Contribution of trabecular and cortical components to the mechanical properties of bone and their regulating parameters

Bone Vol. 31, No. 3 September 2002:351–358

Contribution of Trabecular and Cortical Components to the Mechanical Properties of Bone and Their Regulating Parameters M. ITO,1 A. NISHIDA,1 A. KOGA,2 S. IKEDA,3 A. SHIRAISHI,4 M. UETANI,1 K. HAYASHI,1 and T. NAKAMURA3 1

Departments of Radiology and 2Structural Engineering, Nagasaki University, Nagasaki, Japan Department of Orthopaedic Surgery, University of Occupational and Environmental Health, Kitakyushu, Japan 4 Chugai Pharmaceutical Co., Ltd., Tokyo, Japan 3

Key Words: Finite element analysis (FEA); Microcomputed tomography (micro-CT); Mechanical testing; Three-dimensional (3D) structure.

To evaluate the mechanical contributions of the spongiosa and cortex to the whole rat vertebra, we developed a finite element analysis (FEA) system linked to three-dimensional data from microcomputed tomography (micro-CT). Twenty-eight fifth lumbar vertebrae (L-5) were obtained from 10-month-old female rats, comprised of ovariectomized (ovx, n ⴝ 6), sham operated (n ⴝ 7), and alfacalcidoltreated after ovx (0.1 ␮g/kg [n ⴝ 8] and 0.2 ␮g/kg [n ⴝ 7]) groups. The trabecular microstructure of L-5 was measured by micro-CT. Yield strength at the tissue level (YS), defined as the value at which 0.034% of all elements reached yield stress, was calculated by the FEA. Then, the ultimate compressive load of each specimen was measured by mechanical testing. The YS of the whole bone (YSw) showed a significant correlation with ultimate load (r ⴝ 0.91, p < 0.0001). The YS values of the isolated spongiosa (YSs) and cortex (YSc) were calculated in models with varying amounts of trabecular or cortical bone mass. The mechanical contribution of the spongiosa showed a nonlinear relationship with bone mass, and ovx reduced the mean mechanical contribution of the spongiosa to the whole bone by 13% in comparison to the sham group. YSs had a strong relationship with trabecular microstructure, especially with trabecular bone pattern factor (TBPf) and structure model index (SMI), and YSc had a strong relationship with cortical bone volume. The structural parameters most strongly related to YSw were BV/TV and TBPf. Our micro-FEA system was validated to assess the mechanical properties of bone, including the individual properties of the spongiosa and cortex, in the osteoporotic rat model. We found that the mechanical property of each component had a significant relationship with the respective bone mass, volume, or structure. Although trabecular microstructure has a significant relationship with bone strength, in ovx bone with deteriorated trabecular microstructure, the strength depended mainly on the cortical component. (Bone 31:351–358; 2002) © 2002 by Elsevier Science Inc. All rights reserved.

Introduction The strength of the vertebral body has been shown to be related to the apparent bone density. However, the relative mechanical contribution of the trabecular and cortical bone components to the strength of the whole vertebral bone is unclear and the results of previous studies have not been consistent. In human vertebral bone, Rockoff et al.22 found that 45%–75% of the axial load was transferred by the cortex, whereas Hayes et al.7 found only a 6%–12% reduction in the load-bearing capacity after removal of the cortical bone. This difference was considered due to the different methods used in evaluating the load distribution and the relative amounts of trabecular bone in the specimens. Finite element analysis (FEA) is a simulation method that can reveal the stress distribution when a bone is loaded. Muller et al.18 applied FEA to the images of three-dimensional (3D) human vertebral bone, showing that simulated age- and diseasedependent trabecular bone loss affected the strength of whole bone. However, selective analyses of the stress distribution and strength of the vertebral bone were not performed in their study, perhaps due to the limitation of the FEA system used. We have developed a new 3D FEA system to evaluate the mechanical properties of whole vertebral bone that accounts for the mechanical interactions of the spongiosa and the cortex. The FEA system was linked to micro-CT data, enabling the calculation of bone strength and stress distribution of the spongiosa and cortex using 3D images. We hypothesized that the FEA system would be able to predict the ultimate mechanical compressive strength of the whole lumbar bone of rats and, furthermore, to calculate individually the strengths of the isolated spongiosa and cortex. The purposes of our study were to validate our FEA system for the assessment of the mechanical properties of whole bone, to evaluate the relationship between the individual strength of spongiosa or cortex and bone mass or structure and, finally, to evaluate the mechanical contribution of spongiosa to whole bone using an osteoporotic rat model.

