A Biomechanical Analysis of Ape and Human Thoracic Vertebrae

Home , Thoracic vertebrae

A BIOMECHANICAL ANALYSIS OF APE AND HUMAN THORACIC VERTEBRAE

USING QUANTITATIVE COMPUTED TOMOGRAPHY BASED FINITE ELEMENT

MODELS

DAVID ARTHUR LOOMIS

Submitted in partial fulfillment of the requirements

For the degree of Masters of Science

Thesis Adviser: Christopher J. Hernandez Ph.D.

Department of Mechanical and Aerospace Engineering

CASE WESTERN RESERVE UNIVERSITY

January 2010

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

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candidate for the ______degree *.

(signed)______(chair of the committee)

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(date) ______

*We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents

List of Tables...... iii

List of Figures ...... iv

Acknowledgements ...... v

Abstract ...... vi

Introduction ...... 1

BONE COMPOSITION AND STRUCTURE ...... 1 CLINICAL FRACTURE MORPHOLOGY ...... 3 BIOMECHANICAL MODELING ...... 4 HABITUAL LOADING ...... 5 PREVIOUS WORK ...... 5 OBJECTIVES AND SPECIFIC AIMS ...... 6

Methods ...... 7

SPECIMEN DESCRIPTION ...... 7 QCT SCANNING ...... 8 IMAGE PROCESSING ...... 8 BIOMECHANICAL ANALYSIS ...... 9 BONE LOSS SIMULATIONS ...... 13 STATISTICAL ANALYSIS ...... 16

Results ...... 17

Discussion ...... 24

Appendices ...... 29

APPENDIX I: TABLE OF SPECIMEN IDENTIFICATION, SEX, AND BODY MASS ...... 29 APPENDIX II: ELEMENT INFORMATION, AND ASPECT RATIO COMPARISON FOR FINITE ELEMENT MODELING AMONG APES AND HUMANS ...... 30 APPENDIX III: CONVERGENCE STUDY FOR NUMBER OF MATERIALS USED IN FINITE ELEMENT MODELS ...... 31

Works Cited ...... 32

List of Tables

Table 1. Linear and log-transformed regression models of significant correlations between finite element strength (kN), bone mineral content (g), and body mass (kg) are shown (reduced major axis, RMA, coefficients are also shown)……………………….…….....…..18

Table 2. The results of ANCOVA analyses to evaluate differences among and between species are shown. Multiple comparisons were performed using the Holm post-hoc test.....20

iii

List of Figures

Figure 1: A thoracic vertebrae (T8) is shown with anatomical parts indicated...... 3

Figure 2: Finite element model showing the distribution of elastic modulus in a vertebral body, application of PMMA on the endplates and loading of the vertebral body on the superior surface...... 11

Figure 3: The relationship between porosity (p), and specific surface as determined by Martin is shown [51]. 15

Figure 4: Relationship between specific surface, porosity, and density used in the surfaced-based bone loss model. Solid cubes portray a single density value representative of bone porosity in a given voxel...... 16

Figure 5: Distribution of elastic modulus values in a chimpanzee vertebrae visualized using ABAQUS...... 17

Figure 6: Distribution of elastic modulus values and cross-section view showing von Mises stresses...... 17

Figure 7: Vertebral compressive strength determined through finite element modeling (SFE) is positively correlated with body mass. No significant differences in this regression line were observed among species, but humans showed reduced bone strength relative to body mass as compared to apes (p < 0.01)...... 18

Figure 8: Vertebral compressive strength determined through finite element modeling (SFE) is positively correlated with bone mineral content (g). After accounting for bone mineral content, vertebral compressive strength in humans is less than what would be expected in apes (p < 0.01) as indicated by the different regression lines...... 19

Figure 9: Bone mineral content (g) linearly increases with body mass for all species (kg). No significant differences in bone mineral content were observed among species were after accounting for body mass...... 20

Figure 10: The reduction in finite element strength associated with a 20% reduction in bone mineral content is shown for the surface-based and uniform bone loss simulation methods...... 21

Figure 11: The ratio of finite element strength to body mass was significantly lower in humans as compared to apes (p<0.01)...... 22

Figure 12: Volumetric bone mineral density (vBMD) compared to finite element strength (SFE)...... 23

Figure 13: Relationship between compressive strength determined using composite beam theory (Saxial) and strength determined through finite element modeling (FE Strength). Finite element strength linearly increases with axial rigidity ( r2 = 0.98)...... 23

Figure 14: Faces containing species labels are the “In-Plane” of BMD scans. Orangutan (FMNH) were scanned with a different slice thickness, at Rush Medical Center in Chicago, IL (n = 2)...... 30

Figure 15: Finite element result convergence was analyzed on twelve samples using six different numbers of bin materials. The data showed convergence of finite element compressive strength when the number of materials used for binning exceeds 50 materials per vertebral body...... 31

Acknowledgements

The work herein would not be possible without the combined effort of many

individuals and collaborative institutions. The author would first like to thank the Case

Alumni Association for their support through a BS-MS Scholarship. Also, the author would

like to thank Meghan Cotter, Drew Schifle, and CJ Slyfield for their technical assistance.

Finally, the author would like to thank his parents Jim and Betty Loomis, twin brother Mark

Loomis, and adviser Christopher Hernandez Ph.D. for their continued support, guidance, and

inspiration.

A Biomechanical Analysis of Ape and Human Thoracic Vertebrae Using Quantitative

Computed Tomography Based Finite Element Models

Abstract

DAVID ARTHUR LOOMIS

Spontaneous vertebral fractures are common among humans, but not observed in

apes. Differences in bone structure associated with increased fracture susceptibility among

humans remain unclear. Our aim was to determine how vertebral bone compressive strength

varies among apes and humans, and how bone loss affects differences in vertebral strength.

QCT-based voxel finite element models derived from quantitative computed tomography

(QCT) images of the thoracic vertebrae (T8) were created for apes and humans. Human

vertebrae showed significantly reduced bone strength relative to apes with similar body mass

(p<0.01) and bone mineral content (p<0.01). Bone loss simulations showed no significant

differences in the effect of bone loss on strength among species. Our study suggests human

vertebrae are weaker than ape vertebrae after accounting for bone mass, but are not more sensitive to age-related bone loss. Our results support the idea weaker vertebral bone contributes to the unique susceptibility of humans to vertebral fractures.

Introduction

Vertebral fractures are the most prevalent low-energy fracture in humans. The

clinical standard for assessing vertebral fracture risk uses measures of bone mineral density

(BMD). The most common clinical radiography technique to measure BMD is dual energy

x-ray absorptiometry (DXA), which is a two-dimensional measure, resulting in an “areal”

BMD measurement (aBMD, g/cm2). Although DXA based measures of aBMD are

correlated with bone strength as measured in the laboratory [1, 2] and are a good predictor of

future fracture risk, DXA based measures cannot fully explain fracture risk [3, 4]. As a result

there is interest in other aspects of bone structure and material properties that can contribute

to understanding fracture risk, independent of aBMD. The long-term goal of this research is

to identify aspects of bone structure that are associated with fracture risk independent of

aBMD. Toward this goal the current study explores inter-species differences in bone

structure and strength. While spontaneous vertebral fractures are common in humans they

are not observed in apes [5-8]. Wild apes are, however, susceptible to severe osteopenia [9,

10]. It is unclear why apes might experience vertebral osteopenia yet not be susceptible to

vertebral fractures. One possible explanation is that there are fundamental differences in

bone structure between humans and apes that influence fracture risk.

