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IRC-13-54 IRCOBI Conference 2013

Response of to Dynamic Compressive Loading

Sourabh Boruah, Kyvory Henderson, Damien Subit, Robert S. Salzar, Barry S. Shender, Glenn Paskoff

Abstract Given the rise in incidents of Traumatic Injury (TBI), a validated finite element model (FEM) of the human is necessary for the study, assessment and mitigation of this injury. In this study, dynamic compressive mechanical properties of the human skull have been determined. These properties are suitable for incorporation in an FEM of the skull with a coarse mesh (~ 5 mm) affording greater computational efficiency. Cylindrical through‐the‐thickness specimens (cores) of skull bone were obtained from ten regions of the right calvarium of ten male post‐mortem human surrogates. Potted specimens were compressed using a ramp displacement. The resulting stress vs. strain behavior was used to calculate effective material properties of the skull cores. A micro computed tomography (μCT) study of the cores was performed prior to testing to determine response dependency on microstructure. The modulus of elasticity was determined as 450 ± 135 MPa and the failure stress was estimated as 23 ± 6 MPa. These material properties did not correlate with harvest location or average apparent density in the cores. This study characterizes the combined response of the inner and outer tables and the diploe and provides dynamic material properties to be used in an FEM suitable for high strain rate applications.

Keywords human skull bone mechanical properties, dynamic compressive loading, PMHS, TBI, micro computed tomography

I. INTRODUCTION Historically the study of bone revolved around the long weight bearing of the . Epidemiologically, these are the bones that were most commonly injured. Hardinge [1] extensively studied the mechanical behavior of femoral trabecular bone. Evans [2] studied the regional variation of spongy bone properties. However, perhaps due to the advent of the automobile and increased exposure of human beings to high speed environments, began to become more prevalent. Thurman [3] found that hospitalizations due to severe (TBI) increased by 90 % from 1980 to 1995. Evans [4] tested 56 specimens from embalmed adult human cadavers and estimated the compressive failure strength of the diploe (trabecular bone lying between the cortical tables of the skull) to be 25.1 ± 13.3 MPa. Dempster [5] studied the relative importance of the influence of structural anisotropy (concavity) and material anisotropy (grain orientation) on mechanical response. Robbins [6] tested 70 through the thickness specimens and reported an average elastic modulus of 1.4 GPa and a mean failure stress of 36.54 MPa. McElhaney [7] tested 237 through the thickness skull cores under quasi‐static compression and estimated the elastic modulus to be 2.4 ± 1.5 GPa and failure stress of 73.8 ± 35.2 MPa. These specimens were obtained from both fresh donors and embalmed cadavers. McElhaney attributed the high values of standard deviations to naturally occurring variations in the diploe. It was found that the diploe was isotropic in the tangential direction. McElhaney also developed linear and power law models to correlate density to material properties. The limited studies that were done were all at quasi‐static rates. Peterson [8] conducted transmissibility tests on cranial bone samples from the outer cortical plate and explored its 3‐dimensional anisotropy as a purely elastic substance. The first high strain rate experiments were conducted by Coats [9]. Forty‐six pediatric cranial bone samples were tested under bending and fourteen cranial bone‐‐bone samples were tested under tension in a drop test apparatus and modulus of elasticity, and bending and failure properties were determined. The objective of this study was to investigate pediatric injury due to accidental

S. Boruah is a PhD student at the Center for Applied Biomechanics (CAB) at the University of Virginia (tel: +1‐434‐296‐7288 ext. 115, fax: +1‐434‐296‐3453, e‐mail: [email protected]). K. Henderson is a Researcher, D. Subit is a Senior Research Scientist, and R. Salzar is a Principal Scientist at the Center for Applied Biomechanics at the University of Virginia. B.S. Shender and G. Paskoff are Engineers at the Human Systems Department, Naval Air Warfare Center Aircraft Division, Patuxent River, MD.