Address for correspondence and reprints: Dr. Masako Ito, Department of Radiology, Nagasaki University, 1-7-1 Sakamoto, Nagasaki 852-8501, Japan. E-mail: [email protected] © 2002 by Elsevier Science Inc. All rights reserved.

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Table 1. Microstructural parameters, cortical area, and ultimate load for each sample

Sample 845 846 847 848 849 850 851 853 854 855 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 874 875

Group

BV/TV (%)

Tb.Th (mm)

Tb.N (mm⫺1)

Tb.Sp (mm)

SMI

TBPf (mm⫺1)

Cortical area

Ultimate load (N)

Sham control Sham control Sham control Sham control Sham control Sham control Sham control Ovx control Ovx control Ovx control Ovx control Ovx control Ovx control Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.1 ␮g/kg Ovx ⫹ D3 0.2 ␮g/kg Ovx ⫹ D3 0.2 ␮g/kg Ovx ⫹ D3 0.2 ␮g/kg Ovx ⫹ D3 0.2 ␮g/kg Ovx ⫹ D3 0.2 ␮g/kg Ovx ⫹ D3 0.2 ␮g/kg Ovx ⫹ D3 0.2 ␮g/kg

0.328 0.307 0.295 0.238 0.291 0.333 0.251 0.160 0.217 0.120 0.194 0.194 0.204 0.543 0.512 0.594 0.631 0.634 0.569 0.472 0.684 0.704 0.726 0.740 0.713 0.723 0.670 0.611

0.092 0.097 0.097 0.084 0.091 0.099 0.089 0.081 0.086 0.071 0.087 0.087 0.089 0.131 0.122 0.148 0.152 0.155 0.140 0.116 0.160 0.180 0.182 0.202 0.202 0.190 0.176 0.159

4.875 4.384 4.442 4.415 4.712 4.638 4.242 3.272 3.734 3.073 3.558 3.558 3.293 5.213 5.355 5.292 5.685 5.681 5.314 5.205 6.292 5.532 6.492 6.406 5.716 6.412 5.609 5.205

0.209 0.237 0.230 0.227 0.211 0.225 0.238 0.308 0.267 0.327 0.285 0.285 0.303 0.189 0.183 0.177 0.167 0.179 0.196 0.186 0.153 0.170 0.149 0.141 0.168 0.145 0.184 0.185

0.801 0.723 1.183 1.686 1.186 0.623 1.446 1.948 1.564 2.203 1.812 1.812 1.370 ⫺2.719 ⫺2.043 ⫺3.801 ⫺4.725 ⫺5.045 ⫺3.267 ⫺1.185 ⫺6.593 ⫺7.523 ⫺8.632 ⫺8.961 ⫺7.605 ⫺8.088 ⫺6.266 ⫺4.210

⫺3.702 ⫺1.584 ⫺1.160 0.202 ⫺1.166 ⫺3.307 0.458 4.190 1.752 5.998 2.234 4.323 2.018 ⫺9.804 ⫺10.364 ⫺9.156 ⫺12.215 ⫺13.292 ⫺11.574 ⫺7.090 ⫺17.194 ⫺12.850 ⫺18.466 ⫺18.377 ⫺14.496 ⫺17.613 ⫺14.382 ⫺10.396

0.09 0.08 0.07 0.08 0.08 0.13 0.09 0.05 0.07 0.06 0.07 0.09 0.07 0.12 0.17 0.11 0.21 0.13 0.14 0.08 0.13 0.21 0.15 0.22 0.18 0.17 0.17 0.13

495 395 445 375 445 505 385 240 355 330 305 300 290 660 605 700 735 700 635 420 835 690 735 685 740 860 840 575

