Calcified Tissue International

, Volume 83, Issue 6, pp 368–379

Bone Volume Fraction Explains the Variation in Strength and Stiffness of Cancellous Bone Affected by Metastatic Cancer and Osteoporosis

Authors

  • Ara Nazarian
    • Orthopedic Biomechanics Laboratory, Beth Israel Deaconess Medical CenterHarvard Medical School
    • Institute for Biomedical EngineeringUniversity and ETH Zürich
  • Dietrich von Stechow
    • Orthopedic Biomechanics Laboratory, Beth Israel Deaconess Medical CenterHarvard Medical School
  • David Zurakowski
    • Department of Orthopedic Surgery, Children’s Hospital BostonHarvard Medical School
  • Ralph Müller
    • Institute for BiomechanicsETH Zürich
    • Orthopedic Biomechanics Laboratory, Beth Israel Deaconess Medical CenterHarvard Medical School
    • Department of Orthopedic Surgery, Children’s Hospital BostonHarvard Medical School
    • Orthopedic Biomechanics LaboratoryBeth Israel Deaconess Medical Center
Article

DOI: 10.1007/s00223-008-9174-x

Cite this article as:
Nazarian, A., von Stechow, D., Zurakowski, D. et al. Calcif Tissue Int (2008) 83: 368. doi:10.1007/s00223-008-9174-x

Abstract

Preventing nontraumatic fractures in millions of patients with osteoporosis or metastatic cancer may significantly reduce the associated morbidity and reduce health-care expenditures incurred by these fractures. Predicting fracture occurrence requires an accurate understanding of the relationship between bone structure and the mechanical properties governing bone fracture that can be readily measured. The aim of this study was to test the hypothesis that a single analytic relationship with either bone tissue mineral density or bone volume fraction (BV/TV) as independent variables could predict the strength and stiffness of normal and pathologic cancellous bone affected by osteoporosis or metastatic cancer. After obtaining institutional review board approval and informed consent, 15 patients underwent excisional biopsy of metastatic prostate, breast, lung, ovarian, or colon cancer from the spine and/or femur to obtain 41 metastatic cancer specimens. In addition, 96 noncancer specimens were excised from 43 age- and site-matched cadavers. All specimens were imaged using micro-computed tomography (micro-CT) and backscatter emission imaging and tested mechanically by uniaxial compression and nanoindentation. The minimum BV/TV, measured using quantitative micro-CT, accounted for 84% of the variation in bone stiffness and strength for all cancellous bone specimens. While relationships relating bone density to strength and stiffness have been derived empirically for normal and osteoporotic bone, these relationships have not been applied to skeletal metastases. This simple analytic relationship will facilitate large-scale screening and prediction of fracture risk for normal and pathologic cancellous bone using clinical CT systems to determine the load capacity of bones altered by metastatic cancer, osteoporosis, or both.

Keywords

OsteoporosisSkeletal metastasisCancellous boneMechanical propertyBone volume fractionBone mineral density

The skeleton is the third most common site of metastatic cancer, and one-third to half of all cancers metastasize to bone [1]. There are no proven methods for predicting pathologic fractures in patients with skeletal metastasis [2]. While most clinicians assume that bone mineral density (BMD) is the “best” predictor of fracture risk, noninvasive measurement of BMD by dual-energy X-ray absorptiometry (DXA) or quantitative computed tomography (QCT) provides only a surrogate measure of the strength of the affected bone. The prevention of fractures due to skeletal metastasis depends on objective criteria to evaluate changes in bone structure that reflect the interaction of the metastatic cancer with the host bone. The risk that a bone will fracture through a metastatic lesion depends on the reduction in the load-bearing capacity of the bone induced by the cancer and the loads applied to the bone. From the mechanics of structures, the load-bearing capacity of a bone affected by metastatic cancer depends on the shape and cross-sectional geometry of that bone in addition to its material properties [29]. The increased fragility associated with skeletal metastasis suggests that the strength of the bone tissue adjacent to the metastatic lesion is degraded and/or the stresses generated within the bone during loading are increased due to changes in bone geometry [10]. Therefore, any method that assesses fracture risk must be able to measure both changes in the bone tissue material properties and the bone geometry induced by the cancer. As bone tissue material and cancellous bone microstructure are directly affected by osteoclast and osteoblast activity in response to local and systemic cytokines, growth factors, and hormones regardless of the underlying pathology, our hypothesis is that cancellous bone (normal or pathologic) follows the same analytic relationships between BMD and stiffness that have been previously derived for normal and osteoporotic bone [6, 7, 1118]. However, to the best of our knowledge, this hypothesis has never been validated for metastatic cancer bone tissue. Therefore, the primary aim of this study was to test the hypothesis that a single analytic relationship can predict the strength and stiffness of normal and pathologic cancellous bone affected by osteoporosis or metastatic cancer, where the independent variables were the BMD and bone volume fraction (BV/TV) measured noninvasively by QCT. To accomplish this aim, normal, osteoporotic, and metastatic cancer cancellous bone specimens were imaged using micro-QCT and then tested mechanically by uniaxial compression. Nanoindentation and backscatter emission (BSE) imaging were also performed on the specimens to measure the bone tissue micromechanical properties and bone tissue mineral content. Cancellous bone specimens were then modeled analytically as rigid, open-celled foam [19], where the strength and stiffness of the bone were assumed to be a function of BMD (ρTISSUE, g cm−3), which reflected the contribution of the mineral and organic matrix to the bone tissue material properties and BV/TV (%), which reflected the contribution of the trabecular microstructure to the continuum level and mechanical properties of cancellous bone [20, 21].