- 497 - IRC-13-54 IRCOBI Conference 2013 drops. Motherway [10] obtained 63 specimens from the frontal and parietal bones of fresh and frozen adult crania and tested them under dynamic three point bending. Elastic and failure properties were deduced for rates of up to 2917 %/s. A homogeneous cross‐section was assumed and simple beam theory was used. These yielded elastic moduli of ~10 GPa, which was dominated by the stiff response of the cortical layers and would not be representative of through‐the‐thickness compressive response of the skull. Thus, there were no material properties of skull in the literature that were suitable for high strain rate applications in a Finite Element (FE) Model. This study aims to derive high‐rate material properties of the skull bone, as a composite of the diploe sandwiched between the two cortical layers, that can be used in a skull FE model.

II. METHODS

Subjects

Ten adult male post mortem human surrogates (TABLE I) were chosen to represent the 50th percentile adult male with an upper age limit of 70 years. All specimens were frozen post‐mortem and thawed for use. Kang [11] and Pelker [12] found that multiple freezing‐thawing cycles have no significant effect on mechanical properties. All specimens were screened for hepatitis A, B, C and Human Immunodeficiency Virus and for pre‐existing pathology that may influence bone properties. Pre‐test radiographs and Computed Tomography (CT) scans were analyzed to verify that specimens with existing bone conditions, such as osteoporosis or osteopenia, were excluded from the study. All test procedures were approved by the University of Virginia cadaver institutional review board. Clinical CTs were performed on all subjects at a resolution of 0.625 mm. TABLE I LIST OF SUBJECTS Subject ID Age [y] Height [cm] Weight [kg] 272 58 188 104 273 41 180 71 282 49 175 57 301 51 173 91 499 61 175 204 492 66 178 70 494 59 173 68 504 45 191 73 511 49 175 101 518 70 173 77

Specimen Harvesting Skull clinical CT was used to identify ten anatomical locations (Fig. 1) on the right half of the calvarium for harvesting cores. The locations were chosen to avoid sutures. The locations of the harvested cores were precisely measured. The distance along the intersection of the curved skull outer surface and the Frankfurt plane is denoted X_fp and distance along the outer surface perpendicular to the Frankfurt plane is denoted Y_fp (Fig. 1). These distances were measured from the posterior of the . After removal of the , ten sites on the right side of the calvarium for harvesting cores were identified and marked (Fig. 2). This was guided by the rough designated locations identified from clinical CT and the avoidance of specific anomalies such as deformation and table curvature. The locations were then measured and recorded. The calvarium was then split into two along the mid‐ and removed from the head using an oscillating surgical saw.

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Fig. 1. Harvest locations marked on the skull (1 through 10). Also shown are the reference features and location measurement scheme. Cores of through‐the‐thickness skull samples were obtained from the right half of the calvarium using a drill press (Fig. 2) and a 1‐inch outer diameter diamond abrasive hole saw. The bone was hydrated and cooled with saline solution throughout the coring . The machined cores had a nominal diameter of 18.24 mm. A total of 98 cores were obtained from the right of the ten subjects. The cores weighed 2.53 ± 0.63 g. These were then stored submerged in saline solution inside falcon tubes at 5.5 °C. Fig. 3 shows a sample finished core. The inner cortical table is seen on top.

Fig. 2. Cores being drilled out of the calverium Fig. 3. A sample core, inner cortical table on top. using a vertical drill press using a one inch abrasive bit. Micro Computed Tomography All the cores were imaged prior to testing using a Scanco vivaCT40 scanner (SCANCO Medical AG, Brüttisellen, Switzerland) with an isotropic resolution of 30 μm. A special core holder was used to hold the cores for µCT (Fig. 4). The cores were submerged in saline solution inside a radio‐transparent plastic tube (Fig. 4) during imaging. Image slice direction is shown by the dotted red line. The image resolution allows identification of cortical and trabecular regions on the basis of discernible 3D structure (Fig. 5 and Fig. 6) Thickness of the three layers of the cores were measured by observing the onset of trabecular pores at four fixed 15 x 15 pixel windows on the slice image. Porosity measurements of the three layers were obtained using the SCANCO v1.2a software. A threshold value of 700 mg HA/cm3 for segmentation was chosen since it has been found to satisfactorily separate pore voxels from bone voxels. The distribution of apparent density is bimodal and clearly shows the presence of two phases, viz. bone and pore material, and that they can be discerned by

- 499 - IRC-13-54 IRCOBI Conference 2013 the choice of an appropriate threshold value (Fig. 7). This value has been maintained constant throughout this study for determination of porosity. Porosity is related to the ratio of pore volume to total volume (equation (1)).