Materials and Methods Materials Twenty-eight fifth lumbar vertebrae were obtained from 10month-old female rats (Wistar-Imamichi) that had been ovariectomized (ovx, n ⫽ 21) or sham operated (n ⫽ 7). The ovx rats were divided into three groups: an ovx control group (n ⫽ 6), and groups treated with alfacalcidol (0.1 ␮g/kg [n ⫽ 8] or 0.2 ␮g/kg [n ⫽ 7]) for 6 months. The fifth lumbar vertebrae (L-5) were sampled, cleaned of soft tissue, and frozen at ⫺40°C until required. These samples originated from a study evaluating the effects of alfacalcidol and menatetrenon.25 Table 1 shows the raw data from each group for BV/TV, Tb.Th, Tb.N, Tb.Sp, SMI, cortical area, and ultimate load. Measurement of Bone Mineral Density The bone mineral density (BMD; mg/cm 2) and bone mineral content (BMC; mg) of the fifth lumbar vertebrae were measured by dual-energy X-ray absorptiometry (DCS-600; Aloka, Japan). Microcomputed Tomography (CT) The micro-CT apparatus (␮CT-20) and the analysis software used in this study were provided by Scanco Medical (Bassersdorf, Switzerland).23 The details of this micro-CT scanner have been described previously.17 Briefly, the device has a micro-Xray source (10 ␮m, 25 keV) directed toward the sample. The X-ray beam is analyzed with a line detector (CCD array; 1024 elements) after being attenuated by the apatite crystals contained in the bone. The process is piloted by a DEC ␣-station (Digital Equipment, Marseille, France), and an open VMS system in a

cluster configuration was used to perform the 3D analysis. The whole L-5 body was scanned dorsoventrally using 250 slices with 13 ␮m slice thickness. To obtain the original 3D image of the L-5 body, a threshold value of 180 was used to binarize the spongiosa and cortex in this analysis system.10 This threshold value was selected on the basis of our previous study in comparison to histological evaluation.10 Measurement of Mass and Structure of Spongiosa On the original 3D image, morphometric indices were determined directly from the binarized volume of interest (VOI). The micro-CT allowed a nominal resolution smaller than the thickness of trabeculae, and supplied a voxel size of 13 ␮m. Bone surface area (BS) was calculated using the “marching cubes” method to triangulate the surface of the mineralized bone phase. Bone volume (BV) was calculated using tetrahedrons corresponding to the enclosed volume of the triangulated surface. Total tissue volume (TV) was the volume of the whole sample examined. The values of trabecular bone volume fraction (BV/TV) and trabecular surface density (BS/TV) were then calculated. Mean trabecular thickness (Tb.Th) was determined from the local thickness at each voxel representing bone.8 With this technique, the thickness could be estimated without a model assumption. Trabecular separation (Tb.Sp) was calculated by applying the same technique used for the direct thickness calculation to the nonbone parts of the 3D image. The trabecular number (Tb.N) was calculated by taking the inverse of the mean distance between the middle axes of the structure. These 3D histomorphometric parameters (Tb.Th, Tb.Sp, and Tb.N) are analogous to the traditional histomorphometric parameters measured on two-dimensional (2D) histological sections. Nonmetric parameters can quantify the shape