Since cancer metastatic to bone changes the trabecular structure [22] and introduces inhomogeneities that make it difficult to obtain consistent cancellous bone samples required to measure the material properties of pathologic bone specimens that we intended to measure, a secondary aim was to develop a method to determine the dependence of the mechanical properties of structurally inhomogeneous bone specimens affected by metastatic cancer, osteoporosis, or both on BMD and trabecular microstructure. To this end, we used a mechanical testing and data acquisition device previously validated by us [23, 24] that incorporated stepwise axial compression in combination with time-lapsed micro-computed tomographic (μCT) imaging to study the three-dimensional (3D) failure behavior of cellular solids [25]. From structural mechanics, we adapted Castigliano’s second theorem [26], which states when an axial force, F, is applied to a series of beams comprising a structure, the total deformation of that structure (δ) is given by the sum of individual beam element deformations:
$$ \delta = \sum {F\left( {\frac{{L_{i} }}{{E_{i} A_{i} }}} \right)} $$
(1)
where EiAi/Li is the axial stiffness for each beam element. In this study, we considered each bone specimen to be comprised of a series of stacked, transaxial bone segments of variable stiffness. Since the force applied to the bone specimen was known and the axial displacement for each transaxial segment through the bone specimen was measured after each stepwise force using the time-lapsed μCT imaging system, it was possible to calculate Ei for each transaxial bone segment. Ei was then related to BMD and trabecular microstructure measured on the corresponding transaxial μCT image through the bone specimen. From this analysis it was apparent that the least rigid segment(s) of bone comprising the specimen governed most of the mechanical behavior of the entire specimen.

Materials and Methods

Specimen Preparation

After obtaining institutional review board approval and informed consent from patients with skeletal metastasis, seven females (36–75 years) and eight males (42–83 years), mean age 68 ± 15 years, underwent excisional biopsy of metastatic prostate, breast, lung, ovarian, or colon cancer from the spine or proximal femur at surgery for fracture treatment or at autopsy. A total of 41 cylindrical cancer specimens were cored from the excised bones (Table 1). The specimens were cored along the predominant trabecular orientation (assessed via contact radiography) out of a precut block of the excised bone using a diamond coring tool (Starlite Industries, Rosemont, PA) while completely submerged in 0.9% saline solution. Once cored, both ends of all specimens were cut perpendicular to the longitudinal axis of the specimen between two parallel diamond wafering blades running on a low-speed saw (Isomet; Buehler, Lake Bluff, IL) following previously described protocols [23, 24]. The specimens were cored and cut using a 2:1 ratio (diameter 5.40 ± 0.31 mm, height 10.31 ± 0.28 mm) between length and diameter [27].
Table 1

Distribution of cancer types along with number of donors and specimens per cancer type

Cancer type

Donors (n)

Specimens (n)