Vbone  1 (1) Vtotal where  denotes porosity of the core,

Vbone denotes the volume of bone inside the core,

Vtotal denotes the total volume of the core. Another more standardized measure of bone density is the apparent density. Researchers have found that this metric correlates well to mechanical properties [13]. Apparent density can be measured non‐invasively using CT and, if correlated to mechanical properties, properties of in‐vivo bone can be estimated. The average bone apparent density (measured using μCT and expressed as amount of hydroxyapatite per unit total bone volume) was estimated for each core sample to observe its correlation with mechanical properties.

Fig. 4. Custom core holding jig used for μCT Fig. 5. Top: 3D reconstruction of a skull core; Bottom: imaging with cores submerged in saline solution; Section view (section is perpendicular to skull slice direction shown by the red dotted line. surface).

Distribution Segmentation Threshold Frequency

-500 0 500 1000 1500 3 Apparent Density [mg HA/cm ]

Fig. 6. A sample μCT slice image; Cortical bone on Fig. 7. Distribution of apparent density within a the left and trabecular bone on the right. representative slice of bone; Blue line shows arbitrarily chosen threshold value. Specimen Potting After completion of μCT and before testing, the skull cores were potted in a minimal amount of polyester resin (Bondo, 3M, Maplewood, Minnesota) in order to provide two flat parallel surfaces for mounting the specimen on the test rig. The mass of the cores was measured prior to potting using an electronic scale

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(resolution 0.01 g). The two part filler was mixed using syringes to produce consistent potting material. It was then applied to the inner and outer tables and put in a jig to ensure flat and parallel surfaces (Fig. 8). The total potted thickness was measured using a vernier caliper.

Fig. 8. Potting of skull core in polyester using the jig Fig. 9. Potted cores. device. Experimental Testing The compressibility test setup (Fig. 10) consisted of the Instron 8874 servo‐hydraulic system pushing vertically down on the potted core sample. Instrumentation consisted of a stationary piezo‐resistive load cell (Honeywell model 41, full‐scale 22.24 kN) beneath the specimen and a linear potentiometer (Novotechnik T series) for sensing displacement. Sensor data was acquired at 100 kHz using a DEWE‐2010 data acquisition system (Dewetron, Graz).

Potentiometer

Instron

Sample

Load Cell

Fig. 10. Skull core compression test setup. The test fixture was constructed from aluminum and consisted of a grooved specimen holder to prevent any accidental projectile due to slippage. The groove diameter was 10 % greater than the core diameter and the core specimens were not restricted in the lateral directions during the tests. Also, no glue was used on the specimen boundaries during the compression tests, and the specimen was free to slip. The core specimens were loaded in the setup with the outer table facing the actuator of the Instron machine. A ramp displacement was then applied to the core outer table at a target rate of 15 mm/s which corresponds to a target strain rate of 300 %/s (comparable to blast trauma rates < 1000 %/s [14]). This parameter was limited by the ability of the Instron to respond to a possible overload. The Instron control system was programmed to unload the machine when a force of 6.5 kN was reached. This was done to prevent any damage to the test equipment. Finally a pre‐load of 15 N was applied to ensure the loader was in contact with the core surface to ensure that minimal inertial load was generated when the displacement was applied. The engineering stress, i.e., the force divided by the undeformed area (positive for compressive stress), and

- 501 - IRC-13-54 IRCOBI Conference 2013 the engineering strain, i.e., the displacement divided by the undeformed thickness (positive for compressive strain) are reported in this paper.

III. RESULTS

Results of 84 skull core samples are presented here. Fourteen specimens have been excluded due to unusual size or shape or outlying mechanical response. Core μCT results Total and trabecular thickness were normally distributed (Fig. 12). They varied significantly from subject to subject, but there was no correlation between these parameters and any of the anthropometric data. It was observed that the outer cortical layer was significantly thicker (0.76 mm vs. 0.35 mm) than the inner cortical layer (paired t‐test p<0.001, assuming a normal distribution; Fig. 11). There was no correlation between layer thicknesses and harvest location.