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(structure model index [SMI]9 and the direction (degree of anisotropy [DA]) of the trabeculae, and the characteristics of the trabecular surface (trabecular bone pattern factor [TBPf].4 Cortical area in the lower third of the vertebral body was calculated using the axial micro-CT images and was analyzed using NIH IMAGE software. Bone volume of the spongiosa, cortex, and whole bone was calculated by counting the number of voxels that contained bone components. Finite Element Analysis (FEA) FEA of the original vertebral body image was applied to the region from which the upper and lower endplates had been removed, and the image sizes were adjusted to match those of the specimens undergoing the mechanical tests. The micro-CT data (1024 ⫻ 1024 ⫻ 250 slices) were transformed to (256 ⫻ 256 ⫻ 75 slices) volume data, binarized to separate bone from the other components, and then the noise was reduced with a filter. Next, a FE mesh was generated on the surface of the 3D images with approximately 0.2 million eight noded, isoparametric hexahedral elements. In the analysis, uniaxial compression loading was used, simulating the craniocaudal loading of the specimen. Three mechanical property parameters were calculated using MARC K7.1 software (MSC Software Corp.): reaction force (RF); equivalent von Mises stress (EMS); and yield strength. RF was defined as the force that induces the displacement of unit length (⫽ 1 ␮m) uniformly. The yield strength at the element level (yield strength) was defined as the stress at which individual elements began to show plastic deformation. Yield strength at the tissue level (YS) was defined as the value at which 0.034% of all 0.2 million eight noded elements reached the yield stress. This calculated value was approximately equal to the experimental ultimate load. The formula used to calculate the YS was: YS ⫽ RF/EMS ⫻ 0.00018 (N/mm2).28 Distribution of the EMS is shown in Figure 1B. To determine the most appropriate values of Young’s modulus (⫽ 17 GPa) and Poisson’s ratio (⫽ 0.3) in relation to the biomechanical loading test results, the YS was initially calculated using a range of values for Young’s modulus and Poisson’s ratio. Poisson’s ratio and Young’s modulus were defined as 0.25 and 12.5 ⫾ 0.6 GPa, respectively, in a previous study using synchrotron radiation micro-CT.13 It was confirmed that the results were not significantly different when 0.25 or 0.3 was adopted as the value of Poisson’s ratio in our FEA system. In contrast, the Young’s moduli have varied considerably among published studies. The trabecular tissue modulus of a single trabeculum was determined to be 0.4 –3.6 GPa in tensile testing experiments24 and 10.4 –14.8 GPa in experiments using microtensile testing and ultrasonic techniques.21 The discrepancy between the values obtained can be attributed to the different methods used, or, where a similar method was used, to differences in the spatial resolution used to obtain the microstructural images when using conventional micro-CT or synchrotron radiation CT. The boundary conditions of the FE model varied on the upper, lower, or lateral sides. A displacement of unit length (⫽ 1 ␮m) was applied to the top face, the displacement was fixed at the bottom face, and all other faces of the model were free. This condition simulates a compression test. The computation time was approximately 1 h for the FE analysis of each sample. FE Models With Various Amounts of Bone Mass in the Spongiosa and Cortex To evaluate the mechanical contribution of each bone component to the whole bone, FE models with various amounts of bone mass in isolated spongiosa, cortex, or whole bone were prepared.

Figure 1. Trabecular microstructure and stress distribution. (A) Two representative models of the trabecular microstructure in the rat vertebrae. Trabecular structures in sham-operated and ovx rats are shown on the left and right, respectively. The arrow indicates the region of FE analysis. (B) Stress distribution in these two spines accompanied by their respective cortical bones from (A). Load direction is from left to right in these images, and the light and dark colors represent high and low stress, respectively.

The 3D border of the bone cortex was determined in this study as follows. Two image-processing methods, namely the “border-following by raster scan”3 and the “expansion processing (dilation) methods,”6 were applied to separate the spongiosa and cortex components of bone. The raster scan is a method of scanning—for example, in the top row from left to right, then similarly in the next row, and so on down to the bottom of the image. The dilation method is one of the morphologic techniques that includes dilation and erosion, opening and closing. This expansion processing method involves locally adding voxels to the vicinity (neighborhood) of existing voxels. The process is shown in Figure 2. Figure 2A shows the original 3D image of the rat vertebra. The volume was binarized using the discriminating analysis to separate the bone and nonbone components (Figure 2B). The contour of the bone was detected using a raster scan (Figure 2C). In Figure 2D, the mask volume outside of this contour was prepared based on this contour of the bone. A higher-thanthreshold value was applied to binarize the volume to separate the bone and nonbone components (Figure 2E); then, after filtering and labeling (Figure 2F), the largest connected compo-