Bone Composition and Structure

The skeleton provides mineral storage to maintain calcium homeostasis in the body, protects vital organs including stem cells involved in hematopoiesis, and provides leverage

and attachment points for muscles and ligaments that are necessary for locomotion [11].

Mineralized bone tissue is a composite material consisting of three main components, a

1 mineral component (predominantly hydroxyapatite), an organic component (primarily type I collagen), and water [12, 13]. Bone is further characterized into two types, cortical and cancellous bone. Although both cortical and cancellous bone have the same composition, cortical bone is dense (bone volume fraction > 0.80), and cancellous bone is a more porous and a compliant cellular solid [13, 14]. Cortical bone is the dense outer shell of bones and is found in the diaphysis of long bones, whereas cancellous bone is the more porous bone that occupies the epiphysis of long bones and vertebral bodies [11, 12].

The spine is made up of articulating bony segments known as vertebrae, separated from one another by vertebral disks. Each vertebra consists of the vertebral body which is the primary load bearing section, and the posterior elements which interact with connecting ligaments, muscles, and facet joints (Figure 1). The vertebral body is composed of a cancellous bone core, and a surrounding shell with endplates. The shell and endplates are best described as condensed cancellous bone [15-17]. Studies show that as much as 90% of the compressive load on spinal bones is carried by the vertebral body [18-21]. Within the vertebral body, the cancellous bone core may carry up to 42-62% of the load within the vertebral body [22, 23].

Figure 1: A thoracic vertebrae (T8) is shown with anatomical parts indicated.

Clinical Fracture Morphology

There is no consesnsus on a formal definition for clinical vertebral fractures in humans, which makes their classification difficult. Previous studies have used a reduction of

15 % or more of mean vertebral body height ratios as indicative of a vertebral fracture [24,

25]. Gehlbach used a similar percentage rating system to grade the severity of vertebral deformities from normal to a grade 3 deformity (> 40 % reduction in height or area)[26].

This definition was more specifically quantified by Eastell by replacing the arbitrary percentage above with criterion based on standard deviations [27]. Using these various definitions, clinically noted vertebral fractures occur only on the vertebral body, and an anterior wedge fracture was the most prevalent low-energy fracture [28, 29]. Wedge fractures suggest the primary loading of the human vertebral body is asymmetrical.

Biomechanical Modeling

While measures of bone mineral density based on clinical bone scans are the current

standard for predicting fracture risk and bone strength, biomechanical models, derived

directly from clinical images, are now being used to achieve better predictions of bone

strength than can be achieved from bone mineral density measurements alone. The most

effective of these mechanical modeling approaches is based on three-dimensional images of

bone achieved using quantitative computed tomography (QCT). QCT is a three-dimensional

imaging approach and can be used to provide a true “volumetric” density (g/cm3) in contrast

to the two-dimensional areal bone mineral density measures achieved using dual-energy x-

ray absorptiometry (g/cm2). QCT based density scans are correlated to fracture risk [30], and

to bone strength determined experimentally [31, 32]. The three-dimensional information and

intra-specimen density information provided by QCT scans lend themselves to

biomechanical modeling. Two approaches have been used to determine vertebral bone

strength from QCT images. The first approach utilizes composite beam theory to predict

bone strength (Saxial), using the transverse slice with the lowest stiffness value. Estimates of

bone strength using composite beam theory are well correlated to mechanical testing (r2 =

0.58 to 0.81) [31-33]. The second method of evaluating vertebral bone strength from QCT images is via the finite element method. Finite element models derived from QCT images are well correlated to vertebral bone strength [34]. The standard method of generating finite element models from QCT scans is through direct conversion of each voxel into an 8 noded brick element. This finite element approach has been used on a range of levels, from low- resolution ( > 1 mm cube voxels) models [17, 32, 35, 36], to models which differentiate between the cortical shell and cancellous core [37-39]. In general QCT-based finite element models achieve somewhat improved prediction of bone strength as compared to composite

4 beam theory (r2 range of 0.65-0.80 among studies as compared to 0.58-0.81 with composite beam theory) [37, 40]. Although high-resolution models (voxel size 60-80 m) have been presented [39],predictions of vertebral bone compressive strength using such high resolution models are comparable (<10 % difference) to those using low-resolution models (> 1mm voxels) [36, 37, 41, 42].

Habitual Loading

Bone is an adaptive organ that is modified in internal and external shape during growth and adulthood according to the loads applied to it. Differences in bone morphology among species are therefore commonly due to differences in mechanical demands of habitual loading, primarily locomotion [9]. Human locomotion is distinct from that in apes in that it is upright and bipedal. Although apes exhibit bipedal locomotion, it is not their exclusive form of movement as it is in humans [7]. Habitual bipedal locomotion in humans is believed to be associated with increased loading, relative to body mass, in the spine [9, 43]. It has been proposed that evolutionary adaptations in the spine associated with habitual bipedalism explain why humans are susceptible to spinal diseases such as spondylolysis, idiopathic scoliosis, and spontaneous vertebral fractures while apes are not susceptible to such diseases

[5, 7-9, 44].

Previous Work

Previous work utilized QCT images of vertebral bones from humans and apes to derive estimates of bone strength using composite beam theory. A significant relationship between composite beam theory-based estimates of bone strength (Saxial) and body mass was

found, that was consistent in both humans and apes [45]. Prior work also showed that

vertebral bone mineral density was reduced in humans as compared to apes at a young age,

yet no differences were observed in vertebral strength relative to body mass. Leading to the

conclusion that vertebral bones in humans may be predisposed to develop spinal fractures

because they show reduced bone density even at young ages. If so, the unique susceptibility

of humans to spinal fractures could be a result of the fact that vertebral bone strength in

humans is more sensitive to bone loss, i.e. that if humans and apes experience the same

amount of bone loss, human vertebral strength declines more rapidly.

Objectives and Specific Aims

Although our previous work compared human and ape vertebral bone strength using composite beam theory, because finite element modeling can account for changes in sensitivity, it is possible that more subtle differences in bone strength could be detected using finite element modeling. To date, finite element models have not been used to study differences in strength of ape and human vertebrae. Additionally it is not known if human vertebral bone strength is more sensitive to degradations in the bone mass, as occur during age-related bone loss.

The overall goal of this work is to understand the differences in vertebral bone biomechanics between humans and apes. The specific aims of this study are 1) to determine differences in vertebral bone compressive strength between apes and humans using finite

element modeling and 2) to determine how sensitive vertebral strength is to simulated bone

loss in apes and humans.