Ovarian

2

3

Lung

4

7

Prostate

4

19

Breast

4

9

Colon

1

3

Additionally, 96 noncancer specimens (diameter 5.53 ± 0.26 mm, height 10.44 ± 0.21 mm) were cored from 43 age- (P = 0.64) and site-matched cadaver bones (21 females [26–85 years], 22 males [23–93 years], mean age 65 ± 17 years) employing identical procedures as above. Noncancer specimens were divided between normal and osteoporotic groups. As no patient information regarding the skeletal health of the cadavers was available, areal BMD (aBMD, g cm−2) was measured for all noncancer specimens and compared with site-specific normative aBMD cut-off values for osteoporosis in male and female representatives from the National Health and Nutrition Examination Survey (NHANES) and Hologic (Waltham, MA) data set [28] (female femoral neck aBMD cut-off = 0.600 g cm−2, lumbar spine aBMD cut-off = 0.840 g cm−2; male femoral neck aBMD cut-off = 0.590 g cm−2, lumbar spine aBMD cut-off = 0.816 g cm−2). Specimens that presented with aBMD values less than the cut-off normative data for their respective sex and site were considered osteoporotic (n = 35), and the remaining specimens were considered normal (n = 61).

Specimens underwent cleaning via sonic agitation (Fisher Scientific, Hampton, NH) while suspended in water for 20 minutes, followed by centrifugal removal of excess water and marrow at 9G for 15 minutes. The average mass (m, g) and physical dimensions of each specimen were measured (average of three measurements per case) using precision balance and calipers. Additionally, bone tissue volume (VBONE, mm3) of each specimen was measured via pycnometry (Accupyc 1330; Micromeritics, Norcross, GA). Wet bone tissue density (ρTISSUE, g cm−3) was then calculated as the result of the average mass (m) divided by VBONE.

Specimens underwent μCT imaging and mechanical testing. All tested specimens were sectioned in half axially. One-half of all cancer specimens were used to confirm the presence of skeletal metastasis histologically. The other half of all specimens were prepared for BSE microscopy and nanoindentation. To that end, specimens were dehydrated in ethyl alcohol with increasing concentrations of 70%, 80%, 90%, and 100%. Dried specimens were embedded in low-viscosity epoxy resin (Epo-thin, Buehler) and sanded using silicon carbide abrasive paper of decreasing particle size (600, 800, and 1,200 grit) under irrigation to expose the bony surface. This surface was further polished with alumina suspension (Buehler) with 0.05 μm particle size. The last polishing step was on plain microcloth under deionized water, followed by ultrasonic cleaning to remove surface debris.

Nanoindentation

We obtained bone tissue material properties by means of nanoindentation using a Triboindenter with a Berkovich indenter (Hysitron, Minneapolis, MN). This fully automated hardness testing system makes small indentations at precise positions on a specimen surface while continuously monitoring the loads and displacements of the indenter. The apparatus is enclosed in an insulated cabinet to provide thermal stability and is suspended on an antivibration table to isolate it from external vibrations. The Oliver–Pharr method was used to determine the indentation modulus, hardness, and indenter area function [29, 30]. Measurements of load and displacement were used to determine contact stiffness, and the reduced modulus was determined from the contact stiffness. The elastic properties of the diamond indenter tip, νtip and Etip, are 0.07 and 1,140 GPa, respectively.

Each nanoindentation test was conducted to a maximum load of 6 mN at a constant loading rate of 400 mN/second. The indentation procedure included a linear loading part 15 seconds long, a holding period at maximum load 10 seconds long, and a linear unloading part 15 seconds long. For calculation of elastic properties, 50–95% of the unloading curves was used. Five target areas were selected in each specimen. In each target area, six indents were performed for a total of 30 indents per specimen. The target areas were selected in the trabecular islands or junctions immediately adjacent to the sites of trabecular fracture from conventional mechanical testing.

BSE Imaging

BSE imaging was performed using the XL30 scanning electron microscope (SEM; Philips/FEI, Eindhoven, The Netherlands) with a BSE detector (Philips/FEI). The signal was first calibrated using C (Z = 6) and A1 (Z = 13), and then the settings were changed to increase the contrast of the bone signal (Z ± 10). During the acquisition session, we controlled the drift of the signal using SiO2 as a standard (only for slight adjustments) with beam intensity of 20 kV. Digital images were collected at 100× magnification with each file measuring 2 × 1.5 mm. Images were saved as TIFF files (645 × 484 pixels, pixel size = 3.00 μm), and adjacent images were obtained on each block.

