. Backman developed a structural model of the CH-33 Page 19 Monday, January 22, 2001 2:13 PM

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proximal femur to compare the distribution of stresses in the femoral neck under loads assumed to be associated with gait, muscular contraction, and falls on the greater trochanter. He modeled a cross section of the femoral neck using nonconcentric inner and outer ellipses to represent the cortical shell boundaries, and applied combinations of normal, shear, and bending loads at the femoral head. Although this analysis was limited to the estimation of stresses at a single cross section of the femoral neck, comparison of stresses associated with different loading conditions demonstrated the potential importance of loads that act outside of the frontal plane in producing fractures, and the results suggested that the proximal femur was weakest under these types of loads. Other investigators have incorporated geometric measurements from X-rays into beam-bending calculations to predict either the failure load of the proximal femur39,40,93 or the ultimate stress at the femoral neck.37 The shortcomings associated with early closed-form solutions for determining stress distributions, along with advances in high-speed computing and the contemporaneous development of the finite- element method, led to the use of the finite-element method as a tool for estimating stresses in skeletal structures. Brekelmans et al.135 introduced the finite-element method for use in orthopedic research because of its suitability for structures with complex geometry, material properties, and load conditions. Although early finite-element models of the femur were limited by their two-dimensional nature and simplified material property distributions,134–136 the early work was important as an improvement over previous experimental and analytical techniques. In particular, Rybicki et al.134 compared a two-dimensional finite-element model of the femur with an analysis based on simple beam theory, and noted that a continuum-based (i.e., finite-element) model could improve stress predictions in places where the geometry did not approximate a slender beam (e.g., the femoral neck and intertrochanteric region). Following the introduction of the finite-element method for the analysis of whole-bone structures, investigators focused on the refinement of structural models to improve stress predictions. A natural increase in complexity was the extension of two-dimensional finite-element models to three dimensions. Valliappan et al.137 reported results for a three-dimensional finite-element model of the proximal portion of a human femur, and compared them with results from two-dimensional finite-element analysis and simple beam theory. These comparisons demonstrated significant differences in predicted stresses, particularly in the proximal region of the femur. The work of Rohlmann et al.138 represented further refinement of femur modeling techniques, specifically with the incorporation of limited variations in bone material properties based on density measurements from radiographs, along with increased mesh density. Both Valliappan et al. and Rohlmann et al. attempted validation of their models using surface strain measurements on human femora, with significant differences between experimental and theoretical results. Although these early three-dimensional models represented an important improvement over previous two-dimensional models and beam theory analyses, these authors also recognized the need for improvements in geometry and material property descriptions. An important step in the evolution of structural models of the human femur was from the prediction of stress distributions to the prediction of structural failure. Vichnin and Batterman139 developed a three- dimensional model of a human femur, using a transversely isotropic material model for the diaphyseal cortex. The primary goal of their study was to compare the behavior of a femur with and without a prosthesis. Since only diaphyseal stresses were of interest, this model had limited applicability to proximal femur fracture. However, the investigation represented an early attempt to utilize engineering failure surfaces for bone material in the prediction of failure at the whole-bone level. The work of Lotz and colleagues140,141 was an important step in the prediction of fracture of the proximal femur using finite-element models. These investigators developed models of the proximal femur using geometry and material properties based directly on QCT. Of critical importance in this work was the investigation of fall as well as stance loading conditions, since falls are associated with large numbers of proximal femur fractures among elderly people.24–27 This represented an evolution beyond previous models, which had investigated only stance and gait loading conditions.136–139 Attempts were made to model the inhomogeneity of bone material properties, and care was taken to account specifically for the contribution of the cortical shell in the proximal region. Both linear and nonlinear material models were used. Although comparisons between predicted and measured surface strains showed substantial discrepancies, CH-33 Page 20 Monday, January 22, 2001 2:13 PM

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these models were reasonably effective in predicting both the onset of yielding and bone fracture for both stance and fall loading conditions. Results from these stress analyses pointed to the potential structural importance of the trochanteric and subcapital regions in fracture of the proximal femur, and demonstrated a dramatic difference in stress distributions for stance and fall loading conditions. The desire to predict failure of the proximal femur accurately led to increased sophistication of closed- form stress analyses in parallel with refinements in finite-element models. Raftopoulos and Qassem142 proposed a three-dimensional, composite curved beam model of the human femur for prediction of stresses; however, no numerical results were presented. An alternative approach involved the incorporation of bone mineral data into beam bending calculations. Beck and colleagues95 introduced a computer program to estimate femoral neck cross-sectional areas and moments of inertia from DPA data, and to incorporate these cross-sectional properties into a simple beam bending model. Comparisons between predicted and measured femoral fracture loads suggested that beam bending models incorporating structural geometry from DXA could improve fracture prediction over bone mineral assessment alone. Yoshikawa and co-workers143 proposed a similar beam bending model based on DXA, and expanded the loading conditions to include a fall on the greater trochanter. An important step in the evolution of DXA-based structural models of the proximal femur was the use of a curved beam model to estimate stresses.144 Using a three-dimensional, QCT-derived finite-element model of the femur as a standard of comparison, these authors found that stress predictions based on the curved beam solution were better than those utilizing the conventional flexure formula. Furthermore, the curved beam analysis identified stress peaks at the femoral neck as well as at the medial intertrochanteric region under fall loading conditions, both common sites of femur fracture. Although DXA-based structural models provide information that may be useful in evaluating fracture risk, the DXA imaging technique is intrinsically limited to two dimensions. Therefore, DXA-based structural analyses cannot incorporate loads that lie outside the frontal plane, under which the femur is typically weaker,35,140,141 and under which many proximal femur fractures occur. A natural progression in the refinement of structural models of the proximal femur was the development of improved, QCT-based finite-element models. Substantial effort has been devoted to the development of modeling techniques that incorporate geometry and material property distributions that are unique to a particular bone. Keyak and co-workers145–147 introduced an automated method for generating QCT-based femur models, using cube-shaped elements and density-based material properties (Fig. 33.5). Although this modeling technique produces a suboptimal representation of the bone surface, predictions of femoral stiffnesses and failure load using the technique have been reasonably well correlated with experimental measurements on the same bones.54,55 Alternative QCT-based modeling techniques have allowed for accurate representation of the surface contours of the proximal femur (Fig. 33.6).148–150 Much of the effort in finite-element modeling of the proximal femur has been oriented toward refinements in model geometry and material property distribution that have led to better predictions of stress and failure load. Significant progress has been made in this regard; however, limitations related to current finite-element modeling techniques remain to be addressed. An important issue that has rarely been directly addressed in models of the femur is how to model the metaphyseal shell properly. The geometric and material properties of the cortical shell have been demonstrated to be related to femur fracture risk,113,118 and therefore the cortical shell likely plays an important structural role in the proximal femur. Perhaps the most ambitious attempt at accurately modeling the cortical shell was contributed by Lotz et al.140,141,151 In this series of finite-element studies, the metaphyseal shell was modeled using elements approximately 1mm thick, with material property values based on mechanical tests of metaphyseal bone from the contralateral femur. A set of “reduced” metaphyseal bone material properties was defined for portions of the femur where the cortical shell thickness was less than 1 mm. Using a generic femur geometry, these investigators found that the percentage of total load carried by the cortical shell varied substantially with location in the proximal femur. Under loads associated with both gait and falls, there was a shift in the distribution of load carried by the cortical shell from approximately 30% in the subcapital region to 96% at the base of the femoral neck. Furthermore, the percentages of load transferred by the cortical shell were not in proportion to the local tissue volume. Since differential rates of loss with age may occur between cortical and trabecular bone,152,153 accurate prediction of femoral structural CH-33 Page 21 Monday, January 22, 2001 2:13 PM

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FIGURE 33.5 Voxel-based femur model with 14,534 nodes and 11,604 cube elements measuring 3 mm on a side. (From Keyak, J.H. et al., J. Biomech., 31(2), 125–133, 1998. With permission.)

FIGURE 33.6 Smooth surface femur model of a cadaveric femur. Elements were mostly hexahedral, with tetrahe- dral shapes at the transition region between the shaft and epiphysis. (From Mourtada, F.A. et al., J. Orthop. Res., 14(3), 483–492, 1996. With permission.) CH-33 Page 22 Monday, January 22, 2001 2:13 PM

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capacity (and its changes with age) will likely require detailed modeling of the cortical shell. Current QCT-derived voxel models do not allow for effective modeling of the metaphyseal shell,54,55 which could account in part for discrepancies between predicted and measured failure loads. Furthermore, even smooth-surface models of the femur with material properties derived from QCT data148–150,154 are subject to volume-averaging effects, which could limit the accuracy of cortical shell properties. Although much of the early and current work in structural modeling of the proximal femur for fracture prediction remains method oriented rather than problem oriented, as has been described previously by Huiskes and Chao,155 finite-element models have become sufficiently sophisticated to be used as tools for addressing complex biologic problems. For example, Lotz et al.151 developed a finite-element model to study the effects of age-related density changes on the stress distribution in the proximal femur during gait and falls, independent of variations in geometry. The results of this analysis shed light on the relative contributions of cortical and trabecular bone in load transfer in the proximal femur, and provided insight into theories related to the pathomechanics of osteoporosis. Ford and colleagues33 used a QCT-based model to examine the effects of impact direction on structural capacity during falls, and found that reductions in strength associated with variations in impact direction were comparable to strength reductions associated with age-related bone loss.

33.5.2 Spine Mathematical modeling of the spine, similar to that of the femur, provides a complementary approach to understanding bone behavior and, in particular, to calculating stress levels that are not possible to obtain experimentally or clinically. Comprehensive reviews related to mathematical modeling of spine structures show that early applications of the finite-element method focused primarily on understanding the behavior of intervertebral disks,155,156 and that use of the finite-element method in the spine evolved first in the thoracolumbar region.156–158 Only recently have these efforts shifted toward applications in the cervical spine.156,159–161 The studies presented here focus on the use of mathematical modeling to understand what factors affect the stress distribution in vertebral bodies. Models developed to study the effects of specific clinical interventions (including spinal instrumentation) are beyond the scope of this chapter. Although spine finite-element models have evolved in complexity from two-dimensional models representing vertebral slices to complex multisegment models, this section reviews representative models of single vertebral bodies and single functional spinal units (two vertebrae and interconnecting soft tissue). Several models of single vertebral bodies have been developed to study vertebral body stresses.68,162–166 Ranu’s162 idealized model of a single vertebra showed that under compressive loading, the maximum stresses were at the junction of the pedicles and the vertebral body. High stresses also appeared at the anterior aspect of the vertebra, consistent with the location of wedge fractures. Mizrahi et al.163 developed an idealized model of an isolated lumbar vertebra to examine how material properties affected end plate and cortical shell stresses. Under uniform compressive loading simulating degenerated disks, the model indicated that the peak stresses in the end plate and cortical shell were sensitive to the modulus of the underlying trabecular bone. A 50% reduction in trabecular bone modulus increased the peak stress in the end plate by 74%. In addition, disproportionate reductions in trabecular and cortical bone moduli increased peak stresses in the cortical shell and end plate. The relevance of these modulus changes is that they could reflect those typically seen in patients with osteoporosis. Although these models did not reflect the exact geometry of a vertebral body or local variations in the thickness of the cortical shell and end plate, they provide useful insight into the role of material property changes in determining the stress distribution. The influence of geometric factors on overall strength has been examined in single vertebral body models.68,164,166,167 A three-dimensional finite-element model of L1 with uniform compressive loading was used to examine the effect of the pedicles and posterior arch on strain distributions within the vertebral body.68 Whyne et al.68 found that inclusion of the posterior arch resulted in substantial decreases in maximum strain and posterior wall displacement. Improvements in the geometric and material property representation of a single vertebra were reported in a three-dimensional model of a midcervical vertebra generated from QCT data by Bozic et al.164 The highly refined mesh of this voxel-based model incorporated CH-33 Page 23 Monday, January 22, 2001 2:13 PM

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three-dimensional variation in material properties with moduli derived from QCT data. Under axial compressive loading, this model predicted the initiation of failure in the central cancellous region of the vertebral body, consistent with typical cervical burst fractures. The single lumbar vertebra model developed by Martin et al.167 was also generated based on QCT data from cadaveric specimens and utilized the QCT data to assign material properties. This model was utilized to assess the stiffness and failure load of the vertebral body under a distributed compressive load on the superior end plate, and was successfully validated with experimental measurements. A single cervical vertebra model (C2) developed using the geometry of a cadaveric specimen was reported by Teo et al.166 This model showed that the stress distribution within this vertebra was influenced by the direction (45, 0, 45°) of the applied load on the anterior surface of the odontoid process. The regions of highest compressive stress corresponded with areas of fracture seen clinically. A number of models have been developed to evaluate the load-carrying capacity of the cortical shell and trabecular core,165,168,169 and the effects that these have on the overall stiffness of vertebral bodies.170 Faulkner et al.168 used QCT data to develop patient-specific finite-element models of lumbar vertebral bodies to examine the role of the vertebral cortex in the overall vertebral body strength under distributed compressive axial loading. These models predicted that the shell contributed 12% to the total vertebral strength in healthy individuals and 50% in ones with osteoporosis. In contrast, Burr et al.169 had predicted from a parametric finite-element modeling study that the shell carried about 50% of the vertebral body force in a young individual, and about 90% in an individual with osteoporosis.169 Using a geometrically simple model of a single lumbar vertebral body, Silva et al.165 evaluated parametrically the relative load-carrying roles of the shell and the centrum. The findings from this model supported the notion that the shell accounts for only about 10% of the vertebral strength in vivo and that the cancellous core is the dominant structural component of the vertebral body. This is in contrast to previous studies that had reported a wider range of contribution of the cortical shell toward the overall strength of the vertebral body.82,168,169,171 In a recent study by Liebschner et al.,170 the effects of cortical shell and end plate material property changes on the overall vertebral body stiffness were examined in QCT-based whole vertebral body models. These models showed that vertebral body stiffness was relatively insensitive to end plate modulus variations compared with models that were evaluated with the cortical shell completely removed. Unlike previous models that varied end plate and cortical shell thickness, these models included a constant cortical shell and end plate thickness. These different approaches to examining the contribution of the cortical shell to overall vertebral strength make direct comparison of the studies difficult. Models of single vertebral bodies provide insight into the mechanical behavior of these bones, but modeling a full functional spinal unit (FSU) has been shown to be a more accurate method for evaluating the internal stresses in the spine. With a more complete model, the effect of other spinal structures on the overall strength of vertebrae can be evaluated. In their 1995 review of the state of the finite-element method in spine mechanics, Gilbertson et al.156 summarized pertinent contributions from single FSU models subjected to different kinds of loading. Comparison of predicted stresses and strains from various reported finite-element models with available ultimate stress and strain values indicated that the most vulnerable components under compressive loading were the cancellous bone and the end plate adjacent to the nucleus. This is consistent with findings from prior experimental studies.65,172 Under torsional loading the posterior bony structures, including the junction of the pedicle and the vertebral body and facets, appeared to be the most vulnerable components. In addition, models showed that most of the torsional load was transmitted through the cortical shell and not the cancellous core, thereby making the cortical shell more vulnerable to shear failure under this type of loading. These findings have also been shown in ex vivo cadaveric work under torsional loading.173 One of the landmark publications of finite-element modeling of the spine is that by Shirazi-Adl et al.,174 in which they present an L2-L3 disk-body unit model based on the geometry of a cadaveric specimen (Fig. 33.7). This model showed that under an axial compressive load of about 3000 N, the most vulnerable elements in a disk-body unit with a normal disk were the cancellous bone and the end plate adjacent to the nucleus. Shirazi-Adl et al. extended their disk-body unit to include posterior elements, facet joints, and ligamentous structures to provide a more complete representation of a spinal motion segment and loaded CH-33 Page 24 Monday, January 22, 2001 2:13 PM

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FIGURE 33.7 L2-L3 motion segment model. (From Shirazi-Adl, A. et al., J. Biomech., 19(4), 331–350, 1986. With permission.)

it in the sagittal plane under flexion and extension.175 This model was then evaluated under more complex loading conditions including axial torque and axial torque combined with compression.176 The inclusion of the posterior elements in three-dimensional models of single motion segments of the spine had been done earlier by Hakim and King.177 Although their model was symmetric about the sagittal plane, it included separate element representations for trabecular bone, cortex, end plate, and posterior elements. The model was experimentally validated by comparison with vertebral body surface strains. One of the earliest three- dimensional models to incorporate QCT-derived geometry for development of a finite-element model of a single lumbar motion segment, by Goel et al.,178 incorporated all biomechanically relevant structures of the spine and was validated against experimental data. The recent trend toward voxel-based model generation has been utilized in the spine,164,179,180 but to a lesser extent than in femur models. The midcervical vertebral body model of Bozic et al.164 was voxel-based, but it did not incorporate details of trabecular microstructure. Hollister et al.179 utilized a substructure-based voxel modeling approach to determine the effect of trabecular microstructure on whole vertebral body mechanics. A three-dimensional global finite-element model of a vertebral body was generated, with geometric input from QCT, which utilized as input the effective stiffness predicted from smaller models of trabecular bone cubes. Surface strains obtained from the global finite-element model were used as input for the cube models to determine trabecular-level strains. These smaller models showed that vertical trabeculae experienced mostly axial compressive strains, whereas horizontal trabeculae were subjected to both compressive and tensile strains. CH-33 Page 25 Monday, January 22, 2001 2:13 PM

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Incorporating trabecular-level detail in multisegmental spine models with properly deﬁned material properties for all components is the next logical step in ﬁnite-element modeling of the spine. With this level of detail, it will be possible to increase understanding of the effects of localized trabecular bone loss and changes on overall spine mechanics.

33.5.3 Future Trends in Modeling Skeletal Structures Although automated, patient-specific finite-element models may eventually be clinically useful in the assessment of both femur and spine fracture risk, an additional and potentially powerful application of finite-element models will involve parametric investigation of the factors that contribute to fracture risk. For example, well-constructed finite-element models of the femur could be used to investigate the effects of regional differences in age-related bone loss181 under multiple loading conditions, independent of differences in femur geometry. Similar parametric studies could be performed in the spine, examining the effects of changes in material properties due to either disk degeneration or aging. Finite-element models could also be utilized to examine the structural importance of various geometric parameters that are associated with femur and spine fracture risk, while potentially controlling for the confounding effects of differences in density distribution. Future use of finite-element models for the parametric examination of factors that are difficult or impossible to examine experimentally will contribute to the evolution of the finite-element method in biomechanics from “a tool of technology to a tool of science.”182

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100. Tabensky, A. D., Williams, J., DeLuca, V., Briganti, E., and Seeman, E., Bone mass, area, and volumetric bone density are equally accurate, sensitive, and speciﬁc surrogates of the breaking strength of the vertebral body: an in vitro study, J. Bone Miner. Res., 11(12), 1981, 1996. 101. Mosekilde, L., Vertebral structure and strength in vivo and in vitro, Calcif. Tissue Int., 53(Suppl. 1), S121, 1993. 102. Mosekilde, L. and Viidik, A., Correlation between the compressive strength of iliac and vertebral trabecular bone in normal individuals, Bone, 6(5), 291, 1985. 103. Mosekilde, L. and Danielsen, C. C., Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals, Bone, 8(2), 79, 1987. 104. Snyder, B. D., Piazza, S., Edwards, W. T., and Hayes, W. C., Role of trabecular morphology in the etiology of age-related vertebral fractures, Calcif. Tissue Int., 53(Suppl. 1), S14, 1993. 105. Gordon, C. L., Lang, T. F., Augat, P., and Genant, H. K., Image-based assessment of spinal trabecular bone structure from high-resolution CT images, Osteoporos Int., 8(4), 317, 1998. 106. Cummings, S. R., Black, D. M., Nevitt, M. C., Browner, W. S., Cauley, J. A., Genant, H. K., Mascioli, S. R., Scott, J. C., Seeley, D. G., and Steiger, P., Appendicular bone density and age predict hip fracture in women. The Study of Osteoporotic Fractures Research Group, JAMA, 263(5), 665, 1990. 107. Peacock, M., Turner, C. H., Liu, G., Manatunga, A. K., Timmerman, L., and Johnston, C. C., Jr., Better discrimination of hip fracture using bone density, geometry and architecture, Osteoporos Int., 5(3), 167, 1995. 108. Cummings, S. R., Are patients with hip fractures more osteoporotic? Review of the evidence, Am. J. Med., 78(3), 487, 1985. 109. Hoiseth, A., Alho, A., Husby, T., and Engh, V., Are patients with fractures of the femoral neck more osteoporotic? Eur. J. Radiol., 13(1), 2, 1991. 110. Hayes, W. C., Myers, E. R., Morris, J. N., Gerhart, T. N., Yett, H. S., and Lipsitz, L. A., Impact near the hip dominates fracture risk in elderly nursing home residents who fall, Calcif. Tissue Int., 52(3), 192, 1993. 111. Greenspan, S. L., Myers, E. R., Kiel, D. P., Parker, R. A., Hayes, W. C., and Resnick, N. M., Fall direction, bone mineral density, and function: risk factors for hip fracture in frail nursing home elderly, Am. J. Med., 104(6), 539, 1998. 112. Greenspan, S. L., Myers, E. R., Maitland, L. A., Resnick, N. M., and Hayes, W. C., Fall severity and bone mineral density as risk factors for hip fracture in ambulatory elderly, JAMA, 271(2), 128, 1994. 113. Horsman, A., Nordin, B. E., Simpson, M., and Speed, R., Cortical and trabecular bone status in elderly women with femoral neck fracture, Clin. Orthop., (166), 143, 1982. 114. Beck, T. J., Ruff, C. B., Scott, W. W., Jr., Plato, C. C., Tobin, J. D., and Quan, C. A., Sex differences in geometry of the femoral neck with aging: a structural analysis of bone mineral data, Calcif. Tissue Int., 50(1), 24, 1992. 115. Beck, T. J., Ruff, C. B., and Bissessur, K., Age-related changes in female femoral neck geometry: implications for bone strength, Calcif. Tissue Int., 53(Suppl. 1), S41, 1993. 116. Faulkner, K. G., Cummings, S. R., Black, D., Palermo, L., Gluer, C. C., and Genant, H. K., Simple measurement of femoral geometry predicts hip fracture: the study of osteoporotic fractures, J. Bone Miner. Res., 8(10), 1211, 1993. 117. Nakamura, T., Turner, C. H., Yoshikawa, T., Slemenda, C. W., Peacock, M., Burr, D. B., Mizuno, Y., Orimo, H., Ouchi, Y., and Johnston, C. J., Do variations in hip geometry explain differences in hip fracture risk between Japanese and white Americans? J. Bone Miner. Res., 9(7), 1071, 1994. 118. Gluer, C. C., Cummings, S. R., Pressman, A., Li, J., Gluer, K., Faulkner, K. G., Grampp, S., and Genant, H. K., Prediction of hip fractures from pelvic radiographs: the study of osteoporotic fractures. The Study of Osteoporotic Fractures Research Group, J. Bone Miner. Res., 9(5), 671, 1994. 119. Lawton, J. O., Baker, M. R., and Dickson, R. A., Femoral neck fractures—two populations, Lancet, 2(8341), 70, 1983. CH-33 Page 31 Monday, January 22, 2001 2:13 PM

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120. Eriksson, S. A. and Widhe, T. L., Bone mass in women with hip fracture, Acta Orthop. Scand., 59(1), 19, 1988. 121. Ferris, B. D., Kennedy, C., Bhamra, M., and Muirhead-Allwood, W., Morphology of the femur in proximal femoral fractures, J. Bone Joint Surg. [Br.], 71(3), 475, 1989. 122. Greenspan, S. L., Myers, E. R., Maitland, L. A., Kido, T. H., Krasnow, M. B., and Hayes, W. C., Trochanteric bone mineral density is associated with type of hip fracture in the elderly, J. Bone Miner. Res., 9(12), 1889, 1994. 123. Mautalen, C. A., Vega, E. M., and Einhorn, T. A., Are the etiologies of cervical and trochanteric hip fractures different? Bone, 18(3 Suppl.), 133S, 1996. 124. Dias, J. J., Robbins, J. A., Steingold, R. F., and Donaldson, L. J., Subcapital vs intertrochanteric fracture of the neck of the femur: are there two distinct subpopulations? J. R. Coll. Surg. Edinb., 32(5), 303, 1987. 125. Hinton, R. Y. and Smith, G. S., The association of age, race, and sex with the location of proximal femoral fractures in the elderly, J. Bone Joint Surg. [Am.], 75(5), 752, 1993. 126. Alffram, P., An epidemiologic study of cervical and trochanteric fracture of the femur in an urban population, Acta Orthop. Scand. Suppl., 65, 1964. 127. Dretakis, E., Kritsikis, N., Economou, K., and Christodoulou, N., Bilateral non-contemporary fractures of the proximal femur, Acta Orthop. Scand., 52(2), 227, 1981. 128. Finsen, V. and Benum, P., The second hip fracture. An epidemiologic study, Acta Orthop. Scand., 57(5), 431, 1986. 129. Biggemann, M., Hilweg, D., Seidel, S., Horst, M., and Brinckmann, P., Risk of vertebral insufficiency fractures in relation to compressive strength predicted by quantitative computed tomography, Eur. J. Radiol., 13(1), 6, 1991. 130. Sogaard, C. H., Hermann, A. P., Hasling, C., and Mosekilde, L., Spine deformity index in osteoporotic women: relations to forearm and vertebral bone mineral measurements and to iliac crest ash density, Osteoporos Int., 4(4), 211, 1994. 131. Wolff, J., The internal architecture of normal bone and its mathematical significance, in The Law of Bone Remodeling, Springer-Verlag, Berlin, 1986, chap. 2. 132. Koch, J., The laws of bone architecture, Am. J. Anat., 21, 177, 1917. 133. Toridis, T., Stress analysis of the femur, J. Biomech., 2, 163, 1969. 134. Rybicki, E. F., Simonen, F. A., and Weis, E. B., Jr., On the mathematical analysis of stress in the human femur, J. Biomech., 5(2), 203, 1972. 135. Brekelmans, W. A., Poort, H. W., and Slooff, T. J., A new method to analyse the mechanical behaviour of skeletal parts, Acta Orthop. Scand., 43(5), 301, 1972. 136. Brekelmans, W. A. and Poort, H. W., Theoretical and experimental investigation of the stress and strain situation on a femur, Acta Orthop. Belg., 39(Suppl. 1), 3, 1973. 137. Valliappan, S., Svensson, N. L., and Wood, R. D., Three dimensional stress analysis of the human femur, Comput. Biol. Med., 7(4), 253, 1977. 138. Rohlmann, A., Mossner, U., Bergmann, G., and Kolbel, R., Finite-element analysis and experimental investigation of stresses in a femur, J. Biomed. Eng., 4(3), 241, 1982. 139. Vichnin, H. H. and Batterman, S. C., Stress analysis and failure prediction in the proximal femur before and after total hip replacement, J. Biomech. Eng., 108(1), 33, 1986. 140. Lotz, J. C., Cheal, E. J., and Hayes, W. C., Fracture prediction for the proximal femur using finite element models: Part II—Nonlinear analysis, J. Biomech. Eng., 113(4), 361, 1991. 141. Lotz, J. C., Cheal, E. J., and Hayes, W. C., Fracture prediction for the proximal femur using finite element models: Part I—Linear analysis, J. Biomech. Eng., 113(4), 353, 1991. 142. Raftopoulos, D. D. and Qassem, W., Three-dimensional curved beam stress analysis of the human femur, J. Biomed. Eng., 9(4), 356, 1987. 143. Yoshikawa, T., Turner, C. H., Peacock, M., Slemenda, C. W., Weaver, C. M., Teegarden, D., Markwardt, P., and Burr, D. B., Geometric structure of the femoral neck measured using dual-energy X-ray absorptiometry [published erratum appears in J. Bone Miner. Res., 10(3), 510, 1995], J. Bone Miner. Res., 9(7), 1053, 1994. CH-33 Page 32 Monday, January 22, 2001 2:13 PM

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144. Mourtada, F. A., Beck, T. J., Hauser, D. L., Ruff, C. B., and Bao, G., Curved beam model of the proximal femur for estimating stress using dual-energy X-ray absorptiometry derived structural geometry, J. Orthop. Res., 14(3), 483, 1996. 145. Keyak, J. H., Meagher, J. M., Skinner, H. B., and Mote, C. D., Jr., Automated three-dimensional finite element modelling of bone: a new method, J. Biomed. Eng., 12(5), 389, 1990. 146. Keyak, J. H. and Skinner, H. B., Three-dimensional finite element modelling of bone: effects of element size, J. Biomed. Eng., 14(6), 483, 1992. 147. Keyak, J. H., Fourkas, M. G., Meagher, J. M., and Skinner, H. B., Validation of an automated method of three-dimensional finite element modelling of bone, J. Biomed. Eng., 15(6), 505, 1993. 148. McCarthy, M., Bone Geometry from CAT Scans for Finite Element Analysis—Image Processing Considerations and Modeling Effects, Ph.D. thesis, Cornell University, Ithaca, NY, 1989. 149. Edidin, A., Modeling of Bone Material Properties from CT Scans—Considerations in Biomechanical Structural Models, Ph.D. thesis, Cornell University, Ithaca, NY, 1989. 150. Merz, B., Niederer, P., Muller, R., and Ruegsegger, P., Automated finite element analysis of excised human femora based on precision—QCT, J. Biomech. Eng., 118(3), 387, 1996. 151. Lotz, J. C., Cheal, E. J., and Hayes, W. C., Stress distributions within the proximal femur during gait and falls: implications for osteoporotic fracture, Osteoporos. Int., 5(4), 252, 1995. 152. Riggs, B. L., Wahner, H. W., Seeman, E., Offord, K. P., Dunn, W. L., Mazess, R. B., Johnson, K. A., and Melton, L.J., Changes in bone mineral density of the proximal femur and spine with aging. Differences between the postmenopausal and senile osteoporosis syndromes, J. Clin. Invest., 70(4), 716, 1982. 153. Riggs, B. L. and Melton, L.J., Involutional osteoporosis, N. Engl. J. Med., 314(26), 1676, 1986. 154. Zannoni, C., Mantovani, R., and Viceconti, M., Material properties assignment to finite element models of bone structures: a new method, Med. Eng. Phys., 20(10), 735, 1998. 155. Huiskes, R. and Chao, E. Y. S., A survey of finite element analysis in orthopedic biomechanics: the first decade, J. Biomech., 16(6), 385, 1983. 156. Gilbertson, L. G., Goel, V. K., Kong, W. Z., and Clausen, J. D., Finite element methods in spine biomechanics research, Crit. Rev. Biomed. Eng., 23(5–6), 411, 1995. 157. Goel, V. K. and Weinstein, J., Biomechanics of the Spine: Clinical and Surgical Perspective, CRC Press, Boca Raton, FL, 1990. 158. Yoganandan, N., Myklebust, J. B., Ray, G., and Sances, A., Mathematical and finite element analysis of spine injuries, CRC Crit. Rev. Biomed. Eng., 15(1), 29, 1987. 159. Yoganandan, N., Kumaresan, S., Voo, L., and Pintar, F., Finite element applications in human cervical spine modeling, Spine, 21(15), 1824, 1996. 160. Yoganandan, N., Kumaresan, S. C., Voo, L., Pintar, F. A., and Larson, S. J., Finite element modeling of the C4-C6 cervical spine unit, Med. Eng. Phys., 18(7), 69, 1996. 161. Yoganandan, N., Kumaresan, S., Voo, L., and Pintar, F. A., Finite element model of the human lower cervical spine: parametric analysis of the C4-C6 unit, Spine, 119(1), 87, 1997. 162. Ranu, H. S., A vertebral finite element model and its response to loading, Med. Prog. Technol., 16(4), 189, 1990. 163. Mizrahi, J., Silva, M. J., Keaveny, T. M., Edwards, W. T., and Hayes, W. C., Finite-element stress analysis of the normal and osteoporotic lumbar vertebral body, Spine, 18(14), 2088, 1993. 164. Bozic, K. J., Keyak, J. H., Skinner, H. B., Bueff, H. U., and Bradford, D. S., Three-dimensional finite element modeling of a cervical vertebra: an investigation of burst fracture mechanism, J. Spinal Disord., 7(2), 102, 1994. 165. Silva, M. J., Keaveny, T. M., and Hayes, W. C., Load sharing between the shell and centrum in the lumbar vertebral body, Spine, 22(2), 140, 1997. 166. Teo, E. C., Paul, J. P., and Evans, J. H., Finite element stress analysis of a cadaver second cervical vertebra, Med. Biol. Eng. Comput., 32(2), 236, 1994. 167. Martin, H., Werner, J., Andresen, R., Schober, H. C., and Schmitz, K. P., Noninvasive assessment of stiffness and failure load of human vertebrae from CT data, Biomed. Tech. (Berlin), 43(4), 82, 1998. CH-33 Page 33 Monday, January 22, 2001 2:13 PM

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168. Faulkner, K. G., Cann, C. E., and Hasegawa, B. H., Effect of bone distribution on vertebral strength: assessment with patient-specific nonlinear finite element analysis, Radiology, 179(3), 669, 1991. 169. Burr, D. B., Yang, K. H., Haley, M., and Wang, H.-C., Morphological changes and stress redistribution in the osteoporotic spine, in Spinal Disorders in Growth and Aging, Takahashi, H., Ed., Springer-Verlag, Tokyo, 1995, 127–147. 170. Liebschner, M. A. K., Kopperdahl, D. L., and Keaveny, T. M., Role of vertebral shell and endplate modulus on whole vertebral body stiffness, in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Nashville, TN, 1999, 179. 171. Rockoff, S. D., Sweet, E., and Bleustein, J., The relative contribution of trabecular and cortical bone to the strength of human lumbar vertebrae, Calcif. Tissue Res., 3(2), 163, 1969. 172. Roaf, R., A study of the mechanics of spinal injuries, J. Bone Joint Surg., 42B(4), 810, 1960. 173. Adams, M. A. and Hutton, W. C., The relevance of torsion to the mechanical derangement of the lumbar spine, Spine, 6(3), 241, 1981. 174. Shirazi-Adl, S. A., Shrivastava, A. M., and Ahmed, A. M., Stress analysis of the lumbar disc-body unit in compression: a three-dimensional nonlinear finite element study, Spine, 9, 120, 1984. 175. Shirazi-Adl, A., Ahmed, A. M., and Shrivastava, S. C., A finite element study of a lumbar motion segment subjected to pure sagittal plane moments, J. Biomech., 19(4), 331, 1986. 176. Shirazi-Adl, S. A., Finite element evaluation of contact loads on facets of an L2-L3 lumbar segment in complex loads, Spine, 16(5), 533, 1991. 177. Hakim, N. S. and King, A. I., A three-dimensional finite element dynamic response analysis of a vertebra with experimental verification, J. Biomech., 12, 277, 1979. 178. Goel, V. K., Kim, Y. E., Lim, T. H., and Weinstein, J. N., An analytical investigation of the mechanics of spinal instrumentation, Spine, 13(9), 1003, 1988. 179. Hollister, S. J., Weissman, D. E., and McCubbrey, D. A., A modeling procedure to evaluate vertebral body mechanics from trabecular microstructural properties, in Transactions of the 39th Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, 1993, 176. 180. Fyhrie, D. P. and Hamid, M. S., The probability distribution of trabecular bone strains for vertebral cancellous bone, in Transactions of the 39th Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, 1993, 175. 181. Greenspan, S. L., Maitland, L. A., Myers, E. R., Krasnow, M. B., and Kido, T. H., Femoral bone loss progresses with age: a longitudinal study in women over age 65, J. Bone Miner. Res., 9(12), 1959, 1994. 182. Huiskes, R. and Hollister, S. J., From structure to process, from organ to cell: recent developments of FE-analysis in orthopaedic biomechanics, J. Biomech. Eng., 115, 520, 1993. CH-33 Page 34 Monday, January 22, 2001 2:13 PM

Ch-34.fm Page 1 Monday, January 22, 2001 2:14 PM 34 Noninvasive Measurement of Bone Integrity

Jonathan J. Kaufman 34.1 Introduction ...... 34-1 Mount Sinai School of Medicine and 34.2 X-Ray Densitometry ...... 34-2 CyberLogic, Inc. Absorptiometric Methods • Quantitative Computed Tomography • Limitations of X-Ray Densitometry Robert S. Siffert 34.3 Ultrasonic Techniques ...... 34-6 Mount Sinai School of Medicine Review of Ultrasound Theory • Tissue Characterization • Review of Experimental and Clinical Studies • Computational Methods • Directions for Future Research 34.4 Alternative Techniques...... 34-17 Micro-CT and High-Resolution Magnetic Resonance Imaging • Vibrational Methods • Plain Radiographic Textural and Pattern Analyses • Other Methods 34.5 Summary ...... 34-20

34.1 Introduction

This chapter discusses methods for noninvasively measuring skeletal integrity. The skeleton, a living structure composed of bone tissue in a state of constant turnover, adapts continually to the complex and time-dependent milieu of mechanical forces to which it is subjected. As the body ages, the ability of the skeleton to perform its primary function of weight bearing is diminished, due to a loss of bone tissue. This loss of bone occurs in both the cortical and cancellous portions of the skeleton, thinning cortices and trabeculae, increasing their respective porosities, and leading to overall increases in bone fragility and risk of minimal trauma fractures. Decreases in bone mass may arise from a host of biological, genetic, and biomechanical factors. In women, rapid bone loss occurs during the 5 years following menopause (at about 3% per year), as a result of an increase in the rate of bone remodeling and an imbalance between the activity of osteoclasts and osteoblasts, both due to estrogen deficiency.1 Slower rates of bone loss (for example, in women more than 5 years after menopause and in men after about age 55) occur in part because of an increase in parathyroid hormone levels, which may be a result of decreased calcium absorption or reabsorption.1 Bone loss can also result from biomechanical disuse, such as during extended bed rest or during spaceflight. All people lose bone as they age. Identifying those individuals with excessive bone loss and fragility is important so that preventive and/or therapeutic measures can be instituted. It is also important to be able to monitor effects of treatment. At present, there are more than 28 million individuals in the United States who are at significantly increased risk of experiencing a low-trauma fracture, and the majority of these individuals have not even been identified.2 Low bone mass leads to over 1.5 million

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minimal trauma fractures in the United States alone, with estimated annual health care costs of more than $14 billion.2 The risk of having a low-trauma fracture is inversely related to bone strength; thus, techniques for assessing bone integrity can be useful for identifying the at-risk population. However, the risk of fracture is not solely due to biomechanical properties. Other factors are also important, including genetic and environmental considerations, such as family history and likelihood of falling.3 This focuses solely on the noninvasive measurement of variables that relate directly to underlying bone integrity. The current status of two leading techniques, X-ray and ultrasonic, as well as other methods, will be reviewed, and suggestions for future research will be presented.

34.2 X-Ray Densitometry

Techniques using ionizing X-ray radiation quantitate the amount of bone at a given anatomical site. This is done by measuring the attenuation (i.e., reduction in intensity) of a beam of X-ray as it passes through bone and soft tissue. For a ﬁxed amount of soft tissue, the more attenuated the beam, the more bone mass that is present in its transmission pathway. Bone mass is the primary factor contributing to bone strength. Quantitative relationships between bone mass and biomechanical stiffness and strength have been demonstrated.4–9 Thus, it is not surprising that a number of X-ray densitometric techniques have been developed to assess bone integrity and are currently in clinical use. The primary ones are single and dual-energy X-ray absorptiometry, and quantitative computed tomography.10

34.2.1 Absorptiometric Methods X-ray absorptiometric methods quantitate total bone mineral content (BMC) in grams (g) contained within a three-dimensional (3D) region scanned by an X-ray beam. Absorptiometric methods are projection methods, meaning they summate down to a plane (like a plain X ray) all the information on bone mass contained in a 3D scanned region. Often the BMC is normalized by the projected area (usually a rectangle) of the region scanned, to obtain what is referred to (in the clinical milieu) as areal bone mineral density (BMD), in grams per centimeter squared (g cm2). To avoid confusion, the acronym BMD will be used to denote this areal BMD only, as measured with absorptiometric techniques, to distinguish it from volumetric or apparent density—both expressed in grams per cubic centimeter (g cm3)—which can be measured using other methods. Of fundamental importance is the fact that clinical BMD measurements have been shown to be useful not only for estimating bone strength in vitro, but also for predicting the occurrence of minimal- trauma fractures.11 For example, in a study by Cummings et al.,12 each standard deviation decrease in femoral neck BMD increased the age-adjusted risk of hip fracture 2.6 times. They also showed that women with BMD in the lowest quartile had an 8.5-fold greater risk of hip fracture than those in the highest quartile. Besides its relationship to fracture risk, present X-ray absorptiometry also has very good accuracy and precision.11 This makes the technique a useful clinical tool for noninvasively assessing bone integrity, enabling not only detection of at-risk individuals but also monitoring of the effects of treatment.