Methods

Specimen Description

Thoracic Vertebrae (T8) were selected from museum specimens of adult humans

(Homo sapiens, 9 female and 6 male), chimpanzees (Pan troglodytes, 5 female and 5 male),

gorillas (Gorilla gorilla, 5 female and 5 male), orangutans (Pongo pygmaeus and Pongo abelii, 4 female and 4 male), and gibbons (Hylobates lar, n = 10, a random selection of adult specimens was made because gibbon sex is indeterminable from skeletal remains). Human, gorilla, chimpanzee, and gibbon specimens were obtained from the Hamann-Todd

Osteological Collection at the Cleveland Museum of Natural History in Cleveland, Ohio.

Orangutan specimens were collected from the National Museum of Natural History (n=5), the Field Museum of Natural History (n=2), and the Cleveland Museum of Natural History

(n=1). Gorilla, chimpanzee, orangutan, and gibbon specimens were wild shot animals (see

Appendix I).

Human specimens from the Haman-Todd Collection have recorded cause of death, age, and height obtained within one week of death. Human specimens used in the study were obtained from individuals who suffered from accidental or sudden causes of death to ensure that the specimen did not have bone loss from prolonged immobility. The age range of human specimens (20-40 years old, 31.3 ± 7.3, mean ± SD) was selected to represent skeletal maturity prior to age-related bone loss [46].

QCT Scanning

Quantitative computed tomography scans were taken of all specimens and a liquid

calibration phantom (K2HPO4 calibration phantom, Mindways Software Inc.). A Siemens

Somatom 16 scanner (140 kV, 120 mA, 0.75 mm slice thickness) was used at University

Hospitals Case Medical Center (Cleveland, OH) for specimens from the Cleveland Museum of Natural History and the National Museum of Natural History. Scans of specimens from

the Field Museum of Natural History were obtained at Rush University Medical Center using

a Philips Brilliance 64 scanner (140 kV, 120 mA, 0.625 mm slice thickness).

Craniocaudal axial scans were performed on ten samples at a time secured anterior

side down in custom built fixtures. Carbon fiber pads were used to isolate each vertebra

between polycarbonate fixtures. Bones were submerged in a 20% ethanol solution to ensure

accuracy of density values. A vacuum was applied at 30 in. Hg for 30 minutes to remove any

air bubbles present in the bone cavities.

Image Processing

Computed tomography images were analyzed using custom software written for use

with MATLAB (version 7.8.0, Mathworks Inc., Natick, MA, USA). Image voxels were

3 converted to QCT density (ρQCT, mg/cm ) using the K2HPO4 mineral content. Background

signal associated with the ethanol solution was removed by subtracting a grayscale density

value comparable to one standard deviation below the mean fluid value [32]. Specimens

scanned with the Siemens machine underwent Gaussian filtering during scanning, while

those obtained with the Philips machine were filtered using a custom Gaussian filter. Two sample vertebrae, unaffiliated with the study, were scanned at both locations to ensure compatibility between scanners and filtering approaches. The volumetric bone mineral

density (vBMD, g/cm3) of the test specimen differed by less than 5%. Posterior elements

were manually removed from images. The cranial and caudal endplates were identified and

manually attenuated.

To ensure that analyses were not biased due to differences in voxel size relative to

bone size, image resolution was modified using integer coarsening to reduce variability in voxel aspect ratio and total number of voxels per specimen. For example, gibbon specimens were analyzed with a voxel size of 0.38 mm x 0.38 mm x 0.375 mm and human specimens

were analyzed with a voxel size of 0.94 mm x 0.94 mm x 1.5 mm. A total of 11,535 ± 4,348

elements (mean ± SD) were used for each vertebral body and the aspect ratio (largest voxel

dimension/smallest voxel dimension) ranged from 1.0-1.6 (see Appendix II).

Mineral density values for each voxel were determined using the density calibration

phantom in each image from which measures of bone mineral content (BMC, grams) and

volumetric bone mineral density (vBMD, mg/cm3) were obtained. Volumetric bone mineral density was determined by dividing BMC by the volume of the vertebral body.

Biomechanical Analysis

The elastic modulus of each voxel was determined by first converting the density

obtained through QCT imaging (QCT, determined using the calibration phantom) into ash

density (ρash, ash mass/bulk volume) using the relationship determined experimentally by

Keyak et al. [47]:

ash 0.953* QCT  45.7 , (Eq. 1) where all density measures are mg/cm3. An empirical power-law relationship was then used to relate ash density to elastic modulus [48]:

2.57 E 10.5* ash , (Eq. 2)

3 where E is in GPa, and ρash is in mg/cm . A power-law relation was used due to the large range of bone density values, (i.e. linear relationships are valid for smaller density ranges)

[49].

Finite element models were generated using a technique pioneered by Crawford and colleagues [32, 49]. Each voxel in the image is converted into a linear elastic 8-node brick element. Bone elements are modeled as a transversely isotropic, linearly elastic material with the following engineering constants [50, 51]:

Ex = E y = 0.333 E z (Eq. 3)

υxy = 0.381 (Eq. 4)

υxz = υ yz= 0.104 (Eq. 5)

where z is the cranial-caudal direction, E is the elastic modulus, and υ represents the

Poisson’s ratio. Density values for each element were binned into one of fifty incremental values before determining modulus (see Appendix III). Binning the modulus values reduces the number of different material types in the model (reducing computational expense) and has been shown to have a negligible effect (<5%) on whole bone strength estimates [36, 37].

Any elements with negative modulus values due to very low densities are set to 0.0001 MPa

[36]. To simulate commonly used experimental testing conditions, a layer of elements

10 simulating poly-methyl methacrylate PMMA (E = 2.5 GPa, υ = 0.3, 1.5mm slice thickness) is added to each endplate [52].

Boundary conditions for the finite element models were also assigned based on previous studies [32, 33]. The superior surface of the model was assigned a uniform axial displacement corresponding to 3 % deflection. Previous work has shown a 3% axial displacement to be defining of strength in vertebral bodies [33, 53]. All other translational and rotational degrees of freedom on the superior and inferior surfaces were constrained. A linear analysis using ABAQUS 6.8-3 (Dassault Systèmes Simulia Corp, Providence, RI,

USA) was completed on a 3.40 GHz Pentium® 4 CPU with 2.0 GB of RAM, with a maximum CPU time of 58 seconds per model. ABAQUS was used to calculate the whole vertebral body stiffness (KFE), which is represented as the sum of resultant nodal forces on the cranial surface divided by the applied uniform displacement.

Figure 2: Finite element model showing the distribution of elastic modulus in a vertebral body, application of PMMA on the endplates and loading of the vertebral body on the superior surface.