40 40 Total Outer Table 35 N p =84 Trabecular 35 N p =84 Inner Table 30 30

25 25

20 20

Frequency 15 Frequency 15

10 10

5 5

0 0 2 4 6 8 10 12 0 0.3 0.6 0.9 1.2 1.5 Thickness [mm] Thickness [mm] Fig. 11. Histogram of cortical table thicknesses. Fig. 12. Histogram of total and trabecular thicknesses. There is no discernible organization in the distribution of trabecular porosity (Fig. 14). The distributions of porosity of the cortical tables were skewed to the right (Fig. 13). Logarithmic transformations of the cortical porosities are distributed normally (Fig. 15), allowing estimation of significance of difference. The inner cortical layer was significantly more porous (7.1 % vs. 2.4 %) than the outer cortical layer (paired t‐test for log‐normal distribution p<0.001). No correlation was observed between porosity and any of the anthropometric data, nor did porosity correlate to harvest location. TABLE II shows a summary of findings in terms of means and standard deviations. Average apparent density was 807.7 ± 111.7 mg HA/cm3 and its distribution was skewed to the right (Fig. 16). TABLE II MICRO CT STUDY RESULTS Thickness [mm] Porosity Outer Table 0.76 ± 0.29 0.023 ± 0.017 Inner Table 0.35 ± 0.15 0.071 ± 0.032 Trabeculae 5.08 ± 2.01 0.399 ± 0.194 Core Compression Results At the beginning of the experiments, the displacement was seen to climb very fast compared to the force (Fig. 17 A to B). This corresponds to the shallow non‐linear stress vs. strain response (Fig. 18 A to B). This non‐ linear toe region was followed by a linear region (force and displacement histories in Fig. 17 B to C; and stress vs. strain in Fig. 18 B to C). The reported elastic modulus was the slope of this linear region. To facilitate comparison of stress vs. strain curves, the linear region was extrapolated to zero stress and the remaining strain (Fig. 18 G) was deducted. In effect, the stress strain curve was shifted leftwards until the linear region intersected the origin (as can be seen in the combined plots that follow). The trabecular diploe then failed as indicated by a drop in force (Fig. 17 and Fig. 18 D) and displacement increased at a higher rate. This was sometimes accompanied by ejection of material from the trabecular region (Fig. 19). This was followed by another linear domain (Fig. 17 and Fig. 18 E to F), presumed to be due to the tables coming into contact with the

- 502 - IRC-13-54 IRCOBI Conference 2013 trabecular debris. Due to test equipment limitations, stresses exceeding 24 MPa could not be applied to the skull cores.

40 Outer Table Np =84 Inner Table 35 Np =84 40 30 35 30 25 25 20 20 Frequency Frequency 15 15 10 10 5 5 0 0 0 0.04 0.08 0.12 0.16 0.20 0 0.16 0.32 0.48 0.64 0.80 Porosity Porosity Fig. 13. Histogram of cortical table porosity. Fig. 14. Histogram of trabecular porosity.

40 40 Outer Table 35 Np =84 Inner Table 35 N p =84 30 30

25 25

20 20 Frequency Frequency 15 15

10 10

5 5

0 0 0.006 0.01 0.02 0.05 0.1 0.2 0.3 500 600 700 800 900 1000 Porosity Apparent Density [mg HA/cm3] Fig. 15. Histogram of logarithms of cortical table Fig. 16. Histogram of bone apparent density. porosities. Force Disp. time history for 282_06 Stress vs. Strain for 282_06 7 2.8 30 D 6 2.4 25 D C E 5 2.0 F 20 C E 4 1.6 F 15 3 1.2 B 10 B

Force [kN] Force 2 0.8 Stress [MPa] Stress 5 1 A 0.4 [mm] Displacement A 0 G Modulus 393.19 MPa 0 Force 0.0 Strain Rate 94, 117 %/s Post Collapse Modulus 136.17 MPa Disp. Location 6 Failure Stress 16.33 MPa -1 -5 0 50 100 150 200 0 5 10 15 20 25 30 time [ms] Strain [%] Fig. 17. Typical force and displacement time history Fig. 18. Typical stress vs. strain curve for a failure for a failure case. case.