34.2.1.1 Dual-Energy Methods Dual-energy X-ray absorptiometry (DXA) is able to account for variations in the amount of overlying soft tissue. This is important because soft tissue affects the overall attenuation and can thus lead to errors in estimating BMD. Dual-energy methods compensate for the presence of soft tissue by measuring the

attenuations of X-ray beams at two distinct energies. Let I1 and I2 be X-ray beam intensities at energy 1 and energy 2 after transmission through an anatomical site comprising speciﬁc but unknown amounts

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Noninvasive Measurement of Bone Integrity 34-3

of bone and soft tissue:

() b2db w2dw I2 I02 exp , (34.1)

() b1db w1dw I1 I01 exp . (34.2)

In Eqs. 34.1 and 34.2, I01 and I02 are the transmitted (source) X-ray beam intensities at energy 1 and energy 2, respectively, b1 and w1 are the X-ray attenuation coefﬁcients of bone and soft tissue at energy 1, respectively, b2 and w2 are the X-ray attenuation coefﬁcients of bone and soft tissue at energy 2, respectively, and db and

dw are the (integrated or total) thicknesses of bone and soft tissue, respectively, at the anatomical site of measurement. By taking the natural logarithms of both sides of the two equations and rearranging, the following matrix representation is obtained:

Ax b, (34.3)

where

ln[]I ------01- ln[]I b 1 (34.4) [] ln I02 ------[]- ln I2

b1 w1 A (34.5) b2 w2

and

d x b . (34.6) dw

The only unknowns are the bone and soft tissue thicknesses (represented by the x vector), which may be solved for by inverting Eq. 34.3. The inverse of A exists because the attenuation coefﬁcients for bone and soft tissue have distinct functional dependencies (|A| b1 w2 w1 b2 0). This fact is the basis by which dual-energy methods are able to separate out the confounding effects of soft tissue. The thickness, ≈ 3 db, of bone is multiplied by a standard volumetric density, b ( 1.85 g cm ) of bone, to obtain the BMD (g cm2), or multiplied by both the volumetric density and projected area of the scan to obtain the BMC (g).13 DXA devices have the highest accuracies and precisions of all X-ray-based methods; these range from 0.5 to 2% for precision, and from 3 to 5% for accuracy.14 Scans may be performed at any anatomical site but are usually done at the spine, the proximal femur (hip), or the distal radius. In a typical scan, the X-ray beam is mechanically translated over a body region and detected and processed to create an integrated bone density image at the site; automatic edge detection algorithms operate to locate repro- ducibly a region of interest. Fig. 34.1a displays a DXA scan of the spine together with a region of interest, and Fig. 34.1b shows the associated BMD and BMC values. 34.2.1.2 Single-Energy Methods In contrast to dual-energy methods, single-energy X-ray absorptiometric (SXA) methods measure X-ray absorption at a single energy only, and thus cannot compensate for varying amounts of soft tissue. Mathematically, this is simply a manifestation of the fact that there are two unknowns (the bone and soft tissue thicknesses, respectively) and only one equation (i.e., Eq. 34.1). Therefore, single-energy

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34-4 Bone Mechanics

FIGURE 34.1 (a) DXA scan of the spine, showing the regions of interest for which the areal BMD and BMC will be determined. (b) The BMD and BMC values for the scan of Fig. 34.1a.

techniques are useful at anatomical sites where the amount of soft tissue is either negligible (e.g., at the phalanges) or can be controlled, like the wrist bone (distal radius) measured in a water bath of ﬁxed height. Single-energy methods are also utilized in in vitro laboratory studies, where bones may be cleaned of all soft tissue or can be placed in a ﬁxed-height water bath.

34.2.2 Quantitative Computed Tomography Using a technique known as quantitative computed tomography (QCT), volumetric bone density values can be measured noninvasively.10,14 In this method, which is similar to standard computed tomography, a quantitative cross-sectional image of a bone is obtained. Similar to the absorptiometric techniques described in Section 34.2.1, QCT is also based on measurements of X-ray attenuation. However, in QCT the attenuation measurements are made not from one, but rather from a multitude of angular directions, which permits the tomographic or spatial reconstruction of the attenuation coefﬁcient. A QCT scan of an anatomical site (like the spine) is acquired in conjunction with a calibration phantom that is composed of a small number (usually three to seven) of materials, each material having a speciﬁc “bone-equivalent” value. A quantitative interpolation between the values of the portion of the image associated with the region of interest with the portions associated with the phantom materials allows a bone-equivalent value in g cm3 to be derived. A typical QCT image of a vertebral body is shown in Fig. 34.2, which also displays a rectangular region of interest within the trabecular portion of the vertebra in which the volumetric bone mineral density was computed.

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Noninvasive Measurement of Bone Integrity 34-5

FIGURE 34.2 A QCT scan of a lumbar vertebra, showing the region of interest and the calibration phantom. (From Mirsky, E. C. and Einhorn, T. A., J. Bone Joint Surg., 80-A, 1687–1698, 1998. With permission.)

34.2.3 Limitations of X-Ray Densitometry Notwithstanding the utility of X-ray methods, there are weaknesses. Despite being the most widely used methods in practice, DXA or SXA does not discriminate between cortical and trabecular bone, “lumping together” into a single measurement the bone mass in the cortical and trabecular portions at any particular site. In addition, absorptiometry provides only areal bone mineral density, not volumetric density. Both factors can lead to decreased accuracy when estimating bone integrity and predicting fracture risk. Although QCT can estimate volumetric bone density and discriminate between cortical and trabecular bone, its high radiation dose and cost limit its practical utility. Further, QCT is difficult to use at sites which are extremely heterogeneous and geometrically complex, such as the hip.15 Although bone mass is the most significant component in bone strength, other factors are also important. For example, trabecular bone mass accounts for only about 65% of the observed variation in biomechanical strength in vitro. This can be increased up to 94% by including in the model a measure of bone architecture known as fabric, which quantifies the relative degree of architectural anisotropy.16,17 Other studies have demonstrated the importance of considering structural and bone material properties to assess mechanical integrity.18–21 For example, it has been shown that architecture is needed to specify the biomechanical properties of trabecular bone and that the relative degree of anisotropy is independently (of bone mass) associated with an increase of fracture incidence.22,23 Fatigue damage is another aspect that is not measured in densitometry, but which may also play a role in low-trauma fractures.1 X-ray densitometry does not measure any aspect of architecture, remodeling state, or bone material properties per se; it simply quantifies the total bone mass present at the time of measurement.

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34.3 Ultrasonic Techniques

Unlike X-rays, ultrasound is a mechanical wave and, as such, has the potential to provide more information on mechanical integrity because it interacts with bone in a fundamentally distinct manner. This, combined with the fact that ultrasound involves no radiation, is relatively simple to implement and process, and can easily be used in a portable device, makes ultrasound an attractive alternative to methods based on ionizing radiation. Like bone densitometry using X-rays, ultrasound can be used to measure the attenuation of elastic energy as it passes through bone. However, ultrasound propagation through bone is a highly complex phenomenon dependent not only upon bone mass, but also on bone architecture and material properties.24–26 Since bone strength depends on its mass, architecture, and quality, ultrasound has the unique potential for being able to more accurately assess bone integrity compared with X-ray densitometric methods.27

34.3.1 Review of Ultrasound Theory Ultrasound is a mechanical wave consisting of frequencies above the range of human hearing (20 kHz). When an ultrasound wave is propagated through a medium such as a biological tissue, it will produce regions of temporary compression and rarefaction in the tissue. Various wave modes can be propagated simultaneously, including longitudinal (when the oscillatory motion of the particles in the tissue is parallel to the wave direction), transverse or shear (particle motion is perpendicular to the wave direction), and surface or Rayleigh (propagation of the wave along an interface between two tissues, e.g., muscle and bone, and the particles of the medium execute an elliptical trajectory). In complex heterogeneous materials such as bone, ultrasound waves will generally be multimodal. These ultrasound interactions with bone and other tissues are characterized by the linear viscoelastic wave equation:24

2 w  2  () ------ ----- w  ------w , (34.7) t2 t t 3 t

where is the volumetric density in kg m3; and are the first and second Lamé constants, respectively, in units of N m2, and are the first and second viscosities in units of N s m2; and w w(x,y, z, t) is the material displacement vector as a function of Cartesian coordinates x, y, and z and of time t. For a heterogeneous structure (such as the heel), the material parameters in Eq. 34.7 are functions of the spatial coordinates x, y, and z. For example, in the heel the bone material portions (i.e., the individual trabeculae and cortical shell) may have the following parameter values: 1850 kg m3, 9306 MPa, 3127 MPa, 40 Pa . s, 0.1 Pa . s, while both the marrow spaces and overlying soft tissue within and around the heel bone may have the following values for its material parameters: 1055 kg m3, 2634 MPa, 0 MPa, 0.1 Pa . s, 0 Pa . s.13,25–27 Eq. 34.7 can be solved in closed form in only highly idealized problems. The generation and reception of an ultrasound wave is usually accomplished by a piezoelectric transducer. This transducer utilizes a special material, often a ceramic, and is used to convert an electrical signal into a mechanical vibration, and vice versa.25 For example, by placing a transducer in physical contact with the surface of the skin, an ultrasound wave can be propagated through the underlying bone. Ultrasound waves are almost totally reflected at interfaces with air, and also highly attenuated as they propagate through it. Therefore, ultrasound cannot be used in the same mode as DXA in measuring the bone mass of a thoracic or lumbar vertebra, since air in the lung or bowel would nearly eradicate the acoustic signal. This is the reason that virtually all ultrasound measurements on bone in vivo are carried out at such anatomically accessible sites as the calcaneus, patella, radius, and tibia, where there is minimal overlying soft tissue. Ch-34.fm Page 7 Monday, January 22, 2001 2:14 PM

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FIGURE 34.3 Most common technique used for bone assessment. In this transmission mode, two transducers are used, one for transmitting the ultrasound wave and the other for receiving the signal after it has propagated through the tissue. (From Kaufman et al., J. Bone Miner. Res., 5, 517–525, 1993. With permission.)

34.3.2 Tissue Characterization The ability of an ultrasound wave to provide information about the medium (tissue) through which it is propagating will depend on the way in which the wave is altered by the medium. The most common approach in bone assessment is to use two transducers, one as a transmitter and the other as a receiver, the latter of which measures the ultrasound signal after it has propagated through the medium.27 A typical example is shown in schematic form in measurement of a human heel in Fig. 34.3. Other methods can also be used, such as a backscattered approach.28 In general, two principal changes in an ultrasound signal can occur: (1) the medium can affect the velocity of the wave and (2) the medium can modify the amount of attenuation of the wave. 34.3.2.1 Influences on Ultrasound Velocity The velocity of an ultrasound wave depends not only on the properties of the medium through which it is propagating, but also on its mode of propagation. Longitudinal waves are generally faster than shear waves, and these are faster than surface waves; thus, it is generally necessary to be able to identify not only the velocity but the mode of propagation as well. Most measurements of velocity in vivo have primarily longitudinal components, since soft tissue greatly attenuates other modes of propagation.25 Besides propagation mode, ultrasound can be measured as a phase or group velocity.29 Phase velocity refers to the velocity of a wave that travels through a medium at a single frequency. Group velocity is a term used to describe the velocity of a wave packet or pulse that consists of a finite number of frequencies. Group velocity is the quantity most often reported since pulse measurements are easier to obtain.29 For certain media such as water, the phase and group velocities are essentially equivalent. Media for which the phase or group velocities are not equivalent are known as dispersive. Bone is an example of a dispersive medium, and trabecular bone is significantly more dispersive than compact bone.30,31 Furthermore, for dispersive materials such as bone, both the phase and group velocities are frequency dependent. Ch-34.fm Page 8 Monday, January 22, 2001 2:14 PM

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TABLE 34.1 Ultrasound Velocities for Several Common Materials and Biological Tissues24,29,32,33,36

Material Velocity [m/s]a

Water 1500 Bone, compact, human 2600–3000 Bone, cancellous, human 1530–2100 Bone, cancellous, bovine 1700–2500 Fat 1480 Lung 660 Blood 1530 Aluminum 6420 Steel 5800 Polystyrene 2350 Polymethylmethacrylate 2680 Muscle 1566

a All velocities are longitudinal phase velocities, measured at a nominal frequency of 1 MHz.

Therefore, different values will be obtained depending on the frequency of the ultrasound waveform. Thus, it is important that the speciﬁc experimental conditions used be recognized when comparing or analyzing reported ﬁndings. Table 34.1 displays values of ultrasound velocity for several common materials and biological tissues. Ultrasound velocity can be analytically related to certain biomechanical properties. In the case when the ultrasound wavelength is large with respect to the cross-sectional area of the interrogated object, and for homogeneous and nondispersive media, the relationship between elastic modulus and the ultrasound longitudinal phase velocity, c, is given by the equation:

E c --- , (34.8)

where E and are the Young’s modulus and volumetric density of the material, respectively.32 This equation does not apply to heterogeneous, anisotropic, and dispersive materials such as bone. In this case, no general closed-form solutions exist, but the above equation may still be used to provide ﬁrst-order estimates of the biomechanical properties. Since the elastic modulus of bone can be related to its density, that is,

E k , (34.9)

where k and are constants, equations can also be derived in which E and are related to the velocity, c, namely,

2()1 E k1c (34.10)

and

2()1 k2c , (34.11)

4,5 where k1 and k2 are constants that depend on k and . Using the empirical result that the compressive strength of bone is proportional to its elastic modulus, one can relate the ultimate compressive strength,

Su, to ultrasound velocity as well:

2()1 Su k3c , (34.12)

5 where k3 is another constant. Ch-34.fm Page 9 Monday, January 22, 2001 2:14 PM

Noninvasive Measurement of Bone Integrity 34-9

34.3.2.2 Influences on Ultrasound Attenuation The attenuation of an ultrasound wave occurs by a reduction of its amplitude and results in a loss of acoustic energy. Two primary mechanisms can produce this attenuation: scattering and absorption.33 In scattering, the amplitude of the propagating wave is reduced because the energy has been redistributed in one or more directions. A simple type of scattering, backscattering, occurs when a portion of a transmitted ultrasound wave is reflected back toward the source, such as when an ultrasound wave propagates from one medium to another (e.g., from soft tissue to bone). More complex scattering can arise in a material with acoustic inhomogeneities. Bone is an excellent example of an acoustically inhomogeneous material because it is composed of a cortical shell, a trabecular framework and is filled with a liquid-like material, bone marrow. When an ultrasound wave undergoes absorption, a portion of the energy of the propagating wave is converted directly into heat. This conversion is an extremely complex process and results when the density fluctuations within a medium are out of phase with the pressure fluctuations. This leads to energy loss through phase cancellation and so-called relaxation mechanisms.35 In general, absorption increases with increasing ultrasound wave frequency. In summary, the loss of ultrasound energy in a tissue will consist of the individual contributions from scattering and absorption and is expressed by the equation

s a , (34.13)

where is the attenuation coefficient and s and a are the scattering and absorption coefficients of the medium, respectively. In virtually all cases, the attenuation, , depends on the ultrasound wavelength as well as the acoustic properties of the medium. Attenuation is usually expressed in the units nepers (np) or decibels (dB); 1 np is equivalent to approximately 8.65 dB. A medium that has an attenuation of 1 np will reduce the amplitude of an ultrasound wave to approximately 37% of its initial value. A medium with an attenuation of 3 np will reduce the amplitude to approximately 5%. The attenuation coefficient, , of a medium is related to its thickness, d. This parameter can be used to derive the specific attenuation, , according to the equation:

d. (34.14)

Specific attenuation is usually expressed in the units npcm1 or dBcm1. As noted, ultrasound attenuation is generally a function of frequency, i.e., (f ). For many materials, this relationship is approximately linear over a given frequency range. In these cases, the attenuation coefficient, , can be characterized by its slope, 1, and is expressed in the units nepers per megahertz (npMHz1) or decibels per megahertz (dBMHz1). In ultrasound bone assessment, the slope is a central parameter, and is known by the term broadband ultrasound attenuation (BUA) (i.e., 1 BUA). BUA was originally suggested as a means for characterizing bone by Langton.35 In situations where the attenuation of a material cannot be characterized by a linear dependence on frequency, polynomial functions (including nonintegral exponents) may be necessary to approximate the relationship. All materials, including bone, exhibit some degree of nonlinear behavior if the frequency range of interest is sufficiently broad. Table 34.2 displays representative values of BUA (normalized to material thickness) for several common materials and biological tissues. BUA is computed by evaluating the Fourier transforms of a “bone signal” (the signal that has propagated through the bone tissue and overlying soft tissue if present) and a “reference signal” (a signal that has propagated through a known medium such as water), respectively, and then taking the negative logarithm of the magnitude of their quotient. A straight line is fit over a given frequency interval (nominally 300 to 800 kHz) and a least-squares (regression) estimate of BUA in dBMHz1 determined. The computation typically relies on fast Fourier transformation of the signals.36 Ultrasound velocity is usually computed in the time domain, although phase-dependent (transform) methods should more Ch-34.fm Page 10 Monday, January 22, 2001 2:14 PM

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TABLE 34.2 Differential Speciﬁc Attenuations (BUA normalized to material thickness) for Several Common Materials and Biological Tissues24,29,32,33,36

BUA per unit length Material dB MHz1 cm1 at 1 MHz 2 Water 0.001 (~f ) →→ Bone, compact, human 10 (~f 0.9 2.1 0.5 ) → Bone, cancellous, human 5–40(~f 12 ) Fat 0.6 → Lung 40 (~f 2 1.2 ) Blood 0.3 Aluminum 0.355 (~f 2 ) 2 Steel 0.29 (~f ) Polystyrene 0.35 Polymethylmethacrylate 0.4 Muscle 1.1

Note: Broadband ultrasound attenuation (BUA) is the slope of the ultrasound attenuation, measured in units of dB MHz1 (see text). All attenuations are with respect to longitudinal mode of propagation. The text in parentheses indicate the approximate frequency dependence(s). Thus, for compact bone, the attenuation follows a 0.9 power at lower frequencies, increasing to a 2.1 power, and then decreasing to a 0.5 power. For additional details, consult the references. If not shown, dependence is linear around 1 MHz.

appropriately be used.29 In the former case, times of arrival of the two (bone and reference) signals are deﬁned relative to a leading edge or some other landmark on the signals. Formally, the measurement of BUA and velocity can be represented as follows. Let H(f ) be the complex transfer function associated with the overall path of ultrasound propagation through a tissue of interest, for example, a heel bone. Then

() ()Vf ()f j()f Hf ------() e e , (34.15) Vr f

where V(f ) and Vr(f ) are the Fourier transforms of the bone and reference signals, respectively, (f ) and (f ) are the attenuation and phase (real) functions associated with the overall tissue pathway, and j (1)1/2. The attenuation function, (f ), over a given frequency range, is approximated by an afﬁne function, i.e.,

() () f ln Hf 0 BUA f 8.65 , (34.16)

where values for 0 and BUA are determined by least squares. The group velocity, vg(f ), can be computed from the phase function, (f ):

d()f 1 v ()f 2d ------, (34.17) g df

where d is the overall tissue thickness, and (f ) arg{H(f )} (radians).29,31 As will be seen in Section 34.3.3, less bone mass and increasing fragility are generally associated with smaller values of BUA and velocity. It is important, however, to point out that ultrasound measurements on heterogeneous materials such as bone engender a variety of practical problems that can reduce accuracy and Ch-34.fm Page 11 Monday, January 22, 2001 2:14 PM

Noninvasive Measurement of Bone Integrity 34-11

precision signiﬁcantly. For example, irregular geometry can produce inaccurate readings of attenuation through phase cancellation effects.37 There can also be large variations in measured attenuations and velocities depending on the speciﬁc bone region interrogated by the ultrasound wave due to associated heterogeneity of bone. Soft tissue surrounding the bone can also affect both ultrasound attenuation and velocity estimates, for example, by distorting the received waveform due to multipath interference.31 In summary, ultrasound assessment of bone relies primarily on the measurement of the velocity and attenuation of the ultrasound wave, which are, in general, frequency dependent. From a linear systems theoretic point of view, one may view these parameters as representations of the magnitude and phase, respectively, of a transfer function associated with the ultrasonically interrogated medium (tissue). Ultrasound characterization is based on the fundamental hypothesis that bone in different physical and biomechanical states will have different complex transfer functions. The determination of unique and quantitative relationships between these ultrasound variables and the physical properties of bone and clinical fracture risk, as well as development of reliable measurement means, constitute the critical research goals for this technology.

34.3.3 Review of Experimental and Clinical Studies Two of the earliest attempts to relate ultrasound measurements to bone properties were reported by Lang38 and Abdenshein and Hyatt,39 who found high correlations between mechanically determined and ultrasonically determined elastic moduli. These findings were later reproduced by Ashman et al.40 who studied the elastic properties of cortical bone using a more refined continuous wave technique. More recent studies on trabecular bone samples from human and bovine subjects have shown correlations of ultrasound velocity with ultimate strength ranging from 0.71 to 0.75.41–43 In animal studies, it has been possible to assess the interaction between a physiological event or manipulation and a physical outcome measured by ultrasound velocity assessment. Using a sheep Achilles tenotomy model to mimic biomechanical disuse, Rubin et al.44 studied the changes in ultrasound transmission through the calcaneus over a 12-week period. They noted a 10.2% decline in ultrasound velocity in the experimental limb and this was associated with a 21% reduction in trabecular bone volume. McCarthy et al.45 studied the relationship between ultrasound velocity and the effects of specimen orientation, density, porosity, and temperature in equine cortical bone and showed a positive linear correlation between ultrasound velocity and bone specific gravity, and an inverse relationship with porosity. To determine the ability of ultrasound to detect a therapeutic response, Lees and Hanson46 examined the relationship between ultrasound velocity in the rabbit femora before and after sodium fluoride treatment, which was used as means for treating bone loss. They proposed that an “optimum dose” for fluoride administration could be determined based upon the ability to measure ultrasonically the elastic modulus of bone. Two early ultrasound studies on humans were conducted by Heaney et al.47 and Rubin et al.48 In the study by Heaney et al., ultrasound velocity measurements made across the patella of patients with atraumatic vertebral compression fractures were 3 to 4% lower than in normal (unfractured) controls.47 By assessing fracture incidence, these investigators were able to show that women who had ultrasound velocities below 1825 ms1 were approximately six times more likely to have sustained one or more vertebral fractures than women with velocities above this level. In the study by Rubin et al., longitudinal group velocity measurements were made at the patella and tibia in individuals before and after completion of a marathon.48 The study demonstrated the ability of ultrasound (tibial) velocity to differentiate individuals based on their performance and gender. There was also a 1.6% increase in tibial ultrasonic velocity after the race. Other studies have used ultrasound attenuation to characterize bone tissue. In vitro experiments have compared BUA with X-ray densitometric findings. For example, McKelvie et al.49 compared bone density measured with QCT to BUA in the human calcaneus and showed a correlation of R 0.92. Similarly, McCloskey and co-workers50 examined the relationship between BUA in the os calcis and both BMD determined using QCT and physical density (i.e., the volumetric density of the fluid saturated Ch-34.fm Page 12 Monday, January 22, 2001 2:14 PM

34-12 Bone Mechanics

bone sample); BUA was found to be highly correlated with both densities, R 0.80, P 0.0001 and R 0.85, P 0.001, respectively. Clinical studies using BUA have also compared ultrasound estimates to bone densitometry measurements. In one such study BUA of the calcaneus was reported to be highly correlated with QCT of the spine (R2 0.85, p 0.01).51 Investigators have also assessed bone density using both ultrasound attenuation and velocity measurements. One in vitro study examined the ability of BUA and ultrasound group velocity to detect alterations in bone mineralization on bovine bone samples.52 Using controlled nitric acid attack to demineralize bone sequentially, BUA and velocity were shown to be highly correlated (R values between 0.84 and 0.99) with bone physical density. Another in vitro study determined both the attenuation and phase velocity of ultrasound over frequency ranges of 300 kHz to 3.0 MHz in cancellous bone from the human skull.30 Besides demonstrating that the attenuation and velocity were nonlinear functions of frequency, they also concluded that the dispersion was caused principally by the scattering of ultrasound by the blood and fat-filled interstices of the bone. Clinical investigations have reported measurements of ultrasound attenuation and group velocity in the same subjects.53,54 Correlation coefficients between SXA (BMD) and ultrasound attenuation (BUA) and velocity in the os calcis were found to be 0.53 and 0.72, respectively. A clinical study mathematically combined BUA and velocity to derive a third parameter called “stiffness” (no relation to the biomechanical term).55 These investigators showed that in 23 normal women and 18 women with excessive bone loss, BUA, velocity, and “stiffness” were significantly lower in the latter group of 18 subjects (p 0.001). Of greatest importance is the ability to use ultrasound measurements to predict fracture risk. In one seminal study on 60 women, Langton et al.35 showed that patients who had experienced a hip fracture within 4 weeks of a BUA measurement had a significantly lower BUA than women who had no history of fracture. In addition, they reported a significant decrease in the BUA in relation to age. Values for BUA ranged from a low of about 25 dB MHz1 to a high of almost 90 dB MHz1; the fracture patients had an average BUA of about 40 dB MHz1 and the unfractured patients had an average BUA of about 75 dB MHz1, an almost twofold difference. However, this study did not correct for age, an important consideration in discriminating between fracture and nonfracture subjects, nor did it provide a statistical analysis. More recently, Miller and Porter56 measured BUA in 840 women over the age of 65, 32 of whom had sustained a fracture of the proximal femur during the study period. The mean BUA was significantly lower in the fracture compared to the nonfracture group (P 0.0005). Similar results were reported by Baran et al.,57 who studied ultrasound attenuation of the os calcis in patients with hip fractures and those with established low bone mass (by X-ray absorptiometry), but no history of hip fracture. At ultrasound values of 50 dB MHz1, this study showed sensitivities and specificities on the order of 80% for identifying patients with hip fracture. Most recently and significantly, three independent prospective studies with sample sizes of 6,500, 10,000, and 710 women, respectively, all showed that ultrasound can be used to estimate future fracture risk in older women.58–60 The two ultrasound parameters, BUA and ultrasound velocity, performed about equally well. Results from these studies demonstrated an increase in fracture risk with decreasing BUA and velocity, as shown in Fig. 34.4. For example, a one standard deviation decrease in BUA led to about a twofold increase in risk of hip fractures.58,59 Of special note was the fact that changes in fracture risk were similar to those as determined by X-ray absorptiometry.58 Additionally, it has been claimed that the ability of ultrasound to predict future fractures is independent of predictions based on X-ray-based measures of bone mass (e.g., BMD), although this is a subject of controversy.61 The degree of reproducibility or precision in ultrasonic studies has also been reported. Given the fact that many different types of apparatuses and approaches for measuring ultrasonic attenuation and velocity are being used, there has also been a wide range of precisions reported. For example, in one recent study, an ultrasonic assessment device (Walker-Sonix, now Hologic, Bedford, MA) was used on cadaveric feet.62 They found a precision of 6.1 and 0.8% for the attenuation and velocity, respectively. Coefficients of variation for several different devices and measurement techniques have also been published.63 These authors reported in vivo precisions ranging from 0.93 to 5% for attenuation, and 0.15 to 0.64% for velocity. However, it has been suggested that the coefficients of variation reported for ultrasonic Ch-34.fm Page 13 Monday, January 22, 2001 2:14 PM

Noninvasive Measurement of Bone Integrity 34-13

FIGURE 34.4 The relative risk for hip fractures, comparing BUA, velocity (speed of sound, SOS), and BMD of the femoral neck. The heights of the three bars on the graph indicate the increases in relative risk of hip fractures for each standard deviation decrease in BUA, SOS, or BMD, respectively. As may be seen, the relative risk increases by about a factor of two for each standard deviation reduction in BUA, SOS, or BMD. Also shown on each bar are the associated 95% conﬁdence intervals for relative risk. (From Glüer et al., J. Bone Miner. Res., 8, 1280–1288, 1997. With permission.)

velocity, as well as for attenuation, do not realistically reﬂect effective diagnostic precisions.64 This controversy on precision and accuracy of ultrasound has also led to disagreement on its use for monitoring response due to therapy.61 Notwithstanding, the U. S. Food and Drug Administration has approved three quantitative ultrasound devices for bone assessment in the past 2 years, and several more are likely to receive favorable consideration in the near future.

34.3.4 Computational Methods In view of the complexity of ultrasound propagation through bone, the relative paucity of analytic results, and the practical difficulties and costs associated with experimental and clinical studies, new approaches for clarifying ultrasound interactions with bone are needed. In this regard, a computational technique for simulating propagation of ultrasound through bone has recently been reported by Luo et al.65 Computational methods allow virtually any aspect of the bone–ultrasound interaction to be investigated. For example, it is possible to study the effects of varying viscosity of the marrow, cortical bone, and soft tissue, degree of mineralization, nonparallel surfaces, and refraction, diffraction, and scattering, to name just a few.66–68 In the study by Luo et al., propagation of ultrasound through 15 trabecular bone slices (similar to the one shown in Fig. 34.5) whose respective architectures (i.e., fabrics) and densities (i.e., bone volume fractions) were measured, was simulated using a computer software package (Wave2000, CyberLogic, Inc., New York, NY). The software provides the complete solution on a standard personal computer to a two-dimensional version of the elastic wave equation (Eq. 34.7), using a method of finite differences, modeling all the modes of propagation as well as accounting for material-dependent losses and scattering. A 1-MHz sine wave with a Gaussian envelope was used as the source waveform (Fig. 34.6), which is typical of the waveforms used in present commercial devices. A 1.4-cm source and a 1.4-cm receiver transducer pair was operated in transmission mode with the source–receiver pair in two orientations. The first was with the transducer pair aligned along the main trabecular orientation (“”), and the second was with the transducer pair aligned orthogonal to the main trabecular orientation (“”). Receiver measurements were computed for each of the 15 samples in each of the two directions, for a total of 30 receiver waveforms. The ultrasound velocities (UVs) in the parallel and orthogonal directions

(UV|| and UV , respectively) and mean frequencies (MFs) in the parallel and orthogonal directions (MF|| 67,69 and MF, respectively) were computed for each of the received waveforms. The mean frequency is Ch-34.fm Page 14 Monday, January 22, 2001 2:14 PM

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FIGURE 34.5 A single slice from a calcaneal trabecular bone sample. (From Luo, G. M. et al., Ultrasound Med. Biol., 25(5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.)

FIGURE 34.6 A 1-MHz sine wave with a Gaussian envelope, which was transmitted into the bone samples for the simulation study of Luo et al.65 (From Luo, G. M. et al., Ultrasound Med. Biol., 25(5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.)

related to BUA (i.e., an increase in BUA usually implies a decrease in mean frequency), but is more robust and not as subject to artifacts as BUA.69 Fig. 34.7 shows an instantaneous “snapshot” of the propagating ultrasound wave within the slice of Fig. 34.5. As may be seen, there is a signiﬁcant amount of scattering associated with propagation of the ultrasound wave. The simulated receiver measurements associated with the same sample along the principal direction (i.e., propagation of the ultrasound in the direction parallel to the primary orientation Ch-34.fm Page 15 Monday, January 22, 2001 2:14 PM

Noninvasive Measurement of Bone Integrity 34-15

FIGURE 34.7 An instantaneous “snapshot” at t 7.4 s of an ultrasound wave propagating (from left to right) through the 2D bone slice shown in Fig. 34.5, in the direction orthogonal to the main trabecular orientation. The gray level of the image is proportional to the magnitude of the material displacement at each point in the trabecular bone slice. (From Luo, G. M. et al., Ultrasound Med. Biol., 25 (5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.)

FIGURE 34.8 The simulated received waveform propagated along the principal direction of the trabeculae for the structure represented by Fig. 34.5. (From Luo, G. M. et al., Ultrasound Med. Biol., 25 (5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.)

of the trabeculae) and orthogonal direction (i.e., propagation of the ultrasound in the direction orthogonal to the primary orientation of the trabeculae) are shown in Figs. 34.8 and 34.9, respectively; these measurements show a remarkable similarity to experimental data.31,67 Plots of all the 30 UVs and MFs vs. volume fractions are shown in Figs. 34.10 and 34.11, respectively. Note that different symbols are used to denote propagation in the direction parallel () and orthogonal () to the primary orientation of the trabeculae, respectively. Linear correlation analyses with volume fraction for the two individual velocity curves of Fig. 34.10, i.e., the parallel and orthogonal data sets, resulted in R2 values of 0.98 (P 0.0001) and 0.96 (P 0.0001), respectively. Linear correlation analyses with volume fraction (mass) Ch-34.fm Page 16 Monday, January 22, 2001 2:14 PM

34-16 Bone Mechanics

FIGURE 34.9 The simulated received waveform propagated orthogonal to the principal direction of the trabeculae for the structure represented by Fig. 34.5. (From Luo, G. M. et al., Ultrasound Med. Biol., 25 (5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.)

FIGURE 34.10 Plot of ultrasonic velocity (UV) vs. bone volume fraction (VF). (From Luo, G. M. et al., Ultrasound Med. Biol., 25 (5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.)

FIGURE 34.11 Plot of mean frequency (MF) vs. bone volume fraction (VF). (From Luo, G. M. et al., Ultrasound Med. Biol., 25 (5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.) Ch-34.fm Page 17 Monday, January 22, 2001 2:14 PM

Noninvasive Measurement of Bone Integrity 34-17

for the two individual mean frequency curves of Fig. 34.11, i.e., the parallel and orthogonal data sets, resulted in R2 values of 0.91 (P 0.0001) and 0.90 (P 0.0001), respectively. Correlation analyses were also carried out on the ultrasound data without regard to orientation, that is, with the data grouped together so that there were 30 data points instead of 15 for the mean frequency and velocity linear regressions. This led to much reduced correlations as a result of the fact that the architectural orientation of the bone was not fixed, but varied from sample to sample for each of the ultrasound measurements. The significance of these results is that it demonstrates unequivocally that ultrasound is strongly affected by the direction in which it propagates through bone. This is most readily apparent in Figs. 34.10 and 34.11, since the only difference in the experimental condition for each data pair, that is, for the and ultrasound features associated with each sample, is the trabecular structure itself, as the volume fraction, transducer characteristics, and material properties are entirely unaltered. Previously, both theoretical and in vitro experimental results have demonstrated that ultrasound propagation is direction (i.e., architec- turally) dependent.70,71 The study by Chiabrera et al.70 studied an idealized model of trabecular bone, derived the coefficients of its associated compliance matrix, and evaluated using the Christoffel relations its directionally dependent velocities. The study by Luo et al.65 extended these results by using not idealized but realistic trabecular structures, accurately quantifying mass and architecture and relating them to ultrasound measurements.

34.3.5 Directions for Future Research There are numerous areas to explore with respect to ultrasound assessment of bone. Ultrasound measurements, although of some utility at present, are not extremely well correlated with bone mass or strength, nor are present devices as precise as they should be. Future studies should concentrate on both basic research and developing better clinical devices. Since ultrasound propagation depends on mass, architecture, and material properties, combining it with data related to one or more of these variables may prove useful for improving upon current capabilities. The combination of X-ray densitometric with ultrasonic measurements may provide a reasonable approach for more accurately identifying both density and architecture, and ultimately bone strength and fracture risk.62,72–74 Since age is correlated with bone density, another alternative is to combine age with ultrasound measurements to enhance ultrasound-based density estimation.69,72 It will also be useful to explore nonlinear combinations of ultrasound and other features (e.g., density, age, weight, height), as well as nonlinear combinations of the ultrasound features themselves, as a means to estimate bone strength and fracture risk. This can be pursued, for example, with neural networks.72,75 Most ultrasound measurements at present rely on large, single-element stationary transducers. More recently, imaging techniques have been proposed, both for improving reproducibility and for obtaining additional architectural information. The imaging modalities have included both the mechanical translation of the transducers, or two-dimensional (2D) array methods.76,77 It is expected that ultrasound will become more useful as further research is pursued.

34.4 Alternative Techniques

In addition to X-ray densitometry and quantitative ultrasound, other methods have been proposed and/or studied for noninvasively assessing bone integrity. Although none seem to have the overall capability or potential that is shared by X-ray and ultrasound techniques, it is useful to mention them here.

34.4.1 Micro-CT and High-Resolution Magnetic Resonance Imaging Two techniques that can image the microstructural aspects of trabecular bone have been reported. The ﬁrst, micro-CT, is based on standard X-ray CT principles, but utilizes specialized hardware to obtain bone images at extremely high resolutions (up to ~10 m).78–82 Several such systems have been constructed, the most advanced one being based on extremely narrowband synchrotron radiation.80,81 A 3D image of calcaneal trabecular bone made using such a system is shown in Fig. 34.12. The utility of Ch-34.fm Page 18 Monday, January 22, 2001 2:14 PM

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FIGURE 34.12 A 3D rendered image using micro-CT of a calcaneal trabecular bone sample. (From Luo, G. M. et al., Ultrasound Med. Biol., 25 (5), 823–830, © 1999 by World Federation of Ultrasound in Medicine & Biology. With permission of Elsevier Science.)

micro-CT is that it enables the complete 3D microarchitectural distribution of trabecular bone to be measured, which can help to answer questions related to the role that architecture plays in determining bone strength. Most micro-CT systems, however, have very high radiation doses and may generally be used for small samples only, thus limiting their practical utility in the clinic. From a conceptual point of view, high-resolution magnetic resonance imaging is similar to micro-CT. Using specialized magnetic resonance imaging hardware, namely, high magnetic ﬁeld systems with small radiofrequency surface coils, 3D images of bone that depict trabecular structure can be generated.82–84 An advantage that these systems have over micro-CT is their capability to image bone in arbitrary orientations and to be more suitable in clinical settings (no ionizing radiation and larger bodies allowed); however, their resolution (~100 m) or contrast is not as good as micro-CT. A recent clinical study used high-resolution magnetic resonance imaging of the calcaneus and demonstrated differences in trabecular structure between patients with excessive bone loss and controls.85 Clearly, magnetic resonance imaging is not an economically viable tool in terms of assessing integrity and fracture risk in the population at large, but its use, as with micro-CT, in research settings makes it a useful technique. Both of these imaging modalities, for example, can be used for 2D or 3D histomorphometry (e.g., measuring trabecular connectivity), to elucidate further the role that bone architecture plays in determining bone strength.86,87

34.4.2 Vibrational Methods The ability of bone to conduct low-frequency vibrations (sound) was applied clinically over 50 years ago to identify the presence of fractures, although the technique has become a relatively “lost art” as more-sophisticated X-ray and other imaging techniques have been developed.88 More recently, vibrational methods have been applied to intact bone in an attempt to assess its biomechanical properties.89,90 Ch-34.fm Page 19 Monday, January 22, 2001 2:14 PM

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Although the subject of extensive research, no vibrational methods have yet become useful for assessing integrity in intact bone, although some success has been realized in monitoring fracture healing.88 The basic approach in vibrational assessment is to excite the bone with a mechanical stimulus, and monitor the dynamic response(s) at a given position or set of positions. In this regard, it is not dissimilar to ultrasound methods, although the wavelengths used are much larger (in ultrasound methods, 1 to 3 mm, while in vibrational methods 0.1 to 1 m). However, low-frequency vibrational methods are much more subject to systematic and random errors as a result of large sensitivities with respect to transducer repositioning and skin coupling, differences in boundary conditions of the limb under test, and effects of soft tissue and muscle. These factors have prevented vibrational methods from having any signiﬁcant role in assessing bone loss and integrity.