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Figure 2. Processing to separate spongiosa and cortex. (A) Original 3D image of the rat vertebra. (B) The image binarized using discriminating analysis to separate bone and nonbone components. (C) The contour of the bone using raster scanning. (D) The mask image outside of the contour is prepared. (E) The image applied the higher value than the threshold value to binarize the image to separate the bone and nonbone components. (F) The image after filtering and labeling. (G) The extracted core of the cortex. (H) The expanded cortical core. (I) A new mask image. (J) Isolated cortex. (K) Isolated spongiosa.

nent was extracted as the core of the cortex (Figure 2G). Expansion processing (dilation) was applied to the volume in Figure 2G resulting in Figure 2H. However, the voxels cannot be expanded beyond the contour of the original volume (Figure 2A). The mask volume outside of the contour (Figure 2D) and the expanded cortical core volume (Figure 2H) were combined to make a new mask volume (Figure 2I). Using the volumes in Figure 2A and the new mask volume in Figure 2I, the cortex and spongiosa were extracted. Then, the isolated cortex (Figure 2J) was the zone of overlap between the volumes in Figure 2A and Figure 2I. The isolated spongiosa (Figure 2K) component was obtained by subtracting the isolated cortex from the original volume (Figure 2A).

vanced Visual Systems, Inc., Waltham, MA) running on Windows NT (Microsoft Corp. Redmond, WA). A threshold value of 70 in the AVS software corresponds to the threshold value of 180 used in the micro-CT evaluation software to separate the bone and nonbone components. The threshold value of 150 is the minimum value for eliminating most of the trabecular components while retaining the complete contour of the thin cortex. The values of YS were then calculated in these models and plotted against the threshold values on a graph, with an assumed continuous line connecting the points. Three values of YS were calculated: YS of the whole vertebral body (YSw); YS of the isolated spongiosa (YSs); and YS of the isolated cortex (YSc), with varying amounts of whole vertebral, trabecular, or cortical bone.

Mechanical Contribution of the Spongiosa From the sham-operated (n ⫽ 7), ovx (n ⫽ 6), and alfacalcidoltreated after ovx (0.1 ␮g/kg; n ⫽ 7) groups, 20 vertebrae, with varying amounts of isolated spongiosa, cortex, and whole bone mass, were prepared using different thresholds. The rat vertebrae from the 0.2 ␮g/kg alfacalcidol-treated group were excluded from this analysis as it proved difficult to separate the isolated trabecular and cortical bone components. The border between the trabecular and cortical bone components was unclear due to the greatly increased amount of trabecular bone. To obtain images that had selectively reduced spongiosa or cortical bone mass, the imaging threshold levels were adjusted in nine steps, from 70 to 150. These threshold values were used to reconstruct the 3D micro-CT images using AVS software (Ad-

Mechanical Tests The L-5 vertebral body specimen was fixed with a clamp at the bases of the transverse processes in the holder of a diamond band saw (Exakt, Norderstedt, Germany). By removing the cranial and caudal endplates, approximately 4-mm-high specimens with planoparallel surfaces were obtained for compression testing.19 The vertebral cylinder samples were placed centrally on the smooth surface of a steel disk (10 cm diameter) attached to the material-testing machine (Tensilon UTA-1T, Orientec, Tokyo). A compression force was applied in the craniocaudal direction using a steel disk (1.8 cm diameter) at a nominal deformation rate of 2 mm/min. Load-deformation curves were recorded continually in the computerized monitor linked to the tester. The ulti-

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Figure 3. Relationship between YIELD STRENGTH and ultimate load. There is a significant correlation between ultimate load (N) and YIELD STRENGTH (N) (r ⫽ 0.91, p ⬍ 0.0001)

mate compressive load (N) was obtained directly from the load-deformation curves at the level of maximum load. Statistical Analysis The relationships between the values of YS and compressive load or bone mineral density (BMD) were assessed using regression analysis. The correlations between YS or ultimate load and BMD or bone mineral content (BMC), and the correlations between the percentage mechanical contribution of the spongiosa to the whole bone and the microstructural parameters were also examined by linear regression. The most significant parameters related to YSw, YSs, and YSc were then obtained using stepwise regression analysis. Data are presented as mean ⫾ standard deviation (SD). p ⬍ 0.05 was considered statistically significant. Results Relationship Between YIELD STRENGTH and Ultimate Load There was a significant correlation between ultimate load (N) and EMS (N) (r ⫽ 0.52, p ⬍ 0.005), and YS (N) had a more significant correlation with ultimate load (r ⫽ 0.91, p ⬍ 0.0001) (Figure 3). Relationship Between Ultimate Load or YIELD STRENGTH and BMD or BMC Table 2 shows the correlation coefficients for the ultimate load or YS and BMD or BMC. These relationships were similar, and Table 2. Correlation between the ultimate load or YIELD STRENGTH with BMD or BMC