The compressive strength was derived from the whole bone stiffness determined in the finite element model using a simple column model as described by Crawford and colleagues [32]. Using the column model, the compressive strength determined using finite

11 element modeling (SFE) is related to the ultimate stress of the vertebral bone (σu) at the weakest point in the vertebral body (assumed to be the minimum transverse cross-sectional area, Amin):

SFE = σu Amin . (Eq. 6)

The ultimate strsss of human vertebral cancellous bone has been shown to be related to the yield stress of human vertebral bone (σy) through the following relationship [32, 54]:

σu = 1.20 σy . (Eq. 7) where bone yield stress is defined using the 0.2% offset yield criterion. Using this definition, the yield stress, yield strain (εy), and elastic modulus (E) are related as follows [55]:

σy = E (εy – 0.002) . (Eq. 8)

Combining equations (7 and 8) allows us to relate ultimate stress to elastic modulus and yield strain of bone:

σu = 1.20 E (εy – 0.002) . (Eq. 9)

Furthermore, the compressive stiffness (KFE) and compressive strength (SFE) of a column can be represented as a function of elastic modulus, height (H), and cross-sectional area (A):

KFE = EA . (Eq. 10) H Assuming the cross-sectional area, A is equal to Amin, equations (8-11) can be manipulated to represent vertebral strength:

SFE = 1.2KH (εy – 0.002) . (Eq. 11)

By substituting the mean value of the compressive yield strain of vertebral trabecular bone

(εy = 0.0077) [54] we get:

SFE = 0.0068KH , (Eq. 12)

12 where K is the whole bone stiffness determined using the finite element model and H is the height of the whole column. Crawford and colleagues found the approach to be highly predictive of vertebral bone strength determined experimentally (r2 > 0.80) [32, 49].

Composite beam theory was used as a secondary estimate of bone strength in axial compression. Composite beam theory has been used in prior analyses of human and ape vertebral bone biomechanics[45]. The technique accounts for the effects of vertebral bone cross-sectional area and density distribution and provides a simple indicator of vertebral bone strength. When using composite beam theory to estimate bone strength, the axial rigidity

(EA) of each transverse cross-section of the bone is determined using:

x EAEA  ii. (Eq. 13) i1

Where E is the elastic modulus, A is the cross sectional area, i indicates each individual voxel, and x is the total number of voxels. The transverse slice with the lowest stiffness value was used as an indicator of bone strength and denoted Saxial [31-33, 56].

Bone Loss Simulations

In addition to determining vertebral bone strength in the young adult specimens as described, the possibility that there could be differences among species in terms of the reductions in bone strength relative to reductions in bone mass was also considered. Bone loss was simulated by digitally reducing bone mass within each image. A 20% reduction in bone mineral content was applied to each specimen without modifying the external morphology of the vertebral body. A value of 20% was chosen as it is similar to the reductions in bone mineral content observed between attaining peak bone mass and 65 years of age in humans [57].

Two different methods were used to reduce bone loss: uniform bone loss, and surface-based bone loss. The uniform bone loss method reduced the amount of bone mineral by the same percent in every voxel. The surface-based method assumed that bone loss occurs primarily at the bone surface so that regions of the vertebra with greater bone surface experienced greater bone loss. The amount of bone surface present in a region (i.e. voxel) of the vertebral body was determined using an empirical relationship between the ratio of bone surface to total volume (BS/TV, also known as the specific surface, Figure 3) [58]:

BS/TV = 32.3p – 93.9p2 + 134p3 – 101p4 + 28.8p5 . (Eq. 14) where p is the porosity of the region, which is related to the bone volume fraction (BV/TV) by:

p = 1 – BV/TV . (Eq. 15)

Figure 3: The relationship between porosity (p), and specific surface as determined by Martin is shown [58].

Bone volume fraction is related to the apparent density (total mass/total volume, a common measure in mechanical testing) divided by the density of fully mineralized bone

3 tissue, ρtissue (g/cm ):

BV/ TV = ρ / ρtissue (Eq. 16)

Fully mineralized bone can be treated as the highest density value possible, taken here to be a tissue density of 2.31 g/cm3 [59], which was derived using the ash fraction (α) in the following relationship[58, 60]:

ρtissue = 1.41 + 1.29 * α (Eq. 17) where the ash fraction (ash mass / total mass), was also that for fully mineralized bone (α =

0.70) [58-60]. The ash fraction is also used to relate the ash density of a bone specimen voxel to the apparent density (ρ):

ρ = ρash * α (Eq. 18)

Once the amount of surface area in a region was determined, bone loss was applied per unit bone surface area using the following bone resorption rate relationship [61]:

r (BS/TV) t issue , (Eq. 19) where  is the rate of change of voxel apparent density (g/cm3/unit time), and r is the rate of resorption at the bone surface, or in this implementation the step size in the iteration

(m/unit time).

Bone loss was applied iteratively using the forward Euler technique. In each iteration, the bone volume fraction of each voxel was determined and used to calculate the specific surface (BS/TV). A rate of bone apposition/resorption of r = 1.0 m/unit time was applied using equation (18) to determine the total change in ash density. In the event that the

15 bone loss simulation removes all bone mineral in a voxel the voxel density is set to zero.

Alterations in iteration step size (value of r ) by an order of magnitude resulted in less than

1.5% difference in finite element compressive strength values.

Statistical Analysis

Statistical analyses were performed using commercially available software, JMP 8.0

(SAS Institute Inc Cary, NC). General linear regression models were created to examine the relationships between body mass, bone strength, BMC, and vBMD. Because body mass for many individuals was estimated (see above), the reduced major axis (RMA) approach was used for regression models with body mass as a predictor [62]. Differences in strength relative to body mass, BMC or vBMD among species were determined using ANCOVA analysis with a Holm post-hoc test for multiple comparisons [63]. For parameters not

16 correlated with body mass, BMC or vBMD, differences among species were determined using ANOVA with a Tukey post-hoc test.

Results

Figure 5: Distribution of elastic modulus values in a chimpanzee vertebrae visualized using ABAQUS.

Figure 6: Distribution of elastic modulus values and cross-section view showing von Mises stresses.

Compressive strength determined through finite element modeling (SFE) was significantly related to body mass and bone mineral content (Figure 7, 8, Table 1). Bone

17 mineral content also increased linearly with body mass (Figure 9). Finite element derived compressive strength was found to be significantly less in humans than apes relative to body mass (p < 0.01), and bone mineral content (p < 0.01).

Table 1: Linear and log-transformed least squares regression models between body mass (kg) and either finite element strength (kN) or bone mineral content (g) are shown. Reduced major axis (RMA) regression coefficients are also shown. SFE (kN) Bone Mineral Content (g)

y = ax + bSlope 0.0416 0.045 Intercept 0.5213 0.194 SEE 0.273 0.193 r² 0.72 0.86 RMA Slope 0.07563 0.04933 RMA Intercept 0.02455 ‐0.02466 log₁₀y = b*log₁₀x + aSlope 0.697 1.042 Intercept ‐0.76 1.605 SEE 0.0797 0.05832 r² 0.81 0.947 RMA Slope 1.07 1.07 RMA Intercept 1.56 1.559

Twenty percent reductions in bone mineral content simulated through the surface- based model resulted in a 38.73 ± 3.10% (mean ±SD) reduction in vertebral bone strength. When the same amount of bone loss was applied in the uniform bone loss model, a similar reduction in bone strength of 39.01 ± 0.76% (mean ± SD) was observed (Figure 10).