34.4.3 Plain Radiographic Textural and Pattern Analyses Since architecture is known to play a role in bone strength, techniques that attempt to quantitate trabecular structure noninvasively have also been attempted. The most common modality used in this regard is plain radiography. One of the earliest techniques involved a subjective rating based on the qualitative appearance of trabeculation in the proximal femur.91 The Singh index, as it was called, was developed in an attempt to evaluate those at increased risk of hip fracture, but suffered by its qualitative and subjective nature. In an effort to overcome this limitation, quantitative techniques were developed, which included objective measurements based on texture and fractal analysis.92,93 For example, in one early study using plain radiographs of the calcaneus, textural image features were shown to be affected during periods of biomechanical disuse.93 The features studied included fractal dimension, run length, and co-occurrence measures. Other studies have reported further on the use of fabric, fractal dimension, and Moire patterns to characterize the architectural pattern of trabecular bone.94–97 Quantitative analysis of plain radiographs of the calcaneus in vitro using an architectural measure known as covariance have been reported as well.98 Covariance is similar to fabric in that it is a measure of the anisotropy of a structure; however, it has some additional advantages in that it contains additional structural information.99 Some researchers have also used textural and pattern analyses with other modalities (magnetic resonance imaging, for example) in an attempt to noninvasively extract architectural features from bone.85 An important recent result has demonstrated that architecture measured directly from a 3D (micro-CT) image of calcaneal trabecular bone is directly related to summated patterns, i.e., projec- tions of 3D volumes onto 2D surfaces, of plain radiographs.100 Plain radiographic-based pattern and textural analysis is very attractive because of its inherent low cost and wide availability. However, as of yet, there has been no clear clinical utility of any of the reported methods, although research is continuing.

34.4.4 Other Methods In addition to the previously mentioned techniques, several other methods have been proposed to measure bone integrity noninvasively. One of these, biochemical markers of bone turnover, while it does not directly measure biomechanical integrity, has nevertheless been shown in some studies to provide additional information on clinical fracture risk beyond that provided by X-ray densitometry (e.g., BMD).101 The biochemical markers, of which there are now more than ten different ones, may be measured relatively inexpensively using a subject’s blood and/or urine, and provide a measure of the rate and degree of bone turnover. The markers provide a dynamic assessment of the skeleton and may be expected, in the coming years, to play an important role in assessing skeletal integrity. Another method for bone assessment utilizes nonionizing electromagnetic measurements, similar to electrical impedance tomography or microwave imaging techniques.102,103 In one such in vitro study, electrical conductances were measured on 13 human trabecular bone samples, using a plastic cylinder ﬁlled with a conducting ﬂuid and a pair of 1-cm-diameter silver–silver chloride electrodes (Type 4560, Nikomed, Doylestown, PA) surrounding each trabecular bone sample.104 The impedance magnitude of Ch-34.fm Page 20 Monday, January 22, 2001 2:14 PM

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each bone sample was measured (Model 1260 Impedance Analyzer, Solartron Instruments, Hampshire, UK) at 10 kHz and normalized by the length and area of the sample to obtain its electrical conductance. The bone apparent densities, a, were estimated by air-drying the samples and dividing their dry weight by their total volume. There was a high degree of correlation between the apparent density of the bone samples with measured electrical conductivity (R 0.94, P 0.001). Further work will be necessary to extend this work to in vivo applications. Finally, two additional X-ray-based methods should be mentioned for the sake of completeness. First, measurement of bone geometry obtained either with plain radiographs or some other noninvasive imaging technique has been shown to provide additional information on bone integrity. This is not surprising since induced strains in bone tissue generally will depend on geometric factors. As one example, the lateral cortical thickness of the hip 2 cm distal to the calcar femorale, measured using a plain radiograph, has been shown to be an independent discriminator of hip fracture.105 Similarly, the hip-axis length, the length along the femoral neck axis from below the lateral aspect of the greater trochanter to the caput femoris, has been shown to be an independent discriminator of hip fracture as well.106 Second and last, radiographic absorptiometry, the measurement of bone mineral density using a plain radiograph, is a useful technique for measuring bone mass where there is minimal soft tissue, for example, at the phalanges.14,15 The method generally uses an aluminum calibration wedge, and expresses the BMD in aluminum-equivalent units. Radiographic absorptiometry does not perform as well when sites such as the calcaneus are used, because of its inability to account for varying amounts of overlying soft tissue. However, recent advances have attempted to address this problem, although additional research is still required.107

34.5 Summary

Noninvasive methods for assessing bone integrity are important for diagnosing and managing clinical bone loss, assessing fracture risk, as well as for monitoring the response to therapeutic interventions. Present-day X-ray densitometry techniques are reasonably good at making accurate and reproducible estimates of bone mineral content, and these estimates are correlated with in vitro measurements of bone biomechanical properties and with clinical fracture risk. Such techniques fulﬁll an important public health need. Quantitative ultrasound is another means for assessing bone, and is becoming an important clinical tool as well. Because of the complexity of the human skeleton from biomechanical, geometric, and biological perspectives, the development of new methods and the improvement of existing techniques to assess bone noninvasively requires a multidisciplinary approach. The objective of obtaining accurate and precise noninvasive measurements of skeletal integrity, which are also safe, reliable, and practical, although already achieved with some degree of success, still requires signiﬁcant further research and development.

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73. Njeh, C. F., Kuo, C. W., Langton, C. M., Atrah, H. I., and Boivin, C. M., Prediction of human femoral bone strength using ultrasound velocity and BMD: an in vitro study, Osteoporosis Int., 7, 471, 1997. 74. Lochmuller, E. M., Zeller, J. B., Kaiser, D., Eckstein, F., Landgraf, J., Putz, R., and Steldinger, R., Correlation of femoral and lumbar DXA and calcaneal ultrasound, measured in situ with intact soft tissues, with the in vitro failure loads of the proximal femur, Osteoporosis Int., 8, 591, 1998. 75. Kaufman, J. J., Alves, M., Siffert, R. S., Magee, F. P., and Ryaby, J. T., Ultrasound assessment of trabecular bone density using neural networks, J. Bone Miner. Res., 9, A204, 1994. 76. Roux, C., Fournier, B., Laugier, P., Chappard, C., Kolta, S., Dougados, M., and Berger, G., Broad- band ultrasound attenuation imaging: a new imaging method in osteoporosis, J. Bone Miner. Res., 11, 1112, 1996. 77. Kaufman, J. J., Friess, S. H., Chiabrera, A., Sorensen, J., Ryaby, J. T., and Siffert, R. S., Two- dimensional array system for ultrasonic bone assessment, Trans. Orthop. Res. Soc., 23, 966, 1998. 78. Feldkamp, L. A., Goldstein, S. A., Parﬁtt, A. M., Jesion, G., and Kleerekoper, M., The direct examination of three-dimensional bone architecture in vitro by computed tomography, J. Bone Miner. Res., 4, 3, 1989. 79. Ruegsegger, P. and Koller, B., A micro-CT system for the non-destructive analysis of bone samples, in Proc.10th International Bone Densitomety Workshop, 25, Bomiet, Venice, Italy, 1994. 80. Kinney, J. H. and Nichold, M. C., X-ray tomographic microscopy using synchrotron radiation, Annu. Rev. Mater. Sci., 22, 121, 1992. 81. Kinney, J. H., Lane, N. E., and Haupt, D. L., In vivo, three-dimensional microscopy of trabecular bone, J. Bone Miner. Res., 10, 264, 1995. 82. Lang, T., Augat, P., Majumdar, S., Ouyang, X., and Genant, H. K., Noninvasive assessment of bone density and structure using computed tomography and magnetic resonance, Bone, 22, 149S, 1998. 83. Chung, H., Wehrli, F., Williams, J., Kugelmass, S., and Wehrli, S., Quantitative analysis of trabecular microstructure by 400 MHz nuclear magnetic resonance imaging, J. Bone Miner. Res., 10, 803, 1995. 84. Muller, R., Hildebrand, T., Hauselmann, H. J., and Ruegsegger, P., In vivo reproducibility of three- dimensional structural properties of non-invasive bone biopsies using 3D-pQCT, J. Bone Miner. Res., 11, 1745, 1996. 85. Link, T. M., Majumdar, S., Augat, P., Lin, J. C., Newitt, D., Lu, Y., Nane, N. E., and Genant, H. K., In vivo high resolution MRI of the calcaneus: differences in trabecular structure in osteoporosis patients, J. Bone Miner. Res., 13, 1175, 1998. 86. Cortet, B., Colin, D., Dubois, P., Delcambre, B., and Marchandise, X., Methods for quantitative analysis of trabecular bone structure, Rev. Rhum Engl. Ed., 62, 781, 1995. 87. Parﬁtt, A. M., Bone histomorphometry: proposed system for standardization of nomenclature, symbols, and units, Calcif. Tissue Int., 42, 284, 1988. 88. Siffert, R. S. and Kaufman, J. J., Acoustic assessment of fracture healing: capabilities and limitations of “a lost art,” Am. J. Orthop., 25, 614, 1996. 89. Nokes, L. D. M. and Thorne, G. C., Vibrations in orthopaedics, in CRC Crit. Rev. Biomed. Eng., 15, 1987, 309. 90. Markel, M. D. and Chao, E. Y. S., Noninvasive monitoring techniques for quantitative description of callus mineral content and mechanical properties, Clin. Orthop. Relat. Res., 293, 37, 1993. 91. Singh, M., Nagrath, A. R., and Maini, P. S., Changes in trabecular pattern of the upper end of the femur as an index of osteoporosis, J. Bone Joint Surg. [Am.], 52, 457, 1970. 92. Rockoff, S. D., Scandrett, J., and Zacher, R., Quantitation of relevant image information: automated radiographic bone trabecular characterization, Radiology, 101, 435, 1971. 93. Kaufman, J. J., Mont, M. A., Hakim, N., Ohley, W., Lundahl, T., Soifer, T., and Siffert, R. S., Texture analysis of radiographic trabecular patterns in disuse osteopenia, Trans. Orthop. Res. Soc., 12, 265, 1987. 94. Siffert, R. S., Luo, G. M., and Kaufman, J. J., Moire patterns from plain radiographs of trabecular bone, in Proceedings 17th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, IEEE, New York, 1995. Ch-34.fm Page 25 Monday, January 22, 2001 2:14 PM

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95. Benhamou, C. L., Lespessailles, E., Jacquet, G., Harba, R., Jeannane, R., Loussot, T., Tourliere, D., and Ohley, W., Fractal organization of trabecular bone images on calcaneus radiographs, J. Bone Miner. Res., 9, 1909, 1994. 96. Caliguri, P., Giger, M. L., Favus, M. J., Jia, H., Doi, K., and Dixon, L. B., Computerized radiographic analysis of osteoporosis: preliminary evaluation, Radiology, 186, 471, 1993. 97. Buckland-Wright, J. C., Lynch, J. A., Rymer, J., and Fogelman, I., Fractal signature analysis of macroradiographs measures trabecular organization in lumbar vertebrae of postmenopausal women, Calcif. Tissue Int., 54, 106, 1994. 98. Siffert, R. S., Luo, G. M., Kaufman, J. J., and Cowin, S. C., Quantitative analysis of trabecular architecture in plain radiographs of the human os calcis, in Transactions of the 2nd Combined Meeting of the Orthopaedic Research Societies of U.S.A., Japan, Canada and Europe, Orthopaedic Research Society, Palatine, IL, 1995, 10. 99. Berryman, J. G., Measurement of spatial correlation functions using image processing techniques, J. Appl. Phys., 57, 2374, 1985. 100. Luo, G. M., Kinney, J. H., Kaufman, J. J., Haupt, D., Chiabrera, A., and Siffert, R. S., Relationship of plain radiographic patterns to three-dimensional trabecular architecture in the human calcaneus, Osteoporosis Int., 9, 339, 1999. 101. Khosla, S. and Kleerekoper, M., Biochemical markers of bone turnover, in Primer on the Metabolic Bone Diseases and Disorders of Mineral Metabolism, Favus, M. J., Ed., Lippincott-Williams & Wilkins, Philadelphia, PA, 1999, chap. 22. 102. Dehghani, H., Barber, D. C., and Basarab-Horwath, I., Incorporating a prior anatomical information into image reconstruction in electrical impedance tomography, Physiol. Meas., 20, 87, 1999. 103. Semenov, S. Y., Svensen, R. H., Bulyshev, A. E., Souvorov, A. E., Nazarov, A. G., Sizoz, Y. E., Pavlovsky, A. V., Borisov, V. Y., Voinov, B. A., Simonova, G. I., Starostin, A. N., Posukh, V. G., Tatsis, G. P., and Baranov, V. Y., Three-dimensional microwave tomography: experimental prototype of the system and vector born reconstruction method, IEEE Trans. Biomed. Eng., 46, 937, 1999. 104. Bianco, B., Chiabrera, A., Siffert, R. S., and Kaufman, J. J., Electrical assessment of trabecular bone density: theoretical and in vitro results, Trans. Orthop. Res. Soc., 21, 716, 1996. 105. Peacock, M., Turner, C. H., Liu, G., Manatunga, A. K., Timmerman, L., and Johnston, C.C. Jr., Better discrimination of hip fracture using bone density, geometry and architecture, Osteoporosis Int., 5, 167, 1995. 106. Karlsson, K. M., Sernbo, I., Obrant, K. J., Redlund-Johnell, I., and Johnell, O., Femoral neck geometry and radiographic signs of osteoporosis as predictors of hip fracture, Bone, 18, 327, 1996. 107. Chiabrera, A., Siffert, R. S., and Kaufman, J. J., Plain X-ray bone densitometry apparatus and method, U. S. Patent 5,917,877, issued June 29, 1999.

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35 Bone Prostheses and Implants

Patrick J. Prendergast 35.1 Introduction ...... 35-1 Trinity College Dublin 35.2 Biomaterials...... 35-2 Biocompatibility • Metals • Ceramics • Polymers 35.3 Design of Bone Prostheses ...... 35-5 General Overview • Prosthesis and Implant Systems 35.4 Analysis and Assessment of Implants...... 35-14 Preclinical Tests • Clinical Assessment 35.5 Future Directions ...... 35-19

35.1 Introduction

Replacing or augmenting bone with an implant can relieve the pain caused by trauma or disease. Replace- ment of bone occurs in joint arthroplasty or in bone grafting. Augmentation of bone with fixation devices is required for fracture healing, or for stabilization and fusion of joints, or for alignment/distraction of bones. Bone prostheses must address several design requirements. Among these are 1. Fit a wide anatomical range of patients, 2. Maintain mechanical fixation under cyclic loading, 3. Offer a functional range of motion, 4. Provide the required kinematic stability. The relative importance of the design requirements depends on the function of the implant. Design of surgical procedures and associated instrumentation is also an essential aspect to the development of bone prosthesis systems. The design requirements for bone prostheses are met, first, by the selection of suitable biomaterials. These must have the required biocompatibility, i.e., perform with an appropriate host response in a specific situation.1 Sometimes the implant must remain strictly inert to facilitate removal from the body, e.g., a fixation plate. Other implants must resorb over time, and others are designed to “osseointegrate” with the host bone—osseointegration being a process of bone ingrowth at the implant surface to create a secure bond with the bone.2 Second, the geometry of the implant is a critical factor because it determines the stress distribution at the bone–implant interface and within the surrounding bone.3 In the case of joint replacement prostheses, the geometry of the articulating surfaces determines the range of motion of the prosthetic joint, and the kinematic stability of the articulation.4 The regulatory environment for new implants plays a critical role in determining the evolution of new designs. The Food and Drug Administration (FDA) regulates medical devices in the United States5 and in the European Union regulation is according to the Medical Device Directives.6 Although these

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35-2 Bone Mechanics

systems are fundamentally different, they do have similar implant classification systems. The lowest degree of regulation is reserved for “minimum risk,” Class 1 devices. Class 2 devices require specific control tests. Class 3 devices are “maximum risk,” where no comparison with an existing device can be made. Active devices, such as bone substitutes and prostheses with osseointegratative surfaces, come into Class 3.7 This chapter is concerned with the design and testing of Class 2 and Class 3 prostheses to replace or augment the biomechanical function of bone. In Section 35.2 a review of available biomaterials is given; then in Section 35.3 the design of specific implant systems is overviewed; and finally in Section 35.4 methods of testing implants are described.

35.2 Biomaterials

Metals, ceramics, and polymers are used to replace bone in the human body. Metals have strength and stiffness that make them suitable for many load-bearing applications. Only three metals are commonly used. In order of increasing corrosion resistance, these are stainless steel, cobalt–chromium alloys, and titanium and its alloys. Ceramics—compounds of metallic and nonmetallic elements—have a wide range of properties that make them suitable for implantation; in particular, oxide ceramics are highly wear resistant and calcium phosphate and bioactive glass ceramics have excellent osteoconductive properties. Polymers are most often used in joint replacement prostheses. In all cases, prosthesis materials must have the required biocompatibility.

35.2.1 Biocompatibility In general, an implant will alter the mechanical and chemical environment in its immediate neighborhood (locally) and throughout the body (systemically). Williams8 has classified the components of biocompatibility as follows: 1. Protein absorption. Proteins rapidly cover the surface of an implant and their interaction with the surface of the biomaterial controls the host response, including behavior of cells adjacent to the implant. 2. Material degradation at atomic and molecular level. Corrosion of metals,9 resorption of ceramics,10 and hydrolysis of polymers11 can all occur in vivo. Degradation can be heavily dependent on the physiological environment. 3. Evolution of the local host response. The trauma of implant surgery initiates an inflammatory process in the surrounding tissues, followed by a repair process that will determine eventual stability of the implant. The time course of the repair is influenced by the chemical characteristics of the biomaterial, and by mechanical phenomena such as wear12 and micromotion.13 4. Systemic effects. Occurring remote from the implant, these are primarily mediated by chemical and mass transport phenomena. Small particles released from the implant surface by wear or degradation may be carcinogenic, or interfere with metabolic and immunological systems.14

35.2.2 Metals Surgical stainless steel of speciﬁcation ASTM F138 and F139 (grades 316 and 316L) achieves corrosion

resistance by forming a chromium oxide (Cr2O3) layer on the implant surface. Nickel further improves the corrosion resistance and improves the formability of the metal for manufacturing by stabilizing a face-centered cubic crystal structure. Molybdenum is added as it increases resistance to pitting corrosion. The other elements are added to overcome manufacturing problems (Table 35.1a). Carbon content is low to prevent chromium-carbides from depleting chromium content near the grain boundaries, which would lead to intergranular corrosion. A problem with stainless steel is its slow but ﬁnite corrosion rate. Crevice corrosion can also occur if two stainless steel components are in contact. Possibility of corrosion means that stainless steel is used mainly for temporary implants.9

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Bone Prostheses and Implants 35-3

TABLE 35.1a Composition of Stainless Steel (ASTM F138)

Element %

Chromium 17.00–19.00 Nickel 13.00–15.50 Molybdenum 2.00–3.00 Manganese 2.00 max Iron Balance P, S, Si, Cu, N Trace amounts

TABLE 35.1b Composition of Cobalt–Chromium Alloys (ASTM F75; ASTM F90)

% (F75–92) % (F90–92) Element Cast Wrought (forged)

Chromium 27.0–30.00 19.00–21.00 Nickel 1.0 max 9.00–11.00 Molybdenum 5.0–7.00 — Tungsten — 14.00–16.00 Manganese 1.00 max 1.00–2.00 Silicon 1.00 max 0.40 max Iron 0.75 max 3.00 max Carbon 0.35 max 0.05–0.15 Phosphorus — 0.040 max Sulfur — 0.030 max Cobalt Balance Balance

TABLE 35.1c Composition of a Titanium Alloy (ASTM F136)

Element %

Aluminium 5.5–6.5 Vanadium 3.5–4.5 Iron 0.25 max Titanium Balance H, C, O, N Trace amounts

Cobalt–chromium displays better corrosion resistance than stainless steel. It can be either cast or forged, the latter having much greater fatigue resistance. ASTM F-75 is the casting alloy and ASTM F-90 is the forging alloy, the latter containing tungsten and nickel for forgability (Table 35.1b). Titanium and its alloys have better corrosion resistance than stainless steel or cobalt–chromium alloys.15

This is conferred by a TiO2 layer on the surface. However, its stiffness is lower than either stainless steel or cobalt–chromium making those materials a better choice in certain situations. There is no evidence of pitting or intergranular corrosion with titanium in biological environments. Unalloyed c.p. (commercially pure) titanium is sometimes used for sintering surface layers. The alloy used is commonly called Ti-6Al-4V, although compositions differ from this, for example, ASTM F-136 (Table 35.1c). Porous coatings of wire meshes or beads can be applied to implants to act as an anchor for bone ingrowth. Several layers of beads can be employed to improve the strength of the interface under tension (Fig. 35.1).

35.2.3 Ceramics There are three categories of ceramics used to replace bone. The ﬁrst is structural ceramics (alumina, 16 Al2O3, and zirconia, ZrO2). These have higher stiffness and hardness than metals and much better wear resistance. Pure zirconia can undergo phase transitions on cooling and, to avoid this, it is alloyed with

CaO, MgO, or Y2O3, forming partially stabilized zirconia (PSZ) or tetragonal zirconia (TZP). Both alumina and zirconia are used for heads of hip prostheses.17

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FIGURE 35.1 (a) A monolayer of beads gives adequate resistance to shear loads, and (b) a multibead layer gives superior resistance to tensile loads. (From Cameron, H. U., Bone Implant Interface, Mosby, St. Louis, 1994. With permisson.)

The second category of ceramic used to replace bone is calcium phosphate.18 Hydroxyapatite (HA),

[Ca10(PO4)6(OH)2], is a calcium phosphate that is found naturally in bone. Another calcium phosphate

is tricalcium phosphate (TCP), [Ca10(PO4)6]. TCP biodegrades more quickly than HA, indicating that the amount of TCP should be minimized to slow the dissolution rate of an HA TCP mix.10 Calcium phosphates have useful osteoconductive properties and are used to coat metallic implants that aim to bond to the bone by osseointegration.19 They are also used for synthetic bone graft materials.20 The third category of ceramic is bioactive glass. Ceramics in this category have excellent biocompatibility. Glasses are amorphous materials—they have no long-range atomic order. This results when the cooling from the liquid phase is sufﬁciently rapid to prevent crystallization. Glass bioceramics have large

amounts of SiO2, with amounts of the following compounds: P2O5, CaO, Ca(PO3)2, CaF2, MgO, MgF2, 21 Na2O, K2O, Al2O3, B2O3, and Ta2O5 TiO2. Glass-ceramics used for implantation undergo surface dissolution in a physiological environment, resulting in the formation of a chemical bond with bone. This results in high interfacial strength. However, the toughness of the underlying glass can be low, leading to failure within the bulk material. 35.2.4 Polymers A wide range of polymers is used for implantable devices. The first category is polymers with no cross- linking of polymer chains—called thermoplastics. Well-known examples are polyethylene (PE) and polymethylmethacrylate (PMMA). Ultrahigh-molecular-weight polyethylene (UHMWPE), so-called because it has a very long molecular chain, is very wear resistant and is used as a bearing material for the articulating surfaces of many artificial joints. Radiation sterilization and subsequent aging in storage can change the properties of PE.22 Polyacetal, polyetheretherkeytone (PEEK), and polytetrafluroethylene (PTFE) have been used as components in hip replacement prostheses.23 Bioresorbale polymers are used for pins and screws in treatment of musculoskeletal injuries (poly-L-lactite, PLLA),24 and for bone plugs in modern cementing of implants.25 The second category is polymers with heavy cross-linking of polymer chains (called thermosets), e.g., polyester (PET) is used in the augmentation of soft tissues in the musculoskeletal system.26 Elastomers (e.g., polydimethyl siloxane, commonly called silicone) have occasional cross-linking and are characterized by the physical attribute that they can deform elastically to several hundred percent. This characteristic makes it suitable for one-piece prostheses for low-load-bearing joints such as the metacarpophalangeal,27,28 and metatarsophalangeal29 joints. PMMA is used as an orthopedic bone cement for fixation of prostheses to bone. The material serves to interlock the prosthetic component to the bone. Polymerization takes place during the mixing of powder and liquid components, which is carried out in the operating theater. Mixing is critical to the

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Bone Prostheses and Implants 35-5

removal of pores and increasing the strength.30 Hand-mixing has largely been superseded by vacuum mixing or centrifugation. The cement is injected into the bone using a gun while it is still in a doughy state. Formulations of “low-viscosity” cement, which delay the onset of the doughy stage thereby facili- tating greater cement/bone interdigitation, have been developed.31 As the polymerization reaction progresses, the material solidifies and the prosthesis is fixated into its final position. While PMMA cement has many advantages, there are negative attributes such as thermal necrosis of bone due to the exothermic polymerization reaction,32 and PMMA undergoes damage accumulation as the cyclic load is applied over the lifetime of the patient.33

35.3 Design of Bone Prostheses

35.3.1 General Overview Many strategies have been formulated for engineering design. The design problem may be decomposed into a series of hierarchical steps to be solved separately, e.g., Technical Systems Theory.34 Less prescriptive approaches may include design reviews that integrate user requirements at several steps of the design process, e.g., Total Design.35 All design strategies specify procedural rules that engineers may use as a basis for creating a new product. They may begin with a needs analysis leading to a specification of objectives for the design. Objectives may be categorized into musts and wants. Next, several different solutions are formulated, and the final step is the selection of the design solution that best meets the categorization of objectives. This classical design process is complicated further by the requirements for quality system regulations. These specify the quality of procedures to be followed as part of the design process itself, in respect to documentation at each step, records of review meetings, and the results of implant testing procedures—including those necessary to meet industry standards.36 Furthermore, a risk analysis may be carried out.37 This information forms part of a design history file kept for each new implant design.38 Design issues particular to bone prostheses and implants may be enumerated as follows: 1. Magnitude and direction of the load on an implant changes in a highly complex manner, even during routine daily activities. Telemeterized implants have been used to retrieve in vivo data of loading on prostheses, e.g., hip,39,40 shoulder,41 and spine.42 Telemetry may eventually provide daily loading data sets that can be used for standard assessment of implant performance. 2. Tissues react to the new mechanical environment created by the implant. Algorithms to predict tissue differentiation at implant interfaces43 and fully three-dimensional (3D) predictions of bone remodeling are now available.44 3. Physiological joint kinematics are due to the very complex and synergistic interplay of joint surfaces, ligaments, and musculature. Precise replication of natural joints is impossible, particularly as soft tissues may have degenerated, or need to be excised to insert the implant. Designers must therefore develop new constraint mechanisms that allow functional range of motion, while main- taining kinematic stability. 4. The range of materials available for implantation is limited because of biocompatibility issues (see Section 35.2 above). These include reactivity to the bulk material and to particulate matter generated due to wear. 5. Surgical factors—the prosthesis must be implantable. New developments include surgical innovations in robotic instrumentation and minimally invasive surgery.45,46

35.3.2 Prosthesis and Implant Systems In this section, the various designs of bone prostheses and implants are described. Implants may be classiﬁed as either temporary implants (those that will be removed or resorbed from the body after the bone has healed) or permanent implants (those that are intended to remain in the body indeﬁnitely).

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35-6 Bone Mechanics

FIGURE 35.2 A longitudinal force to compress the bone fragments is created as the screw is tightened to the bone plate. (From Tencer, A. F. and Johnson, K. D., Biomechanics in Orthopaedic Trauma, Martin Dunitz, London, 1994. With permission.)

35.3.2.1 Temporary and Resorbable Implants 35.3.2.1.1 Bone Fixation Systems Devices employed to fixate bone are (1) bone screws, (2) bone plates, (3) intramedullary (IM) nails, and (4) external fixators. There are a large number of these devices employed in orthopedics, reflecting the specific requirements of each bone and the variety of surgical opinion on how to treat a particular fracture. Tencer and Johnson47 give a thorough description of the various systems. Bone screws can be classified into cortical screws or cancellous screws. Design variables for screws are root diameter, pitch (axial motion per revolution), and thread profile.48 Cancellous bone screws have larger threads and pitch than cortical bone screws because of the need to grip widely spaced trabeculae. The pullout strength of bone screws is also determined by the pilot drill-hole, which should not be too small (else screw breakage could occur) or too large (else screw purchase will be reduced).47 Bone plates are screwed directly onto the bone. Among the innovations proposed for these seemingly simple devices is the “compression plate,” which achieves compression between the fracture ends by creating axial motion as the screw is tightened (Fig. 35.2). IM nails are inserted into the intramedullary cavity of the long bones. Proximal and distal interlocking pins are used to stabilize the nail. IM nails are slightly curved to align with the natural curve of the long bone shaft—this, however, creates problems at insertion which can lead to bone splitting.47 The cross section of the IM nail determines the rigidity and ease of insertion.49 External fixators stabilize a fracture by insertion of pins or wires through the skin on either side of the fracture site and connecting the pins with external sidebars. Pin diameter and thread design determine the pullout strength.50 This method of fixation causes less surgical trauma and can facilitate better wound management than other methods.51 Behrens52 has classified fracture fixation devices as uniplanar (with sidebars in the same plane as the bone) and multiplanar (with sidebars surrounding the limb). Uniplanar devices are called unilateral if there is only one sidebar, or bilateral if there are two sidebars on either side of the limb. The advantage of the unilateral fixator is that there are fewer pin insertions through the skin and a correspondingly lower risk of infection—however, the mechanical stability of the bilateral fixator is greater. A multiplanar fixator, such as pioneered by the Russian orthopedic surgeon G. Ilizarov, uses tensioned wires rather than pins, thereby reducing the disturbance to the vascularity of the bone and reducing the problem of refracture at the holes when the fixator is removed.47 Fig. 35.3 illustrates this kind of fixation system. Many experimental,53–55 theoretical,56,57 finite-element,58,59 and animal studies,60,61 have been reported on external fixation systems. CH-35 Page 7 Monday, January 22, 2001 2:16 PM

Bone Prostheses and Implants 35-7

FIGURE 35.3 An external ﬁxation system (circular conﬁguration). (From Chao, E. Y. S. et al., J. Biomech., 15, 971, 1982. With permission.)

All fixation systems alter the mechanical load transferred to bone callus. The mechanical forces transmitted to the callus influence bone regeneration during fracture healing. Beaupré et al.62 showed that, as the callus stiffens, the fixator allows a greater proportion of the load to pass via the bone. It has been proposed63 that the interfragmentary strain between the bone determines the tissue formed: low strains (2%) allow bone formation, higher strain causes cartilage, and excessive strains maintain granulation tissue. Pauwels64 had earlier proposed a more complex theory implicating hydrostatic pressure in cartilage formation; recently, the influence of oxygen tension65 and cell migration66 have been included in biomechanical models of tissue regeneration. CH-35 Page 8 Monday, January 22, 2001 2:16 PM

35-8 Bone Mechanics

35.3.2.1.2 Bone Substitute Materials Bone graft implants are needed as a space filler in reconstructive surgery, or in spinal fusion. The available materials may be listed as follows: autograft taken from the patient, allograft taken from another human (either as chips or morselized67), xenograft taken from another species, or synthetic materials falling into two main categories: 1. Materials from conversion of naturally occurring materials, e.g., coralline materials,68 which have full interconnectivity of pores and good pore distribution. 2. Entirely synthetic materials, e.g., artificially porous hydroxyapatites formed by various processing methods69 or by replication of naturally porous cancellous bone.70 Bone materials have some disadvantages as grafts: autograft causes additional trauma to the patient and allograft and xenograft have risk of disease transmission. Synthetic materials have neither of these problems, but may lack appropriate porosity and pore interconnectivity,71,72 with the exception of materials that directly replicate trabecular bone structure.70 Synthetic materials are made from hydroxyapatite-tricalcium phosphate (HA -TCP) composites. Since -TCP is more resorbable than HA, the resorption rate of the implant can be designed by suitable ratio of these components. Greater porosities also favor more rapid resorption. Knowles and Bonfield73 showed that these materials can be strengthened by addition of a glassy phase, although adding too much reduces the mechanical properties.74 Morphogenetic proteins necessary to induce bone growth and blood vessel penetration of the graft may be added to synthetic materials,75 and recent studies report using synthetic implants as a carrier for cells and growth factors.76 35.3.2.2 Permanent Implants for Total Joint Arthroplasty A degenerated joint can be “cured” by replacing it with a prosthesis. Many attempts to design replacement implants were made over the centuries,77 but serious problems persisted until the British orthopedic surgeon John Charnley advocated the use of PMMA as a fixation material78 and PE as a bearing material.79 Replacement of both sides of a joint creates a total joint arthroplasty, whereas replacement of one side only is called a hemi-arthroplasty. The concepts of conformity and constraint are central to artificial joint design. The healthy hip joint, for example, is a ball-and-socket joint with high conformity and high constraint. The shoulder is also a ball-and-socket joint with highly conforming surfaces but, because the socket is shallow, it has low constraint.80 Joints such as the knee are more complex with significantly different congruencies in different directions.81 Highly constrained articulations can be designed using hinges (constant center of rotation). Hingeless joints can also be designed. Although they run the risk of dislocation, they are better able to reproduce natural joint kinematics. 35.3.2.2.1 Hip Replacement Prostheses Many hundreds of different designs of hip joint prostheses are currently on the market.82 They may be broadly classified into cemented or cementless devices, with fixation in the former achieved by cementing with PMMA (see Section 35.2.4) and in the latter by osseointegration (see Section 35.2.3). If cement is used for the femoral side and cementless fixation for the acetabular side, the implant is a “hybrid” design.83 Fig. 35.4 shows a schematic of a cemented hip replacement. Stillwell et al.84 give a description of the procedures and instrumentation involved. Variations in prosthesis design include the size of the prosthesis head. Charnley 85 described the effect of head size: he proposed a small head because it would create a lower frictional torque than a larger head and thus reduce the potential for loosening (Fig. 35.5). However, smaller heads imply greater contact stresses on the polyethylene cup. The size of the head and the geometry of the neck determine the range of motion of the reconstruction. For a given neck geometry, a larger head size will permit a greater range of motion of the artificial joint.86 As wear progresses, the head penetrates the acetabular cup, decreasing the range of motion. For these reasons, head diameter is a crucial design variable for which a compromise is required. Note also that the head may be removable from the tapered neck (modular prosthesis). The acetabular cup may have “metal-backing” which was introduced to create a more even stress transfer CH-35 Page 9 Monday, January 22, 2001 2:16 PM

Bone Prostheses and Implants 35-9

FIGURE 35.4 Total hip replacement involves replacement of both the acetabular and femoral sides. In this schematic diagram, both sides are ﬁxated with cement. (Adapted from Hardinge, K., Hip Replacement, Oxford University Press, Oxford, 1983. With permission.)

FIGURE 35.5 Illustrating how rotation of the socket against the bone is less likely with a small head and a thick socket than with a large head and a thin socket as a result of the differences in the moment of the frictional force as a result of the differences in radii of the parts. (From Charnley, J., Lancet, 1129, 1961. ©The Lancet Ltd. With permission.)

from the head to the acetabular bone, although this is not confirmed by stress analysis of implanted acetabuli.87 On the femoral side, cementless designs require a “canal-filling” stem of adequate fit with the bone to minimize interfacial micromotion and allow bone ingrowth.88 For cemented femoral stems, the stem cross- sectional shape determines stress concentrations in the cement89—circular cross sections minimize stress concentrations but have the lowest resistance to slip within the cement mantle.90 Stem shape also affects the pressure generated within the bone cement and, therefore, the interdigitation of the bone cement with the cancellous bone.91 Another geometric difference between femoral components is the presence of a collar. The collar can either overhang the bone or just overhang the cement mantle, the latter being termed a semicollar. The taper of the stem is also very different between prosthetic designs. The taper has at least two effects: 1. A steeper taper means that the proximal stem is more rigid than the distal stem. Huiskes and Boeklagen92 have used stem taper as a control variable in an optimization process to minimize cement stresses; the so-called Scientific Hip prosthesis (SHP) was designed on this basis. CH-35 Page 10 Monday, January 22, 2001 2:16 PM

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2. A steeper taper generates a greater wedging action of the stem within the medullary cavity.93 The Exeter prosthesis, for example, facilitates distal movement within the bone cement. This requires a polished stem surface and the absence of a collar.94, 95 Alternatively, if a collar is used with the objective of loading the calcar femorale (a phenomenon not confirmed by structural analyses96,97), it can be argued that a strong cement interface is required to prevent subsidence.98 Chang et al.99 found that such bonded stems have up to 60% lower cement stresses than unbonded stems. Failure of artificial joints is a multifactorial process involving a cascade of biomechanical events. Huiskes100 advances six failure scenarios, which provide a generic approach for viewing failure of all bone/prostheses systems. These failure scenarios are as follows: 1. Accumulated Damage: Accumulation of damage in prosthesis materials occurs during cyclic loading. Proof of damage accumulation in bone cement was provided by Jasty et al.,101 who found partial cracking in autopsy-retrieved specimens. Experimental confirmation that the cracking process is gradual and continuous under bending loads102 and torsional loads103 has been provided. Damage may also accumulate within the prosthesis (leading to stem breakage) or on the interfaces.104,105 Verdonschot and Huiskes106 carried out a computer simulation of damage accumulation in the cement mantle of a hip replacement and found that debonding very much accelerates the damage accumulation rate. Precoating of the stem with a PMMA layer to reduce interfacial porosity may slow the rate of damage.107 2. Particulate Reaction: There are three possible sources of particles in joint replacement: wear of the articulating surfaces, abrasion of the PMMA/prosthesis/bone interfaces, and fretting between metal parts in modular prostheses.108 For example, PE particles have been found at the cement/bone interface in acetabular cups where they initiate a macrophage inflammatory response and subsequent formation of a fibrous tissue layer.109,110 The next event in this failure scenario is increased interfacial micromotion and mechanical loosening. 3. Failed Ingrowth: Failure of osseointegration to occur can be caused by large unbridgeable gaps between prosthesis and bone, or by excessive micromotion. 4. Stress Shielding: The implant takes load formerly transferred to the bone, thereby shielding the bone from the load and causing bone resorption. This process is most probably dependent on mechanical factors,111 and has been observed in the proximal medial bone after hip replacement, and under the tibial component of knee replacements. While more flexible components have been proposed to prevent stress-shielding in the hip,112 finite-element models predict that too flexible a stem creates unsustainable bone/prosthesis or bone/cement interface stresses,113 which may lead to the failure scenario of damage accumulation (cemented implants) or failed ingrowth (cementless implants). 5. Stress Bypass: A prosthesis that is badly designed for a particular bone, or malsized, may transfer the loads in such a way as to bypass part of the bone entirely. Stress bypass may also result from localized osseointegration in uncemented devices—such “spot-welding” causes the load to bypass whatever bone tissue lies between the “weld” and the articulation. 6. Destructive Wear: Wear of the bearing surfaces may proceed to such an extent that the PE component “wears out.” For example, the head may penetrate the acetabular cup in a hip replacement. Obviously, the failure scenarios will proceed simultaneously, and the one that causes failure depends on the rate of progression of the active scenarios in a particular patient. 35.3.2.2.2 Knee Replacement Prostheses The first total knee replacement (TKR) prostheses were hinged designs.114 However, such high-constraint prostheses do not allow for rolling and sliding of the femoral condyles on the tibial plateau, which occurs in the healthy knee—because of this, high stresses are generated in the fixation causing premature loosening and occasional stem breakage.115 Unconstrained designs were developed that replaced the femoral condyles with a metal component and the tibial plateau with a partially conforming PE component supported on a “tibial tray.” The patella is also replaced in many designs. Walker and Sathasivam116 CH-35 Page 11 Monday, January 22, 2001 2:16 PM