BMD vs ultimate load BMC vs ultimate load BMD vs YIELD STRENGTH BMC vs YIELD STRENGTH

r

p

0.96 0.95 0.90 0.87

0.0001 0.0001 0.0001 0.0001

Figure 4. Representative bone models, with varying amounts of trabecular and cortical bone mass, and their respective micro-FEA images. The graph shows the change in YIELD STRENGTH of the isolated spongiosa, cortex, and whole bone as a function of the threshold values.

the correlation coefficients were significantly high (r ⫽ 0.87– 0.96, p ⬍ 0.0001). YIELD STRENGTH in Bone Models With Various Amounts of Spongiosa, Cortex, and Entire Bone Mass The value of the YS decreased with the increase of the threshold value from 70 to 150 in the isolated spongiosa (YSs) and cortex (YSc). In all specimens, YSs decreased with the increase in threshold value, and this was evident graphically as a curve and a plateau, whereas YSc decreased almost linearly. Representative changes in the YS of the isolated spongiosa, cortex, and whole bone as a function of the threshold values are shown in Figure 4. The mean threshold values for YSs at the point of inflection on the curve, together with the YSs value at this threshold, are shown in Table 3 for the sham, ovx, and alfacalcidol-treated rat groups. The mechanical contribution of the spongiosa to the whole bone varied from 11% to 57%; the mean values are also shown in Table 3. In comparison to the sham-operated rats, ovx caused a 13% decrease in the mechanical contribution of the spongiosa to the whole bone, reflecting the microstructural deterioration of bone in the ovx rats. The correlation coefficients for the percent mechanical contribution (%) of the spongiosa and trabecular microstructural parameters are shown in Table 4. When all experimental groups were analyzed together, all trabecular microstructural parameters

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Table 3. YSs at the threshold value showing plateau n sham OVX alfacalcido 0.1 mcg/kg sham vs OVX OVX vs alfacalcido 0.1 mcg/kg

7 6 7

thresholda 68.7 ⫾ 16.9 78.5 ⫾ 13.4 88.3 ⫾ 16.8 ns ns

YSb 262.4 ⫾ 49.1 230.1 ⫾ 42.7 264.4 ⫾ 109.4 ns ns

(50–90) (59–92) (62–105)

% contribution (218.1–367.8) (180.5–292.0) (108.3–389.1)

34.7 ⫾ 12.5 21.4 ⫾ 7.0 35.6 ⫾ 12.0 0.05 0.05

(21.9–51.6) (11.7–31.7) (10.5–56.7)

KEY: thresholda ⫽ threshold values at plateau; YSb ⫽ YIELD STRENGTH of the spongiosa at the plateau: ( ): minimal value ⫺ maximal value

how the bone spongiosa or cortex contributes to the mechanical properties of a whole vertebrae. The measurement of multiple microstructural indices is a precise approach toward the prediction of fracture load and individual fracture risk. Previous studies have investigated those parameters that are significantly related to bone strength. The most important explanatory variables have been considered to be apparent density and anisotropy.12, 17 However, in evaluating the mechanical contribution of the whole bone, the trabecular microstructure is too complex to describe adequately the characteristics of bone structure using one parameter alone. The anisotropy, connectivity, and characteristics of the trabecular surface (TBPf) are not always independent, and they can act in association with one another in the prevention of bone fragility fracture. For example, if structural characteristics are analyzed in a sample group with a variable range of biomechanical properties, small differences in anisotropy, and large differences in connectivity, the most important explanatory parameter could be connectivity rather than anisotropy, and vice versa. Furthermore, the interaction of spongiosa and cortex are complicated biomechanically, and it is not possible to evaluate the bone strength by considering the two components separately.5 Micro-FEA of the entire bone should be a useful tool for evaluating the changes in whole bone biomechanical properties, particularly in studies of drug efficacy, as the individual bone components or structures are not considered separately. Among the previous studies on FEA of bone, there have been several reports evaluating the relationship between macroscopic structure and strength.15 Mizrahi demonstrated that elimination of the cortical shell reduced peak stresses in the endplate by approximately 20%. The changes in voxel-based structure at a microscopic level in the relation to bone strength have been