BSE-generated images were analyzed for the distribution of gray levels, using the Quantimet 500IW system for Image Analysis and Image Processing from Leica (Cambridge, UK). In order to determine the bone mineralization profiles, which are known to vary with age, therapy, and disease, images were segmented into 50 equal bins of increasing intensity (gray levels); the first part of the histograms represents the least mineralized bone (dark gray areas), and the second part contains the distribution of the gray levels corresponding to the most heavily mineralized bone (white areas). The statistical parameters of the histograms—mean, weighted average (BSE-WA), standard deviation, median, mode, skewness, kurtosis, and logit—were determined. In order to estimate the shift to higher mineralization (or lower mineralization), which is a function of the disease, the whole mineralization profiles of the five groups were compared using the logit function: logit = ln[(proportion < 150/proportion > 150)].

Mechanical Testing

A previously described and validated mechanical testing and data acquisition device was employed for this study [23, 24]. This method incorporates stepwise microcompression in combination with time-lapsed μCT to study the 3D failure behavior of cellular solids [25]. Prior to testing, brass end caps (9 mm diameter, 1.2 mm thickness) were glued with cyanoacrylate (American Glue, Taylor, MI) to both ends of the specimens. This reduced end artifact [31] by providing support to the free ends of trabeculae at either end of the specimen. All specimens were preconditioned to eliminate the nonlinear “toe region” [25, 27, 32] at a strain rate of 0.005 s−1 for seven cycles. Specimens were transferred to the μCT scanner to image the trabecular architecture in the undeformed state (0% strain), then mounted in the mechanical testing device and subjected to a monocyclic nominal strain of 2% at a strain rate of 0.01 s−1. Sequential time-lapsed images were acquired after application of 4%, 8%, 12%, 16%, and 20% nominal strain. The specimen was allowed to relax for 20 minutes after each incremental strain step to allow for stress relaxation before imaging.

The discrete stepwise mechanical data for each specimen were reconstructed as described previously [24]. Due to the discontinuous nature of the stepwise testing method and the stress relaxation occurring in the specimen between two measurement segments, the stepwise stress–strain graphs consisted of six discontinuous sections between the seven strain steps from 0% to 20% strain. In order to again introduce continuity in the graphs, straight lines were added to the discontinuous regions [33]. Modulus of elasticity (E, N mm−2) in addition to yield strain (εY, mm/mm) and strength (σY, N mm−2), representing intrinsic properties, were reported for the study. Modulus of elasticity was assessed by measuring the slope of the elastic region of the stress–strain curve, and yield strength was assessed as the point where the stress–strain curve ceased to be linear. Yield point was within the first compression step for all specimens and was calculated using the 0.2% offset method. Specimens remained wet during testing with the humidity sealed within the microcompression device. This was verified upon retrieval of wet specimens at the end of the testing periods.

μCT Imaging

Sequential transaxial images were generated using the μCT 20 system (Scanco Medical, Bassersdorf, Switzerland) [34]. Measurements were stored in 3D image arrays with isotropic voxel sizes of 30 μm at 70 kVp tube voltage and 250 ms integration time. A 3D gaussian filter (σ = 1.2) with a limited, finite filter support (2) was used to suppress the noise in the volumes. These images were segmented to separate bone from background using an iterative thresholding procedure. A component labeling algorithm was applied to these images in order to keep only the largest connected bone component and to remove small particles arising from noise and artifacts.

Each specimen’s intact μCT image was divided along the longitudinal axis into 10 subregions of equal height. For each of these subregions, as well as for the whole specimen, direct 3D indices were computed [35]: BV/TV, bone surface density (BS/TV), specific bone surface (BS/BV), structure model index (SMI), trabecular number (Tb.N), trabecular thickness (Tb.Th), fabric tensor Eigen values (H1–H3), degree of anisotropy (DA = H1/H3), and connectivity density (Conn.D). The subregion with the minimum BV/TV (BV/TVMIN) was identified. Specimens were divided into 10 subregions only to avoid boundary artifacts in the calculations of microstructural indices. Morphometric indices were calculated for the entire specimen and then averaged out over each subregion using a masking procedure (IPL, Scanco Medical). Apparent BMD (volumetric BMD, g/cm3) was calculated as the product of the bone mineral tissue density (ρTISSUE, g/cm3) measured gravimetrically and BV/TVAVG measured by μCT.