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define these TKR types as one of the following: 1. Fixed-bearing condylar replacement with partially conforming surfaces, with or without the posterior cruciate ligament (PCL), 2. Mobile-bearing type, where the PE is free to slide and rotate on the tibial tray, 3. A rotating-platform type, where the PE component is allowed to rotate only about an axis, and is prevented from translating. Knee prostheses with partially conforming surfaces require close attention to stability: the “laxity” of the healthy knee should be maintained while guarding against “dislocation.”117 Delp et al.118 show that TKRs that “substitute” the PCL increase anterior-posterior (AP) stability with higher “tibial spines,” and show also that the radius of the femoral component (posterior part) in the AP direction has a role in preventing dislocation. Knee prostheses with mobile bearings rely on the natural soft tissues and ligaments to limit and direct joint movement. Goodfellow and O’Connor119 report that mobile-bearing prostheses that retain a functional anterior cruciate ligament (ACL) have superior survival rates. Another consideration to be borne in mind is that the moment of the muscles about the knee is determined by the tibiofemoral contact point, which is in turn determined by the radii of the femoral and tibial components in the AP plane and the functionality of the ligaments. The conformity of the surfaces, in both AP and medial-lateral (ML) directions, influences the polyethylene stress—with the ML conformity having more effect.120 Bartel et al.121 substantiate this conclusion with results from a finite-element analysis of eight prosthesis designs that show that nonconforming prostheses generate the greatest polyethylene stresses 1 to 2 mm below the surface. However, Blunn et al.122 suggest more conforming surfaces in the AP direction to reduce cyclic sliding and hence the destructive wear failure scenario. It seems that the cyclic nature of the load must be included in analyses of PE failure, and strain/damage accumulation functions have been used for this purpose.123,124 Fixation of knee components is achieved by intramedullary stems (which may be cemented), or posterior and/or anterior pegs, posts, or blades, often employing porous coating. Furthermore, each “compartment” of the tibia may be replaced separately (bicompartmental prostheses) or only the medial compartment may be replaced (unicompartmental knee replacement). Walker et al.125 analyzed the stability of several configurations of tibial fixations, (Fig. 35.6). Finite-element modeling has also been employed, e.g., to identify stress-shielded regions below the tibial component.126 35.3.2.2.3 Shoulder Replacement Prostheses Early designs of shoulder replacement prostheses were either constrained ball-and-socket arrangements or unconstrained prostheses with shallow glenoid sockets and large humeral heads.127 Considering the biomechanical aspects of total shoulder arthroplasty, Walker128 described the design conflict between the degree of containment required for stability and the need to achieve a physiological range of motion. The required degree of containment (hence, constraint) depends on the quality of the “rotator cuff” surrounding the joint. Recent designs mainly follow the unconstrained concept129 as constrained designs gave unacceptable loosening rates. The main outstanding problem is glenoid component radiolucency, which limits the longevity to such an extent that many surgeons recommend hemi-arthroplasty of the shoulder. Both the humeral and glenoid components may be cemented. Design variations include keeled and pegged designs of the glenoid component. A finite-element analysis by Lacroix et al.130 has shown that pegged designs have lower cement stresses than keeled designs in normal bone, but that the reverse is true if the glenoid bone is of lower density (osteoporotic) (Fig. 35.7). Implant selection therefore depends on an assessment of bone quality. 35.3.2.2.4 Elbow Replacement Prostheses The elbow poses some challenges for replacement because three bones meet at the joint: the humerus on one side articulating with the ulna (trochlea) and the radius (capitellum) on the other. Most often, just the humerus/ulnar articulation is replaced, although some designs replace both. Early designs of hinged (high constraint) prostheses gave high loosening rates.131 Failures occurred due to high forces at the elbow132 and because the range of motion needed for daily activities was not facilitated.133 According CH-35 Page 12 Monday, January 22, 2001 2:16 PM

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FIGURE 35.6 (Top row) From left to right, compartmental components (with two pegs each), compartmental components with an anterior cross-bridge and an anterior blade, and a one-piece component with a central peg. Loading applied by rotation of a bicondylar femoral roller. (Bottom row) Same as above but with metal backing. (From Walker, P. S. et al., J. Bone Joint Surg., 63A, 258, 1981. With permission.)

to Coonrad,134 the artificial constraints produced by the hinge caused high stresses in the cemented fixation, whereas unconstrained designs require intact carpsuloligamentous structures and run the risk of dislocation.134 The solution of semiconstrained designs with various degrees of mediolaterial and rotary laxity has been pursued.135–137 These hinge-type designs are sometimes termed sloppy hinges. Although fixations may still prove problematic,138 the semiconstrained implants do seem to demonstrate a superior long-term performance, with Gill and Morrey137 reporting 86% of results in the “good or excellent” category at 10 to 15 years (Coonrad–Murray design) (Fig. 35.8). 35.3.2.2.5 Ankle Replacement Prostheses Total ankle arthroplasty replaces the joint formed by the tibia and the talus. Early designs were characterized by a rapid failure rate leading to the view that ankle arthrodesis (fusion of the joint) rather than arthroplasty should be used.139 However, more recent studies have reported greater than 70% survivorship at 14 years using cemented fixation and congruent cylindrical surfaces.140 Uncemented, semiconstrained prostheses have also recently reported good results.141 35.3.2.2.6 Wrist Replacement Prostheses Total wrist arthroplasty (TWA) replaces the articulation formed at the radial head and the scaphoid and lunate bones of the wrist. A metacarpal component inserts distally into the intramedullary cavity of the metacarpals and a proximal component inserts into the medullary cavity of the radius. Costi et al.142 describe the various prosthesis designs. One popular design is due to Volz,143 whose design involves resection of the scaphoid and lunate and one half of the capitate in an attempt to maintain the center of rotation of the normal wrist. Other cemented designs (trispherical and biaxial) employ the semiconstrained option, but dislocations have been reported.144 The uncemented design of Meuli145 is shown in Fig. 35.9. Many authors report TWA to be technically demanding, with a high complication rate.145,146 35.3.2.3 Dental Implants “Implantology,” the science of dental implants, is well developed and success rates for dental implants are very high compared with orthopedic implants.147 Implants are used to replace teeth in both the mandible and the maxilla. Most systems operate as follows: a gingival incision is made and exposure of CH-35 Page 13 Monday, January 22, 2001 2:16 PM

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FIGURE 35.7 FE mesh of the scapula, showing a detail of a pegged glenoid prosthesis. (Courtesy of Linda Murphy, Trinity College, Dublin.)

the bone followed by a guide-drilling procedure and a series of subsequent drilling steps to prepare a cavity accurately to the required diameter and depth. The implant is then either screwed or tapped into place. The implant is filled with a temporary cover screw, and the skin sutured to cover the implant. The implant is then left in this unloaded state in the “submerged” position for a period (usually several weeks) allowing the process of ossteointegration to proceed.148 Next the implant is exposed, the covering screw removed, and an abutment placed in position to allow soft-tissue healing before the aesthetic component is finally screwed into position. Stresses and adaptive bone remodeling around dental implants have been reported; see Vander Sloten et al.149 35.3.2.4 Middle-Ear Implants The smallest bones in the body are the three ossicles. The malleus, incus, and stapes (commonly called the hammer, anvil, and stirrup) need to be replaced if they degenerate, which usually happens as a result of fluid retention in the middle ear. Prostheses come in two categories: partial ossicular replacement prostheses (PORPs) and total ossicular replacement prostheses (TORPs).150 A PORP is used if the stapes superstructure is intact—it replaces the malleus and incus by connecting the tympanic membrane to the head of the stapes. A TORP additionally replaces the stapes superstructure and therefore connects the tympanic membrane directly to the stapes foot plate. Materials used for middle-ear implants have been reviewed by Blayney et al.151 and include hyodroxyapatite,152 alumina,153 and various polymers and bioactive glasses.150 The mechanical behavior of the middle ear was thoroughly investigated by von Békésy,154 who identified a lever action for the ossicular chain. A recent analysis has shown that this lever action is not regained in prosthetic reconstruction.155,156 More research is required to optimize the biofunctionality of these implants.157 CH-35 Page 14 Monday, January 22, 2001 2:16 PM

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FIGURE 35.8 Coonrad–Murray elbow replacement design. It has seven degrees of varus-valgus laxity, but this increases as the wear of the polyethylene bushings progresses. (From Gill, D. R. J. and Morrey, B. F., J. Bone Joint Surg., 80A, 1327, 1998. With permission.)

35.4 Analysis and Assessment of Implants

The objective of preclinical testing is to ensure the biofunctionality of new implants, to screen out inferior designs before clinical trials, and to demonstrate the superiority of new designs over competing devices at an early stage of product development. Postoperative assessment also plays a critical role in the process of implant innovation by eliminating inferior designs at the earliest possible stage.100

35.4.1 Preclinical Tests 35.4.1.1 Analytical Methods Analyses of bone/implant systems using the theory of elasticity was reported by Bartel,158 who showed that, among other things, the magnitude of the shear stresses in the cement layer of an intramedullary fixation is of similar magnitude to the normal stresses, and that the Young’s modulus of the prosthesis has a significant influence on cement and bone stresses. Elasticity theory has also been used to determine contact stresses in polyethylene in hip and knee replacement.120 Beams-on-elastic-foundations theory has been used to investigate stress transfer in intramedullary fixation. Huiskes’ comprehensive analyses32 showed that intramedullary fixation could be thought of as having a proximal region of CH-35 Page 15 Monday, January 22, 2001 2:16 PM

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FIGURE 35.9 The Meuli Wrist prostheses, an uncemented design. (From Meuli, H. C., Clin. Orthop., 342, 77, 1997. With permission.)

prostheses-to-bone load transfer, a midregion behaving like a composite beam, and a distal region of bone-to-prosthesis load transfer.

35.4.1.2 Finite Element Methods Finite-element (FE) modeling techniques have advanced rapidly since they were introduced to bone mechanics in 1972.126,159,160 FE analyses of femoral and acetabular hip components, surface hip arthroplasty, knee arthroplasty, arthroplasty of upper extremity joints, external and internal fixation, and structured implant interfaces were reviewed by Prendergast.126 The reasons for recent rapid developments include: 1. Combined with digitized computed tomography (CT) scanning, accurate representation of complex bone geometries can be achieved. Skinner et al.161 use the voxels of the CT image to generate a finite-element model automatically, whereas others use only the boundary definition of the bone, e.g., femur,162 scapula,130 acetabulum.163 2. The method allows parametric variation of design parameters in a way that experimental methods do not—this allows designers to compare the effects of implant geometry rapidly, e.g., hip,99,164,165 tibial plateau,166 and acetabular cup.167 For example, it has been predicted that stiffer hip prostheses generate lower bone cement stresses,168,169 that surface finish affects interface motions,170 and that porous coating can reduce interface motion in cementless hips by more than 50%.171 3. FE models can be combined with bone remodeling algorithms to predict possible long-term tissue reactions around implants. Iterative computations can be used to predict the time course of peri- implant tissue response, including bone remodeling and tissue differentiation. Computer simulation of bone remodeling around implants was first reported by Huiskes et al.,172 who used strain energy density as a remodeling stimulus to compute “surface” remodeling around an intramedullary implant. They showed that higher stiffness prostheses have a greater potential for surface resorption. Further studies showed the influence of prosthesis material properties173 and bonding characteristics174 on bone adaptation around a hip femoral stem in terms of change in density (internal remodeling). Van Rietbergen et al.175 compared remodeling in dogs with 3D external and internal bone remodeling simulation and found excellent correlation. Further 3D remodeling CH-35 Page 16 Monday, January 22, 2001 2:16 PM

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simulations showed the effect of prosthesis stem material162 and extent of porous coating.176 Under certain circumstances, the postoperative stress pattern can predict the evolution of bone density without the need for a simulation.177 Other approaches to predict peri-implant bone remodeling use • An “effective stress” remodeling stimulus,178 • A damage accumulation remodeling stimulus,179,180 • A strain rate remodeling stimulus.181

35.4.1.3 Strain Measurement Methods Strain measurement techniques are often used to determine the stress distribution in bone tissue surrounding an implant, or on the implanted material itself. Strain gauges have been used, despite the problems such as strain gauge misalignment, reinforcement effects of the gauges (e.g., on PE), and the impossibility of measuring strain at a point when the strain gradient is high.182 Optical methods have several advantages, including the possibility of full-field results.183,184 Most often strain gauge analyses are performed on cadaver bone.185–187 Strain gauge measurement of models built to several times life size have been reported, which allow use of embedded strain gauges in the cement mantle, e.g., for the knee188 and hip.189 Recent studies have found excellent correlation between FE and strain gauging.190 Cristofolini191 gives a review of the studies that address stress-shielding in the proximal femur, showing that there are great differences in the boundary conditions in the many studies. An interesting study of strain gauging of implanted femora retrieved at autopsy showed that remodeling had not succeeded in returning strain to “anywhere near normal,” even 7.5 years after surgery.192 35.4.1.4 Simulators Simulators are machines designed to assess the performance of prostheses under cyclic loading. Simulators must replicate the motion and loading on an implant in the biological environment. They may be divided into two classes: those concerned with wear and those concerned with loosening. 35.4.1.4.1 Wear Wear is the progressive loss of material from surfaces due to relative movement. Mechanisms of wear are abrasion, adhesion, and fatigue wear, see Dowson.193 Because of the sensitivity of the wear rate to many extraneous factors, experiments to determine the rate of material removal must replicate the in vivo loading and environmental conditions as closely as possible. According to LaBerge et al.,194 11 hip joint wear simulator designs are in existence, differing in how many tests can be run simultaneously, and in how well in vivo kinematics are approximated. The Leeds hip simulator applies three axes of loading in a complex three-dimensional motion,195 and has been used, for example, to show that traditional metal-on-polymer bearings have a higher wear rate than ceramic- on-polymer articulations.193 The orientation of the articulation during the test, and the precise nature of the lubricant have been reported to be critical.196 Knee simulators have been reviewed by Walker and Blunn.117 Similar considerations of in vivo kinematics and environmental lubricational conditions apply as with hip simulators except that the unconstrained nature of most contemporary knee prostheses poses a special challenge. Walker et al.197 adopted a solution of controlling flexion-extension and restraining other degrees-of-freedom by simulated soft tissues. 35.4.1.4.2 Loosening Loosening due to the damage accumulation failure scenario involves a progressive loss of mechanical integrity of the implant/bone construct. Devices to measure the 3D relative motion of the femoral stem and the bone under cyclic loading have been developed.88,198–201 Studies which apply a form of muscle loading have also been reported.192,202,203 However, the difficulty of applying physiological loading and the problems of reproducible prosthesis implantation204 and of establishing a failure criterion makes quantitative simulation of loosening a difficult prospect. CH-35 Page 17 Monday, January 22, 2001 2:16 PM

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35.4.2 Clinical Assessment Ideally, a randomized clinical trial (RCT) should form part of a clinical assessment but RCT is problematic in surgery for the following reasons:205 1. It is difficult if not impossible to blind patients in surgical vs. nonsurgical treatments. 2. Sham surgical procedures are not considered ethically acceptable by many. 3. Patients may refuse to accept randomization. 4. There is a “learning curve” to an operative technique, which will confound the results. Unbiased scientific assessment of implants is all the more critical to the innovation process because of the difficulties with RCT.206 35.4.2.1 Gait Analysis Gait analysis has the potential to aid outcome assessment of lower-limb joint replacement.207 For example, Andriacchi et al.208 report a study showing a change in the stride-length/walking relationship after TKR. In a clinical study, Hilding et al.209 reported that patients whose knee prosthesis were in the risk category for loosening had increased knee flexion moments compared with nonrisk patients; other gait parameters such as gait speed or stride length were unaffected. They advocated gait analysis to identify these patients prior to surgery. 35.4.2.2 Radiographic Assessment Radiographic assessment of a bone prosthesis is used to identify implant “loosening,” and to determine bone reactions around the implant. Radiolucent lines between the implant and the bone can be interpreted as indicating a loosening process, such as the formation of a soft fibrous tissue. Brand et al.210 have drawn attention to the qualitative nature of this assessment. Dual-energy X-ray absorptiometry (DEXA) is more accurate, and is frequently used to assess bone remodeling around implants. For example, Ang et al.211 compared bone remodeling around a metallic hip stem and a polymeric hip stem using DEXA and showed greater bone mineral density around the polymeric stem. Cohen and Rushton212 describe how errors can occur during DEXA measurements. Finally, image analysis, in combination with FE modeling, has the potential for highly accurate assessment of bone reactivity, including architectural changes, in vivo. 35.4.2.3 Roentgen Stereophotogrammetry Analysis Radiostereometry analysis, or RSA, is a method of measuring the relative movement of two rigid bodies. Originally used by Dr. Göran Selvik213 to measure the relative motion of bones, it can also be applied to determination of the relative movement between prostheses and bone. Huiskes and Verdonschot44 give a simple description of how RSA works. Two X-ray tubes are placed so as to project an image of an object onto two X-ray films. The object to be studied has tantalium pellets attached to it (because tantalium has high density) and is surrounded by a “calibration cage.” This cage has markers on a control plane, which are used to determine the foci of the X-ray beams and markers on a fiducial plane used to define the laboratory coordinate system. When the foci and laboratory frame are known, the position of the object (i.e., the position of its marker pellets) can be calculated as the intersection point of the two lines joining the foci to the image point cast by the pellet on each X-ray film. Several developments have been made to optimize the procedure.214 Kiss et al.215 employ a method that does not have pellets on the prosthesis but instead uses prosthesis landmarks (e.g., center of the head) to define its position. RSA has been applied to THR and TKR to determine both migration (permanent movement of the prosthesis) and inducible displacement (recoverable deflection under load). For example, Ryd et al.216 studied a screw-fixated tibial component in TKA and found migrations and inducible displacement of the order of 0.6 and 0.3 mm, respectively. Kärrholm and co-workers report RSA of hip femoral stems for cementless217 and cemented fixation.218 In the latter study of 84 hips, they correlated subsidence rates of 1.2 mm or more at 2 years with a greater than 50% probability of revision. RSA has also shown the complex nature of cemented stem migration within the femur.219 CH-35 Page 18 Monday, January 22, 2001 2:16 PM

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TABLE 35.2 The Harris Hip Score

Factor Score

Pain (seven categories with points for each) 0–40 Function (Gait, 33 points and activities, 14 points) 0–47 Range of motion 0–5 Absence of deformity 0–8 Total 0–100

FIGURE 35.10 Survival curves for the acetabular and femoral components in 444 Lubinus arthroplasties in 398 patients. (From Partio, E. et al., Clin. Orthop., 303, 140, 1994. With permission.)

35.4.2.4 Retrieval Analysis Retrieval of prostheses at revision (e.g., knee,220 hip221,222) or after death223 allows inspection of failure phenomena such as wear.224 Strain analysis to determine if the fixation was performing adequately can also be carried out.112,192 35.4.2.5 Outcome Analysis Outcome analysis measures how well an implant is functioning by combining patient information on pain and mobility with surgical results. For example, with hip replacement there are various “hip scores.” One widely used score is the Harris hip score,225 in which the status of the hip is given a single number (Table 35.2). For example, Edidin et al.226 report a mean Harris hip score of 91 at 51 months for a hip replacement where the femoral component was cemented in the proximal region only. Murray227 gives a review of the Harris, Charnley, Iowa, and Mayo hip scores. 35.4.2.6 Survival Analysis Survival analysis measures the time to some end point—usually the revision of the prosthesis. Problems encountered are loss of patients to follow-up, the small numbers of patients, and the difficulty of defining the end point. Recently published results from national hip registries in Europe, such as the Swedish registry,228 have removed the first two problems. However, the third—the difficulty of defining an end point—can be controversial; different decisions of when to revise are possible. Fig. 35.10 shows survival curves for the Lubinus prosthesis (W. Link, Hamburg, Germany) where revision is taken as the end point.229 In this study, different modifications to the stem and cup are compared, and failure rates associated with the femoral and acetabular sides have been differentiated. Hench and Wilson230 present an extensive review of the performance of bone prostheses and implants in orthopedics, dentistry, and otolaryngology. CH-35 Page 19 Monday, January 22, 2001 2:16 PM

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35.5 Future Directions

This chapter has shown that replacement or augmentation of bone by prostheses has led to a proliﬁc number of devices with one common aim—to alter the load transfer in bone tissue. Bone prostheses and implants will continue to be used until the capability for growing replacement tissues outside the body by tissue engineering becomes well established. Even when that happens, implants will almost certainly be required as scaffolds in many cases, and determination of the appropriate load sharing between the scaffold and the tissue will still require a thorough understanding of the issues raised in this chapter.231 These implants will be biomechanically “active” in the sense that they will act in synergy with the cells in the surrounding bone.232 Modeling the performance of these implants prior to animal trials and clinical trials will become more important,233 and attention will be further focused on preclinical testing methods.234

Acknowledgments

Dr. David C. Tancred and Dr. Suzanne A. Maher are thanked for their comments on the content of this chapter.

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138. Sjödén, G.O., Lundberg, A., and Blomgren, G.A., Late results of the Souter-Strathclyde total elbow prosthesis in rheumatoid arthritis. 619 implants loose after 5 years, Acta Orthop. Scand., 66, 391, 1995. 139. Hamblen, D.L., Editorial: can the ankle joint be replaced? J. Bone Joint Surg., 67B, 689, 1985. 140. Kofoed, H. and Sørensen, T.S., Ankle arthroplasty for rheumatoid arthritis and osteoarthritis. Perspective long term study of cemented replacements, J. Bone Joint Surg., 80B, 328, 1998. 141. Pyevich, M.T., Saltzman, C.L., Callaghan, J.J., and Alvine, F.G., Total ankle arthroplasty: a unique design, J. Bone Joint Surg., 80A, 1410, 1998. 142. Costi, J., Krishnan, J., and Pearcy, M., Total wrist arthroplasty: A quantitative review of the last 30 years, J. Rheumatol., 25, 451, 1998. 143. Volz, R.G., Total wrist arthroplasty: a clinical and biomechanical analysis, in Symposium on Total Joint Replacement of the Upper Extremity, Inglis, A.E., Ed., CV Mosby, St. Louis, 1982, chap. 23. 144. O’Flynn, H.M., Rosen, A., and Weiland, A.J., Failure of the hinge mechanism of a trispherical total wrist arthroplasty. A case report and review of the literature, J. Hand Surg., 24A, 156, 1999. 145. Meuli, H.C., Total wrist arthroplasty. Experience with a noncemented prosthesis, Clin. Orthop., 342, 77, 1997. 146. Gellman, H., Hontas, R., Brumfield, R.H., Tozzi, J., and Conaty, J.P., Total wrist arthroplasty in rheumatoid arthritis. A long term clinical review, Clin. Orthop., 342, 71, 1997. 147. Norton, M., Dental Implants, Quintessence Publishing, London, 1995, 33. 148. Albrektsson, T., Brånemark, P.-I., Hansson, H.A., and Lindström, J., Osseointegrated titanium implants, Acta Orthop. Scand., 52, 155, 1981. 149. Van der Sloten, J., Hobatho, M.-C., and Verdonck, P., Applications of computer modelling for the design of orthopaedic, dental and cardiovascular biomaterials, Proc. Inst. Mech. Eng. Part H, 212, 489, 1998. 150. Kobel, K.D., Ossicular replacement prostheses, in Clinical Performance of Skeletal Prostheses, Hench, L.L. and Wilson, J., Eds., Chapman & Hall, London, 1996, chap. 13. 151. Blayney A.W., Williams, K.R., Erre, J.-P., Lesser, T.H.J., and Portmann, M., Problems in alloplastic middle-ear reconstruction, Acta Otolaryngol. (Stockholm), 112, 322, 1992. 152. Grote, J.J., Reconstruction of the middle-ear with hydroxyapatite implants.: Long term results, Ann. Otol. Rhinol. Laryngol., 144, 12, 1990. 153. Yamamoto, E. and Iwanaga, M., Soft tissue reaction to ceramic ossicular replacement prostheses, J. Laryngol. Otol., 101, 897, 1987. 154. von Békésy G., Experiments on Hearing, McGraw-Hill, New York, 1960. 155. Prendergast, P.J., Ferris, P., Rice, H.J., and Blayney, A.W., Vibroacoustic modelling of the middle ear using the finite-element method, Audiol. Neurootol., 4, 185, 1999. 156. Ferris, P. and Prendergast, P.J., Middle-ear dynamics before and after ossicular replacement, J. Biomech., 33, 581, 2000. 157. Hüttenbrink, K.-B., Ed., Middle-Ear Mechanics in Research and Otosurgery, Dresden University of Technology, Dresden, 1997. 158. Bartel, D.L., Stress analysis: effects of geometry in bone-implant systems, Bull. Hosp. Joint Dis., 40, 90, 1977. 159. Huiskes, R. and Chao, E.Y.S., A survey of finite element models in biomechanics: the first decade, J. Biomech., 16, 385, 1983. 160. Gilbertson, L.G., Goel, V.J., Kong, W.Z., and Clausen, J.D., Finite element models in spine biomechanics research, Crit. Rev. Biomed. Eng., 23, 411, 1995. 161. Skinner, H.B., Kim, A.S., Keyak, J.H., and Mote, C.D., Jr., Femoral prosthesis implantation induces changes in bone stress that depend on the extent of porous coating, J. Orthop. Res., 12, 553, 1994. 162. Husikes, R., Weinans, H., and van Rietbergen, B., The relationship between stress shielding and bone resorption around total hip stems and the effects of flexible materials, Clin. Orthop., 274, 124, 1992. CH-35 Page 26 Monday, January 22, 2001 2:16 PM

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185. Oh, I. and Harris, W.H., Proximal strain distribution in the loaded femur, J. Bone Joint Surg., 60A, 75, 1978. 186. Huiskes, R., Janssen, J.D., and Slooff, T.J., A detailed comparison of experimental and theoretical stress analyses of the human femur, in Mechanical Properties of Bone, Cowin, S.C., Ed., American Society of Mechanical Engineers, New York, 1981, 211. 187. Bourne, R.B. and Finlay, J.B., The influence of tibial component intramedullary stems and implant- cortex contact on the strain distribution of the proximal tibia following total knee arthroplasty, Clin. Orthop., 208, 95, 1986. 188. Little, E.G., Kneafsey, A.G., Lynch, P., and Kennedy, M., The design of a model for a three dimensional stress analysis of the cement layer beneath a tibial plateau of a knee prosthesis, J. Biomech., 18, 157, 1985. 189. Colgan, D., McTague, D., O’Donnell, P., and Little, E.G., The effect of the transverse component of the hip reaction on cement mantle stresses in a model of an implanted Exeter prosthesis, J. Strain Anal., 31, 205, 1996. 190. Stolk, J., Verdonschot, N., Cristofolini, L., Firmati, L., Toni, A., and Huiskes, R., Strains in composite hip reconstructions obtained through FEA and experiments correspond closely, Trans. Orthop. Res. Soc., 25, 0515, 2000. 191. Cristofolini, L., A critical analysis of stress shielding evaluation of hip prostheses, Crit. Rev. Biomed. Eng., 25, 409, 1997. 192. Engh, C.A., O’Connor, D., Jasty, M., McGovern, T.F., Bobyn, J.D., and Harris, W.H., Quantification of implant micromotion, strain shielding, and bone resorption with porous-coated anatomic medullary locking femoral prostheses, Clin. Orthop., 285, 13, 1992. 193. Dowson, D., A comparative study of the performance of metallic and ceramic femoral head components in total replacement hip joints, Wear, 190, 171, 1995. 194. LaBerge, M., Medley, J.B., and Rogers-Foy, J.M., Friction and wear, in Handbook of Biomaterials Evaluation, 2nd ed., van Rencum, A.F., Ed., Taylor & Francis, London, 1999, 171. 195. Bigsby, R.J. A., Hardaker, C.S., and Fisher, J., Wear of ultra-high molecular weight polyethylene acetabular cups in a physiological hip joint simulator in the anatomical position using bovine serum as a lubricant, Proc. Inst. Mech. Eng. Part H, 211, 265, 1997. 196. Wang, A., Essner, A., Polineni, V.K., Sun, D.C., Stark, C., and Dumbleton, J.H., Lubrication and wear of ultra-high molecular weight polyethylene in total joint replacements, in New Directions in Tribology, Hutchings, I.M., Ed., Mechanical Engineering Publications, London, 1997, 443. 197. Walker, P.S., Blunn, G.W., Broome, D.R., Perry, J., Watkins, A., Sathasivam, S., Dewar, M.E., and Paul, J.P., A knee simulating machine for performance evaluation of total knee replacements, J. Bio- mech., 30, 83, 1997. 198. Schneider, E., Kinast, C., Eulenberger, J., Wyder, D., Eskilsson, G., and Perren, S.M., A comparative study of the initial stability of cementless hip prostheses, Clin. Orthop., 248, 200, 1989. 199. Berzins, A., Sumner, D.R., Andriacchi, T.P., and Galante, J.O., Stem curvature and load angle influence the relative bone-implant motion of cementless femoral stems, J. Orthop. Res., 11, 758, 1993. 200. Bühler, D.W., Berlemann, U., Lippuner, K., Jaeger, P., and Nolte, L.-P., Three dimensional primary stability of cementless femoral stems, Clin. Biomech., 12, 75, 1997. 201. Maher, S.A., Prendergast, P.J., Waide, D.V., Reid, A.J., and Lyons, C.G., Development of an experimental procedure for pre-clinical testing of cemented hip replacements, in Advances in Bioengi- neering, American Society of Mechanical Engineers, New York, 1999, 139–140. 202. Burke, D.W., O’Connor, D.O., Zalenski, E.B., Jasty, M., and Harris, W.H., Micromotion of cemented and uncemented femoral components, J. Bone Joint Surg., 73B, 33, 1991. 203. Munting, E. and Verhelpen, M., Mechanical simulator for the upper femur, Acta Orthop. Belg., 59, 123, 1993. 204. Maher, S.A., Prendergast, P.J., Reid, A.J., Waide, D.V., and Toni, A., Design and validation of a machine for reproducible precision insertion of femoral prostheses for pre-clinical testing, J. Biomech. Eng., 122, 203, 2000. CH-35 Page 28 Monday, January 22, 2001 2:16 PM

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Ch-36.fm Page 1 Monday, January 22, 2001 2:17 PM 36 Design and Manufacture of Bone Replacement Scaffolds

Scott J. Hollister 36.1 Introduction ...... 36-1 The University of Michigan 36.2 Designing Bone Scaffolds ...... 36-2 36.3 Fabricating Bone Scaffolds ...... 36-6 Tien-Min Gabriel Chu 36.4 Bone Scaffolds: An Example from The University of Michigan Design to Testing ...... 36-9 John W. Halloran 36.5 Conclusion...... 36-11 The University of Michigan Stephen E. Feinberg The University of Michigan

36.1 Introduction

Each year a large number of surgical cases require reconstruction of bone defects in the craniofacial and appendicular skeleton. These defects may be congenital or result from disease or trauma. The ultimate surgical goal is to replace the defect with a functioning material that will last the patient’s lifetime. The two classic methods of defect reconstruction are bone grafting and synthetic material reconstruction, each having advantages and disadvantages. Bone grafting offers a biological tissue reconstruction that can undergo functional remodeling. Disadvantages of grafting include morbidity associated with a second surgical site, a limit on the amount of usable material, the need for hardware to ﬁx the graft, and possible mismatches between graft and defect shape, requiring additional surgical time. Synthetic material reconstruction offers the advantages of not having a second surgical site, no limit on usable material, and shapes speciﬁcally manufactured for a given reconstruction. Disadvantages include the inability of synthetic materials to integrate completely with biological tissue, leading to risks of loosening between material and tissue, and the inability of the synthetic material to adapt and remodel with the host tissue to its functional environment. Although both bone grafting and synthetic material reconstruction have been successful in many applications, their shortcomings have motivated a third approach to bone reconstruction, tissue engineering. Tissue engineering combines biologic regenerative factors, like stromal cells or growth factors, with biodegradable material scaffolds, like calcium phosphate ceramics and polylactic and polyglycolic acid polymers. The scaffold provides initial function but slowly degrades as healing bone tissue gradually takes over more function. In theory, tissue engineering provides the best of bone grafting and synthetic material reconstruction. Like synthetic reconstruction, tissue engineering requires no second surgical site and is not restricted by a limited amount of material. Like bone grafting, tissue engineering reproduces natural bone tissue that can adapt to functional demands.

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36-2 Bone Mechanics

FIGURE 36.1 Overall strategy for patient speciﬁc tissue reconstruction from initial image to ﬁnal manufactured scaffold.

Scaffold–biologic factor interaction is critical for successful bone tissue engineering. Many studies have noted that scaffold pore size and material can significantly influence bone vs. cartilage regeneration.1–4 Furthermore, it is not sufficient that the scaffold have the right pore diameter for bone regeneration; those pores must have adequate connectivity and orientation so that the regenerated bone tissue can carry mechanical load. Bruder et al.5 noted that calcium phosphate ceramics with uncontrolled pore architecture produced poor biomechanical properties, even though there was a large amount of regenerate bone tissue. In addition to internal architecture, it is necessary that the scaffold can replicate complex external shapes, especially in craniofacial reconstruction. The need to control internal scaffold architecture and external scaffold shape depends on the ability to design and manufacture complex three-dimensional (3D) topologies. Although significant research has been performed on the biologic6–8 and material fabrication9,10 aspects of bone tissue engineering, controlled 3D scaffold design and fabrication have only recently received attention. The ideal goal in bone tissue engineering is to combine design and automated manufacturing techniques to create patient- specific tissue reconstruction strategies (Fig. 36.1). This chapter discusses current work on scaffold design and fabrication for bone tissue engineering, in three sections: (1) design, (2) fabrication, and (3) overall concept from design to in vivo testing.

36.2 Designing Bone Scaffolds

Designing bone scaffolds requires that one can design both complex, external 3D geometry to ﬁt anatomical shapes and complex, internal 3D architecture for cell invasion and tissue regeneration. There are two computational design methodologies for creating complex 3D topology: traditional computer-aided design (CAD) and image-based design (IBD). CAD uses mathematical entities like points, lines, and surfaces to represent 3D topology. Advantages of CAD include the ability to theoretically represent topology with exact precision and the ability to represent complex structures with small amounts of data.

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Design and Manufacture of Bone Replacement Scaffolds 36-3

Disadvantages of CAD include difficulties in representing extremely complex 3D topologies, the significant amount of user time needed to create complex 3D designs, and the necessity to preprocess image data like computed tomography (CT) scans. The last point is especially relevant to bone scaffold design, since one goal is to design and fabricate patient-specific scaffolds from CT or magnetic resonance imaging (MRI) data. IBD utilizes the idea of defining 3D topology by density distributions within voxel data sets. Advantages of IBD are the ability to represent any complex 3D topology and the speed with which 3D topology designs can be created. In addition, multiple 3D topologies can be combined easily using Boolean techniques. Disadvantages compared with CAD include the significantly large amounts of data needed to represent 3D topology and the fact that 3D topology can only be represented within a fraction of the smallest voxel resolution. Weighing the relative merits of CAD and IBD, the authors have pursued IBD11,12 based on its robustness for 3D topology representation. IBD techniques encompass any mathematical or imaging technique that can create a density distribution within a 3D voxel array. IBD can be applied to create both scaffold interior architecture and external scaffold shape. In addition, IBD allows easy combination of internal architecture and external shape designs through Boolean operations. Indeed, the use of Boolean operations provides the foundation for scaffold design using IBD. There are three basic steps to create scaffold topology by IBD: (1) creation of the exterior shape design to fit the anatomical defect including accommodation for surgical fixation, (2) creation of an internal architecture design to allow cell migration and tissue regeneration, and (3) Boolean combination of the external design with the internal architecture design to create the final scaffold. Advantages of IBD are readily apparent when creating the exterior shape design. Using a patient’s CT or MRI image, the user may outline the defect within the patient’s anatomy on a slice-by-slice basis using image visualization programs such as Interactive Design Language (IDL, Research Systems, Inc., Boulder, CO), Advanced Visualization System (AVS, AVS, Inc., Waltham, MA), and PV-Wave (Visual Numerics, Inc., Boulder, CO). Combining the slices creates the exterior shape design volume. Next, holes for screw fixation are created by Boolean intersection of voxel representations of cylinders with the exterior shape outlined on a slice-by-slice basis. The purpose of having screw fixation is to allow the surgeon to attach the scaffold to the mandibular ramus that remains after surgical resection of the original degenerated mandibular condyle. An example mandibular condyle exterior design utilizing the Visible Human Female CT data set is shown in Fig. 36.2. The next step in scaffold design is creation of the interior scaffold architecture. One way to create interconnected pore architectures is by periodic repetition of a base unit cell. If the unit cell has channels running through each side, the resulting internal architecture will have complete connectivity for tissue ingrowth. Distributing voxel density according to basic geometric shapes can create these connected cells. One of these basic shapes is an ellipsoid, represented by

x2 y2 z2 ---- ------ 1 (36.1) a2 b2 c2

were x is the x coordinate, y is the y coordinate, z is the z coordinate, a is the ellipsoid radius in the x direction, b is the ellipsoid radius in the y direction, and c is the ellipsoid radius in the z direction. If the voxel densities are set high when Eq. 36.1 is less than 1, connected ellipsoid shaped struts are obtained (Fig. 36.3a). Conversely, if voxel densities are set low when Eq. 36.1 is less than 1, interconnecting ellipsoidal voids are obtained (Fig. 36.3b). Another method of creating scaffold architecture using IBD is simply to image an existing tissue microstructure, for example, porous trabecular bone. Zysset et al.13 demonstrated the ability to design and manufacture scaffolds directly from micro-CT images of trabecular bone. This creates a naturally biomimetic scaffold architecture. The trabecular bone microstructure can be created either by micro-CT or by micro-MRI scanning.

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FIGURE 36.2 External shape design of a mandibular condyle scaffold generated from Visible Human data. Note holes created in exterior design to allow for screw ﬁxation of scaffold to surrounding tissue.

FIGURE 36.3 Sixteen combined unit cells of an ellipsoid architecture created using Eq. 36.1. (a) An ellipsoidal strut; (b) an ellipsoidal pore.

The ﬁnal step in scaffold design is Boolean combination of the exterior scaffold shape and interior scaffold architecture. To do this within IBD, the voxel resolution of the exterior shape must be the same as that of the interior architecture design. In general, the exterior shape voxel resolution may be lower than the interior architecture voxel resolution. The exterior shape resolution can be made equivalent through standard trilinear or cubic interpolation schemes. Once the data resolutions are equivalent, the voxel locations are then found within the 3D interior architecture data set that represents the interior architecture scaffold topology. The corresponding voxel indices within the exterior shape design data set are then set equal to the density of the interior architecture data set. The ﬁnal mandibular condyle scaffold design is shown in Fig. 36.4.

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TABLE 36.1 Designed Polymer Scaffold Properties E1(MPa) E2(MPa) E3(MPa) G23(MPa) G13(MPa) G12(MPa) 23 13 12 Base polymer 2000 2000 2000 769 769 769 0.3 0.3 0.3 Polymer scaffold 154 154 200 17.8 17.8 18.2 0.09 0.09 0.14

Note: The ﬁrst row gives the base polymer material isotropic properties. The second row gives the effective transversely isotropic properties that result from building the architecture in Fig. 36.3b from the polymer.

FIGURE 36.4 Final mandibular condyle scaffold design created by a Boolean intersection of external scaffold shape (Fig. 36.2) and internal ellipsoid pore (Fig. 36.3b).

Since scaffold design determines the deformation and ﬂow environments of invading and seeded cells in addition to global mechanical function, it is desirable to analyze scaffold designs computationally before fabrication. If scaffold architecture is created by repetition of a base unit cell, homogenization analysis14 can be used to calculate the effective scaffold properties that result from the scaffold material and architecture. Effective properties are those that would be obtained by testing a cube containing many unit cells, as opposed to the properties of the materials that make up the unit cell. For example, consider the ellipsoid void architecture in Fig. 36.3b. If it is assumed that the scaffold is made from a polyanhydride15 that is isotropic with a Young’s modulus of 2 GPa and a Poisson’s ratio of 0.3, the effective engineering constants are anisotropic (Table 36.1). The polymer may be stiffened by adding hydroxyapatite (HA) particles in the mixture. This is readily accomplished using IBD by using a random number generator to set voxels to HA. If 25% of the scaffold volume is HA particles, with a Young’s modulus of 100 GPa, the effective constants are obtained by homogenization (Table 36.2). These results demonstrate that image-based methods can be readily used to assess scaffold mechanics in addition to generating scaffold design. They indicate how architecture, base material, and composite mixtures affect scaffold properties. It is also possible to apply image-based topology design methods16 that have been used to design materials to optimize scaffold design with respect to mechanical performance. However, without extensive experiments on scaffold architecture effects on tissue regeneration, it is difﬁcult to know the most appropriate objective function for scaffold optimization.

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TABLE 36.2 Designed Hybrid Polymer/HA Scaffold Properties E1(MPa) E2(MPa) E3(MPa) G23(MPa) G13(MPa) G12(MPa) 23 13 12 Base polymer 2000 2000 2000 769 769 769 0.3 0.3 0.3 Base HA 100,000 100,000 100,000 38,491 38,491 38,491 0.3 0.3 0.3 particles Hybrid polymer 529 476 787 44 44 55 0.09 0.09 0.14 HA scaffold

Note: The ﬁrst row gives the base isotropic polymer properties. The second row gives the base isotropic properties of HA ceramic particles used to reinforce the polymer. The third row gives the effective orthotropic properties that result from building the architecture in Fig. 36.3b from the polymer/HA composite.