(except for Tb.Th) correlated significantly with the percent contribution of the spongiosa to the whole bone. However, when the ovx group was analyzed separately, no significant correlation was noted between any of the trabecular microstructural parameters and percent contribution of spongiosa (Table 4). Structural Parameters Most Strongly Related to YSw, YSs, and YSc The microstructural parameters most strongly related to YSw and YSs are listed in Table 5. These were analyzed using stepwise regression. In the pooled sample analysis, BV/TV and TBPf were related most strongly to YSw, whereas SMI was related most strongly to YSs. In the sham group, no parameter showed a significant relationship with YSw, whereas TBPf was significantly related to YSs. In the alfacalcidol-treated group, BV/TV was the parameter most strongly related to YSw and, in the ovx group, trabecular bone volume was strongly related to YSw and YSs. The cortical bone volume (r ⫽ 0.60, p ⬍ 0.001) was more strongly related to YSc than the cortical area (r ⫽ 0.24, not significant) in the pooled sample analysis. The correlation coefficients of YSc with cortical bone volume were 0.66 (p ⬍ 0.05), 0.63 (p ⬍ 0.05), and 0.91 (p ⬍ 0.005) in the sham, ovx, and alfacalcidol-treated groups, respectively, whereas those with cortical area were 0.22, 0.33, and 0.15 (all nonsignificant), respectively. Discussion 3D trabecular microstructural analysis, using micro-CT and 3D micro-FEA, can be applied to investigate the relationship between structure and biomechanics, and micro-FEA can determine

Table 4. Correlations between trabecular microstructural parameters and the % contribution of spongiosa to the mechanical properties of whole bone groups sham OVX alfacalcidol 0.1 mcg/kg all samples a

S/V

BV/TV

SMI

Th

Sp

N

TBPf

⫺0.38 0.06 ⫺0.09 ⫺0.49a

0.58 0.01 2.51 0.68c

⫺0.58 0.00 ⫺0.52 ⫺0.70c

0.37 0.02 ⫺0.24 0.31

⫺0.57 0.08 ⫺0.47 ⫺0.61b

0.58 ⫺0.08 0.56 0.69c

⫺0.56 0.01 ⫺0.47 ⫺0.67b

p ⬍ 0.05, bp ⬍ 0.01, cp ⬍ 0.001

Table 5. The trabecular microstructural parameters most strongly related to YSw, YSs and YSc. These parameters were analyzed using the stepwise regression sample groups