Fig. 19. Ejection of material from failed trabecular region; Left: Before compression; Right: After compression.

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The compressive elastic modulus of the through‐the‐thickness skull core samples is normally distributed (Fig. 22). The average modulus was 450 ± 135 MPa. No correlation between modulus and or anatomical location was observed. The second linear domain (after failure) had an average slope of 112.5 ± 55.8 MPa (Fig. 23). Out of the 84 tests, failure of trabecular bone occurred in 16 cases. No location or subject specific trend for the mechanical properties was observed (Fig. 20, Fig. 21). Stress vs. Strain for Sub. 301 Stress vs. Strain for Loc. 6

30 Skull Core Compression UVa NAVAIR 2012 30 Skull Core Compression UVa NAVAIR 2012

25 25

20 20 Loc. 1 Sub. 272 15 Loc. 2 15 Sub. 273 Loc. 3 Sub. 282 Loc. 4 Sub. 301

Stress [MPa] Stress 10 Loc. 5 [MPa] Stress 10 Sub. 492 Loc. 6 Sub. 494 Loc. 7 Sub. 499 5 Loc. 8 5 Sub. 504 Loc. 9 Sub. 511 0 Loc. 10 0 Sub. 518

0 5 10 15 20 25 30 0 5 10 15 20 25 30 Strain [%] Strain [%] Fig. 20. Representative stress vs. strain curves from Fig. 21. Representative stress vs. strain curves from different harvest locations of the same subject. the same harvest location of different subjects.

40 10

Np =16 35 Np =84 8 30

25 6 20 4 Frequency 15 Frequency

10 2 5

0 0 280 440 600 760 920 50 80 110 140 170 200 230 260 Modulus [MPa] Post Collapse Modulus [MPa] Fig. 22. Histogram of compressive elastic modulus. Fig. 23. Histogram of post collapse modulus.

IV. DISCUSSION

Quasi‐static compressive modulus of the composite skull reported by Robbins [6] and McElhaney [7] (TABLE III) are an order of magnitude higher than the findings of this study. This may be due to absence of trabecular diploe in the specimens (diploe is known to be absent near sutures; [7]). Although the composite response is dominated by the trabecular compliance, it can be expected to be stiffer than pure trabecular bone because of the presence of stiffer cortical bone. Also, the trabecular diploe in the composite will itself exhibit stiffer response because it is constrained at the ends by the cortical bone ([18]). However, many studies have been conducted on pure trabecular bone (TABLE III). The stiffness of the composite response of the skull (in the through‐the‐thickness direction) that has been reported in this paper, is comparable to the stiffness of the pure trabecular bone from the proximal ([18]; TABLE III). This is perhaps due to the fact that the tibia is a load bearing member of the and is stiffer due to stress induced bone remodeling. Compared to vertebral trabecular bone study ([16], [17]; TABLE III), it is surprising that the skull is so much stiffer. Being load bearing members, the vertebral trabecular bone would be expected to be stiffer. Even more surprising is the stiffness reported by McElhaney [7]. The failure stress found in this study is close to the failure stress of diploe reported by Evans [4] and composite failure stress reported by Robbins [6] and McElhaney [7] (TABLE III). The failure stress of pure trabecular bone [16], [18] is much less compared to the failure stress of the composite material. Mechanism of failure may be different for these two cases. Being constrained by the compact bone may prevent the failure of trabecular bone via the failure mechanism in the latter case resulting in a much higher failure stress.