36.3 Fabricating Bone Scaffolds

In many studies involving fabricated bone scaffolds,17–23 the scaffold interior architecture and external scaffold shape are not designed using computational techniques, but rather are determined by material processing and casting. In the case of corraline HA scaffolds, the internal architecture is determined by the chemical conversion of the original coral structure. For polymer or polymer–ceramic composites interior architecture is often determined by embedding a high density of salt crystals into the dissolved polymer. The dissolved polymer is then poured into a mold and treated under heat and pressure to form the external shape. Once the external shape is formed, the salt particles are leached out to leave porous interconnecting interior channels. Running the salt crystals through a sieve to obtain a specific range of crystal diameters controls the pore size.17 These crystal diameters have been shown to correlate with scaffold pore diameters.17 As with chemical conversion of corraline HA, there is little control over the orientation and connectivity of the internal pore architecture. Connectivity can only be assured by having a high density of salt particles. Polymer and polymer–ceramic scaffolds fabricated using salt-leaching technique have been frequently tested both in vitro and in vivo. Ishaug et al.18 seeded osteoblasts on poly-lactic/poly-glycolic copolymers with pore sizes in 150 to 300, 300 to 500, and 500 to 700 m range. They found no difference in matrix deposition as measured by alkaline phosphatase activity and mineralized matrix for the three pore size ranges. Because of the high compliance of degradable biopolymers, Marra et al.19 incorporated HA particles into blends of poly(caprolactone) and poly(D,L-lactic-co-glycolic acid) polymers. Using a sieved NaCl particle size of 150 to 250 m and a HA granule size of ~10 m, they produced 12-mm-diameter disks that were 80% porous. They noted a five times increase in scaffold stiffness by incorporating 10% HA granules over the polymer alone. This fivefold increase is similar to the approximately fourfold increase predicted using the homogenization image-based analysis using random particle generation. Marra et al. also found that these scaffolds supported stromal cell growth and collagen matrix deposition. Laurencin et al.20 fabricated porous scaffolds from a polyphosphazene polymer using the salt-leaching technique. They produced an average pore size of 165 m, and stated that the scaffolds had a recon- necting porous network under scanning electron microscopy (SEM), but did not state an overall porosity. They found that osteoblasts grew and proliferated on the scaffolds, as indicated by alkaline phosphatase activity. While in vitro studies typically use simple scaffold geometry, many in vivo studies utilizing salt-leached internal scaffold architectures have molded the scaffolds into specific shapes. Thomson et al.21 implanted 4-cm3 volumes of stacked porous wafers of poly(D,L-lactic-co-glycolic acid) polymer on sheep ribs. Some implanted volumes also contained bone graft particles. They noted that all implanted scaffolds supported vascularized tissue ingrowth. However, only those volumes containing bone particles showed bone tissue regeneration. The polymer alone did not generate osseous tissue. Mikos et al.22 studied scaffold pore diameter effects on scaffold vascularization using poly(L-lactic acid) porous polymers implanted in rat mesentery. They noted that the rate of vascularized tissue ingrowth increased as the scaffold porosity and/or pore size increased. Noritaka et al.23 used a woven mesh of polyglycolic acid fibers with 15-m

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Design and Manufacture of Bone Replacement Scaffolds 36-7

fiber diameters and pore sizes of 75 to 100 m to mold replicas of human phalanges. The polyglycolic acid was dissolved in a solvent and cast into vinyl polysiloxane molds. A porous woven mesh scaffold with the external shape of the phalange was obtained after solvent evaporation. These scaffolds were seeded with periosteum in the bulk of the scaffold and chondrocytes on the ends of the scaffold. The scaffolds were then implanted in athymic mice. After implantation for 20 weeks, a mineralized construct in the shape of the phalange with a cartilage cap was formed. The results of both in vitro and in vivo studies demonstrate the feasibility of fabricating functional scaffolds by dissolving polymers with embedded salt crystals into a mold, allowing the solvent to evaporate and leaching out the salt particles to form an internal porous architecture. One difficulty with scaffold architecture fabrication by salt leaching is that there is little control over the architectural topology other than average pore diameter by controlling salt crystal size and rudimen- tary control over pore connectivity by high salt crystal packing density. However, studies such as those by Bruder et al.5 and Mikos et al.22 demonstrate that controlling internal scaffold architecture is crucial to controlling scaffold vascularization and regenerate tissue mechanical properties. Simultaneous control over external scaffold shape and internal scaffold architecture requires the use of computational design techniques such as those discussed at the beginning of this chapter. These computational techniques, however, typically generate a bone scaffold topology that presents a significant manufacturing challenge due to the complicated 3D exterior shape and interior architecture. The only feasible way to manufacture such scaffolds is using a class of techniques known as solid free-form fabrication (SFF). All SFF techniques manufacture complicated 3D structures using a layered fabrication approach. SFF techniques create components in general by material addition as opposed to traditional manufacturing techniques that create 3D structures by removing material to create the final part. A basic premise of SFF methods is that a material in either powdered or liquid form is solidified one layer at a time in a pattern determined by a computer-generated file. Once the layer is complete, it is lowered by a specified depth and the process is repeated. In addition, supports may be generated to buttress material within the structure not supported by material from a previous layer. The mode in which material is processed depends upon the commercial system. In stereolithography (denoted as SLA, 3D Systems, Inc.) a laser is guided along the surface defined in a computer file that polymerizes a photopolymerizable material in a vat. In fused deposition modeling (FDM, Stratsys, Inc.), a viscous solution of a polymer melt is squeezed onto the layer by a guided nozzle. The nozzle path is determined by the computer-defined surface. A third method, Selective Laser Sintering (SLS, DTM Corporation, Austin, TX), uses a laser to sinter powdered material that is placed on a given layer. As with SLA, the laser is guided by a surface model defined in a computer file. A fourth method, by the Sanders Prototype, Inc. uses a thermoplastic ink-jetting technology to essentially print wax analogous to the manner in which laser printers deposit ink. A fifth method, 3D printing (3DP) prints or deposits a binder on powdered material. A sixth process, called layered object manufacturing (LOM), uses a thin sheet of paper that is rolled into the build area and laminated onto previous layers using heat and pressure. A laser is then used to cut area regions not within the surface model. The reader should consult other references for more details on SFF processes.24,25 Medical applications of SFF sprung up soon after the techniques were developed. The earliest uses of SFF in medicine were for surgical planning and modeling. This mimics the progression of SFF in other industrial applications, which began by using SFF to build planning prototypes before moving on to the manufacture of functional parts. Indeed, SFF techniques are commonly known as rapid prototyping, a reference to the original use of SFF for prototyping and planning purposes. A unique application of SFF procedures is the manufacture of bone tissue microstructure, as in the study of Zysset et al.13 Since the base manufacturing material is homogeneous, in this case an epoxy resin for SLA, one may separate the effect of architecture from tissue properties on the effective stiffness of trabecular bone. Zysset et al.13 showed that the base epoxy resin had properties in the range of those reported for trabecular tissue.26,27 They measured orthotropic effective prototype bone properties and found those also to be within the range of reported trabecular bone effective properties.28 This suggests manufacture of bone tissue microstructure prototypes may be another approach to help understand bone tissue structure function.

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Biomedical applications of SFF have progressed from making surgical planning models and tissue prototypes to making functional parts from biomaterials that can actually be seeded with cells for tissue engineering or used as drug-delivery devices. Wu et al.29 described the use of the 3DP technique to fabricate polymers for drug delivery. They noted that manufactured microstructures significantly influenced drug-delivery rates. An early application of SFF in tissue engineering was the work of Kim et al.30 testing the feasibility of regenerating liver tissue using hepatocytes on SFF-manufactured scaffolds. A significant limitation to engineering critical liver tissue mass is the limited oxygen and nutrient diffusion in scaffolds that lack designed interconnected porosity. To address this issue, Kim et al.30 used a 3DP process to create scaffolds with designed interconnected porosity from a copolymer of polylactide-coglycolide acid. The polymer powder was also packed with salt particles that were then leeched out with distilled water. The resulting 3D scaffold was 8 mm in diameter and 7 mm in height. The fabricated porosity consisted of interconnected channels 800 m in diameter. Additional porosity with micropores ranging from 45 to 150 m were created by the leeching process. The total porosity was 60%. Kim et al. then seeded hepatocytes on the scaffolds under both static and flow conditions, showing hepatocyte attachment to the scaffold and significantly increased partial oxygen pressure under flow conditions. Bone replacement scaffolds can be fabricated from either biopolymers or bioceramics. Vail et al.31 used SLS to fabricate calcium phosphate scaffolds from a mixture of monocalcium phosphates and dicalcium phosphates as raw materials. They manufactured a cylindrical test specimen 8.9 mm in height and 8.9 mm in diameter to determine effects of processing and sintering on mechanical properties. The bulk manufactured material had a stiffness of 231.0 33.8 MPa and a compressive strength of 48.3 7.3 MPa. Fox et al.32 used this approach to manufacture scaffolds to replace alveolar ridge defects. The constructed an implant 3 6.6 15.3 mm with hexagonal macropores 2 mm in diameter. Porous scaffolds with hexagonal macropores were manufactured to augment alveolar ridge defects in canines. Animals sacrificed between 4 and 12 months indicated significant bone ingrowth and no adverse reaction. The amount of ingrowth was not reported. The authors’ group at the University of Michigan11,33,34 has used a process for SLA ceramic manufacturing developed by Chu, Halloran, and colleagues35,36 to manufacture bone tissue scaffolds from HA. In this case, the HA powder is mixed in the photopolymerizable suspension. The laser then cures the polymer that binds the ceramics particles. The polymer is then burned out during the ceramic-sintering process to leave only the ceramic. This ceramics SLA process combined with IBD provides the ability to manufacture complex ceramic microstructures, including actual trabecular bone microstructure for biomimetic scaffolds (Fig. 36.5). In addition to direct manufacturing of biomaterial scaffolds on SFF systems, one may use SFF to manufacture a mold into which a biomaterial is cast. This approach was taken by Chu et al.34 to manufacture HA scaffolds. In this process, a 3D mold is made of the inverse of the scaffold. In other words, the scaffold pores are solid in the mold, and vice versa. A HA slurry is then pored into the mold.

FIGURE 36.5 An 8 scale 3 3 3 mm section of human trabecular bone built from alumina oxide on a stereolithography machine. Ch-36.fm Page 9 Monday, January 22, 2001 2:17 PM

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The polymer mold is burned out at a temperature of 500C, following which the ceramic is sintered at a temperature of 1200C.

36.4 Bone Scaffolds: An Example from Design to Testing

Although great strides have been made in design and free-form fabrication of biomaterials, the ultimate test of these scaffolds is how they perform in vivo. There are a number of steps that must be taken to ensure the biological, mechanical, and material integrity of these scaffolds before they can be used for clinical applications (Fig. 36.6). For example, the SFF procedures often use materials during processing that are not retained in the final material. However, if even trace amounts persist in the final product, they may be toxic to cells. Therefore, it is prudent to perform biocompatibility tests on the final processed material. Surgical reconstruction using manufactured bone tissue scaffolds will require standard assays to be developed in areas of biocompatibility, mechanical testing, and in vivo models. Only by linking a set of reproducible assays with design and material fabrication can the notion of patient-specific reconstructions via design and fabricated tissue engineering scaffolds be realized. The authors11,12 have recently begun work that demonstrates a potential path to bring design and manufactured scaffolds to clinical use by linking design and fabrication of HA scaffolds with an in vivo porcine mandibular defect model. Since this was a feasibility study focused on issues of architectural effects on bone ingrowth and compatibility, noncritical-sized defects were utilized that could be repro- ducibly created using a trephine. In this study, the exterior shape of the scaffold was a cylinder 8 mm in diameter and 6 mm long. Two design patterns, an orthogonal cylindrical pore design (denoted as orthogonal) and a radial pore design (denoted as radial), were constructed using IBD techniques. Since an indirect method was used, the inverse of the pore patterns was created. In other words, the scaffold channels were solid in the mold (Fig. 36.7). The voxel design representation was then converted into surface .stl format (Voxelcon, Voxel Computing, Inc., Ann Arbor, MI). The .stl file for each scaffold design was verified and molds were built on a 3D Systems SLA 250/40 machine from Ciba-Geigy 5170 resin. Following the procedure of Chu et al.,35 a HA slurry was prepared and pored into the resin molds. The slurry mold composite was then heated to 500C to burn out the resin. Following burnout, the slurry was then heated to 1200C to sinter the ceramic. X-ray diffraction confirmed that the final sintered ceramics was a form of HA known as oxy-hydroxyapatite. The final manufactured oxy-HA scaffolds closely replicated the initial designs (Fig. 36.8).

FIGURE 36.6 Research steps that must be addressed for successful scaffold-based bone tissue engineering. Ch-36.fm Page 10 Monday, January 22, 2001 2:17 PM

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FIGURE 36.7 Image-based designs of scaffold molds. (a) Radial pore design; (b) orthogonal pore design.

FIGURE 36.8 Comparison of scaffold mold design (a) and manufactured HA scaffold (b) (oriented at right angle to mold) shows that the manufactured scaffold replicates the design. Note that the solid beams in the mold (a) become the pores in the cast scaffold (b).

The scaffolds were implanted bilaterally in porcine mandible defects. Six animals were operated on under general anesthesia in sterile conditions at the Lone Star Veterinary Hospital in Seguin, TX. Animals were allowed unrestricted mobility on a farm and ate a normal diet 3 days following surgery. Three animals were sacrificed at 1 month and the other three at 2 months following surgery. The mandibles were retrieved following sacrifice, sectioned, and embedded in methacrylate for thick sectioning. Sections were processed for either backscattered SEM or stained with toludine blue. Upon resection, there were no visible signs of inflammation or adverse reaction to the scaffold material. Backscattered SEM analysis confirmed these observations showing excellent integration between ingrown bone tissue and the oxy-HA scaffold (Fig. 36.9). Furthermore, bone formation closely followed the existing pore architecture, demonstrating that the designed scaffolds can guide tissue regeneration to form specific tissue architectures. Sections stained with toludine blue (Fig. 36.10) showed bone and fibrous tissue formation within the scaffold, but no cartilage. This suggests that bone formation within the scaffolds occurred by intramembranous ossification rather than by endochondral ossification. At 2 months, the orthogonal pore design had 19 9% of pore volume filled with bone while the radial design had 14 4% of pore volume filled with bone. This amount of bone fill is comparable with Ch-36.fm Page 11 Monday, January 22, 2001 2:17 PM

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FIGURE 36.9 Bone ingrowth on manufactured scaffolds 2 months in vivo shown by SEM. (a) Bone ingrowth in orthogonal design; (b) bone ingrowth into radial designs. Both designs show bone integration into the scaffolds. The orthogonal design had slightly more ingrowth.

FIGURE 36.10 Toludine blue-stained sections of tissue ingrowth in manufactured scaffolds. (a) Larger section shows how scaffold channels guide the architecture of forming bone; (b) close up of the same region shows ﬁbrous tissue formed ahead of mineralized tissue.

studies using corraline HA materials for bone reconstruction in other species in different anatomical sites. For example, Holmes and Hagler37 found similar amounts of bone ingrowth in corraline HA implanted in canine calvaria. Although the amount of bone formed was similar in this design to conventional HA materials, it is critical to remember that, unlike the designed scaffolds, conventional HA bone replacement materials offer little control over regenerate tissue architecture.

36.5 Conclusion

Research on bone tissue engineering has shown that aspects of the scaffold material and structure can signiﬁcantly affect regenerate tissue structure and function. Therefore, the ability to control scaffold architecture through design and fabrication could be a critical factor in the future clinical success of bone tissue engineering. Current fabrication techniques have primarily utilized either corraline converted phosphate ceramics or cast polymers salt-leached to develop porosity. The desire to have better control over scaffold architecture has led to the introduction of SFF techniques to manufacture scaffolds. Current work has clearly demonstrated the capability of designing and manufacturing bone tissue replacements from degradable biomaterials using SFF techniques. In addition, IBD techniques allow rapid design and analysis of complex 3D scaffold topology that can even mimic natural bone structure. The most apparent Ch-36.fm Page 12 Monday, January 22, 2001 2:17 PM

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application of this technology is surgical reconstruction of complex defects. However, two other research areas could significantly benefit from the design and manufacture of biomimetic bone structures. One application is the study of bone fragility. One can create multiple copies of the same bone structure built from materials close in property to mineralized bone. This will allow the multiple failure testing needed to define a failure surface. The second application is the study of mechanotransduction. Currently, studies of mechanotransduction occur either in in vivo or in vitro systems. In vivo models encapsulate all systems involved in transducing mechanical signals but are too complex to analyze completely. In vitro systems allow for carefully controlled experiments, but provide an environment that lacks the complexity of the in vivo situation. 3D culture environments could easily be manufactured using biomaterials to mimic bone structures, providing a bridge between in vivo and traditional in vitro studies.

References 1. Sampath, T.K. and Reddi, A.H., Importance of geometry of the extracellular matrix in endochondral bone differentiation, J. Cell Biol., 98, 2192, 1984. 2. Kuboki, Y., Saito, T., Murata, M., Takita, H., Mizuno, M., Inoue, M., Nagai, N., and Poole, A.R., Two distinctive BMP-carriers induce zonal chondrogenesis and membranous ossiﬁcation, respectively; geometrical factors of matrices for cell-differentiation, Connect. Tissue Res., 32, 219, 1995. 3. Kuboki, Y., Takita, H., Kobayashi, D., Tsuruga, E., Inoue, M., Murata, M., Nagai, N., Dohi, Y., and Ohgushi, H., BMP-induces osteogenesis on the surface of hydroxyapatite with geometrically feasible and nonfeasible structures: topology of osteogenesis, J. Biomed. Mater. Res., 39, 190, 1998. 4. Tsuruga, E., Takita, H., Itoh, H., Wakisaka, Y., and Kuboki, Y., Pore size of porous hydroxyapatite as the cell-substratum controls BMP-induced osteogenesis, J. Biochem., 121, 1997. 5. Bruder, S.P., Kraus, K.H., Goldberg, V.M., and Kadiyala, S., Critical-sized canine segmental femoral defects are healed by autologous mesenchymal stem cell therapy, in Transactions of the 44th Annual Meeting of the Orthopaedic Research Society, 1998, 147. 6. Caplan, A.I. and Bruder, S.P., Cell and molecular engineering of bone regeneration, in Principles of Tissue Engineering, Lanza, R.P., Langer, R., and Chick W.L., Eds., Academic Press, New York, 1997. 7. Reddi, A.H., Initiation of fracture repair by bone morphogenetic proteins, Clin. Orthop., 355, S66, 1998. 8. Krebsbach, P.H., Kuznetsov, S.A., Satomura, K., Emmons, R.V.B., Rowe, D.W., and Robey, P.G., Bone formation in vivo: comparison of osteogenesis by transplanted mouse and human marrow stromal ﬁbroblasts, Transplantation, 63, 1059, 1997. 9. Bostrom, R.D. and Mikos, A.G., Tissue engineering of bone, in Synthetic Biodegradable Polymer Scaffolds, Atala, A. and Mooney, D.J., Eds., Birkhauser, Boston, 1996, chap. 12. 10. Yazemski, M.J., Payne, R.G., Hayes, W.C., Langer, R.S., and Mikos, A.G., Evolution of bone transplantation: molecular, cellular, and tissue strategies to engineer human bone, Biomaterials, 17, 175, 1996. 11. Hollister, S.J., Chu, T.M., Guldberg, R.E., Zysset, P.K., Levy, R.A., Halloran, J.W., and Feinberg, S.E., Image based design and manufacture of scaffolds for bone reconstruction, in Synthesis in Bio Solid Mechanics, Pedersen, P. and Bendsoe, M.P., Eds., Kluwer Academic Press, Dordrecht, 1999, 163. 12. Hollister, S.J., Levy, R.A., Chu, T.M., Halloran, J.W., and Feinberg, S.E., An image-based approach for designing and manufacturing craniofacial scaffolds, Int. J. Oral Maxillofac. Surg., 29, 67, 2000. 13. Zysset, P.K., Marsan, A.L., Chu, T-M.G., Guldberg, R.E., Halloran, J.W., and Hollister, S.J., Rapid prototyping of trabecular bone for mechanical testing, in BED-Vol. 35, ASME Bioengineering Conference, American Society of Mechanical Engineers, New York, 1997, 387. 14. Hollister, S.J. and Kikuchi, N., Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue, Biotechnol. Bioeng., 43, 586, 1994. 15. Muggli, D.S., Burkoth, A.K., and Anseth, K.S., Crosslinked polyanhydrides for use in orthopedic applications: degradation behavior and mechanics, J. Biomed. Mater. Res., 46, 271, 1999. Ch-36.fm Page 13 Monday, January 22, 2001 2:17 PM

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16. Bendsoe, M.P., Optimization of Structural Topology, Shape and Material, Springer-Verlag, Berlin, 1995. 17. Jen, A.C., Peter, S.J., and Mikos, A.G., Preparation and use of porous poly(a-hydroester) scaffolds for bone tissue engineering, in Tissue Engineering Methods and Protocols, Morgan, J.R. and Yarmush, M.L., Eds., Humana Press, Totowa, NJ, 1999, chap. 11. 18. Ishaug, S.L., Crane, G.M., Miller, M.J., Yasko, A.W., Yaszemski, M.J., and Mikos, A.G., Bone formation by three-dimensional stromal osteoblast culture in biodegradable polymer scaffold, J. Biomed. Mater. Res., 36, 17, 1997. 19. Marra, K.G., Szem, J.W., Kumta, P.N., DiMilla, P.A., and Weiss, L.E., In vitro analysis of biodegradable polymer blend/hydroxyapatite composites for bone tissue engineering, J. Biomed. Mater. Res., 47, 324, 1999. 20. Laurencin, C.T., El-Amin, S.F., Ibim, S.E., Willoughby, D.A., Attawia, M., Allcock, H.R., and Ambrosio, A.A., A highly porous 3-dimensional polyphosphazene polymer matrix for skeletal tissue regeneration, J. Biomed. Mater. Res., 30, 133, 1996. 21. Thomson, R.C., Mikos, A.G., Beahm, E., Lemon, J.C., Satterfield, W.C., Aufdemorte, T.B., and Miller, M.J., Guided tissue fabrication from periosteum using preformed biodegradable polymer scaffolds, Biomaterials, 20, 2007, 1999. 22. Mikos, A.G., Sarakinos, G., Lyman, M.D., Ingber, D.E., Vacanti, J.P., and Langer, R., Prevascular- ization of porous biodegradable polymer, Biotechnol. Bioeng., 42, 716, 1993. 23. Noritaka, I., Landis, W., Kim, T.H., Gerstenfeld, L.C., Upton, J., and Vacanti, J.P., Formation of phalanges and small joints by tissue-engineering, J. Bone Joint Surg., 81A, 306, 1999. 24. Jacobs, P.F., Rapid Prototyping and Manufacturing: Fundamentals of Stereolithography, Society for Manufacturing Engineers, Dearborn, MI, 1992. 25. Kai, C.C. and Fai, L.K., Rapid Prototyping: Principles and Applications in Manufacturing, John Wiley Press, New York, 1997. 26. Mente, P.L. and Lewis, J.L., Experimental method for the measurement of the elastic modulus of trabecular bone tissue, J. Orthop. Res., 7, 456, 1989. 27. Choi, K., Kuhn, J.L., Ciarelli, M.J., and Goldstein, S.A., The elastic moduli of human subchondral, trabecular and cortical bone tissue and the size-dependency of cortical bone modulus, J. Biomech., 23, 1103, 1990. 28. Keaveny, T.M. and Hayes, W.C., A 20-year perspective on the mechanical properties of trabecular bone, J. Biomech. Eng., 115, 534, 1993. 29. Wu, B.M., Borland, S.W., Giordano, R.A., Cima, L.G., Sachs, E.M., and Cima, M.J., Solid free-form fabrication of drug delivery devices, J. Controlled Release, 40, 77, 1996. 30. Kim, S.S., Utsunomiya, H., Koski, J.A., Wu, B.M., Cima, M.J., Sohn, J., Mukai, K., Griffith, L., and Vacanti, J.P., Survival and function of hepatocytes on a novel three-dimensional synthetic biodegradable polymer scaffold with an intrinsic network of channel, Ann. Surg., 228, 8, 1998. 31. Vail, N.K., Swain, L.D., Fox, W.C., Aufdlemorte, T.B., Lee, G., and Barlow, J.W., Materials for biomedical application, Mater. Design, 20, 123, 1999. 32. Fox, W.D., Swain, L.D., Aufdemorte, T.B., Lee, G., Vail, N.K., and Barlow, J.W., Custom formed synthetic bone implants in vivo, in Transactions of the 45th Orthopaedic Research Society Meeting, Anaheim, CA., 1999, 527. 33. Levy, R.A., Chu, T.M.G., Halloran, J.W., Feinberg, S.E., and Hollister, S.J., Computed tomography- generated porous hydroxyapatite orbital floor prosthesis as a prototype bioimplant, Am. J. Neuro- radiol., 18, 1522, 1997. 34. Chu, T.-M., Halloran, J.W., Hollister, S.J., and Feinberg, S.E., Hydroxyapatite with controlled internal architecture by acrylic polymerization, J. Mater. Sci. Mater. Med., in press. 35. Chu, T.-M., Halloran, J.W., and Wagner, W.C., Ultraviolet curing of highly loaded hydroxyapatite suspension, in Bioceramics: Materials and Applications, R.P. Rusin and G.S. Fishman, Eds., Ceramic Transactions, Vol. 65, American Ceramic Society, Westerville, OH, 1995, 57. Ch-36.fm Page 14 Monday, January 22, 2001 2:17 PM

36-14 Bone Mechanics

36. Chu, T.-M. and Halloran, J.W., Hydroxyapatite for implant fabrication by stereolithography, in Case Studies of Ceremic Product Development, Manufacturing and Commercialization, A. Ghosh, B. Hiremath, and R. Barks, Eds., Ceramic Transactions, Vol. 75, American Ceramic Society, Wester- ville, OH, 1997. 37. Holmes, R.E. and Hagler, H.K., Porous hydroxyapatite as a bone graft substitute in cranial reconstruction: a histometric study, Plast. Reconstruct. Surg., 81, 662, 1988.

9117_frame_index Page 1 Monday, February 5, 2001 11:51 AM

Index

signal transduction, 31-5 A site dependence, 31-4 Aarhus data, 15-10 stress- and strain-based measures, 31-3 to 31-4 ABAQUS, 23-16 time dependence, 31-4 to 31-5, 31-7 to 31-8 Acoustic emission (AE), 17-14 to 17-15 boundary element method, 31-8 Acoustic impedance mapping, 7-22 continuum and micro-level approaches, 31-6 to 31-7 Acoustic microscopy, 7-21, 10-11 correlation of mechanical parameters, 31-35 to 31-37 Acoustic testing, 7-20 to 7-24, See Ultrasonic methods cortical bone, 31-8 to 31-21 Acoustic vibrational methods, 34-18 to 34-19 adaptive elasticity, 31-11 to 31-12, 31-15 to 31-16 Actin filaments, 28-8 cell dynamics model, 31-12 to 31-16 Actin stress fibers, 21-6, 21-12 curvature reduction application, 31-11, 31-18 Activation frequency, 1-32, 1-34 flexure-neutralization theory, 31-9 to 31-11 Adaptation, 1-34 to 1-47, 22-16, 26-1 to 26-26, 28-1 to 28-2, See homogeneous surface stresses, 31-18 also Bone regeneration; Remodeling site-dependent strain energy density model, 31-16 to adaptivity of youthful changes, 19-9 to 19-11 31-18 age-related modulation of mechanically induced bone strength optimization, 31-20 to 31-21 formation, 26-16 stress-shielding, 31-18, 31-19 animal immobilization models, 1-37 to 1-41 three-way rule, 31-9 to 31-11 animal models of loading, 1-41 to 1-47, See also Animal ulnar osteotomy applications, 31-12, 31-16, 31-21 models error-driven control, 26-17, 31-3, 26-17 aging and exercise, 1-41 to 1-42 fine element methods, 31-8 cancellous bone and exercise, 1-42 mechanistic approach, 31-6, 31-12 to 31-16, 31-32 to 31-34 exercise and bone strength, 1-44 mechanotransduction, 31-5, 31-12 to 31-16, 31-32 to 31-34 in vivo loading, 1-44 to 1-46 null hypothesis algorithm, 31-37 time-course of exercise response, 1-43 to 1-44 optimization approach, 31-6, 31-18 to 31-21, 31-37 applied electromagnetic fields, 26-18 phenomenological approaches, 31-6, 31-9 to 31-12, 31-16 bone loss under disuse conditions, 26-3 to 26-10, See also to 31-18, 31-37 Bone loss strain trajectory theory, 31-23 damage and repair models, 18-22 to 18-23 test suite of example problems, 31-37 dietary effects, 26-17 trabecular bone, 31-21 to 31-34 externally induced loading, 26-12 to 26-16 adaptive elasticity, 31-21 to 31-29 histology, 19-9 to 19-11 bone-lining cells, 31-34 hormonal modulation, 26-5, 26-17, 26-20, See also specific boundary element implementation, 31-34 hormones fabric reorientation application, 31-24 to 31-26 increased functional loading, 26-10 to 26-16 femoral head application, 31-28 to 31-29 interstitial fluid flow and, 22-17 mechanistic model for osteocyte, 31-32 to 31-34 long-term modeling changes, 26-17 to 26-18 mergers/separations and strain rate, 31-34 matrix microdamage, 26-15 skeletal morphogenesis, 31-26 to 31-29 mechanical modulation of bone repair, 26-20 to 26-25, See trabecular density and orientation models, 31-26 to 31-29 also Bone repair discrete structures application, 31-30 to 31-32 mechanostat, 1-36 to 1-37 spatial influence function, 31-32 to 31-34 mineralization and, 5-21 strain energy dependence, 31-29 to 31-31, 31-34 non-mechanical agents, 1-36 Adaptive elasticity, 31-11 to 31-12, 31-15 to 31-16 osteocyte mechanosensation/mechanotransduction model, cortical bone, 31-11 to 31-12, 31-15 to 31-16 26-18 to 26-20, 29-1 to 29-9, See also Lacuno- trabecular bone, 31-21 to 31-29 canalicular system; Mechanosensation; Adeno-associated virus (AAV), 3-11 Mechanotransduction; Osteocytes Adenovirus-based gene transfer, 3-11 to 3-12 physiological exercise effects, 26-10 to 26-12 Adhesives, 8-4 to 8-5 role of strain, 22-16 Adipocytes, 1-15 Roux’s concept, 30-1 to 30-2 Adrenergic nerve fibers, 21-8 strain protection effects, 26-7 to 26-9, 26-21 β-Adrenergic receptor kinase, 4-1 stress trajectories and trabecular architecture, 30-1 to 30-14, Advanced glycation end (AGE) products, 13-4 See Wolff’s law Aging theoretical models, See Adaptation, theoretical models AGE products, 13-4 transport-based remodeling model, 22-18 animal loading adaptation model, 1-41 to 1-42 Utah paradigm, 1-36 to 1-37 bone blood flow and, 21-3 Wolff’s law, 30-1 to 30-14, See Wolff’s law bone loss and, 1-49 to 1-55 Adaptation, theoretical models, 31-1 to 31-38 bone mineral composition and, 5-9 assumptions and concepts, 31-2 to 31-6 cancellous and cortical mechanical properties, 10-17 adaptive impacts, 31-5 cross-sectional moment of inertia changes, 33-17 control of adaptive process, 31-3 estrogen and male bone maintenance, 1-53 linear elasticity, 31-7 factors influencing bone loss and fracture risk, 1-50 to 1-55

I-1 9117_frame_index Page 2 Monday, February 5, 2001 11:51 AM

I-2 Bone Mechanics

maturation and mechanical properties, 19-5 to 19-8 osteocytes, 1-24, 1-55, 2-4, 28-10 microcrack accumulation, 17-10, 19-4 remodeling, 2-4 muscle loss, 26-7 Archimedes’ principle, 7-2 osteocyte loss, 2-4 Archiving, 7-28 remodeling defects, 19-12 Areal bone mineral density (aBMD), osteoporosis definition, trabecular bone strength and, 16-3, 33-16 1-47 Albumin, 1-21, 5-16 Arteries, 1-7, 21-1 to 21-4 Alkaline phosphatase, 1-15, 1-17, 1-21, 2-3 to 2-4, 5-15, 5-18 Arterioles, 1-7, 21-1 to 21-4 knockout model, 4-10 Arthritis, 7-25 to 7-26, 26-2 Alligator, 8-26, 8-33 gene therapy, 3-11 Allografts, 35-8 Articular cartilage, 1-3 Allografts, bone treatment effects, 20-1, 20-12 Ash density, 5-2 ethylene oxide sterilization, 20-15 Ash fraction, cortical and cancellous bone composition, 10-4 freeze-drying, 20-13 to 20-14 Ash weight, 5-2, 5-9 freezing, 20-8, 20-12 Atomic absorption spectrometry, 5-3 irradiation, 20-3, 20-15 to 20-18 Atomic force microscopy (AFM), 22-13, 22-15 methanol and chloroform, 20-18 Attractor stress stimulus, 1-37 remodeling, 20-18 Autoclaving, 20-20 thermal sterilization, 20-19 to 20-20 Avascular necrosis, 21-4 Alumina, 35-3 Avian models, 19-13 to 19-14 Aluminum, 5-10 calcium requirements and bone loss, 26-17 Androgen receptors, 2-11 isolated ulnar model, 1-45, 26-7, 26-9 to 26-10, 26-14 to Angiography, 21-1 26-15, 26-18 Animal models, See also specific animals strain measurement studies, 8-22 to 8-25, 8-32 to 8-33, 26-5, biomechanical testing, 7-24 to 7-726 26-11 choice of model, 7-24 mice measurements, 7-24 osteoarthritis treatment evaluation, 7-25 to 7-26 B osteoporosis treatment evaluation, 7-24 to 7-25 surgical remedy evaluation, 7-26 Backscatter electron imaging, 5-7 bone mass adaptation to exercise, 1-41 to 1-45 Basic fuchsin staining, 16-32, 17-8 to 17-9, 17-13 disuse osteopenia, 26-5 to 26-10 Basic multicellular unit (BMU), 1-28 to 1-33 functional adaptation to externally induced loading, 26-12 Bats, 8-24, 8-33 to 26-16 Beam hardening artifact, 9-4 immobilization, 1-37 to 1-41 Bears, 19-12 to 19-13 in vivo loading, 1-44 to 1-46 Bed rest, 26-4 knockout, See Knockout models Bending, 6-17 to 6-18, 7-11 to 7-15 loading-related modeling changes, 1-46 beam-bending formula, 7-12 necrotic bone studies, 20-3, 20-4 bone damage histology, 17-13 to 17-14 ontogenetic changes, 19-10 to 19-14 bone damage model, 18-15 to 18-17, 18-21 osteoporosis research, 1-48 to 1-49, 5-12 to 5-13 cancellous bone elastic constants and, 15-19 spatial resolution considerations, 9-2 to 9-3 cancellous tissue modulus measurement, 10-10 strain measurement results, various species and activities, combined shear stress mechanostimulus system, 27-16 8-10 to 8-34, See also Strain gauge measurements externally induced mechanostimulation studies, 26-15 and methods four-point loading, 7-12, 26-15, 27-7 to 27-8, 27-16 3D microstructural analysis, 9-13 to 9-14 fracture prediction model, 33-20 transgenic, See Transgenic mouse models freeze-drying effects, 20-13 Anisotropy, 6-2, See also Orthotropy in vitro mechanostimulus systems, 27-7 to 27-8 assumptions for trabecular bone strength microtesting, 7-20 bone damage models and, 18-3, 18-5 streaming potential data, 24-9 cancellous bone elastic properties and, 15-3, 15-11 to 15-12 viscoelasticity studies, 11-5 Darcy’s law and, 25-3 Bending strength fabric model, 34-5, 34-19, 31-23, See Fabric tensor freezing effects, 20-7 global approach, 12-13 irradiation effects, 20-15, 20-16 poroelasticity and, 23-12 maturation effects, 19-5 simulated bone atrophy, 9-16 to 9-17 Beta-3 integrin, 4-10 three-dimensional quantification methods, cancellous bone Betti numbers, 14-6 architecture, 14-7 to 14-10 Biglycan, 1-21, 5-16, 5-18 yield strains and trabecular bone strength, 16-10 knockout model, 4-7, 4-10, 4-13, 5-20, 13-10 Ankle replacement prosthesis, 35-12 Bingham plastic model, 25-14 Annexin V, 5-18 Bioactive glass, 35-4 Antisense oligodeoxynucleotides, 3-13 Biomaterials, 35-2 to 35-5, See also Implants; Prostheses; specific Antler, 11-7, 26-5, 26-6, 26-17 materials Apatite, 5-1, 12-1, See also Hydroxyapatite tissue engineering and scaffold design, 36-1 to 36-2, 36-6 to collagen-apatite porosity, 23-4, 23-7, 23-18, 23-22, 29-6 36-8 collagen bonding, 12-16 waterproofing, 8-3 to 8-4 nucleators, 5-17 to 5-18 Biomechanical testing methods, 7-1 to 7-28, See also Imaging preferred bone mineral terminology, 23-7 methods; specific measures, methods Apoptosis acoustic testing, 7-20 to 7-24, See also Ultrasonic methods hormone effects, 1-17, 2-8, 2-9, 2-11 animal models, 7-24 osteoblasts, 2-8 bending tests, 7-11 to 7-15, 10-10 to 10-11, See also Bending osteoclasts, 1-13, 2-9 cancellous bone characterization, 10-8 to 10-15 9117_frame_index Page 3 Monday, February 5, 2001 11:51 AM