The sequential 3D images of each compression step were combined into an animation to illustrate the mode and location of failure for each specimen. For this purpose, the 3D images were initially aligned relative to the bottom end of the specimen, which was fixed during the experiment. Each aligned 3D data set was then visualized under the same conditions (orientation, light settings) using an extended Marching Cubes algorithm [36]. The resulting images were turned into an animation to visualize the region(s) where most of the specimen deformation occurred (Fig. 1). The deformation of the subregion with the minimum BV/TV relative to the other subregions comprising the specimen (including the deformation of individual trabeculae) was tracked during sequential compression steps to identify the weakest (least rigid) subregion of the specimen.
https://static-content.springer.com/image/art%3A10.1007%2Fs00223-008-9174-x/MediaObjects/223_2008_9174_Fig1_HTML.gif
Fig. 1

a Schematic of the screw-driven mechanical testing and data acquisition system that translates the rotation of a stepper motor into a controlled, incremental compressive displacement. b When the specimen is transferred from the load frame to the μCT for imaging, the displacement applied to the specimen by the actuator is maintained by a custom jig. By sequentially coupling μCT imaging after application of incremental displacement, the failure behavior of the trabecular microstructure is visualized directly. LVDT: linear variable differential transformer

Data Analysis

The continuous data were tested for normality using the Kolmogorov-Smirnov test. A power analysis indicated that the sample sizes of cancer (n = 41) and noncancer (n = 96) specimens provided 80% power to measure the correlation between bone tissue and structural properties and measures of bone strength with a 95% confidence interval (CI) around a moderate Pearson correlation coefficient of 0.60 (nQuery Advisor, version 6.0; Statistical Solutions, Saugus, MA). Multivariable analysis was performed using a linear mixed model strategy, which tests the effects of tissue type (cancer, normal, osteoporosis) and site (spine, proximal femur, distal femur) while controlling for density and bone volume fraction as covariates in the model on E and σY [37]. Multiple specimens from the same donor were handled using a compound symmetry covariance structure, which produced excellent fit to the data as judged by Schwarz’s Bayesian criterion [38]. As part of this methodology, statistical significance between tissue types and sites was evaluated using F-tests with multiple comparisons according to the Bonferroni procedure to minimize the risk of false-positive results (Type I errors). Rather than using empirically derived regression models that best fit the experimental data, we used a simple regression model of the general form y = m x z + b (m = slope and b = y-intercept, x and z independent variables, and y dependent variable), based on the theory that cancellous bone can be analytically modeled as an element comprised of a series of breakable subelements to predict E and σY as functions of ρTISSUE, BV/TVAVG, BV/TVMIN, or vBMD [19, 39].

Since the effective length to width ratio governs the structural behavior of a column, the ratio of effective trabecular length oriented in the principal trabecular direction to mean trabecular thickness was formed to evaluate whether the microstructure of the trabeculae accounted for the variation in BV/TVAVG and BV/TVMIN and further explained the dependence of E and σY on bone volume fraction [40]. The coefficient of determination (R2) was used as the criterion to compare the different regression models. Our strategy was based on the Fisher r-to-z transformation with a back-transformation of the bounds to produce a 95% CI for the difference between the correlations being compared. This strategy includes the 95% CI and Z test with a two-sided P value to test for differences between the correlations [41, 42]. The slopes for the different regression models were compared using generalized estimating equations (GEEs) with the appropriate Wald test for comparing slopes between groups (analogous to analysis of covariance where BV/TV and vBMD and slenderness ratio are treated as covariates).

The SPSS statistical package (version 15.0; SPSS, Inc., Chicago, IL) was used for data analysis. All reported P values are two-tailed, with P < 0.05 considered statistically significant.

Results

BSE results demonstrated that cancer specimens were hypomineralized in comparison to normal and osteoporotic noncancer specimens (Table 2): The average ρTISSUE of cancer specimens was 11% lower than that of normal and osteoporotic noncancer specimens (P < 0.001); the BSE-WA mineral content of the cancer specimens was 19% and 15% lower than the normal and osteoporotic noncancer specimens, respectively (P < 0.001). Additionally, the mineralized tissue comprising the cancer specimens was 50% less hard (H) and less rigid (ENANO) than the normal and osteoporotic noncancer specimens (P < 0.001).
Table 2

Material and structural properties for cancer and noncancer specimens (mean ± standard deviation)

Variable

Unit

Metastatic cancer (n = 41)

Normal (n = 61)

Osteoporosis (n = 35)