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TABLE III TRABECULAR BONE PROPERTIES REPORTED IN THE LITERATURE Age Range [y] Elastic Modulus [MPa] Failure Stress [MPa] Skull composite [4] embalmed not reported 25.1 ± 13.3 Skull composite [7] 56‐73 and embalmed 2413 ± 1448 73.77 ± 35.16 Skull composite [6] unknown 71.71 to 3654 5.3 to 108.2 [16] 15–87 67 ± 45 2.4 ± 1.6 Proximal tibia [18] 59–82 445 ± 257 5.3 ± 2.9 Bovine proximal tibia [19] Not applicable 2380 ± 777 24 ± 8.3 Correlation of Material properties to density metrics No correlation of compressive elastic modulus with density has been observed. The sixteen failure cases show weak correlation of failure stress to the density metrics (Fig. 24, Fig. 25). Coupled effects with other variables have not been analyzed. Since the trend does not resemble a particular non‐linear function, a linear model to predict failure stress given any particular trabecular porosity has been developed (equation (2); (Fig. 24)).

 f  92.2974.34  (2) where  denotes the porosity,

 f denotes the failure stress. Since all specimens could not be tested up to failure, a direct estimate of failure stress is not possible. But assuming trabecular porosity is the dominant factor, the average failure stress can be predicted on the basis of distribution of trabecular porosity (Fig. 14). Using average trabecular porosity of 0.394 ± 0.195, failure stress can be estimated at 23 ± 6 MPa (from equation (2)).

  195.0394.0   f   623 MPa (3) where  denotes the porosity,

 f denotes the failure stress. Although the average apparent density correlates well with the threshold segmentation based porosity metric (F‐statistic against constant model p<0.01; Fig. 26), it does not correlate to mechanical properties (F‐statistic against constant model p>0.05; Fig. 25). This is contrary to observations made by other researchers [13] who have observed power law relationships. They have observed that coefficients vary from one anatomic location to another. However, power law relationships have only been developed for weight bearing bones (such as the vertebral body, femoral trochanter and proximal tibia). Wolff’s law hypothesizes that trabecular bone remodels itself to ensure isotropic strain by stiffening itself in load bearing directions [15]. Since there is little load on the skull, there might be very limited trabecular bone remodeling in the skull resulting in this difference. This hypothesis is also reinforced by McElhaney’s observations about the tangential isotropy of skull diploe [7]. Core Mass Analysis A linear regression between core mass prior to potting and the total potted thickness intercepts the thickness axis at 0.11 mm confirming that the polyester layer is much thinner than the core itself (Fig. 27). Toe Region The toe region in the stress vs. strain response may exist due to slightly imperfect alignment of the mounting of the cores, or may be an actual characteristic of the response. Hypothetically, the misalignment δ (Fig. 28) leads to a small area of contact at the beginning of the experiment and, hence, a softer response. As the area of contact increases, the response becomes stiffer. This may be understood by splitting the core into several parts shown as blue boxes in Fig. 28 left. The response of each part is shown by the blue lines in Fig. 28 right. The total response shown by the red line exhibits the non‐linear toe region observed in the experiments. The linear region of the red line (green shaded area in Fig. 28 right) represents the response that the same core would have shown, had there been no misalignment. This toe region would have resulted in a spurious non‐ uniform strain field with a peak magnitude of 1.37 ± 1.1 %. Peak strain produced in the experiments was 9.93 ±

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5.44 %. Thus, the spurious non‐uniform strain field may be considered negligible compared to the peak strains produced in the experiments, and the assumption of uniform strain field inside the core may be considered valid.

25 25

Slope 2.171e-02 Slope -29.924 Intercept 1.373 Intercept 34.736 Adjusted R2 0.132 Adjusted R2 0.274 20 20 F - st at i st i c v s. F-statistic vs. constant model const ant model p = 0.0219 Sub. 272 Sub. 272 p = 0.0919 Sub. 273 N p =16 Sub. 273 Sub. 282 Np =16 Sub. 282 Sub. 301 Sub. 301 15 Sub. 492 15 Sub. 492 Sub. 494 Sub. 494 Failure Stress [MPa] Stress Failure Failure Stress [MPa] Stress Failure Sub. 499 Sub. 499 Sub. 504 Sub. 504 Sub. 511 Sub. 511 Sub. 518 Sub. 518

10 10 0.4 0.5 0.6 0.7 0.8 0.9 1 500 550 600 650 700 750 800 850 900 Trabecular Porosity Apparent Density [mg HA/cm3] Fig. 24. Correlation of failure stress to porosity. Fig. 25. Correlation of failure stress to average apparent density.