Index I-3

compression, 7-9 to 7-11, See also Compressive loading chemical regulation, 21-9 to 21-10 cortical bone characterization, 10-5 to 10-7 fluid mechanical regulation, 21-11 to 21-13 cross-sectional moment of inertia, 7-3 to 7-5 marrow, 1-55 density measurement, 7-2 neuronal control, 21-8 elastic and inelastic buckling, 10-8 Q measure, 221-16 to 21-21 equipment, 7-8 to 7-9 shear stress and regulation, 21-12 fatigue testing, 7-18 to 7-19, 10-14 to 10-15 viscosity, 21-14 FEM back-calculation, 10-13 to 10-14 Bone biopsy, 9-9 to 9-10 fracture mechanics testing, 7-17 to 7-18 Bone cells, See Bone-lining cells; Osteoblasts; Osteoclasts; histomorphometry, 7-5 to 7-6 Osteocytes collagen orientation, 7-5 to 7-6 connected network, See Connected cellular network; porosity, 7-5 Lacuno-canalicular system indentation, 7-17, 7-20, 10-5, 10-11 to 10-13, See in vitro systems, 2-14 to 2-15, See Cell cultures Indentation testing life cycles and regulation, 2-6 to 2-9 in vitro mechanostimulus methods, 27-1 to 27-16 properties and functions, 2-2 to 2-6 axisymmetric substrate distension, 27-8 to 27-12 regulators and function, 2-9 to 2-14 bending, 27-7 to 27-8 local factors, 2-9 to 2-11 combined stimuli, 27-15 to 27-16 systemic factors, 2-9 to 2-11 computational fluid dynamics, 27-16 Bone cements or adhesives, 8-4 to 8-5, 35-4 to 35-5 direct platen contact, 27-4 to 27-5 Bone chamber intravital microscopy, 21-19 hydrostatic compression, 27-2 to 27-4 Bone composition, 1-6 to 1-7, 5-1 to 5-2, See also Bone mineral longitudinal substrate distension, 27-6 to 27-7 content; Collagen; Hydroxyapatite; shear stress, 27-12 to 27-15 Mineralization; Noncollagenous proteins in vivo induced overload analytical methods, 5-2 to 5-8, See also under Bone mineral invasive techniques, 26-12 to 26-13 comparison of cancellous and cortical bone, 10-4 matrix microdamage induction, 26-15 to 26-16 composite models, 12-1 to 12-17, See Composite models noninvasive techniques, 26-15 heterogeneity, 5-8 to 5-13 transcutaneous implants, 26-13 to 26-16 age effects, 5-9 microtesting or nanotesting, 7-20, 10-5 to 10-7, 10-11 to diseases, 5-11 to 5-13 10-13, 19-5 gender effects, 5-9 to 5-10 outcome measures, 7-6 to 7-8 nutrition and, 5-10 to 5-11 pure shear tests, 7-17 to 7-18 trabecular bone properties and, 14-17 quality assurance, 7-26 to 7-28 Bone damage, 17-1 to 17-15, 18-1 to 18-24, 19-4, See also Bone site-specific tests, 7-16 to 7-17 repair; Fracture(s) specimen handling, 7-2 acoustic emission measure, 17-14 to 17-15 specimen preparation, 7-8 to 7-9 adequacy of orthotropic model, 18-5 strain, See Strain gauge measurements and methods age effects, 17-10, 19-4 strain rate, 7-2 biomechanical consequences, 16-32 tension, 7-9, 10-8 to 10-9, See also Tensile loading causes of mechanical decline, 19-11 to 19-12 torsion testing, 7-15 to 7-16, See also Torsion composite models, 18-16 to 18-17, 18-21 ultrasound, 10-11, See Ultrasonic methods continuum mechanics model, 18-2 to 18-3 Bioresorbable polymers, 35-4 damage and repair models, 18-22 to 18-23 Birds, See Avian models; specific birds definition, 17-1 Birefringence, collagen orientation, 7-5 to 7-6 elastic model, 18-5 to 18-7 Bisphosphonates, 1-15, 1-20 to 1-21, 5-15 elastic-plastic and elastic-viscoplastic models, 18-9 to 18-11 bone mineral properties and, 5-13 fatigue damage models, 18-12 to 18-15 osteoclasts and, 2-9 finite element models, 18-19 to 18-20, 18-21 Blood-bone barrier, 21-9, 21-21 Fondrk model, 18-6, 18-14 to 18-15 Blood flow, 1-7 to 1-8, 19-2, 21-1 to 21-21 functional adaptation, See Adaptation; Remodeling aging and, 21-3 high-energy vs. low-energy fracture effects, 26-21 blood-bone barrier, 21-9, 21-21 histological measures, 17-1, 17-8 to 17-14 bone fluid exchange, 23-6 damage and degradation relationship, 17-13 to 17-14 bone loss and, 1-55 in vivo accumulation, 17-9 to 17-10 circulatory morphology, 21-1 laboratory mechanical tests, 17-10 to 17-13 afferent vessels, 21-1, 21-2 to 21-4 in vivo studies, 17-9 to 17-10, 19-4 efferent vessels, 21-1, 21-5 Kachanov model, 18-6, 18-14 to 18-15 lymphatics, 21-7 mechanically induced microdamage model, 26-15 to 26-16 microvasculature, 21-5 to 21-7 mechanical property degradation, 17-1, 17-2 to 17-8 collateral circulation, 21-7 mechanisms for trabecular bone, 16-30 to 16-32 distribution of, 21-7 to 21-8 consequences of damage, 17-3 to 17-5 endothelial mechanosensitivity, 28-8 experimental methods, 17-5 to 17-8 extravasation techniques, 21-18 inelasticity, 17-2 to 17-3 fluid mechanical aspects, 21-13 to 21-21 moduli, 17-5 to 17-7 axial blood flow measurement, 21-16 to 21-19 residual strains, 17-8, 18-7 hydrostatic pressure measurement, 21-15 to 21-16 micromechanical models, 18-20 to 18-22, 18-23 microvascular flow measurement, 21-19 to 21-21 nonhomogeneous loading applications, 18-15 nutrient exchange, 21-21 bending, 18-15 to 18-17 transmural transport, 21-21 torsion, 18-17 to 18-19 humoral control, 21-8 to 21-9 normal bone biology and, 18-2 interstitial pressure effects, 22-12 one-dimensional models, 18-5 to 18-12 local microcirculation control, 21-9 to 21-13 osteocyte-mediated osteoclast response, 28-11 blood element regulation, 21-10 to 21-11 perfect damage modulus, 17-5 to 17-6 9117_frame_index Page 4 Monday, February 5, 2001 11:51 AM

I-4 Bone Mechanics

postmortem effects, See Postmortem bone changes osteon microstructural and mechanical analysis, 10-7 post-yield mechanical behavior, 16-27 to 16-30, 17-2 Bone hydration, 24-4 preservation effects, See Bone preservation effects freezing effects, 20-7 principle of strain equivalence, 18-4 mechanical properties and, 7-2 relevance of models, 18-1 to 18-2 viscoelasticity and, 11-5 state variable models, 18-3 to 18-5 Bone-lining cells, 1-22 to 1-23, 2-1, 2-5, 28-3, 29-2 strain rate relationship, 16-32 function, 1-14, 1-23 viscoelastic models, 18-7 to 18-8, 18-18 hydraulic conductivity, 22-13 viscoplastic models, 18-8 to 18-11 mineral supply function, 23-5 Zysset and Curnier model, 16-29, 18-11 to 18-12, 18-20 network interconnections, 28-4, See also Lacuno- Bone density, See also Bone mineral density canalicular system biomechanical testing for mice, 7-24 strain energy density model, 31-34 cancellous bone elastic constants and, 15-13 to 15-16 Bone loss, See also Osteoporosis comparison of ultrasound and QCT results, 34-11 to 34-12 AGE products and, 13-4 electrical conductance-based measurement, 34-19 to 34-20 age-related, 1-49 to 150 fracture risk and, 33-13 to 33-18 blood flow and, 1-55 marrow and, 7-3 dietary effects, 26-17 measurement methods, 7-2 to 7-3 electric fields and, 26-7, 26-18 porosity measurement, 7-5 estrogen deficiency and, 1-51 strain energy dependence, 31-29 to 31-31 imaging applications, 9-17 to 9-18 trabecular bone adaptation models, 31-26 to 31-34 immobilization models, 1-37 to 1-41 skeletal morphogenesis, 31-26 to 31-29, 31-37 microstructural analysis, 9-13 spatial influence function, 31-32 to 31-34 noninvasive assessment methods, 34-1 strain energy dependence, 31-29 to 31-32 nutritional factors, 1-53, 1-55 trabecular bone strength relationship, 16-5 to 16-7, 16-21 osteoporotic, 1-47 to 1-49, See Osteoporosis to 16-24 reduced loading (disuse) conditions, 26-3 to 26-10 tubularity and, 9-9 disuse remodeling mode, 1-32 ultrasonic velocity and, 34-8 generalized reduced loading, 26-4 to 26-5 X-ray densitometry, 34-2 to 34-5, See Dual-energy X-ray implants, 26-9 to 26-10 absorptiometry; Quantitative computed localized, 26-5 to 26-10 tomography seasonal osteopenia, 26-5, 26-17 Bone fixation systems, 35-6 to 35-7 simulated bone atrophy, 9-16 to 9-17 Bone fluid, See Interstitial fluid flow strain protection, 26-7 to 26-9, 26-21 Bone formation, 1-18 to 1-21, 1-24 to 1-33, 5-13 to 5-21, 19-1 Bone marrow edema syndrome (BMES), 21-11 to 19-4, See also Bone regeneration; Bone repair; Bone marrow removal, 7-3 Mineralization; Modeling; Remodeling; Skeletal Bone mass, See also Bone density; specific measures development accretion rate, 19-2, 19-3 adaptation to mechanical usage, 1-34 to 1-47, See applied electromagnetic fields and, 26-18 Adaptation; Remodeling bone surface morphology, 1-9 animal models of loading, 1-41 to 1-47 cell biology, 28-2 to 28-5 immobilization models, 1-37 to 1-41 comparison of modeling and remodeling, 1-25 mechanostat system, 1-35 crystal formation chemistry, 5-13 to 5-14 age-related bone loss, 1-49 to 1-50 direct and indirect processes, 32-1 estrogen and, 1-48, 1-51, 1-53 endochondral ossification, 1-25, 26-22, 26-24, 32-1, 32-2, loss of, See Bone loss 32-7 osteoporosis, 1-47 to 1-49, See Osteoporosis factors controlling initial deposition, 5-14 to 5-20 Bone matrix proteins, 2-3 to 2-4, See also Noncollagenous fetal development, 1-24 proteins free-floating bone, 19-3 Bone mineral, 5-1 to 5-21, See also Bone mineral content; Bone functional adaptation, See Adaptation mineral density; Mineralization hormonal stimulation, 2-10, 2-11 analysis of, 5-2 to 5-8, See also Imaging methods imaging applications for rate calculations, 9-17 acoustic methods, See Ultrasonic methods intramembranous ossification, 1-24, 1-24, 26-24, 32-1, atomic absorption spectrometry, 5-3 32-2, 36-10 backscatter electron imaging, 5-7 lining cell function, 1-23 computed tomography, 5-8, See Computed markers, 1-18 tomography matrix formation, 1-18 energy dispersive X-ray microanalysis (EDAX), 5-3 mineral deposition, 5-21, See Mineralization gravimetry, 5-2 to 5-3 nucleation process, 5-13 to 5-14 infrared spectroscopy, 5-4 to 5-7 osteoblast function, 2-2 to 2-4 neutron activation analysis, 5-3 rate, 1-18 NMR, 5-7, See Magnetic resonance imaging regeneration mechanics, 32-1 to 32-10, See Bone Raman microspectroscopy, 5-7 regeneration X-ray diffraction, 5-3 to 5-4 remodeling, 1-31, 19-4, See Remodeling X-ray methods, See Radiographic methods; specific resorption coupling, 1-31 techniques stages, 1-18 collagen bonding, 12-14, 12-16, 13-1 typical sequence for long bone, 1-33 to 1-34 composition, 5-1 to 5-2, See Bone composition; within scaffold, 36-10 to 36-11 Hydroxyapatite Bone grafting, 36-1 hydration shell, 13-6 to 13-7 Bone hardness, 10-5, See Bone density; Bone mineral density; ion substitution effects, 13-7 to 13-8 Elastic modulus; specific measures mechanical consequences of changes, 13-6 to 13-8 indentation measures, See Indentation testing noncollagenous protein bonding, 13-7 to 13-9 9117_frame_index Page 5 Monday, February 5, 2001 11:51 AM

Index I-5

preferred terminology, apatite vs. hydroxyapatite, 23-7, See mechanical environment and, 26-22 to 26-23, 32-3 also Apatite mechanical variables influencing, 26-23 to 26-25 zeta potential, 24-8 mechanics of regeneration, 32-1 to 32-10, See Bone Bone mineral content (BMC) regeneration age, species, and tissue differences, 5-9 strength optimization for cortical bone, 31-20 to 31-21 avian ulnar model, 26-7 tissue differentiation models, 26-24 to 26-25 bisphosphonates and, 1-21 Bone replacement scaffolding, 36-1 to 36-12 exercise effects, 5-10 applications, 36-12 heterogeneity, 5-8 to 5-13 bone formation, 36-10 to 36-11 age effects, 5-9 computational analysis, 36-5 diet and, 5-10 to 5-11 computer-aided design, 36-2 to 36-3 diseases, 5-11 to 5-13 fabrication, 36-6 to 36-9 gender effects, 5-9 to 5-10 image-based design, 36-2 to 36-5, 36-11 microgravity conditions and, 26-4 porcine mandibular defect model, 36-9 to 36-11 osteoporosis definition, 1-47 pore size, 36-2 vertebral fracture risk prediction, 33-14, 33-18 salt leaching, 36-6 to 36-7 X-ray densitometry, 34-2 to 34-5, See Dual-energy X-ray screw fixation, 36-3 absorptiometry solid free-form fabrication, 36-7 to 36-9, 36-11 Bone mineral density (BMD), See also Bone density Bone samples, 9-9 to 9-13 areal (aBMD), osteoporosis definition, 1-47 Bone screws, 35-6 exercise and osteoporosis, 26-4 to 26-5 Bone sialoprotein (BSP), 1-7, 1-14, 1-15, 1-17, 1-20, 1-21, 2-3, femoral fracture prediction, 34-2 5-16 formalin fixation effects, 20-10 knockout model, 4-7, 5-20 fracture risk prediction, 33-13 to 33-18 mineral deposition and, 5-17, 5-18 plain radiographic absorptiometry, 34-20 Bone specimen handling, 7-2 X-ray densitometry, 34-2 to 34-5, See Dual-energy X-ray Bone strength, 7-7 to 7-8, See also Bone density; Trabecular bone absorptiometry; Quantitative computed strength; specific measures tomography animal exercise model, 1-44 Bone morphogenetic proteins (BMPs), 1-19, 1-22, 2-7, 2-11 to cancellous bone elastic properties and, 15-1, See also 2-12 Cancellous bone, elastic properties of; Trabecular BMP-2, 32-2, 32-4 bone strength BMP-4, 4-8, 32-4 degradation measurement, 17-7 to 17-8 BMP-7, 4-10 failure modes, composite models, 12-15 to 12-16 distraction osteogenesis and, 32-4 hydration and, 7-2 fracture healing and, 32-2 irradiation effects, 20-15, 20-17 knockout model, 4-10 measurement, See Biomechanical testing methods receptors, 2-11 mineral characteristics and, 1-21 transgenic overexpression model, 4-8 necrotic bone, 20-4 Bone plates, 35-6 preservation effects, See Bone preservation effects Bone plug, 35-4 strain rate and, 11-8 Bone preservation effects, 20-1 to 20-20 terms and definitions, 16-2 allograft bone treatment effects, 20-1, 20-3, 20-12 to 20-20 testing, See Biomechanical testing methods chemical fixation, 20-3, 20-9 to 20-12 thermal effects, 20-20 ethylene oxide sterilization, 20-15 trabecular bone, See Trabecular bone strength freeze-drying, 20-13 to 20-14 ultrasonic assessment, See Ultrasonic methods freezing, 20-3, 20-6 to 20-8, 20-12 Bone structure and morphology, 1-2 to 1-24, See also Cancellous irradiation, 20-3, 20-15 to 20-18 bone architecture; Trabecular architecture; methanol and chloroform, 20-18 specific anatomical features thermal sterilization, 20-19 to 20-20 biodiversity, 26-1 Bone proteins, See Collagen; Noncollagenous proteins; specific bone surfaces, 1-9 proteins cancellous and cortical bone, 1-3 to 1-4, 1-10 Bone regeneration, 32-1 to 32-10 cancellous bone architecture quantification, 14-1 to 14-17, cyclic loading and, 32-3 See Cancellous bone architecture, quantification direct and indirect bone formation, 32-1 of distraction osteogenesis, 32-4 cells, 1-11 to 1-24, See Osteoblasts; Osteoclasts; Osteocytes; fracture healing phases, 32-1 to 32-2 Bone-lining cells growth factors and, 32-2 comparison of cortical and cancellous bone, 9-2 to 9-4, 10-2 mechanical environment and, 32-3 to 10-4 mechanobiological models of cell differentiation, 32-4 to composite models, 12-1 to 12-17, See Composite models 32-10 hierarchical levels of organization, 12-1, 12-2 deformation pressure models, 32-7 to 32-8 porosity microstructure, 23-3 to 23-4, See also Porosity fluid flows and cell responses, 32-8 to 32-10 relating in vivo fracture risk and ex vivo structural interfragmentary strain theory, 32-6 to 32-7 properties, 33-2 Pauwels’ theory, 32-4 to 32-6 proximal femur, 33-18 to 33-22 Bone remodeling unit (BRU), 1-28 to 1-33 spine, 33-22 to 33-25 Bone repair, 1-54, 26-20 to 26-25, 32-1 to 32-4, See also Bone streaming potentials and, 24-9 regeneration; Fracture healing; Remodeling structural unit, 1-10, See Osteons direct (primary) repair, 26-20 to 26-22 trabecular, See Cancellous bone architecture; Trabecular fixation stiffness and, 26-22 architecture gap healing, 26-21 vascular system, 1-7 to 1-8, See Blood flow indirect repair, 26-22 to 26-23 viscoelasticity relationship, 11-10 to 11-12 interstitial fluid flow and, 22-17 woven and lamellar bone, 1-4 to 1-5 9117_frame_index Page 6 Monday, February 5, 2001 11:51 AM

I-6 Bone Mechanics

Bone substitute materials, 35-8, See also Biomaterials; Bone Cancellous bone, elastic properties of, 15-1 to 15-19 replacement scaffolding anisotropic properties, 15-3, 15-9 to 15-13 Bone surface area, 9-11 orthotropy assumption, 15-9 to 15-10, 15-12 Bone turnover, 1-27, 1-32, See Remodeling structure role, 15-11 to 15-12 markers, bone integrity assessment, 34-19 assessment of, 15-6 to 15-9 Bone volume calculation, 9-11 mechanical symmetries, 15-9 Boundary element method, 31-8, 31-34 micro-finite-element analyses, 15-7 to 15-8, 15-12, Bradykinin, 21-9, 21-11, 21-12 15-17 to 15-19 Broadband ultrasound attenuation (BUA), 34-9 to 34-14 stiffness tensor, 15-3 to 15-4, 15-6, 15-9 Buckling tests, cancellous bone, 10-8, 15-19 healthy and osteoporosis data sets, 15-10 to 15-11 Bulk modulus, 23-18 mechanical characterization, 15-2 to 15-6 compressive properties, 15-6 to 15-7, 15-9 elastic constants and restrictions, 15-3 to 15-6 C tensile loading, 15-6, 15-19 specimen machining effects,15-19 Calcitonin, 1-15 structural relationships, 15-12 to 15-18 bone blood circulation and, 21-9 anisotropic properties, 15-11 to 15-12 hydraulic conductivity, 22-13 density relationships, 15-13 to 15-16 knockout model, 4-10 determination of, 15-13 receptors, 2-9 to 2-10 fabric tensors, 15-16 to 15-18 Calcium, 5-1 tissue properties and, 15-19 45Ca, 22-10, 22-15 Cancellous bone architecture, 1-3 to 1-4, 1-10, 15-2, See also cortical and cancellous bone composition, 10-4 Trabecular architecture deficiency, 1-53, 5-10 composition effects, 14-17 dietary effects on functional adaptation, 26-17 Culmann and Meyer drawings, 30-2 to 30-3 mechanosensation/mechanotransduction mechanisms, elastic properties and, 15-12 to 15-18, See Cancellous bone, 28-8 to 28-9, 29-7, 29-8 elastic properties of streaming potentials and, 24-14 fabric reorientation model, 31-24 to 31-26 trans-interfacial transport, 23-5 finite element model for damage accumulation, 18-20 Calcium-deficient hydroxyapatite (CDHA), zeta potential, 24-8 mean intercept length (MIL), 14-7 to 14-9, 15-2, 15-9, 15-17 Calcium phosphate ceramics, 8-34, 35-4, 36-1, 36-2, 36-8 to 15-18 Calibration, 7-27 Wolff’s trajectorial theory, 30-1 to 30-14, 31-23, See Wolff’s Callus formation, 26-22, 26-23, 32-2 law Canaliculi, 1-5, 11-11, 23-4, 28-3, See also Lacuno-canalicular system Cancellous bone architecture, quantification of, 14-1 to 14-17 cement lines and, 23-5 ad hoc methods, 14-16 interfaces, 23-4, 23-5 connectivity, 14-16 mechanosensation function, 28-5 to 28-6 trabecular thickness, 14-16 remodeling model, 28-9 to 28-12 connectivity, 14-5 to 14-6, 14-10 to 14-13, 14-16 strain-generated potential location, 22-13, 22-14, 23-22 to star volume, 14-5 23-23, 24-14 to 24-19, 28-5 to 28-6, 29-5 to 29-6, stereological methods, 14-2 to 14-6 31-5 structure model index, 9-11 to 9-12, 14-14 transport-based remodeling model, 22-19 surface density, 14-3 to 14-4 Cancellous bone (trabecular bone) 3D methods, 14-7 adaptive hypertrophy, 26-17 anisotropy, 14-7 to 14-10 animal model for biomechanical testing, 7-25 connectivity, 14-10 to 14-13 bone damage histology, 17-12 to 17-13 trabecular dimensions, 14-13 to 14-14 in vivo accumulation observations, 17-9 to 17-10 traditional histomorphometry, 14-14 to 14-16 comparison with cortical bone, 10-1 to 10-18 volume fraction, 14-2 to 14-3, 15-2, 15-13, 15-14 age-related changes, 10-17 Canine models compositional differences, 10-4 bone heating effects, 20-19 mechanical properties, cancellous bone, 10-8 to 10-15 freezing effects, 20-7 mechanical properties, cortical bone, 10-5 to 10-7 functional adaptation to induced overloading, 26-12 microstructure and morphology, 10-2 to 10-4 immobilization, 1-37 specific bone mechanical properties, 10-9 methanol-chloroform effects, 20-18 compressive testing problems, 7-10 osteoarthritis model, 7-25 distribution in specific bones, 1-3 postmortem bone changes, 20-3 freeze-drying effects, 20-13, 20-14 strain gauge studies, 8-10, 8-18 to 8-19, 8-30 to 8-31 functional adaptation models, 31-21 to 31-34, See also Capillaries, 1-8, 21-1, 21-3, 21-5 to 21-7 Adaptation, theoretical models blood viscosity, 21-14 heating effects, 20-19 pressure, interstitial pressure and, 22-12 intrinsic permeability, 25-1, 25-9 to 25-12, See Permeability Carbonate-to-phosphate ratio, 5-13 mean age, 1-27 Carbon dioxide metabolism, 21-9 mechanical properties, 10-8 to 10-15 Cartilage bending test, 10-10 to 10-11 AGE products and, 13-4 determinants of modulus, 10-15 to 10-17 endochondral ossification, 1-25 elastic and inelastic buckling, 10-8 Catenins, 2-14 fatigue properties, 10-14 to 10-15 Cathepsin K, 2-6, 4-10 FEM back-calculation, 10-13 to 10-14 Cbfa-1, 2-8, 4-10 microindentation and nanoindentation, 10-11 to 10-13 CD44, 2-4 ultrasonic testing, 10-11 Cell biology, See Bone cells; Bone-lining cells; Osteoblasts; uniaxial tensile testing, 10-8 to 10-9 Osteoclasts; Osteocytes 9117_frame_index Page 7 Monday, February 5, 2001 11:51 AM

Index I-7

Cell cultures, 2-15 homogenization theory, 12-5, 12-8, 12-11 to 12-12 immunoseparation, 28-7 interfacial bonding, 13-8 to 13-9 mechanosensory models, 28-6 to 28-9 localization, 12-12 to 12-13 mechanostimulus testing methods, 27-1 to 27-16, See mechanical properties, 12-3 to 12-5 Biomechanical testing methods, in vitro mineralized collagen and hierarchical approach, 12-1, mechanostimulus methods 12-8 to 12-13 mineralization studies, 5-18 to 5-19 theories, 12-6 to 12-14 osteocytes in, 28-6 to 28-7 mineral-organic phase bonding, 12-14, 12-16, 13-1 plate systems for mechanostimulus testing, 27-10 to 27-10 noncollagenous proteins, 13-8 to 13-11 viscosity effects, 28-9 representative volume element, 12-4 to 12-5, 23-8 Cell death, See Apoptosis viscoelasticity models, 12-14 to 12-15 transport-based remodeling model, 22-18 Compressive loading, 6-17, 7-9 to 7-11 Cell dynamics model, 31-12 to 31-16 bone damage histology, 17-10 to 17-12 Cell-free solution studies, mineralization, 5-17 to 5-18 cancellous bone elastic properties and, 15-6 to 15-7, 15-9 Cell polarity, 2-2 composite material failure, 12-15 Cellular interface, 23-4 formalin fixation effects, 20-10 Cellular solid theory, 16-7, 16-11 to 16-16, 16-26 in vitro mechanosensitivity, 28-7 to 28-8 Cement lines, 10-4, 11-11 in vitro mechanostimulation, 27-2 to 27-4 interfaces, 23-4, 23-5 to 23-6 microtesting, 7-20 microcrack formation and, 17-9 osteocyte mechanosensitivity, 28-7 to 28-8, 29-3 to 29-4 Ceramics, 8-34, 35-2, 35-3 to 35-4, 36-1, 36-2, 36-8 residual strains, 16-29 c-fos, 2-8, 3-5, 3-7, 4-10, 21-12, 29-5 spinal loads, 33-5, 33-9 to 33-12, 33-22 Charnley hip, 21-1 strain measurement results, various animals and activities, Chemical fixation, 20-3, 20-9 to 20-12 8-10, 8-12 to 8-26, 8-29 to 8-33, See also Strain Chicken models, 8-23 to 8-24, 8-32 to 8-33, 26-5, 26-11, 26-14 gauge measurements and methods to 26-15, 26-17 thermal effects, 20-20 Chloroform, 20-18 tissue formation model for bone repair, 26-24 Cholinergic nerve fibers, 21-8 trabecular bone damage types, 16-30 Chondrocalcin, 5-16 viscoelasticity studies, 11-5 Chordin, 2-7 Compressive strength Ciliary neutrotrophic factor (CNTF), 2-13 anisotropy ratio, trabecular bone strength and, 16-3 Circular morphology, 21-1 to 21-7, See Blood flow; Vasculature embalming effects, 20-11 c-jun, 21-12 freeze-drying effects, 20-13 Cobalt-chromium alloys, 35-2, 35-3 irradiation effects, 20-15 Collagen, 1-6, 11-11, 1-19, 22-1 methanol-chloroform effects, 20-18 aging effects, 19-7, 19-12 postmortem effects, 20-4 to 20-5 bone hydration states and, 24-4 to 24-5 trabecular bone creep and fatigue and, 16-33 to 16-34 bone quality relationship, 13-2 vs. tensile strength for trabecular bone, 16-8 to 16-9 cross-links and biomechanical properties, 13-2 to 13-3 Compton scattering, 33-13 diseases, 12-1, 12-3 Computational fluid dynamics, 27-16 freeze-drying effects, 20-13 Computed tomography (CT), 5-8, 9-2 to 9-6, See also glycosylation, 13-3 to 13-4 Microcomputed tomography; Quantitative hierarchical approach and composite theories, 12-1, 12-8 to computed tomography 12-13, See also Composite models artifacts, 9-4 histomorphometry of orientation, 7-5 bone-implant system analysis, 35-15 hydration, 13-2 cellular activity, 9-18 interstitial fluid mechanics and, 22-13 comparison with conventional histomorphometry, 9-12 irradiation effects, 20-16 to 20-17 micro-CT, See Microcomputed tomography knockout model, 4-10, 5-19 to 5-20 QCT, See Quantitative computed tomography mechanical consequences of changes, 13-2 to 13-6 resorption and, 2-10 microstructural morphology, 10-3 spatial resolution limitations, 9-3 mineralization and, 5-14, 5-16 to 5-18, 5-21, 12-14, 12-16, synchrotron-CT, 9-5 to 9-6, 9-13 to 9-14, 9-17, 9-18 13-1 Computer-aided design (CAD), 36-2 to 36-3 orthotropic assumptions, 12-6, 12-9 Computer-aided optimization (CAO), 31-18 osteoblast secretion, 1-15 Computer assisted tomography (CT), 5-8, See also Quantitative pathologies, 13-4 to 13-6, See also Osteogenesis imperfecta computed tomography tendon biomechanical properties and, 13-2 Conductance-based bone integrity measurement, 34-19 to thermal effects, 20-20 34-20 transgenic model, 4-8 to 4-9 Connected cellular network (CCN), 29-2 to 29-3, See also type X transgenic model, 5-20 Lacuno-canalicular system viscoelasticity, 11-11 attributes, 29-8 zeta potentials and, 24-9 mechanosensation/mechanotransduction and, 29-3 to Collagen-apatite porosity, 23-22, 23-4, 23-7, 23-18, 29-6 29-8, See Mechanosensation strain-generated potentials source, 23-22, 29-5 to 29-6 signal processing and integration, 29-7 to 29-8 Collateral circulation, 21-7 Connectivity density, 15-15 Compliance tensor, 15-3 to 15-4, 15-9, 15-18 ConnEulor principle, 14-6, 14-11 Composite models, 12-1 to 12-17, 13-1 to 13-11 Connexins, 2-4, 29-2, 3-13, 4-10, 29-2 collagen template change, mechanical consequences, 13-2 Conservation remodeling, 1-32 to 13-6 Continuum damage mechanics model, 18-2 to 18-3 damage accumulation, 18-16 to 18-17, 18-21 Core-binding factor-α1 (Cbfa1), 1-17 failure modes, 12-15 to 12-16 Corraline hydroxyapatite, 36-11 global approach, 12-13 to 12-14 Corrosion resistance, 35-2 to 35-3 9117_frame_index Page 8 Monday, February 5, 2001 11:51 AM

I-8 Bone Mechanics

Cortical bone Dexamethasone, 1-13 comparison with cancellous bone, 10-1 to 10-18, See also freezing effects, 20-7 Cancellous bone mechanical properties and, 7-2 age-related changes, 10-17 Diabetes, 5-11 compositional differences, 10-4 DIANA, 23-16 mechanical properties, cancellous bone, 10-8 to 10-15 Diaphyseal pressures, 21-16 mechanical properties, cortical bone, 10-5 to 10-7 Diet, See Nutrition microstructure and morphology, 10-2 to 10-4 Differential display, 3-8 to 3-9 specific bone mechanical properties, 10-9 Differential staining, 17-9 computed tomography issues, 9-2 Differential thermal gravimetric analysis (DTA), 5-2 distribution in specific bones, 1-3 Diffusion-convection equation, 22-7 freeze-drying effects, 20-13, 20-14 Diffusive molecular transport, interstitial fluid, 22-7 to 22-19 heating effects, 20-19 Dilatant fluids, 25-14 in vivo damage accumulation observations, 17-9 Diphtheria toxin, 4-13 mean age, 1-27 Direct (primary) fracture repair, 26-20 to 26-22 remodeling models, 31-8 to 31-21, See also Adaptation, Distal radius theoretical models osteoporosis fracture sites, 9-6 structure, 1-3 to 1-4, 1-10, See also Bone structure and 3D imaging, 9-7 morphology; Osteons Distraction osteogenesis, 32-4 viscoelastic properties, 11-1 to 11-12, See also Viscoelasticity Disuse osteopenia, See Bone loss; Immobilization models Covariance, 34-19 Disuse remodeling, 1-32 to 1-33 COX-II (cyclooxygenase), 2-11, 26-20, 28-9 DNA chip, 3-10 Creep, 11-1, 11-2, 11-7 Dominant-negative transgenics, 4-4 compliance, 11-2 Drag force model, streaming potentials, 24-18 to 24-19 damage, 18-1, 18-6 to 18-7 Drag theories, 25-7 to 25-9 skull deformability, 11-4 Dual-energy projection radiography, 33-13 stretched exponential and Debye model, 11-10 Dual-energy X-ray absorptiometry (DEXA), 5-2, 7-4, 9-1 torsional, 11-9 fracture risk prediction, 33-14, 33-15 to 33-16, 33-20 trabecular and cortical bone behavior, 15-3 implant site remodeling assessment, 35-17 trabecular bone strength, 16-33 to 16-34 limitations of, 34-5 Critical angle analysis, 7-21 space flight study, 26-4 Critical stress intensity factor, 7-17 strain protection bone loss, 26-7 Dual photon absorptiometry (DPA), 33-13, 33-14 Cross-sectional moment of inertia (CSMI), 7-3 to 7-5 Duck, 19-3 age and gender relationships, 33-17 Dynamic shear compliance, postmortem changes, 20-4 c-sac, 4-10 Dynamic strain similarity, 26-10 Culmann and von Meyer drawings, 30-2 to 30-3, 30-12 Dynamic viscosity, 25-13 Curvature reduction application, 31-11, 31-18 Cutting cones, 1-31 Cyanoacrylates, 8-4 to 8-5 Cyclical loading, bone mechanical property degradation and, E 17-3 to 17-5 Ecdysone, 4-13 Cyclo-oxygenase (COX-II), 2-11, 26-20, 28-9 Ectopic gene expression, 4-2 Cynomolgus monkeys, 7-25 Effective medium approach, 23-7, 23-8, 23-10, 23-19 Cytochalasin B, 28-8 Egg laying, 26-17 Cytoskeleton, 22-10 Elastic buckling, trabecular, 10-8 cyto-matrix sensation-transduction processes, 29-5 Elastic compliance matrix, 6-13 endothelial stress fibers, 21-6 Elastic model of bone damage, 18-5 to 18-7 osteoclasts and integrins, 2-6 Elastic modulus, See also Young’s modulus apparent density and, 7-5 backcalculation using finite-element model, 10-13 to 10-14 D cancellous bone properties, 10-8 to 10-17, 15-3, 15-6 to 15-7, 15-13 to 15-14, See Cancellous bone, elastic Damage accumulation, See Bone damage properties of Damage repair, See Bone repair; Fracture healing composite model, 12-6 to 12-8, 12-4 Damping, 11-2, 11-11, See Viscoelasticity cortical bone characterization, 10-5 to 10-7, 10-12 to 10-13 Darcy, Henri, 25-2 drained vs. undrained, poroelasticity considerations, 23-13 Darcy’s law, 25-2 to 25-3, 25-9 effective isotropic elastic constants, 23-17 lower limit, 25-5 ethanol fixation effects, 20-9 upper limits, 25-4 to 25-5 fetal bone, 19-5 Debye model, 11-6, 11-9 to 11-10 freeze-drying effects, 20-13 Decorin, 1-21, 3-13, 5-16, 5-19 freezing effects, 20-6 Deer heat-induced changes, 20-19 antler, 11-7, 26-5, 26-6, 26-17 indentation testing, 10-5 neonatal and maternal bone properties, 19-10 to 19-11 irradiation effects, 20-15, 20-16 Deformation pressure models, bone regeneration, 32-7 to 32-8 maturation effects, 19-5 Dehydroepiandrosterone (DHEA), 1-55 measurement, See Biomechanical testing methods Density, See Bone density; Bone mineral density porosity and, 7-5 Dental implants, 35-12 to 35-13 postmortem changes, 20-4 to 20-5 Dentine, 12-13, 22-16 3D connectivity, 9-14 Derivative notation, 6-21 ultrasonic velocity and, 34-8 Deviatoric stress, 32-7 Elastic strain-stress relations, 6-14, 6-23 9117_frame_index Page 9 Monday, February 5, 2001 11:51 AM

Index I-9

Elastic wave propagation, 23-19 pig model for architectural and mechanical changes, 19-13 Elasticity, See also Viscoelasticity to 19-14 adaptive elasticity model for cortical bone, 31-11 to 31-12, Experimental protocols, 7-26 31-15 to 31-16 External fixators, 35-6 adaptive elasticity model for trabecular bone, 31-21 to Extracellular matrix, 22-1 to 22-2, See also Bone mineral; 31-29 Collagen; Hydroxyapatite; Mineralization bone-implant system analysis, 35-14 Extracellular matrix vesicles (ECMVs), 5-15 functional adaptation models, 31-7 inelasticity and bone damage accumulation, 17-2 to 17-3 orthotropic elasticity theory, 6-22 to 6-24 F Elastomers, 35-4 Elbow replacement prosthesis, 35-11 to 35-12 Fabric, 34-5 Electric fields, externally applied, 26-18, 29-6 Fabric reorientation model, 31-24 to 31-26 bone loss and, 26-7, 26-18 Fabric tensor, 14-9, 14-10, 15-16 to 15-18, 31-23 Electrical conductance-based bone integrity measurement, Tsai-Wu criterion and trabecular bone strength, 16-21, 34-19 to 34-20 16-24 Electrical impedance tomography, 34-19 Tsai-Wu quadratic criterion, 16-21 Electromechanical potentials, See Strain-generated potentials; F-actin stress fibers, 21-6, 21-12 Streaming potentials Failure biomechanics, 33-1 to 33-25, See Bone damage; Electromyography (EMG), 33-5 Fracture(s) Electron microscopic tomography, 5-8 cellular solid theory, 16-11 to 16-16, 16-26 Electroporation, 3-11 femoral loading and failure properties, 9-6, 33-2 to 33-9, Embalming, 20-10 to 20-11 33-13 to 33-14, 33-16 to 33-17, 33-18 to 33-22 Endochondral ossification, 1-25, 26-22, 26-24 trabecular bone strength, 16-2, 16-3, 16-9 to 16-16, See also bone regeneration and, 32-1, 32-2, 32-7 Trabecular bone strength Endocortical bone envelope, 31-4 Fall loading conditions, 33-4 to 33-5 Endosteal surface, 1-9 Fat, dietary, 5-10 Endosteum, 1-3 Fatigue, 18-12 to 18-15, See also Bone damage cellular interface, 23-4 characterizing cancellous and cortical bone, 10-14 to 10-15 Endothelial cells, 21-5 to 21-7 damage and repair models, 18-22 to 18-23 fluid flow sensitivity, 28-8, 29-4 osteocyte-mediated osteoclast response, 28-11 Endothelium-derived relaxing factor (EDRF), 21-12 remodeling stimulus, 29-3 Energy dispersive X-ray microanalysis (EDAX), 5-3 testing, 7-18 to 7-19 Epifluorescence, 17-9 trabecular bone, 16-33 to 16-34 Epinephrine (adrenaline), 21-9 trabecular bone, post-yield behavior, 16-27 to 16-30 Epiphyseal arteries, 21-2, 21-3 Feline models, 20-7, 20-10 Epiphyseal plate, 1-3 Femoral fracture risk, 34-2 Epiphysis, 1-3 Femoral head, 31-28 to 31-29 Epoxy resins, 8-4, 8-5 Femoral, loading and failure properties, 9-6, 33-2 to 33-9, 33-13 Equipment calibration, 7-27 to 33-14, 33-16 to 33-17, 33-18 to 33-22 Erythrocytes (RBCs), 21-10 Ferrets, 7-25 E-selectin, 21-11 Fetal bone, 1-24, 19-5, See also Bone formation; Woven bone Estrogens Fetal skull, 19-5 antler growth and, 26-5 Fetuin, 5-16 apoptosis and, 2-9, 2-11 Fibroblast growth factors (FGFs), 1-19, 1-20, 2-7, 2-12 bone blood circulation and, 21-9 fracture healing and, 32-2 bone formation and bone loss effects, 26-20 knockout model, 4-10 deficiency, 1-51 Fibroblasts, 1-15 genes affected by, 3-7 Fibrolamellar bone, 19-2 male bone maintenance and, 1-53 Fibromodulin, 1-21 osteocyte apoptosis and, 1-24 Fibronectin, 1-21, 2-3, 21-7, 21-14 receptors, 2-11, 3-7 Fibular hypertrophy, 31-8 to 31-9 replacement therapy, 1-48 Fimbrin, 28-8 resorption inhibition, 1-15 Finite-element models (FEMs), 12-5 Ethanol fixation, 20-9 adaptive elasticity application, 31-12 Ethylene oxide sterilization, 20-15 bone damage models, 18-19 to 18-20, 18-21, 18-23 EU-BIOMED I study, 15-10 bone/implant system analysis, 35-15 to 35-16 Euler equation, for elastic buckling, 10-8 "checkerboard" patterns, 31-30 to 31-32 Euler number, 14-5 to 14-6, 14-10 to 14-14 computer-aided optimization (CAO), 31-18 Evolution, 26-1 femoral failure risk models, 33-19, 33-20, 33-22, 33-25 Exercise hydrostatic pressure and bone regeneration, 32-8 age-related bone loss and, 1-54 interstitial fluid flow, 22-14 animal loading adaptation model, 1-41 to 1-45 poroelasticity, 23-16 aging and, 1-41 to 1-42 remodeling theory computational implementation, 31-8 bone strength, 1-44 site-dependent strain energy density model, 31-16 cancellous bone and, 1-42 spinal loading models, 33-22 to 33-25 time course, 1-43 to 1-44 strength optimization, 31-21 bone mass maintenance and, 26-4 to 26-5 trabecular/cancellous bone, 31-20, 31-28 bone mineral composition and, 5-10 adaptation, 21-21, 31-24 to 31-26 bone viscoelasticity and, 11-4 architecture and bone strength, high-resolution model, functional adaptation, 26-10 16-19 to 16-21 9117_frame_index Page 10 Monday, February 5, 2001 11:51 AM