Figure 10: The reduction in finite element strength associated with a 20% reduction in bone mineral content is shown for the surface-based and uniform bone loss simulation methods.

Table 2: The results of ANCOVA analyses to evaluate differences among and between species are shown. Multiple comparisons were performed using the Holm post-hoc test.

Y SFE SFE SFE Saxial Bone Bone Bone Body X Mineral Mineral Mineral Mass Content Density Content

Human v. Non‐Human p < 0.01 p < 0.01 NS p < 0.01

Multiple Comparisons Human NS a a a Chimpanzee NS b c b Gorilla NS b bb Orangutan NS b a cb Gibbon NS a b da b a Species with the same letter are not significantly different from one another NS Not significant

The ratio of finite element bone strength to body mass was found to be significantly reduced in humans as compared to apes (p < 0.01, Figure 11). Previous studies have used bone mineral density and composite beam theory measures, denoted as Saxial, as indicators of

21 bone strength. Volumetric bone mineral density of humans was significantly less than in apes

(p < 0.05, Figure 12). Additionally, a significant relationship was found between strength

2 estimated from composite beam theory, Saxial, and finite element strength (p<0.01, r = 0.98,

Figure 13).

Figure 11: The ratio of finite element strength to body mass was significantly lower in humans as compared to apes (p<0.01).

Figure 12: Volumetric bone mineral density (vBMD) compared to finite element strength (SFE).

Discussion

Our aim was to determine differences in vertebral bone strength between apes and humans, and how simulated bone loss affects vertebral bone strength. Our finite element analyses suggest that human vertebrae are weaker than those of apes after accounting for differences in bone mineral content. A subtle, but significant reduction in vertebral bone strength relative to animal body mass was observed in humans as compared to apes.

Moreover, we found humans to have a significantly lower ratio of finite element strength to body mass when compared to apes (p < 0.01). This suggests that human thoracic vertebrae are not as well adapted to habitual loading, assuming that habitual loading relative to body mass is the same among species. Our simulations of bone loss suggest that a 20% reduction in bone mineral content is expected to have the same effect on human vertebral bone strength as it does on ape vertebral bone strength. These findings suggest that the vertebrae in young adult humans (20-40 years of age) are weaker than expected compared to similarly sized apes, but are not more sensitive to age-related bone loss.

Given the rarity of many of these specimens and available museum collections, the study included a large sample size of wild-shot apes (n = 38) and humans (n=15). Moreover, this study utilized a large number of specimens per species (n = 8 to 15), which allowed us to account for variability within species. Previous comparative biomechanical analyses of long bones used as few as one specimen per species [64]. Secondly, body mass was estimated for each specimen, which allowed for statistical comparisons of inter-species variation. Previous studies have used average weights for each species [65, 66]. Using QCT scans of vertebral bodies allowed us to account for internal mass distribution, measure bone mineral content, and establish finite element estimates of bone strength. The use of finite element modeling

24 provides a more sensitive analysis of vertebral bone strength than our prior study which utilized composite beam theory [45, 67]. We are not aware of other studies that have performed biomechanical analysis of vertebrae from apes using finite element modeling.

Several limitations exist that must be taken into consideration with this study. First, only compressive strength of the vertebral bodies were considered in this study, differences in posterior elements, facet joints, and connective soft tissues were not examined. However, the vertebral body is the primary load carrying component of vertebrae [15, 21], and clinical studies have only shown fractures to be present in the vertebral body[25] [29]. Additionally, measures of the vertebral body in humans have been shown to be predictive of future fracture risk [68], thus the biomechanical analysis of the vertebral body is a useful indicator of whole bone strength. Second, due to the limited populations of ape species in this study, destructive mechanical testing could not be reasonably considered, therefore QCT-based finite element analyses of museum specimens was the only available approach. Furthermore, this study only considered the effects of a symmetrical axial load, but clinical studies showing wedge fracture deformities imply a more asymmetrical load is more realistic. Futher work is needed to examine the effects of a more realistic and complex loading profile.

As with other image-based biomechanical analyses, strength estimates were derived from empirical relationships using human bone tissue. Relationships of QCT density, ash density, elastic modulus, and yield strain from experimental studies in human bone were utilized because such relationships are not available for apes. Because the species included in our study are closely related, considerable variations in the relationship between cancellous bone density and elastic modulus are not expected [12]. Additionally, strength is determined from finite element models utilizing a vertebral cancellous bone yield strain value

25 determined experimentally in humans (εy = 0.0077) [69]. Vertebral cancellous bone yield strain shows little variation among individuals, but has been shown to differ among regions of the human skeleton [54]. Due to the rarity in specimens, it is not known if there are differences in vertebral cancellous bone yield strains between humans and apes. In humans, differences in trabecular microarchitecture among skeletal sites have been attributed to trabecular microarchitecture [70]. Because a recent study in our laboratory showed only minor differences in trabecular microarchitecture among humans and apes [71], the use of yield strain from humans for strength estimates in all species is not expected to greatly influence our conclusions.

Due to large inter-specimen variation in vertebrae size, integer coarsening was used to achieve an equivalent number of voxels per specimen while also minimizing aspect ratio among species. Previous studies have shown bone strength using coarsened voxels up to

4mm in size only differ by less than 5% from uncoarsened finite element strength [36, 41].

Additionally, only a linear model was applied within the finite element analysis. Prior work suggests that a non-linear model would more precisely represent whole bone strength [33,

34]. Because the differences between linear and fully-nonlinear finite element models in predicting whole bone strength are small (r2 = 0.86 with the non-linear model as compared to r2 = 0.80), we do not expect the differences in predictive ability between non-linear and linear modeling to greatly influence our conclusions.

The bone loss models did not account for longitudinal changes in bone external morphology. Gender related differences in humans are well documented, including the continued periosteal apposition [72] of bone in males, which leads to a slight increase (<

10%) in cross-sectional area, as well as a higher propensity for trabecular fenestration among

26 women after an increased period of bone loss[16, 73, 74]. This expansion in cross-sectional area was observed to be 9.8% in male and 3.3% in female humans, and was not included as a parameter in the bone loss model due to the relatively weak relationship between age and vertebral body cross-sectional area in humans (r2 < = 0.26) [73]. Furthermore, it has been shown that human bone composition within the vertebral body changes with aging, tending to have a higher initial percentage of cancellous bone (70%) compared to cortical shell (30%)

[75], whereas with aging the vertebral body bone is composed predominantly of cortical shell

(70%) [76]. Image resolution in the current study was too low to differentiate between the cortical shell, endplates and cancellous center[77]. A recent study showed variations in trabecular microarchitecture among apes and humans to have no significant variation in degree of anisotropy and density among the whole bone between apes and humans [71].