1 5 Slope 0.366 Slope -1.337e-03 4.5 Intercept -0.039 0.8 Intercept 1.483 Adjusted R2 0.798 2 4 Adjusted R 0.609 F -st at i st i c v s. const ant model F-statistic vs. constant model p = 1.87e-30 0.6 p= 2.1e-18 3.5 Sub. 272 N p =84 N =84 Sub. 272 p Sub. 273 3 Sub. 273 Sub. 282 Sub. 282 Sub. 301 0.4 [g] Mass 2.5 Sub. 301 Sub. 492 Sub. 492 Sub. 494 Sub. 494 Trabecular Porosity Trabecular 2 0.2 Sub. 499 Sub. 499 Sub. 504 Sub. 504 Sub. 511 1.5 Sub. 511 Sub. 518 Sub. 518

0 1 500 600 700 800 900 1000 1100 1200 1300 2 4 6 8 10 12 14 Apparent Density [mg HA/cm3] Thickness [mm] Fig. 26. Correlation of bone apparent density to Fig. 27. Correlation of core mass (prior to potting) to threshold segmentation based porosity. measured total potted thickness.

δ

Fig. 28. Toe region in stress vs. strain plot caused by misalignment. Dependency on strain rate The average strain rate in the elastic domain experienced by the cores was 83.88 ± 27.12 %/s (ranging from 30 to 180 %/s; Fig. 29). Material and structural properties presented in this paper are relevant at these strain rates. It was observed that elastic modulus decreased with increasing strain rate. This effect could have been a characteristic of the test setup. Due to time constraints, the test machine could not be tuned to deliver a specific strain rate for each particular core and was tuned to one representative core sample. Thus, a softer core (decreasing elastic modulus) may have resulted in the test setup loading it faster (increasing strain rate). Due to the large specimen‐to‐specimen variation, rate‐dependent properties could have been deduced only if each individual core was tested at different speeds. The material properties are not expected to vary significantly in the narrow range of speeds it was tested in, and the properties derived are valid in this range.

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40 1000 Slope -3.739e+ 00 Sub. 272 35 Np =84 Intercept 763.638 Sub. 273 Adjusted R2 0.561 Sub. 282 800 Sub. 301 30 N p =84 Sub. 492 CORRELATION Sub. 494 25 600 MAY BE ARTIFACTUAL Sub. 499 Sub. 504 20 Sub. 511 400 Sub. 518 Frequency 15 Modulus [MPa] Modulus 10 200 5

0 0 30 60 90 120 150 180 20 40 60 80 100 120 140 160 180 Strain Rate [%/s] Strain Rate [%/s] Fig. 29. Histogram of strain‐rate in the first linear Fig. 30. Correlation of elastic modulus to strain rate; domain. This dependence may be artifactual and a characteristic of the test machine.

V. CONCLUSIONS Composite material properties applicable to a coarse mesh FE model of the adult male human calverium have been developed in this study. These properties are applicable at strain rates of the order of 100 %/s. A total of 84 skull core specimens harvested from 10 adult male post mortem human surrogates have been tested. The material properties deduced are comparable to recent publications about properties of trabecular bone. The following geometric properties of the adult human calverium have been obtained from this study: 1. Outer cortical layer is significantly thicker than inner cortical layer (0.76 mm vs. 0.35 mm; p<0.001) (Fig. 11). 2. Inner cortical layer is significantly more porous than outer cortical layer (7.1 % vs. 2.4 %; p<0.001) (Fig. 15). 3. Trabecular layer is 5.08 ± 2.01 mm thick. There is no significant dependence on anatomical location. The following material properties for the composite response of the adult human calverium have been deduced: 1. Compressive Elastic Modulus of through‐the‐thickness skull specimen is 450 ± 135 MPa (Fig. 22). 2. Elastic Modulus does not correlate with Porosity, Thickness, Location, anthropometric data or apparent density. 3. Failure Stress of skull core specimen correlates with Trabecular Porosity (p<0.05); hypothetical mean Failure Stress (using Figure 85) is 23 ± 6 MPa. 4. Post Collapse Modulus of through‐the‐thickness skull specimen is 112.5 ± 55.8 MPa (Fig. 23). These material parameters are applicable to an FE model of the skull where strain rates of the order of 100 %/s is seen.

VI. REFERENCES

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