I-10 Bone Mechanics

architecture and bone strength, lattice-type model, Freeze-drying, 20-13 to 20-14, 20-16 16-16 to 16-18 Freezing, 20-3, 20-6 to 20-8, 20-12 elastic constant assessment, 15-7 to 15-8, 15-12, 15-17 Functional adaptation, See Adaptation to 15-19 Fused deposition modeling, 36-7 mechanical properties, 10-13 to 10-14 transport-based remodeling model, 22-18 Fish strikes, 8-21, 8-32 G Fixation devices, 26-4, 26-9, 26-22, 35-1, 35-6 to 35-7 Flexercell systems, 27-9 to 27-10 Gait, See Locomotion Flexure-neutralization theory, 31-9 to 31-11 Galago, 8-20, 8-31 Flight, strain measurement results, 8-24 to 8-25, 8-33 Gallium, 5-10 Fluid flows, See Blood flow; Hydrostatic pressure; Interstitial Gancylovir, 4-13 fluid flow Gap healing, 26-21 Fluid mechanics, 21-13 to 21-21, See also Interstitial fluid flow Gap junctions, 1-5, 2-4, 28-4, 29-2 to 29-3, 29-8 axial blood flow measurement, 21-16 to 21-19 in vitro model for mechanosensation, 28-7 cellular mechanosensitivity, 28-8 to 28-9 resorption inhibition mechanism, 1-54 to 1-55 hydrostatic pressure measurement, 21-15 to 21-16 Gelatinase B, 5-15 microvascular flow measurement, 21-19 to 21-21 Gender differences nutrient exchange, 21-21 osteocyte mechanosensation/transduction process, 29-5 bone mineral composition, 5-9 to 5-10 Q measurement, 221-16 to 21-21 cross-sectional moment of inertia, 33-17 transmural transport, 21-21 Gene deletion, See Knockout models Fluorescent bone markers, 1-18 Gene discovery methods, 3-8 to 3-10 Fluoride, 5-13 differential display, 3-8 to 3-9 bone mechanical properties and, 13-7 to 13-8 microchip technology (DNA chip), 3-10 osteoporosis treatment issues, 7-25 representational differentiation analysis, 3-9 Fluorosis, 1-21 serial analysis, 3-9 to 3-10 Focal adhesion kinase (FAK), 2-14 subtractive hybridization, 3-9 Fondrk model, 18-6, 18-14 to 18-15, 18-20 to 18-21 Gene expression, measurement techniques, 3-1 to 3-14, See also Food and Drug Administration (FDA), 1-48, 35-1 Transgenic mouse models Force, 6-2 array technology, 3-7 Formaldehyde, 20-9 gene discovery, 3-8 to 3-10 Formalin fixation, 20-9 to 20-10 gene inactivation, 3-13, See also Knockout models Fourier transform IR (FTIR), 5-4 to 5-7 gene transfer, 3-10 to 3-12, See also Transgenic mouse Four-point bending, See Bending models Fractal analysis, 9-11, 14-14, 34-19 adenovirus-based techniques, 3-11 to 3-12 Fracture(s), See also Microcracks nonvirus-based, 3-11 age and, 19-7 retrovirus-based techniques, 3-12 composite models, 12-15 in situ hybridization, 3-5 to 3-6 factor of risk, 33-1 Northern blotting, 3-2 to 3-3 factors influencing age-related bone loss, 1-50 to 1-55 gap size, 26-23 reverse transcriptase-PCR, 3-3 to 3-5, 3-8 greenstick, 7-6, 19-8 ribozymes, 3-13 high-energy vs. low-energy fracture effects, 26-21 RNase protection assay, 3-6 to 3-7 mechanical testing outcome measures, 7-6 Gene therapy, 3-10, 3-11 osteoporotic, common sites, 1-47 Gibbon, 8-20 to 8-21, 8-31 to 8-32 prevention and protection issues, 1-48, 33-1 Glass bioceramics, 35-4 testing, 7-17 to 7-18 Gli 2, 4-10 ultrasound attenuation and risk, 34-12 Gli 3, 4-10 Fracture(s), relating risk and ex vivo structural behavior, 33-2 Glucocorticoids, 2-8, 2-10 to 2-11 ex vivo behavior and imaging parameters Glucokinase, 4-9 proximal femur, 33-6 to 33-8, Glucose, 22-15 spine, 33-10 to 33-12, 33-14 to 33-16 Glutamate-secreting nerve fibers, 21-8 in vivo loads Glutaraldehyde, 20-9 proximal femur, 33-2 to 33-5 Glycocalyx, 23-7, 23-22, 29-6 spine, 33-5, 33-9 Glycoproteins, 22-2 in vivo risk and imaging parameters Glycosylation, collagen, 13-3 to 13-4 proximal femur, 33-16 to 33-17 Goats, 7-25, 8-19 to 8-20, 8-31 spine, 33-18 Gradient notation, 6-21 fall loading conditions, 33-4 to 33-5 Grafting, 36-1 loading rate, 33-5 Granite porosity, 23-17 structural model development proximal femur, 33-18 to 33-22 Granulocyte/macrophage colony-forming unit (GM-CFU), spine, 33-22 to 33-25 1-11 Fracture fixation devices, 26-4, 26-9, 26-22, 35-1 Granulocyte/macrophage-colony stimulating factor Fracture healing, 32-1 to 32-4, See also Bone repair (GM-CSF), 2-8 direct (primary) fracture repair, 26-20 to 26-22 knockout model, 4-10 gap size and, 26-23 Greenstick fractures, 7-6, 19-8 indirect fracture repair, 26-22 to 26-23 Growth factors, 1-19, See specific substances interstitial and venous pressure effects, 22-17 Growth hormone (GH), 1-53, 4-8 mechanical environment and, 26-22 to 26-23, 32-3 Growth plate-metaphyseal complex, 1-3 mechanical variables influencing, 26-23 to 26-25 Guinea pigs, 7-25 phases, 32-1 to 32-2 Gulls, 19-13 to 19-14 9117_frame_index Page 11 Monday, February 5, 2001 11:51 AM

Index I-11

H Hypophosphatasia, 2-4, 5-15 Hypophosphatemia, 1-21, 13-8 Halpin-Tsai (HT) equations, 12-9 to 12-10 Hypothalmic-pituitary axis, aging effects, 1-53 Hanging-drop tensile loading method, 27-2 Haversian canals (osteonal canals), 21-3, 21-5, 22-3, 22-6, 23-3 to 23-4, 28-3 I local voltage gradients, 23-23 molecular transport mechanisms, 22-8 Iguana, 8-26 to 8-27, 8-33 pressure gradients, 22-11 Image-based design (IBD), 36-2 to 36-5, 36-11 streaming potentials and, 24-9 to 24-16 Imaging methods, 9-1 to 9-20, 34-1 to 34-20, See also specific vascular porosity, 23-6 techniques Haversian system, 1-5, 1-10, 19-3, See Osteons acoustic techniques, See Ultrasonic methods Heel strike transient, 26-4 applications Helmholtz Smoluchowski equation, 24-5 to 24-7 postmenopausal osteoporosis, 9-15 to 9-16 Hemiosteon, 1-10 simulated bone atrophy, 9-16 to 9-17 High-fat diets, 5-10 bone samples, 9-9 to 9-13 High-resolution finite-element modeling, trabecular bone cellular level studies, 9-18 strength and uniaxial loading, 16-19 to 16-21 comparison of histomorphometry and micro-CT, 9-12 High-resolution magnetic resonance imaging, 34-18 CT, 9-4 to 9-6, See Computed tomography High-voltage electron-microscopic tomography, 13-4 measuring time, 9-3 Hingeless joints, 35-8 MRI, 9-6, See Magnetic resonance imaging Hip fracture, 1-47 patient examinations, 9-6 to 9-9 biomechanical tests, 7-16 plate and rod models, 9-10, 9-12 Hip joint forces, 33-3 to 33-4 radiography, See Radiographic methods; specific techniques Hip replacement prostheses, 33-3 to 33-4, 35-8 to 35-10 small animal models, 9-13 to 9-14 outcome analysis, 35-18 spatial resolution, 9-2 to 9-3 Histamine, 21-9, 21-11, 21-12 ultrasonic techniques, 34-6 to 34-17, See Ultrasonic Histomorphometry, 7-5 to 7-6 methods Hodgkin-Huxley theory, 30-1 to 30-2, 30-13, 30-14 whole-bone failure loading studies, 33-6 to 33-18 Homogenization theory, 12-5, 12-8, 12-11 to 12-12, 36-5 X-ray densitometry, 34-2 to 34-5, See Dual-energy X-ray Hooke’s law, 6-2, 6-13 to 6-14, 11-1 absorptiometry; specific methods thermodynamic restriction, 6-15 to 6-16 Immobilization models, 1-37 to 1-41, 26-4 Hormone replacement therapy, 1-48 bone mineral composition and, 5-10 Horses, 19-11, 26-12 localized bone loss, 26-5 exercise and bone volume, 26-12 Immunoglobulin cell adhesion molecules (ICAMs), 21-11 strain measurement results, 8-14 to 8-17, 8-29 to 8-30, 8-31 Immunoseparation, 28-7 Howship’s lacunae, 1-11, 1-31 1-11 to 1-13 Implants, 35-1 to 35-19, See also Bone replacement scaffolding; α Prostheses 2 HS glycoprotein, 1-21, 5-16 Human growth hormone, 4-8 cements or adhesives, 8-4 to 8-5, 35-4 to 35-5 Human immunodeficiency virus (HIV), 20-15, 20-19 artificial joint failure, 35-10 Hyaluronan, 1-21 associated bone loss, 26-9 to 26-20 Hydration shell, 13-6 to 13-7 biocompatibility, 35-2 Hydraulic radius theories, 25-6 to 25-7, 25-10 biomaterials, 35-2 to 35-5 Hydrostatic loading methods, 27-2 to 27-4 bone cement, 35-4 Hydrostatic pressure, 23-6, 23-20, 27-2 to 27-4, See also Fluid bone regeneration around, 32-10 mechanics clinical assessment, 35-17 to 35-18 bone regeneration relationships, 32-5, 32-7 to 32-8 design, 35-5 to 35-14 bone-venous pressure relationship, 22-12, 23-6, 23-20 ankle replacement, 35-12 hypertension and fracture repair, 22-17 bone fixation systems, 35-6 to 35-7 intramedullary pressure, 21-16, 21-17, 22-12 bone substitute materials, 35-8 measurement, 21-15 to 21-16 dental, 35-12 to 35-13 osteocyte mechanosensitivity, 28-7 to 28-8, 29-3 to 29-5, See elbow replacement, 35-11 to 35-12 also Interstitial fluid flow hip replacement, 35-8 to 35-10 tissue differentiation models for bone repair, 26-24 to 26-25, knee replacement, 35-10 to 35-11 32-5 middle-ear, 35-13 Hydroxyapatite, 1-6 to 1-7, 1-19, 5-1, 5-13, 11-11, 13-6, 22-1, permanent for total joint arthroplasty, 35-8 to 35-12 35-4, See also Apatite shoulder replacement, 35-11 bone scaffolding materials, 36-6, 36-8, 36-9, 36-11 temporary and resorbable, 35-6 to 35-8 calcium-deficient, zeta potential, 24-8 wrist replacement, 35-12 corraline, 36-11 experimental external loading systems, 26-13 to 26-15 cortical and cancellous bone comparison, 10-4 finite-element methods, 35-15 to 35-16 osteoclast-facilitated dissolution, 2-5 to 2-6, See also government regulation, 35-1 to 35-2 Osteoclasts; Resorption osseointegration, 35-1 to 35-2 oxy-hydroxyapatite, 36-9 outcome analysis, 35-18 preferred bone mineral terminology, 23-7, See also Apatite preclinical tests, 35-14 to 35-16 "shielding" from fluid phase, 22-15 simulators, 35-16 tricalcium phosphate composites, 35-8 strain measurement methods, 35-16 zeta potential, 24-8 stress shielding, 35-10 24-Hydroxylase, 4-7, 4-10 survival analysis, 35-18 Hyp mouse, 13-8 Wolff’s law and computational modeling, 30-13 Hyperparathyroidism, 1-53, 9-2 Indentation testing, 7-17, 10-5 Hypertension, and fracture repair, 22-17 cortical bone characterization, 10-5 to 10-7, 10-12 to 10-13 9117_frame_index Page 12 Monday, February 5, 2001 11:51 AM

I-12 Bone Mechanics

fetal bone, 19-5 molecular transport mechanisms microtesting, 7-20, 10-5, 10-11 active transport, 22-10 to 22-11 nanotesting, 7-20, 10-5 to 10-7, 10-12 to 10-13, 19-5 convection and other non-diffusive mechanisms, 22-10 Indirect fracture repair, 26-22 to 26-23 lacunocanalicular system model, 22-13 to 22-14, See Indomethacin, 26-20 also Canaliculi; Lacunae; Lacuno-canalicular Infrared spectroscopy (IR), 5-4 to 5-7 system In situ hybridization, 3-5 to 3-6 loading effects, 22-15 Insulin-like growth factor binding proteins (IGFBPs), 1-20, 2-12 non-mechanically loaded bone, 22-7 to 22-10 Insulin-like growth factors (IGFs), 1-19, 1-20, 2-12 outflow dilution method, 22-9 age-related bone loss and, 1-53 to 1-54 passive diffusion, 22-6 to 22-10 fracture healing and, 32-2 remodeling model, 22-18 to 22-19 knockout model, 4-10 osmotic pressure, 22-13 osteoblast regulation, 2-7 periosteal barrier, 23-4 transgenic model, 4-8 permeability, See Permeability Integrins, 1-14, 2-4, 21-6 to 21-7, 2-13 to 2-14 poroelasticity theory, 22-11, 23-1 to 23-25, See cyto-matrix sensation-transduction processes, 29-5 Poroelasticity knockout model, 4-10 porosity levels, 22-2, See also Porosity neutrophil receptors, 21-11 pressure, See Hydrostatic pressure osteoclasts and, 2-6 quiescent bone tracer studies, 22-8 to 22-10 transgenic model, 4-9 signal transduction, 22-16 to 22-17, 26-20, See also Intercurrent disease, 1-55 γ Mechanotransduction Interferon , 4-8 streaming potential theory development, 24-17 to 24-19 Interfragmentary strain theory, 26-24, 32-3, 32-6 to 32-7, 32-9 tissue and bone fluid components compared, 22-2 to 22-3 Interleukins, 1-20 vascular fluid exchange, 23-6 IL-1, 1-20, 2-13, 21-11 Interstitial lamellae, 1-5 fracture healing and, 32-2 Intertrabecular space porosity, 23-4, 23-7 osteoclastogenesis stimulation, 2-8 Intracortical porosity, 26-9 to 26-10, 26-21 receptor knockout model, 4-10 resorption and, 2-5 Intramedullary nails, 35-6 IL-1β, 1-13 Intramedullary pressure (IMP), 21-16, 21-17, 22-12 IL-4, 4-8 Intramembranous ossification, 1-24, 26-24, 36-10 IL-6, 1-20, 2-13 bone regeneration and, 32-1, 32-2 fracture healing and, 32-2 Intravital microscopy, 21-19 knockout model, 4-10 Ion substitution effects, 13-7 to 13-8 osteoclastogenesis stimulation, 2-8 Irradiation, 20-3, 20-15 to 20-18 transgenic models, 4-7, 4-8 Ischemic osteonecrosis, 21-4, 21-15 IL-11, 1-13 Isostress model, 12-4, 12-6 Intermittent hydrostatic compression (IHC), osteocyte mechanosensitivity, 28-7 to 28-8, 29-3 to 29-4 Interstitial fluid flow, 22-1 to 22-19 J bone fluid composition, 23-6 bone fluid functions, 23-1 to 23-2 Joint arthroplasty, 35-1, See Implants; Prostheses; Total joint arthroplasty bone growth and, 22-17 bone hydration states, 24-4 to 24-5 indentation testing, 7-17 bone regeneration models, 32-8 to 32-9 bulk modulus, 23-18 compartmentalization, 22-2 to 22-3, 24-5 K convective flow model, 23-10 Kachanov model, 18-6, 18-14 to 18-15 elastic wave propagation, 23-19 Kinematic viscosity, 25-13 electromechanics, 12-12 to 12-13, 22-14 to 22-15, 23-21, See Klotho, 4-9 also Strain-generated potentials Knee replacement prosthesis, 35-10 to 35-11, 35-17 finite-element models, 22-14 Knockout models, 3-4 to 3-7, 4-4 to 4-7, 4-10, 26-15 fracture repair and, 22-17 animal husbandry, 4-6 to 4-7 functional adaptation and, 22-17 collagen deletion, 4-10, 5-19 to 5-20 hydraulic conductivity, 22-13 in vitro model, 28-6 DNA integration effects, 4-13 influx and efflux pathways to bone tissue, 22-3, 22-6 DNA preparation, 4-4 to 4-5 limiting dimensions for vascular and extravascular spaces, double knockouts, 4-13 22-4 to 22-5 embryonic stem cells, 4-5 to 4-6 measurement, 22-13 to 22-16 examples, 4-7 to 4-9 ex vivo studies, 22-13 growth factors, 4-10 in vitro studies, 22-13 matrix-gla protein, 5-15 to 5-16 in vivo studies, 22-16 noncollagenous proteins, 4-7, 4-10, 4-13, 5-20, 13-10 to model-based approximations, 22-13 to 22-15 13-11 mechanical loading effects, 22-11 osteopetrosis, 2-6 medullary-vascular interactions, 22-12 point mutations, 4-11 molecular transport, 22-15 src, 5-20 pressure gradients, 22-11 to 22-12 tissue-specific model using Cre-recombinase, 4-9 to 4-11 mechanosensory system, 23-2, 28-5 to 28-6, See also Kozeny-Carman model, 25-7, 25-10 Lacuno-canalicular system; Mechanosensation; Kozeny model, 25-6, 25-11 Streaming potentials KWW model, 11-6, 11-8, 11-9 to 11-10 9117_frame_index Page 13 Monday, February 5, 2001 11:51 AM

Index I-13

MARC, 31-17 L Marching cubes algorithm, 9-11, 15-8 Lactation, 19-8, 26-17 Marrow blood flow, 1-8, 1-55, 21-4, 21-5, 21-4, 21-5 Lacunae, 1-5, 11-11, 28-3, See also Lacuno-canalicular system intramedullary pressure, 21-16, 21-17, 22-12 comparison of cortical and cancellous bone, 10-3 to 10-4 Marrow removal technique, 7-3 Lacuno-canalicular system, 22-2, 22-3, 28-3, See also Canaliculi; Marrow space volume fraction, 14-3 Connected cellular network; Osteons Mastication, strain measurement results, 8-20 to 8-21, 8-31 to interfaces, 23-4, 23-5 8-32 mechanosensation-transduction function, 22-17, 28-5 to Matrices, stress, 6-5 to 6-8 28-6, 29-5 to 29-6, See also Mechanosensation; Matrix-gla protein (MGP), 1-21 Mechanotransduction; Streaming potentials knockout model, 5-15 to 5-16 remodeling model, 28-9 to 28-12 Matrix metalloproteinases, 2-6 signal processing, 29-7 to 29-8 McCune Albright syndrome, 3-13 molecular transport model, 22-6, 22-13 to 22-14 Mean intercept length (MIL), 14-7 to 14-9, 15-2, 15-9, 15-17 to porosity, 23-4, 23-5, 23-6 to 23-7, 23-16 to 23-18, 23-20, 15-18 29-5 Mechanical properties, comparison of cancellous and cortical pressure gradients, 22-11 bone, 10-1 to 10-2, See also specific properties resorption inhibition mechanism, 1-55 age-related changes, 10-17 strain-generated potentials, 22-13, 22-14, 23-22 to 23-23, bending test, 10-10 to 10-11 24-14 to 24-19, 28-5 to 28-6, 29-5 to 29-6, 31-5 cancellous bone properties, 10-8 to 10-15 shielding by organic phase, 22-15 cortical bone properties, 10-5 to 10-7 transport-based remodeling model, 22-19 determinants of modulus, 10-15 to 10-17 Lambda (λ) phage, 4-9 elastic and inelastic buckling, 10-8 Lamellar bone, 1-4 to 1-5 fatigue properties, 10-14 to 10-15 Lamellar structure, 1-5, 12-9 to 12-11 FEM back-calculation, 10-13 to 10-14 composite models, 12-1 microindentation and nanoindentation, 10-11 to 10-13 microcrack formation and, 17-9 microstructural and morphological differences, 9-2 to 9-4 viscoelastic properties and, 11-11 ultrasonic testing, 10-11 Laminar bone, 19-2 uniaxial tensile testing, 10-8 to 10-9 Laser Doppler flowmetry, 21-16, 21-19 Mechanical properties, composite materials, 12-3 to 12-5, 13-1 Laser scanning confocal microscopy, 16-31 to 16-32 to 13-11 Layered object manufacturing, 36-7 mineralized collagen and hierarchical approach, 12-1, 12-8 Lead-uranyl acetate, 17-9 to 12-13 Leukocytes, 21-11 theories, 12-6 to 12-14 LIF receptor, 4-10 Mechanical properties, ontogenetic changes, 19-4 to 19-9, See Lining cells, See Bone-lining cells Adaptation; Aging; Remodeling; Skeletal Linseed oil, 25-12, 25-14 development, ontogenetic changes Lipids, 20-18, 22-2 Mechanical properties, postmortem and preservation changes, proteolipids (protein complexes), 5-18 20-1 to 20-20, See Bone preservation effects; removal, 20-18 Postmortem bone changes Load-displacement curve, 7-6 Mechanical testing techniques, See Biomechanical testing Local structure tensor, 15-9 methods Locomotion Mechanical usage, bone mass adaptation to, 1-34 to 1-47, See efficiency, 19-9 to 19-10 Adaptation exercise and bone development, 26-11 to 26-12 mechanostat system, 1-35 to 1-36 gait analysis for prosthesis assessment, 35-17 Mechanics, 6-1 to 6-24, See also specific mechanical properties, hip joint forces measurement, 33-3 measures loading cycle time course, 31-4 axial deformation, 6-9 to 6-11 strain measurement results (various species), 8-10 to 8-20, boundary-value problems, 6-23 to 6-24 8-35 to 8-36, 26-5, 26-11 compression, See Compressive loading Longitudinal structure index (LSI), 7-6 derivatives and gradients, 6-21 Low-frequency vibrations, 34-18 to 34-19 displacement vector, 6-20 LWX model, 12-9 to 12-10 elastic modulus, See Elastic modulus Lymphatics, 21-7, 22-3 equilibrium, 6-4 Lymphocytes, 21-11 force, 6-2 Lyophilization, 20-13 matrices, 6-5 to 6-8 Lysyl oxidase, 13-3 multiaxial loading, 6-12 to 6-13 orthotropic elasticity theory, 6-22 to 6-24 primary laws of, 6-1 to 6-2 M strain-displacement relations, 6-22, 6-23 strains, 6-8 to 6-9, See Strain Macaque, 8-20, 8-31 stresses, 6-4 to 6-8, 6-16 to 6-19, See also specific parameters Macrophage colony-stimulating factor (M-CSF), 1-13, 2-8 axial loading, 6-18 to 6-19 Magnesium, 5-1, 5-10, 5-12 centric compression, 6-17, See also Compressive loading Magnetic resonance imaging (MRI, NMR), 5-7, 9-2 equilibrium equations, 6-22 to 6-24 high-resolution MRI, 34-18 pure bending, 6-17 to 6-18, See also Bending micro-MRI, 9-6, 10-13 torsion, 6-19, See also Torsion osteoporosis applications, 9-15 tension, See Tensile loading signal-to-noise ratio, 9-6 testing methods for bones, See Biomechanical testing spatial resolution, 9-3 methods Malnutrition, 1-55 torsion, See Torsion Marble porosity, 23-17 translation, rotation, and deformation, 6-19 to 6-22 9117_frame_index Page 14 Monday, February 5, 2001 11:51 AM

I-14 Bone Mechanics

vectors, 6-2 to 6-3, 6-7 Mineralization, 1-18, 5-1 to 5-21, 10-2 to 10-3, 19-4, 28-3, See Mechanoelectricity, 24-1, See Strain-generated potentials; also Bone formation; Bone mineral; Streaming potentials Hydroxyapatite Mechanoreception, 29-1 age-related hypermineralization, 19-12 Mechanosensation, 28-1 to 28-12, 29-1 to 29-9, See also bone age and, 19-4 Interstitial fluid flow; Mechanotransduction; bone development, 5-21 Strain-generated potentials bulk modulus, 23-18 cellular network, 28-2 to 28-9, 29-2 to 29-8, See also collagen cross-links, 13-3 Lacuno-canalicular system; Osteocytes collagen knockout and, 5-19 to 5-20 cell-cell communication, 29-7 control of, 1-20 cyto-matrix sensation-transduction processes, 29-5 cortical and cancellous bone comparison, 10-4 fluid flow and, 23-2, 29-5, See Interstitial fluid flow crystal formation chemistry, 5-13 to 5-14 network integrity, 28-9 crystal size regulation, 5-20 to 5-21 remodeling model, 28-9 to 28-12 extracellular matrix vesicles (ECMVs), 5-15 comparison of bone and non-osseous processes, 29-6 factors controlling initial deposition, 5-14 to 5-20 future research problems, 29-9 animals with genetic defects, 5-19 to 5-20 mechanism in bone, 28-5 to 28-6 cell culture studies, 5-18 to 5-19 mechanostat system, 1-35 to 1-36 cell-free solution studies, 5-17 to 5-18 uniqueness of osseous system, 29-6 collagen template, 5-14, 5-16 to 5-17 second messengers and, 28-8 to 28-9, 29-7, 29-8 ion concentrations, 5-14 to 5-15 streaming potentials and, 28-5, 29-5 to 29-6, See also noncollagenous proteins as regulators, 5-17 to 5-20 Streaming potentials removal of mineralization inhibitors, 5-15 to 5-16 Mechanostat system, 1-35 to 1-36 gene expression, 5-18 Mechanotransduction, 22-16 to 22-17, 26-18 to 26-20, 29-1, mechanical consequences of changes, 13-6 to 13-8 29-4 to 29-8, 31-5, See also Mechanosensation mechanical effects of cell death and, 20-3 to 20-4 bone replacement scaffold applications, 36-12 nucleation process, 5-13 to 5-14 cellular network, See under Mechanosensation osteoblast function, 2-2, 2-3 to 2-4 electromechanical effects (streaming potentials/SGPs), osteogenesis imperfecta model, 13-4 22-17, 26-20, 29-5 to 29-6, See Strain-generated pathological models, 13-2, See also Osteopetrosis; potentials; Streaming potentials Osteoporosis exogenous electric field strength, 29-6 remodeling cycle, 1-31 fluid flow and, 22-17, 26-20, 29-5 shielding from fluid phase, 22-15 lacuno-canalicular network integrity and, 28-9, See also Mineralization front, 1-18 Lacuno-canalicular system Minimum effective strain (MES), 1-25, 1-35 noninvasive experimental methods, 26-15 Minipigs, 7-25 signal processing and integration, 29-7 to 29-8 Mixture theory approach, 23-7 to 23-10 steps, 28-2 MMMP-9, 5-15 stretch- and voltage-activated ion channels, 29-4 to 29-5 Modeling, 1-25 to 1-27, See also Bone formation; Bone tentative synthesis, 29-8 regeneration; Remodeling Medical Device Directives, 35-1 animal loading adaptation model, 1-46 Medullary blood supply, 21-4, 21-5, 22-6 comparison with remodeling, 1-25 intramedullary pressure (IMP), 21-16, 21-17, 22-12 linear elasticity formulation, 31-7 Mesenchymal stem cells, 2-6 long-term adaptation, 26-17 to 26-18 Metal biomaterials, 35-2 to 35-3 threshold, 1-25, 1-27 Metalloproteinases, 5-15 Utah paradigm, 1-36 Metals, viscoelasticity of, 11-12 Modulation transfer function (MTF), 9-3 Metaphyseal arteries, 21-2, 21-3 Modulus-dependent trabecular bone strength asymmetry, 16-8 Methanol, 20-18 Mohr’s circles, 30-10 Meyer, G. H., 30-2 to 30-3 Molecular biology techniques, 3-1 to 3-14, See Gene expression, Microchip technology (DNA chip), 3-10 measurement techniques Microcomputed tomography (micro-CT), 7-4, 9-4 to 9-5, 9-9 Moment of inertia, cross-sectional, 7-3 to 7-5 to 9-13, 10-13 to 10-14, 34-17 to 34-18 Monkey models, 7-25 bone atrophy simulation, 9-16 osteoporosis, 5-13 bone formation rate measurement, 9-17 strain measurement results, mastication and brachiation, comparison with conventional histomorphometry, 9-12 8-20 to 8-21, 8-31 to 8-32 small animal models, 9-13 Monocytes, differentiation into osteoclasts, 2-8 Microcracks, 17-1 to 17-2, 17-9, See Bone damage Morphology of bone, See Bone structure and morphology age effects, 17-10, 19-4 Mouse models, 7-24, See also Transgenic mouse models cement lines and, 17-9 biomechanical testing, 7-24 mechanical testing, 17-10 to 17-13 bone-in-spleen model, 26-3 post-yield mechanical behavior, 16-27 to 16-32, 17-2 externally-induced mechanostimulation studies, 26-15 quantification, 17-8 to 17-9, 17-13 gene deletion, See Knockout models Microfilaments, 22-10 gene-targeted models for noncollagenous proteins, 13-9 to Micro-finite element models, elastic constant assessment, 15-7 13-11 to 15-8, 15-12, 15-17 to 15-19 mineralization defects, 13-8 Microgravity conditions, 26-4 osteogenesis imperfecta, 13-4 to 13-6 Microindentation, 7-20, 10-5, 10-11 transgenic, See Transgenic mouse models Micro-MRI, 9-6, 10-13 Mov13 mouse, 13-6 Microperoxidase, 23-5 Muscle contraction, as bone load, 29-4, 33-3 to 33-4 Microsphere technique, 21-17 Muscle fiber loss, 26-7 Microtubules, 22-10 Muscle mass, age-related bone loss and, 1-54 Middle-ear implants, 35-13 Myloperoxidase, 3-9 9117_frame_index Page 15 Monday, February 5, 2001 11:51 AM

Index I-15

cell dynamics model for functional adaptation of bone, N 21-12 to 31-16 Nanoindentation, 7-20 cultures, 2-15 cortical bone, 10-5 to 10-7, 10-12 to 10-13 differentiation, 1-21 to 1-22, 1-24, 2-6 to 2-7, 28-2 to 28-3 fetal bone, 19-5 glucocorticoids and, 2-10 to 2-11 Narwhal tusk, 12-13 estrogen-androgen receptors, 2-11 Navier-Stokes (N-S) equation, 21-13 function, 1-18 to 1-21, 2-2 Necrosis, 20-3 genes, 2-7 necrotic bone in living organisms, 20-4 hydraulic conductivity, 22-13 Nerve system, 1-8 to 1-9, 21-8 in vitro mechanosensory model, 28-6 to 28-9 Neural network, 29-7 in vitro methods and growth, 28-6 to 28-7 Neutron activation analysis, 5-3 life cycle, 1-15 to 1-17, 2-6 to 2-8 Neutrophils, 21-11, 21-12 lining cell development and, 1-22, 2-5 Newtonian laws, 6-1 to 6-2 matrix synthesis and secretion, 2-2 to 2-3 NF-KB1, 4-10 mechanosensation function, 29-3, 29-4 NF-KB2, 4-10 mineralization and, 2-2, 2-3 to 2-4 Nitric oxide (NO), 21-10, 21-12, 26-20, 28-8, 29-4 morphology, 2-2 NMR, 5-7, See Magnetic resonance imaging neuronal control, 21-8 NMR microscopy, 9-6 osteoclast development, 1-21 to 1-22, 28-5 Noggin, 2-7 phenotypic markers, 1-15, 1-17 to 1-18 Noncollagenous proteins, 1-7, 1-19 to 1-20, 1-21, 13-8 to 13-11, polarity, 2-2 See also specific proteins receptors, 1-15 function, 1-21 regulation of, 1-17, 2-7 to 2-8 gene-targeted models, 13-9 to 13-11 signal processing and integration, 29-7 to 29-8 knockout models, 4-7, 4-10, 4-13, 5-20, 13-10 to 13-11 Osteocalcin, 1-7, 1-15, 1-17, 1-21, 2-3, 2-4 mineral deposition and, 5-16, 5-17 to 5-20 knockout model, 4-7, 4-10, 5-20, 13-10 mineral interfacial bonding, 13-8 to 13-9 mineral deposition and, 5-16, 5-17, 5-18 Nonhuman primate models, 1-48, 1-49, 7-25 Osteoclast activating factor, 2-13 strain measurement results, mastication and brachiation, Osteoclast differentiation factor (ODF-OPG-L), 1-13, 1-22, 2-8, 8-20 to 8-21, 8-31 to 8-32 See also RANKL Noninvasive measurement methods, 34-1 to 34-20, See Imaging Osteoclastogenesis inhibiting factor (OCIF-OPG), 1-13, 1-22 methods; specific techniques Osteoclasts, 1-9, 1-11 to 1-15, 2-1, 2-5 to 2-6, 28-2 Non-Newtonian fluid, 21-2, 21-14, 25-5, 25-14 apoptosis, 1-13, 2-9 NONSYS, 31-17 cell dynamics model for functional adaptation of bone, Norepinephrine (noradrenaline), 21-9, 21-10 21-12 to 31-16 Normal gaitloading cycle time course, 31-4 defects, 2-6, See also Osteopetrosis Northern blotting, 3-2 to 3-3 differentiation, 2-8 Nuclear magnetic resonance (NMR), 5-7, See Magnetic function, 1-14 to 1-15, See also Resorption resonance imaging hormonal control, 1-12 to 1-15, 2-8, 2-10 Nucleation process, 5-13 to 5-14 integrins and cytoskeleton, 2-6 Nutrient arteries, 21-2, 21-3, 21-7 to 21-8 lineage, 2-8 to 2-9 Nutrition markers and receptors, 1-12, 1-15 age-related bone loss and, 1-55 matrix degradation, 2-6 bone mineral properties and, 5-10 to 5-11 mineral dissolution, 2-5 to 2-6 deficiencies, 1-53 morphology, 2-5 noncollagenous proteins and, 5-21, 13-10 origin, 1-21 to 1-22 O osteoblast/osteocyte-mediated control, 1-15, 26-16, 28-5, α 28-9 to 28-12 1 ,25(OH)2, 1-13, 1-15 Octahedaral shear stress, 32-7 remodeling cycle and, 1-29 to 1-31 oim-oim mouse, 13-4 Osteocytes, 1-23 to 1-24, 2-1, 2-4, 28-3, 29-2, See also Canaliculi; Ontogenetic changes, See under Skeletal development Lacuno-canalicular system Optimization models of functional adaptation, 31-6, 31-18 to age-related loss, 2-4 31-21, 31-37 apoptosis, 1-24, 1-55, 2-4, 26-16, 28-10 Organ culture, 2-14 avian ulna model, 26-18 Orthotropic elasticity theory, 6-22 to 6-24 cell culture considerations, 28-6 to 28-7 Orthotropy, 6-2, 6-11, See also Anisotropy cytoskeleton structure, 22-10 assumptions for mineralized collagen, 12-6, 12-9 function, 1-24, 2-4 bone damage model, 18-5 mechanosensitivity/mechanotransduction model, 28-4 to cancellous bone assumptions, 15-9 to 15-10, 15-12 28-9, 29-2 to 29-8, See also Mechanosensation, Hooke’s law for, 6-13 to 6-14 cellular network Oscillating flow, in vitro cellular response, 28-8 to 28-9 molecular transport mechanisms, 22-6 to 22-10, 22-14 Osmotic pressure, 22-13 morphology, 2-4 Osteoadhedrin, 1-21 origin and fate, 1-24 Osteoarthritis, 7-25 to 7-26, 26-2 osmotic pump, 22-13 indentation testing, 7-17 osteoclast function and, 1-15, 26-16, 28-5, 28-9 to 28-12 Osteoblast stimulating factor-1, 4-8 spatial influence function model for trabecular bone Osteoblasts, 1-9, 1-15 to 1-22, 2-1, 2-2 to 2-4, 10-2, 28-2, 29-2 remodeling, 31-32 to 31-34 apoptosis, 2-8 surrounding bone structure, 1-5, See Canaliculi; Lacunae blood-bone barrier and, 21-9, 21-21 transport-based remodeling model, 22-18 to 22-19 9117_frame_index Page 16 Monday, February 5, 2001 11:51 AM

I-16 Bone Mechanics

Osteogenesis imperfecta, 3-13, 5-12, 5-16, 5-19, 12-3, 13-4 to 13-6 P similarities to irradiation effects, 20-17 to 20-18 Paget’s disease, 5-12 Osteogenic index (OI), 32-8 Parathyroid hormone (PTH) Osteoid, 1-9, 1-15, 1-24, 2-2, 5-21 apoptosis regulation, 2-8 cement lines and, 23-5 bone blood circulation and, 21-9 Osteoid seam, 1-18, 1-31 bone formation-resorption stimulation, 2-10 Osteomalacia, 5-10, 12-3 hydraulic conductivity, 22-13 Osteonal bone envelope, 31-4 osteoblast receptors, 1-15 Osteonal canals, See Haversian canals osteoclast regulation, 1-12, 1-13, 1-15, 2-8, 2-10 Osteonectin, 1-7, 1-20, 1-21, 2-3 osteoporosis treatment issues, 7-25 knockout model, 5-20 receptor knockout model, 4-10 mineral deposition and, 5-16, 5-17, 5-18 receptors, 2-9 to 2-10 transgenic model, 13-10 resorption and, 2-5 Osteons, 1-5, 1-10, 10-2, 10-3, 19-2 to 19-3, 23-4 transgenic model, 4-8 age-related mineral differences, 5-9 Partial ossicular replacement prostheses (PORPs), 35-13 biomechanical micro- and nanotesting, 7-20 Partial volume artifacts, 9-4 blood supply, 21-6 Pauwels, Friedrich, 32-4, 32-9 collagen orientation, 7-5 to 7-6 PB model, 12-9 to 12-10 composite models, 12-1 Perfect damage modulus, 17-5 to 17-6 convective flow model, 23-10 Periosteal blood vessels, 1-7, 21-1, 21-2, 21-7 to 21-8, 21-15, FTIR microspectroscopy, 5-4, 5-5 22-3 intramembranous ossification process, 1-24 Periosteal bone envelope, 31-4 microstructural and mechanical analysis, 10-7, 12-8 to Periosteal fibroblasts, mechanosensitivity, 28-7 to 28-8, 29-4 12-13 Periosteum, 1-3, 23-4 microstructure and viscoelastic properties, 11-11 Peripheral quantitative computed tomography (pQCT), 7-4, mineralization density gradient, 19-4 9-4, 9-7, 9-16 porosity microstructure, 23-3 to 23-4 Permeability, 25-1 to 25-15, See also Porosity pressure gradients, 22-14 cancellous bone, 25-9 to 25-12 strain-generated potentials and, 23-22 to 23-23, 24-9 to fluid channel shape, 25-10 24-16 porosity range, 25-9 to 25-10 Osteopenia, 12-3, See Bone loss previous investigations, 25-10 to 25-12 diabetic, AGE products and, 13-4 specimen size, 25-10 disuse conditions, 26-3 to 26-10, See also under Bone loss Darcy’s law, 25-2 to 25-3 disuse remodeling mode, 1-32 lower limit, 25-5 seasonal, 26-5, 26-17 upper limits, 25-4 to 25-5 Osteopetrosis, 1-21, 5-12, 5-20, 7-6 drag theories, 25-7 to 25-9 transgenic mice models, 4-7 Osteopontin, 1-7, 1-14, 1-20, 1-21, 2-3, 3-9 experimental guidelines, 25-5 to 25-6 apatite nucleation, 5-16, 5-17, 5-18 hydraulic radius-based theories, 25-6 to 25-7, 25-10 knockout models, 4-7, 4-10, 13-10 linseed oil measurements, 25-12 Osteoporosis, 1-47 to 1-49, 9-1, 26-3 non-laminar 25-5 animal models, 1-48 to 1-49 prosthesis design considerations, 25-1 bone mineral properties, 5-12 Reynolds number and, 25-4 to 25-5, 25-9 treatment effects, 5-13 theories, 25-6 to 25-9 cause, 1-47 units, 25-4 collagen cross-links and biomechanical properties, 13-2 to viscosity, 25-13 to 25-15 13-3 pH effects, 5-15 data set for cancellous bone elastic constants, 15-10 to 15-11 Phenomenological models of functional adaptation, 31-9 to definitions and classifications, 1-47 31-13, 31-16 to 31-18, 31-6, 31-37 exercise effects on bone mass, 26-4 to 26-5 Phosphorus and phosphate fracture sites, 9-6 bone mechanical properties and, 13-7 to 13-8 genetic factors, 1-48 cortical and cancellous bone composition, 10-4 imaging applications, 9-15 to 9-16 32P labeling, 3-2, 3-5 muscle fiber loss, 26-7 33P labeling, 3-5 postmenopausal, 1-47 streaming potentials and, 24-14 prevention and treatment, 1-48, 1-49 trans-interfacial transport, 23-5 Singh index, 9-1 Piezoelectric coupling, viscoelasticity and, 11-11 spine deformity index, 33-18 Piezoelectric effects, 22-12, 24-1, 24-7 transgenic models, 4-7 Piezoelectric tensor, 24-2 to 24-3 treatment evaluation Piezoelectric transducers, 7-21, 10-5 animal model, 7-24 to 7-25 Pig models, 1-45, 7-25, 19-13 biomechanical tests, 7-16 bone scaffolding, 36-9 to 36-11 Osteoprotegerin (OPG), 1-13, 2-8, 5-21 functional adaptation to induced overloading, 26-12 knockout model, 4-7, 410 strain measurement results, 8-17, 8-30 ligand (OPG-L), 1-13, 4-10 Pigeon flight model, 8-25, 8-33 transgenic overexpression model, 4-8 Plain radiographic textural and pattern analyses, 34-19 Ostwald viscometer, 25-14 Plakoglobin, 2-14 Ovariectomized animal models, 1-49, 5-13, 7-25 Plastic modulus Owl monkey, 8-21, 8-31 freeze-drying effects, 20-13 Oxygen metabolism, 21-19 irradiation effects, 20-15 Oxyhydroxyapatite, 36-9 Plasticity model of bone damage, 18-8 to 18-11 9117_frame_index Page 17 Monday, February 5, 2001 11:51 AM