These factors could not be considered with the current bone loss model, but they may be important in understanding the effects of bone loss on vertebral fracture susceptibility.

Lastly, the bone loss simulation approaches were identical among all species. It remains possible, therefore, that differences in sensitivity to bone loss among species could be present if there were large differences in patterns of bone loss or bone loss incidence in the overall population. Future studies will examine differences in rate of bone loss, differences in how bone is lost, and how common bone loss is in the species.

Finite element estimates of bone strength achieved in the current study were comparable, relative to age, to previous studies that included both QCT-derived finite element models and mechanical testing of human vertebrae [32, 33]. Additionally, estimates of bone strength based on composite beam theory, Saxial, were well correlated with finite

2 element derived strength estimates (r = 0.98), and in agreement with earlier findings of Saxial

27 for apes and humans [45, 67]. However, using finite element bone strength, we were able to detect a subtle yet significant difference between vertebral bone strength relative to body mass among humans compared to apes, which we did not find in our previous work. The differences between humans and apes found between our finite element estimates of strength as compared to composite beam theory are most likely due to the ability of finite element modeling to account for the effects of the whole vertebral body instead of estimating the strength from the minimum transverse cross-sectional area.

As mentioned earlier, humans were found to have a significantly lower ratio of finite element strength to body mass when compared to apes (p < 0.01). Assuming that habitual loading, relative to body mass is the same among species then this finding suggests that human thoracic vertebrae are underbuilt in terms of compressive strength, i.e. that the bone structure is not as well adapted to habitual loading in humans. Alternatively the differences in bone strength relative to body mass could imply that human vertebrae are not under built but that habitual axial loading in the human thoracic vertebrae is less relative to body mass than in apes. Because bipedal locomotion in humans requires an upright posture we consider it less likely that habitual compressive loading is less in human vertebrae, relative to body mass. White et. al. argues that habitual axial loading of human vertebrae is actually greater, relative to body mass, than in apes [21]. As a result it is considered more likely that vertebral bone strength in modern humans is underbuilt for habitual loading. That human vertebral bones are weaker relative to body weight at a young age may make human vertebrae predisposed to the development of spinal fractures during aging, potentially contributing to the unique susceptibility of humans to spontaneous vertebral fractures.

Appendices

Appendix I: Table of Specimen Identification, Sex, and Body Mass

Species Specimen Sex Age Body Mass Race Number (kg) Homo sapiens HTH0074 MALE 35 63.90 Black Homo sapiens HTH0243 FEMALE 40 63.50ⁿ White Homo sapiens HTH0249 FEMALE 40 56.60 White Homo sapiens HTH0339 FEMALE 38 81.65ⁿ White Homo sapiens HTH0439 FEMALE 35 54.43ⁿ Black Homo sapiens HTH0561 FEMALE 25 56.25ⁿ Black Homo sapiens HTH1208 FEMALE 23 46.72ⁿ Black Homo sapiens HTH1785 FEMALE 32 54.43ⁿ Black Homo sapiens HTH1787 FEMALE 40 54.43ⁿ Black Homo sapiens HTH2085 MALE 23 63.50ⁿ Black Homo sapiens HTH2104 MALE 20 65.77ⁿ Black Homo sapiens HTH2169 FEMALE 24 61.23ⁿ Black Homo sapiens HTH2193 MALE 25 54.43ⁿ Asian Homo sapiens HTH2206 MALE 31 64.86ⁿ White Homo sapiens HTH2831 MALE 38 73.18 White Gorilla gorilla HTB1710 FEMALE ADULT 80.91 Gorilla gorilla HTB1765 FEMALE ADULT 79.39 Gorilla gorilla HTB1797 MALE ADULT 172.77 Gorilla gorilla HTB1798 FEMALE ADULT 88.83 Gorilla gorilla HTB1859 MALE ADULT 163.05 Gorilla gorilla HTB1992 FEMALE ADULT 94.59 Gorilla gorilla HTB1997 FEMALE ADULT 77.35 Gorilla gorilla HTB2741 MALE ADULT 201.40 Gorilla gorilla HTB3391 MALE ADULT 140.50 Gorilla gorilla HTB3404 MALE ADULT 141.13 Pan troglodytes HTB1719 FEMALE ADULT 51.30 Pan troglodytes HTB1720 FEMALE ADULT 36.32 Pan troglodytes HTB1722 MALE ADULT 66.14 Pan troglodytes HTB1758 MALE ADULT 61.86 Pan troglodytes HTB1766 FEMALE ADULT 68.56 Pan troglodytes HTB1770 FEMALE ADULT 37.55 Pan troglodytes HTB1880 FEMALE ADULT 64.45 Pan troglodytes HTB2027 MALE ADULT 51.91 Pan troglodytes HTB2072 MALE ADULT 60.12 Pan troglodytes HTB3552 MALE ADULT 54.37 Hylobates lar HTB3883 -- ADULT 6.80 Hylobates lar HTB3884 -- ADULT 5.08 Hylobates lar HTB3885 -- ADULT 6.95 Hylobates lar HTB3887 -- ADULT 6.50 Hylobates lar HTB3889 -- ADULT 5.35 Hylobates lar HTB3893 -- ADULT 5.72 Hylobates lar HTB3902 -- ADULT 5.31 Hylobates lar HTB3903 -- ADULT 5.23 Hylobates lar HTB3906 -- ADULT 7.46 Hylobates lar HTB3911 -- ADULT 6.17 Pongo pygmaeus HTB1055 FEMALE ADULT 47.83 Pongo pygmaeus FMNH033533 FEMALE ADULT 49.83 Pongo pygmaeus FMNH033536 FEMALE ADULT 41.58 Pongo pygmaeus USNM 145308 FEMALE ADULT 32.72ⁿ Pongo abelii USNM 143590 MALE ADULT 86.36ⁿ Pongo abelii USNM 143593 MALE ADULT 72.72ⁿ Pongo pygmaeus USNM 145301 MALE ADULT 90.9ⁿ Pongo pygmaeus USNM 145304 MALE ADULT 84.09ⁿ ⁿ Body mass measures recorded at death used instead of estimates from regression models.

Appendix II: Element Information, and Aspect Ratio Comparison for Finite Element Modeling Among Apes and Humans

Figure 14: Faces containing species labels are the “In-Plane” of BMD scans. Orangutan (FMNH) were scanned with a different slice thickness, at Rush Medical Center in Chicago, IL (n = 2).

Table 3: Number of elements and dimensions used for each species. # of ElementsElement Aspect Mean SD Dimensions (mm) Ratio Gorilla 11827 4839 1.02 x 1.02 x 1.5 1.48 Human 12254 2214 0.94 x 0.94 x 1.5 1.6 Chimpanzee 6567 1747 0.94 x 0.94 x 1.5 1.6 Orangutan ‐ FMNH 8420 2188 0.94 x 0.94 x 1.25 1.33 Orangutan 10030 2011 0.94 x 0.94 x 1.5 1.6 Gibbon 16659 3335 0.4 x 0.4 x 0.375 1.07

All Species 11535 4348

Appendix III: Convergence Study for Number of Materials Used in Finite Element Models

A sub-study was conducted to determine the convergence of finite element strength using different numbers of materials. Two specimens were selected randomly from each species, and finite element strength was determined using 10, 20, 35, 50 and 100 materials. Finite element strength converged to within 3.2% for 50 or more materials.