n

YSw

YSs

all samples sham OVX alfacalcidol 0.1 mcg

20 7 6 7

BV/TV, TBPf – trabecular bone volume BV/TV

SMI TBPf trabecular bone volume TBPf

YSc cortical cortical cortical cortical

bone bone bone bone

volume volume volume volume

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investigated in a local part of the spongiosa.18, 30 In these studies, micro-CT-based FEA revealed the importance of the DA to the mechanical properties of bone. Furthermore, at the trabecular level, the FEA technique showed that the relationship between the microscopic structure and its strength (i.e., basic multicellular units [BMUs]) is strain-regulated in the osteon as well as in the trabeculae,14 and that there is a relationship between the activity of osteoclasts or osteoblasts and deformation of local bone tissue during remodeling.27 Previous studies have demonstrated that vertebral ash density declines with age and appears to be nonlinearly related to the vertebral compression strength.16 In aged vertebrae, the remaining vertical trabeculae reach a critical size such that elastic buckling and bending forces dominate, resulting in a dramatic failure in vertebral bone strength.2, 29 The nonlinear relationship between YSs and the trabecular bone mass indicates that there may be a critical point for bone strength during the loss of trabecular mass and deterioration of trabecular structure. A significant relationship was demonstrated between microstructural parameters and the mechanical properties of bone. It is of interest that, in bone with a deteriorated structure, such as that in the ovx rat group, the mechanical properties depend mostly on trabecular bone volume among all of the relevant trabecular component indices. The microstructural deterioration due to ovx reduced the mechanical contribution of spongiosa to whole bone by 13%, whereas ovx reduced BV/TV by 38%. Standard spinal quantitative CT (QCT), performed in 179 patients clinically and in 5 cadavers, in combination with biomechanical testing, revealed the contributions of the spongiosa and the cortical shell to spinal bone strength.1 In addition to the spongiosa, the cortical shell plays an important role in the load-bearing capacity of the vertebral body. If the spongiosa is weakened due to a loss of bone mass, the residual load-bearing capacity of the vertebral bodies is increasingly shouldered by cortical bone. In this study, in bone with a deteriorated trabecular microstructure, the stress was distributed mostly in the cortical shell (Figure 4). The contribution of the cortical shell to the stability of the entire bone may be important and a transfer of load bearing from the spongiosa to the cortex occurs if the spongiosa is deteriorated. Our previous study showed that YSw values correlated significantly with all spongiosal parameters and cortical area in specimens with BV/TV values of ⬎0.25 (n ⫽ 13). On the other hand, the YSw values correlated only with cortical area in specimens with BV/TV values of ⬍0.25 (n ⫽ 12).11 These data indicate that, in osteoporosis, the competence of cortical bone is essential for the prevention of spinal compression. The cortex serves as a constraint on the internal porous trabecular structure, but its relative contribution to the strength of the vertebra has been debated. Several investigations have examined the respective influence of cortical and trabecular compartments using FEA. Mizrahi et al.15 found that the stresses in the shell increased as the trabecular core modulus decreased. Silva et al.26 reported that the shell supported approximately 10% of the load under uniform stress loading and as much as 64% under uniform displacement. A nonlinear microstructural model for the trabecular core showed that the shell played an important role in load-bearing ability of the human vertebral body; the load ratio ranged from roughly 38% to 83%, depending on age and curvature of the lateral wall of the cortex.20 Kinney et al. suggested that the importance of trabecular bone had been underestimated, and that there was a synergy between the cortical shell and trabecular bone. Their FEA models linked with synchrotron radiation CT showed that ovx caused a 40% decline in trabecular modulus, and the cortical bone accounted for roughly 75% of the total bone stiffness in all treatment groups.13

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In the current study of rat vertebrae, FEA revealed that the mechanical contribution of the spongiosa to the whole bone varied from 11% to 57%, and suggested that the mechanical contribution of the spongiosa depended on the trabecular microstructure. The separate assessments of YS in each bone component indicated that the parameters regulating the mechanical properties of each component were different; the spongiosa was regulated by nonmetric trabecular microstructural parameters (TBPf, SMI), the cortex by cortical bone volume, and the whole bone by metric (BV/TV) and nonmetric (TBPf) trabecular parameters. In conclusion: 1. We have developed a micro-FEA system to evaluate the mechanical properties of whole bone composed of spongiosa and cortex. This FEA system was found to be useful in the analysis of bone mechanical properties in the osteoporotic rat model. 2. Using this FEA system, the YIELD STRENGTH values of the isolated spongiosa, cortex, and whole bone were calculated. The parameters regulating the mechanical properties of each component were different: spongiosa was regulated by nonmetric trabecular microstructural parameters; cortex was regulated by cortical bone volume; and whole bone was regulated by metric and nonmetric trabecular parameters. 3. The microstructural deterioration due to ovx reduced the mechanical contribution of the spongiosa to whole bone by 13%. In bone with a deteriorated trabecular microstructure, the stress was distributed mostly in the cortical shell.

Acknowledgments: This work was supported in part by grants-in-aid from the Research Society for Metabolic Bone Diseases, Japan.

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Date Received: March 19, 2001 Date Revised: December 14, 2001 Date Accepted: May 20, 2002