Index I-17

Plate and rod models, for calculating structural indices, 9-10, porosities, 23-6 to 23-7 9-12 permeability measurement problems, 25-9 to 25-10 Platelet-derived growth factors (PDGFs), 1-19, 1-20, 2-7, 2-12 pore sizes, 23-18 fracture healing and, 32-2 Skempton pore pressure coefficient, 23-13 Platelets, 21-11 strain-generated potentials and, 28-5 to 28-6 Platen loading system, 27-4 to 27-5 viscoelasticity and, 11-11, See also Poroelasticity Plexiform bone, 19-2 Porous media, 25-1, See Permeability; Porosity Poiseuille equation, 21-14 Positron emission scattering, 5-8 Poisson’s ratio, 6-11 Positron emission tomography (PET), 21-16, 21-19 bone volume fraction and, 15-14 Postmenopausal bone loss, 1-51, 9-15 to 9-16 cancellous bone elastic constants and, 15-7, 15-18, 15-19 Postmortem bone changes, 20-1, 20-2 to 20-5, See also Bone effective isotropic elastic constants, 23-17 preservation effects elastic modulus calculation for cortical bone, 10-6 necrotic bone in living organisms, 20-4 Poke stimuli, 27-4 non-preserved bones, 20-3 to 20-5 Polar bears, 19-12 to 19-13 preservation effects, 20-2 to 20-3, See Bone preservation Polar moment of inertia, 7-4 effects Polyacetal, polyetheretherketone (PEEK), 35-4 Post-yield mechanical behavior, trabecular bone, 16-27 to 16-30 Polyester, 35-4 Post-yield region, 7-8 Polyethylene, 35-4, 35-8 Pregnancy effects, 19-8 to 19-9 Polyglycolic acid polymers, 36-1, 36-6 to 36-7 Preosteoblasts, 1-18 Polylactic polymers, 36-1, 36-6 Preosteoclasts, 1-8 Polymerase chain reaction (PCR), 3-3 to 3-5, 4-2 Pre-osteoprogenitor cells, 21-7 Polymers, 35-4 to 35-5 Preservation effects, See Bone preservation effects scaffold materials, 36-1, 36-6 to 36-8 Pre-yield region, 7-8 viscoelastic properties, 11-12 Procion red, 23-5 Polymethyl methacrylate (PMMA), 8-5, 25-1, 35-4, 35-8 Prostacyclin (PGI2), 21-9, 21-10, 21-12 Polytetra fluoroethylene (PTFE), 8-5, 35-4 Prostaglandin G-H synthase (PGHS), 2-11 Pore size, 23-18 Prostaglandin synthetase inhibitors, 26-20 bone replacement scaffolds, 36-2 Prostaglandins, 26-20 Pore volume fraction, 23-11 mechanoadaptive cell signaling, 28-7, 28-8 Poroelasticity, 11-11, 22-11 to 22-12 PGE , 1-13, 2-11, 28-7 anisotropy effects, 23-12 2 antiapoptotic effects, 1-17 Biot’s theory, 22-11, 23-11 osteoclastogenesis stimulation, 2-8 bone regeneration around implants, 32-10 PGI (prostacyclin), 21-9, 21-10, 21-12, 28-7 constitutive equations, 23-11 to 23-14 2 receptors, 2-11 drained vs. undrained elastic moduli, 23-13 Prostheses, 35-1 to 35-2, See also Implants; Bone replacement effective medium approach, 23-7, 23-8, 23-10, 23-19 scaffolding elastic wave propagation, 23-19 associated bone loss, 26-10 finite-element models, 23-16 damage accumulation, 35-10 homogenization derivations, 23-10 design, 35-5 to 35-14 ideal, 23-11 ideal, field equations, 23-14 to 23-16 ankle replacement, 35-12 microstructure, 23-3 to 23-7, See also under Porosity bone fixation systems, 35-6 to 35-7 mixture theory approach, 23-7 to 23-10 bone substitute materials, 35-8 notation, 23-2 to 23-3, 23-11 to 23-12 elbow replacement, 35-11 to 35-12 parameter values, 23-16 to 23-18 hip replacement, 35-8 to 35-10 peak fluid pressure, 23-20 knee replacement, 35-10 to 35-11 representative volume element, 23-7, 23-8 permanent for total joint arthroplasty, 35-8 to 35-12 single-porosity model applications, 23-18 to 23-19 permeability considerations, 25-1 solution methods for equations, 23-16 shoulder replacement, 35-11 strain-generated potentials, 23-1, 23-21 to 23-24 temporary and resorbable, 35-6 to 35-8 strain magnitude and Eulerian vs. Lagrangian approaches, wrist replacement, 35-12 23-9 material biocompatibility, 35-2 thermodynamical approach, 23-10, 23-12 radiographic assessment, 35-17 thermoelasticity, 23-16 retrieval analysis, 35-18 two-porosity model, 23-19 to 23-20, 23-23 simulators, 35-16 Porosity, See also Permeability; Poroelasticity Protamine sulfate, 24-14 age and, 19-6 Protein S, 1-21 bone maturation and, 23-5 Proteoglycans, 5-15, 5-16, 5-17, 5-18, 22-2, 26-18, See also collagen-apatite porosity, 23-22, 23-4, 23-7, 23-18, 29-6 Noncollagenous proteins; specific glycans intracortical, 26-9 to 26-10, 26-21 Proteolytic enzymes, 2-6 lacunar-canalicular porosity, 23-4, 23-5, 23-6 to 23-7, 23-16 Proximal femur, loading and failure properties, 33-2 to 33-9, to 23-18, 23-20, 29-5 33-13 to 33-14, 33-16 to 33-17, 33-18 to 33-22 lacuno-canalicular mechanotransduction and, 28-9 P-selectin, 21-11 levels of, 22-2 Pseudoarthrosis, 31-8, 32-1 limiting dimensions for vascular and extravascular spaces, Pseudoplastic fluids, 25-14 22-4 to 22-5 Pulsatile fluid flow, osteocyte mechanosensitivity, 28-7 to 28-8, measurement, 7-5 29-3 to 29-4 microstructure, 23-3 to 23-7 Pycnodysostosis, 2-6 interfaces, 23-4 to 23-6 Pyridoxine, 13-3 osteon structure, 23-3 to 23-4 Pyrophosphate, 5-15 9117_frame_index Page 18 Monday, February 5, 2001 11:51 AM

I-18 Bone Mechanics

Q reversal (coupling), 1-31 damage-repair models, 18-22 to 18-23 Quality assurance, 7-26 to 7-28 equilibrium states, 31-3, 31-11, 31-27 archiving, 7-28 fracture healing phases, 32-2 experimental protocols, 7-26 free-boundary problem, 31-7 record keeping, 7-27 to 7-28 functional adaptation models, 31-1 to 31-38, See standard operating procedures, 7-26 to 7-27 Adaptation, theoretical models testing standards and data veriﬁcation, 7-27 implant site, 35-17 Quantitative computed tomography (QCT), 5-8, 34-4 mechanical modulation of bone repair, 26-20 to 26-25, See comparison with ultrasound density results, 34-11 to 34-12 also Bone repair cross-sectional moments of inertia measurement, 7-4 mechanosensation/mechanotransduction models, 22-14, femoral structural capacity model, 33-13, 33-20 28-9 to 28-12, 29-1 to 29-9, See also limitations of, 34-5 Mechanosensation; Mechanotransduction peripheral QCT (pQCT), 7-4, 9-4, 9-7, 9-16 mechanostat hypothesis, 1-35 spinal loading models, 33-22 to 33-24 microdamage repair, 1-54 vertebral fracture risk prediction, 33-13 to 33-16, 33-18 modeling comparison, 1-25 noncollagenous protein knockout models, 13-10 nutritional effects, 5-10 R simulated bone atrophy, 9-16 to 9-17 stimulus for, 29-3 Rabbit models, 7-25 strain remodeling potential, 31-12 to 31-16 functional adaptation to induced overloading, 26-12 time dependence, 31-4 to 31-5, 31-7 to 31-8 strain measurement results, mastication, 8-21, 8-32 transport-based theory, 22-18 to 22-19 Radiographic absorptiometry, 34-20 unifying theory, 1-33 Radiographic methods viscoelastic properties and, 11-4 bone geometry and bone integrity measurement, 34-20 Wolff’s biases, 30-4 CT, See Computed tomography Wolff’s law and computational modeling, 30-13 DEXA, See Dual-energy X-ray absorptiometry Remodeling-dependent bone gain, 1-33 energy dispersive X-ray microanalysis (EDAX), 5-3 Remodeling-dependent bone loss, 1-31, 1-34 plain radiographic absorptiometry, 34-20 Remodeling map, 1-32 plain radiographic textural and pattern analyses, 34-19 Remodeling space, 1-32 prosthesis assessment, 35-17 Renkin-Crone equation, 21-18, 21-21 QCT, See Quantitative computed tomography Representational differentiation analysis, 3-9 single-energy X-ray absorptiometry (SXA), 7-4, 34-3 to Representative volume element (RVE), 12-4 to 12-5, 23-7, 23-8, 34-4, 34-5 30-7, 30-9 small-angle X-ray scattering (SAXS), 5-8 Reptiles, 8-26 to 8-27, 8-33 Radiostereometry analysis, 35-17 Residual modulus, 16-29 Raman spectroscopy, 5-7, 13-9 Residual strain, 16-27 to 16-30, 17-8, 18-7, 18-8 RANKL, 1-14, 2-5, See also Osteoclast differentiation factor Resorption, 1-14 to 1-15, 2-5, See also Osteoclasts; Remodeling Rat models activation, 1-55 freeze-drying effects, 20-13 drifts, modeling and, 1-25 freezing effects, 20-6 formation coupling, 1-31 functional adaptation to induced overloading, 26-12 hormonal regulation, 2-10 immobilization, 1-37 intercellular communication mechanism for inhibition, mechanically induced microdamage model, 26-15 to 26-16 1-54 to 1-55 necrotic bone study, 20-4 lining cells and, 2-5 osteocyte-mediated remodeling responses, 28-11 osteoblast/osteocyte-mediated control, 1-15, 26-16, 28-5, osteoporosis, 1-48 to 1-49 28-9 to 28-12 skeletal loading, 1-41 to 1-47 stimulating agents, 2-5 strain measurement results, exercise, 8-21 to 8-22, 8-32 Resorption cavities, 1-11, 1-31, 22-2 trabecular bone loading and remodeling, 26-17 Retinoid receptors, 2-10 Record keeping, 7-27 to 7-28 Retrovirus-based gene transfer, 3-12 Red blood cells (RBCs), 21-10 Reuss ("isostress") model, 12-4, 12-6, 12-10 Regeneration, See Bone regeneration Reverse transcriptase-PCR, 3-3 to 3-5, 3-8 Regional acceleratory phenomenon (RAP), 1-37 Reynolds number (Re), 21-13, 25-4 to 25-5, 25-9 Rehydration, mechanical properties and, 7-2 RFEM3D, 31-12, 31-16, 31-24 to 31-26 Relaxation, 11-1, 11-2, 11-3 Rheopectic ﬂuids, 25-15 Remodeling, 1-27 to 1-28, 10-2, 19-4, See also Adaptation; Bone Rickets, 12-13, 13-8 formation; Bone regeneration; Bone repair; RNase protection assay, 3-6 to 3-7 Resorption Rock porosities, 23-17 activation frequency, 1-32, 1-34 Rod and plate models, 10-3 age-related defects, 19-12 Rooster model, 8-23 to 8-24, 8-33, 26-5, 26-11, 26-15 allograft bone and, 20-18 Rotated beam loading protocol, 7-18 to 7-19 apoptosis and, 2-4 Roux, W., 30-1 to 30-2, 30-4 to 30-5, 31-8 conservation and disuse modes, 1-32 to 1-33 Ruthenium red, 23-5 cycle (bone remodeling unit), 1-28 to 1-33, See also Bone formation; Mineralization; Resorption activation, 1-29 to 1-31 S bone turnover, 1-32 formation and mineralization, 1-31 Saline, bone storage effects, 20-3, 20-4 resorption, 1-31 Salt leaching, 36-6 to 36-7 resting, 1-28 Sandstone porosity, 23-17 9117_frame_index Page 19 Monday, February 5, 2001 11:51 AM

Index I-19

Scaffolds, See Bone replacement scaffolding Space flight, 26-4 Scientific Hip prosthesis (SHP), 35-9 Spatial influence function, 31-32 to 31-34 Screw pullout force, 20-7, 20-18 Spatial resolution, 9-2 to 9-3 Screws, 35-6, 36-3 Spectral decomposition method, 15-14 Seasonal osteopenia, 26-5, 26-17 Spectral modeling, 11-10 Secant modulus, 16-29, 17-5 to 17-7 Spinal fracture, 1-47 residual modulus and, 16-29 Spinal loading and failure properties, 33-5, 33-10 to 33-12, Secondary osteons, 10-2, 19-2 to 19-3, 23-5 33-14 to 33-16, 33-18, 33-22 to 33-25 mineralization density gradient, 19-4 osteoporosis fracture sites, 9-6 resorption control, 28-5 rat raised cage model, 1-45 Seepage velocity, 25-2, 25-9 Spine deformity index (SDI), 33-18 Selectins, 21-11 Spring constant, 6-10 to 6-11 Selective Laser Sintering (SLS), 36-7 src knockout, 5-20 Selenium deficiency, 5-10 Staining methods, microcrack evaluation, 17-8 to 17-9 Serial analysis of gene expression (SAGE), 3-9 to 3-10 Stainless steel, 35-2 Shear failure model, 12-15 Standard operating procedures, 7-26 to 7-27 Shear moduli, 6-11 Star volume method, 14-5, 14-10 bone volume fraction and, 15-14 Starling resistor, 21-16 Shear strain Stereological methods, cancellous bone architecture calculation from strain gauge measurements, 8-8 to 8-9 quantification, 14-2 measurement results, various animals and activities, 8-10, connectivity, 14-5 to 14-6 8-12 to 8-21, 8-23, 8-25 to 8-26, 8-30 to 8-33, See star volume, 14-5 also Strain gauge measurements and methods surface density, 14-3 to 14-4, 14-7 Shear strength, trabecular bone, 16-5 volume fraction, 14-2 to 14-3, 14-7, 15-2, 15-13, 15-14 Shear stress, 6-5, See also Torsion Sterilization, 20-3, 20-13 to 20-20, See Allografts, bone bone regeneration models, 32-4 to 32-5, 32-7 treatment effects in vitro mechanostimulus systems, 27-12 to 27-16 Steroid receptors, 2-10 microcirculation control and, 21-12 Stiffness, See also specific measures osteocyte mechanosensation/transduction process, 29-5 degradation, measurement of, 17-5 to 17-7 remodeling stimulus, 29-3 intrinsic and extrinsic, 7-9, 7-13 torsion testing, 7-15 to 7-16 mechanical testing outcome measures, 7-6 to 7-7 torsional model of damage accumulation, 18-17 tensor, cancellous bone elastic constant assessment and, Tsai-Wu criterion and trabecular bone strength, 16-24 15-3 to 15-4, 15-6, 15-9, 15-18 Shear testing, 7-17 to 7-18 Strain, See also Elastic modulus; Poisson’s ratio; Young’s Shear thickening, 25-15 modulus; specific measures Sheep models, 1-45, 7-25, 8-10, 8-12 to 8-14, 8-29, 19-10, 20-10 bending calculations, 7-12 to 7-13 Shoulder replacement prosthesis, 35-11 dynamic strain similarity, 26-10 Signal transduction, See Mechanotransduction energy per unit volume, 6-15 Silicone rubber, 8-3 fading memory concept, 31-5 Singh index, 9-1, 34-19 fatigue damage models, 18-12 to 18-15 Single-energy X-ray absorptiometry (SXA), 34-3 to 34-4, 34-5 fracture gaps and, 26-23 Single photon X-ray absorptiometry, 7-4 inelasticity and bone damage, 17-2 to 17-3 Skeletal development, 1-24 to 1-33, See also Bone formation interfragmentary theory, 26-24, 32-3, 32-6 to 32-7, 32-9 functional adaptation, See Adaptation interspecies variation, 26-10 modeling, 1-25 to 1-27, See also Modeling matrix, 6-8 ontogenetic changes, 19-1 to 19-14 measurement, 7-10, 8-1 to 8-37, See Biomechanical testing adaptive changes, 19-9 to 19-11, See also Adaptation methods; Strain gauge measurements and adaptivity of youthful changes, 19-9 to 19-11 methods animal models, 19-10 to 19-14 measures for modeling signaling for adaptive response, 31-3 causes of mechanical decline, 19-11 to 19-12 mechanosensation, 28-2, 28-5, See Mechanosensation fetal bone, 19-5 mechanostat, 1-35 histology, 19-11 mechanotransductive role, 22-16 to 22-17 locomotory efficiency, 19-9 to 19-10 multiaxial loading, 6-12 to 6-13 maturation and aging, 19-5 to 19-8 remodeling stimulus, 29-3 mechanical properties, 19-4 to 19-9 residual, 16-27 to 16-30, 17-8, 18-7, 18-8 mineralization, 19-4 translation, rotation, and deformation, 6-19 to 6-22 pregnancy and lactation, 19-8 to 19-9 viscoelastic properties, 11-1, See also Viscoelasticity primary bone development, 19-1 to 19-4, See also Bone Voigt model, 12-4, 12-6, 12-10 formation Strain-displacement relations, 6-22, 6-23 remodeling, 19-4 Strain energy, remodeling stimulus, 29-3 whole-bone behavior, 19-12 to 19-14 Strain energy density, 31-3, 31-16 to 31-18, 31-29 to 31-31, remodeling, 1-27 to 1-28, See also Remodeling 31-34, 31-37 Skeletal subdivisions, 1-2 Strain equivalence principle, 18-4 Skempton pore pressure coefficient, 23-13 Strain gauge measurements and methods, 8-1 to 8-37, 26-2, Skull, fetal, 19-5 26-26, See also Biomechanical testing methods Skull, neonatal deformability, 11-4 alternative in vivo techniques, 8-34 Sliding filament model, 30-1 to 30-2, 30-13, 30-14 attachment to bone, 8-4 to 8-5 Sloppy hinges, 35-12 avian activities, 8-22 to 8-24, 8-32 to 8-33, 26-5, 26-11 SMAD, 2-11 bat flight, 8-24 to 8-25, 8-33 Small-angle X-ray scattering (SAXS), 5-8 bonded resistance gauge development, 8-2 Smoluchowski equation, 24-5 to 24-7 bone site selection/preparation, 8-4 Solid free-form fabrication (SFF), 36-7 to 36-9, 36-11 complicating factors, 8-2 9117_frame_index Page 20 Monday, February 5, 2001 11:51 AM

I-20 Bone Mechanics

daily strain history quantification, 8-33 to 8-34 piezoelectric tensor, 24-2 to 24-3 data collection, 8-7 remodeling-associated cellular signaling, 22-14 dummy gauges, 8-7 reverse piezoelectric measurement, 24-3 to 24-4 early bone studies, 8-2 sign reversal, 24-7 to 24-8 external loading systems, 26-14 Smoluchowski equation, 24-5 to 24-6 fish strikes, 8-21, 8-32 stressed wet bone measurements, 24-5 human gait, 8-10 to 8-12, 8-29 summary of early data, 24-7 to 24-9 implant evaluation methods, 35-16 viscosity and conductivity relationship, 24-5 to 24-7 interspecies similarities, 8-35 Wolff’s law and, 24-1, 24-2 large mammal and canine gait, 8-10, 8-12 to 8-20, 8-29 to zeta potential, 24-8 8-31 Strength optimization, 31-20 to 31-21 nonhuman primate mastication and brachiation, 8-20 to Stress, 6-4 to 6-8, 6-16 to 6-19, See also Shear stress; specific 8-21, 8-31 to 8-32 measures normal and shear strain calculation, 8-8 to 8-9 axial loading, 6-18 to 6-19 principal strain calculation, 8-8 bending calculations, 7-12 to 7-13 rat exercise, 8-21 to 8-22, 8-32 centric compression, 6-17, See also Compressive loading reptile locomotion, 8-26 to 8-27, 8-33 deformation pressure model for bone regeneration, 32-7 to selected in vivo results, 8-10 to 8-34 32-8 strain history studies, 8-33 to 8-34 equilibrium equations, 6-22 to 6-24 telemetry methods, 8-6 modeling signaling for adaptive response, 31-3 types of gauges, 8-2 to 8-3 normal, 6-4 to 6-5 verification of function, 8-6 to 8-7 pure bending, 6-17 to 6-18, See also Bending waterproofing, 8-2 to 8-3 Reuss ("isostress") model, 12-4, 12-6, 12-10 wiring and strain relief, 8-5 to 8-6 state variable model for damage accumulation, 18-4 zero strain, 8-7, 8-8 torsion, 6-19, See also Torsion Strain-generated potentials (SGPs), 22-17, 22-12, 23-21, 24-14, units of, 6-4 28-5, 31-5, See also Streaming potentials viscoelastic properties, 11-1, See also Viscoelasticity cell-to-cell communication, 29-7 Stress fibers, 21-6, 21-12 glycocalyx and, 29-6 Stress matrix, 6-5 to 6-7 in vitro measurement, 22-15 Stress relaxation, 11-2 location, 22-13, 22-14, 23-22 to 23-23, 24-14 to 24-19, 28-5 Stress shielding, 31-18, 31-19 to 28-6, 29-5 to 29-6, 31-5 implant design issues, 35-10 osteonal experiments, 23-23 Stress-strain curve, 7-7 to 7-8 poroelasticity and, 23-21 to 23-24 bone damage accumulation and, 17-2 to 17-4 two-porosity model and, 23-23 viscoelasticity and, 11-6 Strain history, strain gauge studies, 8-33 to 8-34 Stress-strain relations, 6-14, 6-23 Strain localization tensor, 15-9 Stress trajectories, Wolff’s theory and trabecular architecture, Strain measurement transducer, 7-8 30-1 to 30-14, See Wolff’s law Strain protection bone loss, 26-7 to 26-9, 26-21 Stress vectors, 6-7 Strain rate, 31-3 Stretch-activated ion channels, 29-4 to 29-5 bone damage relationship, 16-32 Stretch testing systems bone strength and, 11-8 axisymmetric distension, 27-8 to 27-12 cancellous bone elastic properties and, 15-3 combined shear stress mechanostimulus system, 27-15 to fracture healing relationship, 26-22, 32-3 27-16 measurement results, various animals and activities, 8-10, longitudinal distension, 27-6 to 27-7 8-12 to 8-33, See also Strain gauge measurements Stretched exponential (KWW) model, 11-6, 11-8, 11-9 to 11-10 and methods Strontium-to-calcium ratio, 5-10 mechanical properties and, 7-2 Structural model index (SMI), 9-11 to 9-12, 14-14 remodeling stimulus, 29-3 Structure, See Bone structure and morphology strain energy density, 31-3, 31-16 to 31-18, 31-29 to 31-31, Subtractive hybridization, 3-9 31-34, 31-37 Sulfur-35 (35S) labeling, 3-5 trabecular bone strength and, 16-32 Surface density approach, cancellous bone architecture viscoelastic properties and, 11-3 quantification, 14-3 to 14-4, 14-7 Strain remodeling potential, 31-12 to 31-16 Surgical remedies, animal models, 7-26 Strain-stress relations, 6-14, 6-23 Swimming, 1-45 Streaming potentials, 22-12 to 22-13, 22-17, 23-1 to 23-19, Synchrotron-CT, 9-5 to 9-6, 9-13 to 9-14, 9-17, 9-18, 10-13 23-21, 24-14 to 24-19, 26-20, 28-5, 29-5 to 29-6, See also Stress-generated potentials bone morphology relationship, 24-9 T canalicular wall permeability and, 24-18 drag force model, 24-18 to 24-19 Tartrate-resistant acid phosphatase, 4-10 dry bone piezoelectric measurements, 24-2 to 24-3 Temperature effects in vitro microelectrode studies, 24-9 to 24-12 bone mechanical properties and, 7-2, 20-5 in vitro models, 24-14 to 24-17 thermal sterilization, 20-19 to 20-20 in vivo data, 24-13 to 24-14 viscoelasticity and, 11-5 in vivo theory development, 24-17 to 24-19 Tenascin-C, 1-21 location, 22-13, 22-14, 23-22 to 23-23, 24-14 to 24-19, 28-5 Tendon, 13-2 to 28-6, 29-5 to 29-6, 31-5 Tensile loading, 6-9 to 6-11, 7-9 measurements, transition from dry to wet bone, 24-2 to bone damage histology, 17-12, 17-14 24-6 cancellous bone, 10-8 to 10-11, 15-6, 15-19 noncellular phenomena, 24-8 damage accumulation, 17-2 to 17-5 oscillations, 24-14 elastic model of bone damage, 18-5 to 18-7 9117_frame_index Page 21 Monday, February 5, 2001 11:51 AM

Index I-21

hanging-drop technique, 27-2 boundary element implementation, 31-34 in vitro mechanostimulation, 27-2 finite element model for damage accumulation, 18-20 microtesting, 7-20 heterogeneity, 16-2 strain measurement results, various animals and activities, mechanical testing considerations, 10-10 8-10, 8-12 to 8-15, 8-17 to 8-21, 8-23 to 8-26, 8-29 quantification, 14-1 to 14-17, See also Cancellous bone to 8-33, See also Strain gauge measurements and architecture, quantification of methods redundant trabeculae, 14-5 tissue formation model for bone repair, 26-24 vertebral fracture risk and, 33-16 yield stress calculation, 12-15 Wolff’s stress trajectories theory, 30-1 to 30-14, See Wolff’s Tensile strength, 12-15 to 12-16 law age and, 19-6, 19-7 Trabecular bone, See Cancellous bone compressive strength for trabecular bone, 16-8 to 16-9 envelope, 31-4 deer development model, 19-11 pattern factor, 14-16 embalming effects, 20-11 strength, See Trabecular bone strength Tensors, 6-6 structural unit, 1-10 Testing methods, biomechanical, See Biomechanical testing structure, See Cancellous bone architecture; Trabecular methods architecture Testosterone, 1-53, 26-5 Trabecular bone strength, 16-1 to 16-35, See also Bone density; Tetracycline, 1-18, 4-13, 9-17 Bone strength; Cancellous bone architecture; Tetranectin, 1-21 Trabecular architecture Texture analysis, 7-8, 34-19 age effects, 16-3 Thawing effects, 20-6 creep and fatigue, 16-33 to 16-34 Thermal sterilization, 20-19 to 20-20 damage mechanisms, 16-30 to 16-32 Thermoelasticity, 11-11, 23-16 multiaxial behavior, 16-21 Thermoplastics, 35-4 multiaxial behavior, mechanistic analysis, 16-26 to 16-27 Thermosets, 35-4 multiaxial behavior, Tsai-Wu criterion, 16-21 to 16-26 Thixotropic fluids, 25-14 to 25-15 fabric-based formulation, 16-24 to 16-26 Three-dimensional connectivity, 9-11, 9-14 normalized stresses, axial-shear loading, 16-24 Three-dimensional imaging, See Imaging methods strength-density relations, 16-21 to 16-24 Three-dimensional reconstruction, cancellous bone on-axis/off-axis loading orientations, 16-2, 16-7 architecture, 14-7 to 14-14 orthotropy assumptions and coordinate systems, 16-2 anisotropy, 14-7 to 14-10 post-yield mechanical behavior, 16-27 to 16-30 connectivity, 14-10 to 14-14 power law model, 16-5, 16-6 mean intercept length, 14-7 to 14-9, 15-2, 15-9, 15-17 to problems with phenomenological approaches, 16-26 15-18 shear strength, 16-5 star volume distribution, 14-10 strain rate effects, 16-32 volume orientation, 14-9 terms and definitions, 16-2 Three-way rule, 31-9 to 31-11 uniaxial properties, 16-2 Thrombin, 21-12 cellular solid theory, 16-7, 16-11 to 16-16, 16-26 Thrombospondin, 1-21, 2-3 failure strains, 16-9 to 16-10 knockout model, 13-11 heterogeneity and anisotropy, 16-2 to 16-5 Thyroid hormone receptors, knockout model, 4-10 high-resolution FEM, 16-19 to 16-21 Tissue culture, 2-14 to 2-15, See Cell cultures lattice-type finite-element modeling, 16-16 to 16-18 Tissue engineering, 36-1 to 36-2 micromechanical modeling, 16-10 to 16-21 scaffold design and manufacture, 36-1 to 36-12, See Bone potential clinical applications, 16-10 replacement scaffolding strength-density relations, 16-5 to 16-7 Titanium, 26-10, 35-2, 35-3 tensile vs. compressive strengths, 16-8 to 16-9 TK gene, 4-13 von Mises yield criterion, 16-19 Tomographic methods, 5-8, See Computed tomography; yield strain homogeneity, 16-9 Quantitative computed tomography yield strain isotropy, 16-10 Torsion, 6-19, 7-15 to 7-16 Zysset and Curnier model, 16-29, 18-11 to 18-12, 18-20 bone damage histology, 17-12 Trabecular bone volume fraction, 14-2 to 14-3, 14-7, 15-2, bone damage model, 18-17 to 18-19 15-13, 15-14 damage accumulation and, 17-8 Trabecular grain, 15-14 Torsional strength, osteogenesis imperfecta model, 13-4 Trabecular packet, 1-10, 10-3 Torsional viscoelasticity, 11-8 to 11-9 Trabecular surface density, 14-3 to 14-4 Tortuosity, 25-6 to 25-7 Trabecular thickness, 14-13 to 14-16 Total ankle arthroplasty, 35-12 FEM for bone strength, 16-16 to 16-18 Total hip replacement, 35-17 machining effects, 15-19 load redistribution and bone loss, 26-10 measurement, 9-7, 9-11 Total joint arthroplasty Tracer methods, interstitial molecular transport, 22-7 to 22-10 implant and prosthesis design, 35-8 to 35-12 TRANCE, 2-8 permeability considerations, 25-1 Transduction, See Mechanotransduction Total knee replacement, 35-10 to 35-11, 35-17 Transfection, 3-10 to 3-12, See also Gene transfer methods; Total ossicular replacement prostheses (TORPs), 35-13 Knockout models; Transgenic mouse models Total shoulder arthroplasty, 35-11 Transforming growth factor-β (TGF-β), 1-13, 1-19, 1-20, 1-21, Total wrist arthroplasty, 35-12 1-51, 2-7, 2-11 to 2-12 Trabeculae, 1-5, 1-24 arthritis gene therapy, 3-11 definition, 14-5 estrogen effect on gene, 3-7 Trabecular architecture, 10-3, 15-2, See also Cancellous bone fracture healing and, 32-2 architecture osteoclasts and, 2-9 bone strength relationships, See Trabecular bone strength receptors, 2-11, 4-4 9117_frame_index Page 22 Monday, February 5, 2001 11:51 AM

I-22 Bone Mechanics

TGF-β1 knockout model, 4-10 Vertebral loading and failure properties, 33-5, 33-10 to 33-12, TGF-β2 transgenic model, 4-8, 4-9 33-14 to 33-16, 33-18, 33-22 to 33-25 Transgenic mouse models, 3-10, 13-9 to 13-11, 26-15 Vibrational methods, 34-18 to 34-19 animal husbandry, 4-6 to 4-7 Villanueva staining, 17-9 DNA integration effects, 4-13 Viscoelasticity, 7-2, 11-1 to 11-12, See also Cancellous bone, DNA preparation, 4-4 to 4-5 elastic properties of; Creep dominant-negative transgenics, 4-4 acoustic frequency and, 11-1, 11-6 to 11-7 double knockouts, 4-13 axial properties of bone ectopic expression, 4-2 linear viscoelasticity, 11-5 to 11-7 embryonic stem cells, 4-5 to 4-6 nonlinear viscoelasticity, 11-7 to 11-8 examples with skeletal phenotypes, 4-7 to 4-9 bone damage models, 18-7 to 18-8, 18-18 gene-targeted (knockout) mice construction, 4-4 to 4-7 bone hydration and, 11-5 inducible gain of function, 4-13 cancellous bone mechanical characterization, 15-2 to 15-6 osteogenesis imperfecta model, 13-6 collagen, 11-11 point mutations, 4-11 comparison of bone and other materials, 11-4, 11-12 tissue-specific expression, 4-4 composite models, 12-14 to 12-15 tissue-specific knockout using Cre-recombinase, 4-9 to 4-11 constitutive equation, 11-3 type X collagen, 5-20 damage accumulation and, 17-8 TRAP, 4-7, 4-8 Debye model, 11-6, 11-9 to 11-10 Treadmill running model, 1-41 to 1-44, 26-12 frequency components, 11-4 Tricalcium phosphate, 35-4, 35-8 Hooke’s law, 11-1 Tubularity, 9-9 inelasticity and bone damage accumulation, 17-2 to 17-3 Tumor necrosis factor (TNF-α), 1-13, 1-51, 21-11, 2-13 infant skull deformability, 11-4 osteoclastogenesis stimulation, 2-8 porosity and, 11-11, See also Poroelasticity transgenic model, 4-8 shear property and, 11-8 to 11-9 Turkey models, 1-45, 26-15, 26-16, 26-17 strain rate and, 11-3 strain measurement results, 8-22, 8-32 stress-strain curves, 11-6 Turner’s syndrome, 5-20 stretched exponential (KWW) and Debye model, 11-6, 11-8, 11-9 to 11-10 structure and causal mechanisms, 11-10 to 11-12 U temperature effects, 11-5 thermoelastic coupling, 11-11 Ulnar osteotomy, 31-12, 31-16, 31-21 torsional, 11-8 to 11-9 Ultrahigh-molecular-weight polyethylene (UHMWPE), 35-4 wave propagation, 23-19 Ultrasonic methods, 5-8, 10-5, 34-7 to 34-11 Viscoplastic models of bone damage, 18-8 to 18-11 acoustic biomechanical test methods, 7-20 to 7-24 Viscosity, 25-13 to 25-15 architectural dependence of propagation, 34-17 blood, 21-14 broadband ultrasound attenuation, 34-9 to 34-14 osteoblastic response to fluid flow and, 28-9 cancellous bone elastic constant determination, 15-7 Vitamin A excess, 5-10

cancellous bone mechanical properties, 10-11 Vitamin B6 deﬁciency, 5-10, 13-3 cancellous tissue modulus measurement, 10-11 Vitamin D computational methods, 34-13 to 34-17 deﬁciency, 1-53, 5-10

experimental and clinical studies, 34-11 to 34-13 1,25(OH)2D3, 2-10 fracture risk estimation, 34-12 receptor knockout model, 4-10 future research issues, 34-17 receptor transgenic overexpression model, 4-8 influences on attenuation, 34-9 to 34-11 24,25-vitamin D hydroxylase knockout, 5-20 precisions, 34-12 to 34-13 Vitamin E deficiency, 5-10 tissue characterization, 34-7 to 34-11 Vitamin K deficiency, 1-55 Ultrasonic velocity, and bone viscoelastic properties, 11-6 to Vitronectin, 1-14, 1-21, 2-14 11-7 Voight model, 12-4, 12-6, 12-10 Utah paradigm, 1-36 to 1-37 Volkmann channels, 28-3, 23-6 Voltage-activated ion channels, 29-4 to 29-5 Volume fraction, trabecular architecture quantification, 14-2 to V 14-3, 14-7, 15-2, 15-13, 15-14 Volume orientation method, 14-9 Vacuum-based distension system, 27-9 Von Mises equivalent stress, 31-4 Vascular endothelial growth factor (VEGF), 2-5 Von Mises yield criterion, 16-19 Vascular porosity, 23-4, 23-5, 23-6, 23-16 to 23-17, 23-18, 23-20 Von Willebrand factor, 21-12 Vasculature, 21-1 to 21-7, See also Blood flow afferent vessels, 21-1, 21-2 to 21-4 efferent vessels, 21-1, 21-5 W lymphatics, 21-7 microvasculature, 21-5 to 21-7 Walking, See Locomotion Vasoactive intestinal peptide (VIP), 1-8, 21-8 Water content, cortical and cancellous bone composition, 10-4 Vectors, 6-2 to 6-3, 6-7 Waterproofing, 8-3 to 8-4 Veins, 21-1, 21-5 Wing bones, 19-13 Venous drainage, 1-7 Wolff, Julius, 30-1, 30-3, 31-1 Venous pressure biases of, 30-4 bone fluid pressure and, 22-12, 23-20 Culmann and von Meyer drawings and, 30-3 fracture repair and, 22-17 real contributions, 30-4 Venules, 21-1, 21-5 Wolff’s law, 11-4, 22-16, 26-2, 26-3, 31-1, 31-8 Versican, 1-21 Culmann and von Meyer drawings, 30-2 to 30-3, 30-12 9117_frame_index Page 23 Monday, February 5, 2001 11:51 AM

Index I-23

fabric tensor, 31-23 Yield strain or stress false premise in, 30-1, 30-10 to 30-12 bone in tension, 12-15 homogeneous and continuum terminology, 30-6 to 30-7 damage accumulation and, 17-8 implications and relevance, 30-13 to 30-14 homogeneity, trabecular bone, 16-10 length restriction on trajectorial theory, 30-12 to 30-13 isotropy, trabecular bone, 16-10 mechanoelectricity and, 24-1, 24-2 Yield strength, continuum damage mechanics model, 18-2 to on-axis loading assumptions for trabecular bone strength, 18-3 16-7 Young’s modulus, 6-9 to 6-11 origin, 30-2 to 30-5 acoustic testing, 7-20 to 7-21 phenomenological model, 30-13 age and, 19-6 previous critiques, 30-5 to 30-7 bending calculations, 7-12 to 7-13 Roux and, 30-1 to 30-2, 30-4 to 30-5, 31-8 bone hydration and, 7-2 stress trajectory constructions, 30-7 to 30-10 bone-implant system analysis, 35-14 supporters, 30-4 to 30-5 cancellous bone compressive strength and, 15-6 to 15-7 Work to failure measure, 7-6 cancellous bone elastic constants and, 15-14, 15-19 World Health Organization (WHO), 1-47 compressive testing issues, 7-9 to 7-10 Woven bone, 1-4 to 1-5, 1-24, 19-2 deer development model, 19-10 to 19-11 free-floating bone, 19-3 effective isotropic elastic constants, 23-17 Wrist fracture, 1-47 fetal bone, 19-5 Wrist replacement prosthesis, 35-12 indentation testing, 7-17, 7-20, 10-5 strain rate, 7-2 temperature and, 7-2 X testing, 6-11, See Biomechanical testing methods Xenograft, 35-8 ultrasonic velocity and, 34-8 X-linked hypophosphatemic mouse, 13-8 viscoelasticity and, 11-7 X-ray diffraction, 5-3 to 5-4 X-ray methods, See Radiographic methods; specific techniques X-ray spectrophotometry, 33-13 Z Zeta potential, 24-8 to 24-9 Y Zinc deficiency, 5-10 Zirconia, 35-3 Yield point, 7-8 Zysset and Curnier model, 16-29, 18-11 to 18-12, 18-20 9117_frame_index Page 24 Monday, February 5, 2001 11:51 AM