Works Cited

1. Singer, K., et al., Prediction of Thoracic and Lumbar Vertebral Body Compressive Strength - Correlations with Bone-Mineral Density and Vertebral Region. Bone, 1995. 17(2): p. 167-174. 2. Tabensky, A.D., et al., Bone mass, areal, and volumetric bone density are equally accurate, sensitive, and specific surrogates of the breaking strength of the vertebral body: an in vitro study. Journal of Bone and Mineral Research, 1996. 11(12): p. 1981-8. 3. Cummings, S.R., et al., Improvement in spine bone density and reduction in risk of vertebral fractures during treatment with antiresorptive drugs. Am J Med, 2002. 112(4): p. 281-289. 4. Nguyen, T.V., J.R. Center, and J.A. Eisman, Femoral neck bone loss predicts fracture risk independent of baseline BMD. J Bone Miner Res, 2005. 20(7): p. 1195-201. 5. Latimer, B., The perils of being bipedal. Ann Biomed Eng, 2005. 33(1): p. 3-6. 6. Mensforth, R.P. and B.M. Latimer, Hamann-Todd Collection aging studies: osteoporosis fracture syndrome. Am J Phys Anthropol, 1989. 80(4): p. 461-79. 7. Lovejoy, C.O., The natural history of human gait and posture - Part 1. Spine and pelvis. Gait & Posture, 2005. 21(1): p. 95-112. 8. Lovell, N.C., Patterns of injury and illness in great apes. 1990, Washington DC: Smithsonian Institution Press. 224. 9. Gunji, H., et al., Extraordinarily low bone mineral density in an old female chimpanzee (Pan troglodytes schweinfurthii) from the Mahale Mountains National Park. Primates, 2003. 44(2): p. 145- 149. 10. Sumner, D.R., M.E. Morbeck, and J.J. Lobick, Apparent age-related bone loss among adult female Gombe chimpanzees. Am J Phys Anthropol, 1989. 79(2): p. 225-34. 11. Bartel, D.L., D.T. Davy, and T.M. Keaveny, Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems. 2006: Prentice Hall. 12. Currey, J.D., Bones: Structure and Mechanics. 2002, Princeton, NJ, USA: Princeton University Press. 13. Currey, J.D., Mechanical properties of vertebrate hard tissues. Proc Inst Mech Eng H, 1998. 212(6): p. 399-411. 14. Keaveny, T.M., Strength of trabecular bone, in Bone mechanics handbook, S.C. Cowin, Editor. 2001, CRC press: Boc Raton, Fl. p. 16-1-42. 15. Mosekilde, L., et al., Vertebral Structure and Strength in-Vivo and in-Vitro. Calcified Tissue International, 1993. 53: p. S121-S126. 16. Mosekilde, L., The effect of modelling and remodelling on human vertebral body architecture. Technology and Health Care, 1998. 6: p. 287-297. 17. Homminga, J., et al., Osteoporosis changes the amount of vertebral trabecular bone at risk of fracture but not the vertebral load distribution. Spine, 2001. 26(14): p. 1555-61. 18. Silva, M.J., T.M. Keaveny, and W.C. Hayes, Load sharing between the shell and centrum in the lumbar vertebral body. Spine, 1997. 22: p. 140-150. 19. Schendel, M.J., et al., Experimental measurement of ligament force, facet force, and segment motion in the human lumbar spine. Journal of Biomechanics, 1993. 26(4-5): p. 427-38. 20. Asano, S., et al., The mechanical properties of the human L4-5 functional spinal unit during cyclic loading. The structural effects of the posterior elements. Spine, 1992. 17(11): p. 1343-52. 21. White, A.A. and M.M. Panjabi, Clinical biomechanics of the spine. 2nd ed. 1990, Philadelphia: Lippincott. xxiii, 722. 22. Eswaran, S.K., et al., Cortical and trabecular load sharing in the human vertebral body. J Bone Miner Res, 2006. 21(2): p. 307-14. 23. Cao, K.D., M.J. Grimm, and K.H. Yang, Load sharing within a human lumbar vertebral body using the finite element method. Spine (Phila Pa 1976), 2001. 26(12): p. E253-60. 24. Melton, L.J., et al., Epidemiology of vertebral fractures in women. Am J Epidemiology, 1989. 129(5): p. 1000-1011. 25. Melton, L.J., et al., Prevalence and incidence of vertebral deformities. Osteoporos Int, 1993. 3(3): p. 113-9. 26. Gehlbach, S.H., et al., Recognition of vertebral fracture in a clinical setting. Osteoporos Int, 2000. 11(7): p. 577-82.

27. Eastell, R., et al., Classification of vertebral fractures. Journal of Bone and Mineral Research, 1991. 6(3): p. 207-215. 28. Wasnich, R.D., Vertebral fracture epidemiology. Bone, 1996. 18(3 Suppl): p. 179S-183S. 29. Jackson, S.A., A. Tenenhouse, and L. Robertson, Vertebral fracture definition from population-based data: preliminary results from the Canadian Multicenter Osteoporosis Study (CaMos). Osteoporos Int, 2000. 11(8): p. 680-7. 30. Mosekilde, L. and L. Mosekilde, Sex differences in age-related changes in vertebral body size, density and biomechanical competence in normal individuals. Bone, 1990. 11(2): p. 67-73. 31. Whealan, K.M., et al., Noninvasive imaging predicts failure load of the spine with simulated osteolytic defects. J Bone Joint Surg Am, 2000. 82(9): p. 1240-51. 32. Crawford, R.P., C.E. Cann, and T.M. Keaveny, Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography. Bone, 2003. 33(4): p. 744-50. 33. Buckley, J.M., K. Loo, and J. Motherway, Comparison of quantitative computed tomography-based measures in predicting vertebral compressive strength. Bone, 2007. 40(3): p. 767-74. 34. Crawford, R.P., J. Brouwers, and T.M. Keaveny, Accurate Prediction of Vertebral Strength using Voxel-Based Non-Linear Finite Element Models. Trans. Ortho. Res. Soc., 2004. 29: p. 1123. 35. Keaveny, T.M., et al., Effects of teriparatide and alendronate on vertebral strength as assessed by finite element modeling of QCT scans in women with osteoporosis. J Bone Miner Res, 2007. 22(1): p. 149-57. 36. Crawford, R.P., W.S. Rosenberg, and T.M. Keaveny, Quantitative computed tomography-based finite element models of the human lumbar vertebral body: effect of element size on stiffness, damage, and fracture strength predictions. J Biomech Eng, 2003. 125(4): p. 434-8. 37. Liebschner, M.A., et al., Finite element modeling of the human thoracolumbar spine. Spine, 2003. 28(6): p. 559-65. 38. Haidekker, M.A., R. Andresen, and H.J. Werner, Relationship between structural parameters, bone mineral density and fracture load in lumbar vertebrae, based on high-resolution computed tomography, quantitative computed tomography and compression tests. Osteoporos Int, 1999. 9(5): p. 433-40. 39. Eswaran, S.K., et al., Multi-scale modeling of the human vertebral body: comparison of micro-CT based high-resolution and continuum-level models. Pac Symp Biocomput, 2009: p. 293-303. 40. Crawford, R.P., C.E. Cann, and T.M. Keaveny, Voxel-based finite element models predict vertebral fracture strength better than quantitative computed tomography. Trans. Orthop. Res. Soc., 2003. 28: p. 1094. 41. Wijayathunga, V.N., et al., Development of specimen-specific finite element models of human vertebrae for the analysis of vertebroplasty. Proc Inst Mech Eng H, 2008. 222(2): p. 221-8. 42. Ladd, A.J., et al., Finite-element modeling of trabecular bone: comparison with mechanical testing and determination of tissue modulus. Journal of Orthopaedic Research, 1998. 16(5): p. 622-8. 43. Shi C., N.S.A.K., Endo B, A comparative morphological analysis of vertebral bodies in humans and some other mammals. Anthropologic Science, 1995. 103: p. 467-484. 44. Lowe, T.G., et al., Etiology of idiopathic scoliosis: current trends in research. J Bone Joint Surg Am, 2000. 82-A(8): p. 1157-68. 45. Hernandez, C.J., et al., Biomechanical Allometry in Hominoid Thoracic Vertebrae. J Hum Evol, 2009. 56: p. 462-470. 46. Heaney, R.P., et al., Peak bone mass. Osteoporos Int, 2000. 11(12): p. 985-1009. 47. Keyak, J.H., I.Y. Lee, and H.B. Skinner, Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. Journal of Biomedical Materials Research, 1994. 28(11): p. 1329-36. 48. Keller, T.S., Predicting the compressive mechanical-behavior of bone. J Biomech, 1994. 27(9): p. 1159-1168. 49. Kopperdahl, D.L., E.F. Morgan, and T.M. Keaveny, Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone. Journal of Orthopaedic Research, 2002. 20(4): p. 801-805. 50. Mosekilde, L., J. Kragstrup, and A. Richards, Compressive strength, ash weight, and volume of vertebral trabecular bone in experimental fluorosis in pigs. Calcified Tissue International, 1987. 40(6): p. 318-22.

51. Ulrich, D., et al., The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone, 1999. 25(1): p. 55-60. 52. Lewis, G., Properties of acrylic bone cement: state of the art review. J Biomed Mater Res, 1997. 38(2): p. 155-82. 53. Kopperdahl, D.L., J.L. Pearlman, and T.M. Keaveny, Biomechanical consequences of an isolated overload on the human vertebral body. Journal of Orthopaedic Research, 2000. 18: p. 685-690. 54. Morgan, E.F. and T.M. Keaveny, Dependence of yield strain of human trabecular bone on anatomic site. J Biomech, 2001. 34(5): p. 569-577. 55. Keaveny, T.M., et al., Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. Journal of Biomechanics, 1994. 27: p. 1137-1146. 56. Recker, R., et al., Characterization of perimenopausal bone loss: A prospective study. J Bone Miner Res, 2000. 15(10): p. 1965-73. 57. Gudmundsdottir, H., et al., Vertebral bone density in Icelandic women using quantitative computed tomography without an external reference phantom. Osteoporos Int, 1993. 3(2): p. 84-9. 58. Martin, R.B., Porosity and specific surface of bone. Crit Rev Biomed Eng, 1984. 10(3): p. 179-222. 59. Robinson, R.A., Physiocochemical structure of bone. Clinical Orthopaedics and Related Research, 1975. 53(112): p. 263-315. 60. Hernandez, C.J., et al., The influence of bone volume fraction and ash fraction on bone strength and modulus. Bone, 2001. 29(1): p. 74-78. 61. Beaupre, G.S., T.E. Orr, and D.R. Carter, An approach for time-dependent bone modeling and remodeling--theoretical development. Journal of Orthopaedic Research, 1990. 8(5): p. 651-61. 62. Sokol, R.R. and F.J. Rohlf, Biometry. Third ed. 1995, New York: W.H. Freeman and Co. 63. Glantz, S.A. and B.K. Slinker, Primer of Applied Regression & Analysis of Variance. 2nd ed. 2001, New York: McGraw-Hill. 64. McMahon, T.A., Allometry and biomechanics: Limb bones in adult ungulates. Amer Nat, 1975. 109(969): p. 547-563. 65. Selker, F. and D.R. Carter, Scaling of long bone fracture strength with animal mass. Journal of Biomechanics, 1989. 22(11-12): p. 1175-83. 66. McMahon, T.A., Using body size to understand the structural design of animals: quadrupedal locomotion. J Appl Physiol, 1975. 39(4): p. 619-27. 67. Schifle, A.L., et al. A biomechanical study of vertebral allometry in primates. in American Soceity of Biomechanics. 2007. Stanford, CA, USA. 68. Melton, L.J., 3rd, et al., Structural determinants of vertebral fracture risk. J Bone Miner Res, 2007. 22(12): p. 1885-92. 69. Morgan, E.F., et al. Dependence of yield strain on anatomic site for human trabecular bone. in Adv. Bioeng. 1999. Nashville TN. 70. Hernandez, C.J., A. Gupta, and T.M. Keaveny, A biomechanical analysis of the effects of resorption cavities on cancellous bone strength. J Bone Miner Res, 2006. 21(8): p. 1248-55. 71. Cotter, M.M., et al., Trabecular microarchitecture of hominoid thoracic vertebrae. Anat Rec 2009. 292(8): p. 1098-106. 72. Thomsen, J.S., E.N. Ebbesen, and L. Mosekilde, Relationships between static histomorphometry and bone strength measurements in human iliac crest bone biopsies. Bone, 1998. 22(2): p. 153-63. 73. Duan, Y., et al., Sexual dimorphism in vertebral fragility is more the result of gender differences in age-related bone gain than bone loss. J Bone Miner Res, 2001. 16(12): p. 2267-75. 74. Mosekilde, L., Age-related changes in bone mass, structure, and strength--effects of loading. Z Rheumatol, 2000. 59 Suppl 1: p. 1-9. 75. Eastell, R., et al., Proportion of human vertebral body bone that is cancellous. Journal of Bone and Mineral Research, 1990. 5(12): p. 1237-1241. 76. Sandor, T., et al., Compact and trabecular components of the spine using quantitative computed tomography. Calcified Tissue Research, 1992. 50: p. 502-506. 77. Silva, M.J., et al., Direct and Computed-Tomography Thickness Measurements of the Human, Lumbar Vertebral Shell and End-Plate. Bone, 1994. 15(4): p. 409-414.