Tissue density (ρTISSUE), pycnometry

g cm−3

1.68 ± 0.22*

1.82 ± 0.12

1.81 ± 0.11

Average bone volume fraction (BV/TVAVG), µCT

%

24.29 ± 12.26*

36.46 ± 15.38

25.03 ± 6.22*

Gray level weighted average (BSE-WA), BSE

114.82 ± 15.75*

142.91 ± 13.84

135.36 ± 12.14

Hardness (H), nanoindentation

GPa

0.24 ± 0.03*

0.52 ± 0.09

0.47 ± 0.08

Tissue elastic modulus (ENANO), nanoindentation

GPa

0.22 ± 0.03*

0.47 ± 0.07

0.42 ± 0.07

Modulus of elasticity (E), mechanical testing

MPa

201.5 ± 59.68*

356.2 ± 89.7

189.9 ± 95.4*

Yield strength (σY), mechanical testing

MPa

40.4 ± 10.1*

100.5 ± 21.8

40.5 ± 22.4*

P < 0.05, where the reported values for the metastatic cancer and osteoporosis groups are different from normal

The bone volume fraction of the cancer specimens was 33% lower than that of the normal specimens (P = 0.001) and not different from that of the osteoporotic specimens (P = 0.45). Consistent with the pathophysiology of osteoporosis, which affects trabecular structure but not bone tissue mineralization [43, 44], BV/TVAVG of the osteoporotic specimens was 31% lower than that of the normal noncancer specimens (< 0.01) but ρTISSUE (P = 0.65), BSE mineral content (P = 0.24), H, and ENANO were not different between the osteoporotic and normal noncancer specimens (P > 0.05) (Table 2).

Sequential μCT images acquired after each incremental stepwise application of compressive strain demonstrated that the least rigid segment of the specimen where the most deformation occurred was at the subregion with the minimum BV/TV (Fig. 2).
https://static-content.springer.com/image/art%3A10.1007%2Fs00223-008-9174-x/MediaObjects/223_2008_9174_Fig2_HTML.gif
Fig. 2

Specimen (normal specimen shown here) is subdivided into 10 equal-sized transaxial segments (superimposed onto the 3D image of the entire specimen). The relative BV/TV value for each segment is demonstrated by the bar graph. Frames I–V portray the progressive deformation of the trabecular microstructure for the entire specimen. Most of the deformation occurs at the segments with the lowest BV/TV values (segments 4–7). The predominant mode of failure appears to be bending and/or buckling of individual trabeculae. While our results are based on uniaxial compression tests, failure of trabeculae by bending is an important mode of failure even when cancellous bone is subjected to torsion or tension [33, 81, 82]. A (red) representative trabecula (randomly selected from trabeculae that can be easily identified and highlighted in all images) in the magnified image sequence demonstrates the bending of an individual trabecula in response to progressive displacement

A multivariate, linear, mixed model tested the effects of tissue type (cancer, normal, osteoporosis) and anatomic site (spine, proximal femur, distal femur) while controlling for ρTISSUE and for BV/TV as covariates. Only BV/TV and anatomic site were independently predictive of the mechanical properties E and σY (P < 0.001). While three specimen groups were distinguished—normal, osteoporotic, and metastatic cancer—linear regression analyses were performed on the cancer and noncancer specimens, combining the normal and osteoporotic noncancer specimens together as parts of the same continuum [11], and on all the specimens (cancer and noncancer combined) to identify single analytic relationships (Table 3). ρTISSUE was poorly predictive of either E (R2 = 0.13) or σY (R2 = 0.11) when considered as the independent variable in the linear regression analysis. In comparison, the variation in BV/TVAVG accounted for 79% and 78% of the variation in E and σY, respectively, for all specimens combined regardless of pathology or skeletal site. However, the variation in BV/TVMIN accounted for 84% of the variation in E (Fig. 3a) and 83% of the variation in σY (Fig. 3b) for all specimens combined regardless of pathology or skeletal site.
Table 3

Mechanical properties of combined cancer and noncancer bone specimens expressed as function of ρTISSUE, BV/TVAVG, BV/TVMIN, or vBMD

Dependent variable

Equation

R2

E

E = 240 · ρTISSUE – 202

0.13

E = 889 · BV/TVAVG + 5.32

0.79

E = 1,050 · BV/TVMIN + 22.3

0.84

E = 1,060 · vBMD + 21.0

0.85

σY

σY = 7.6 · ρTISSUE – 8

0.11

σY = 30.0 · BV/TVAVG – 1.98

0.78

σY = 35.6 · BV/TVMIN – 1.4

0.83

σY = 36.5 · vBMD – 1.5

0.84

Models using BV/TVMIN as the independent variable predicted E and σY significantly better (< 0.01) than models using BV/TVAVG, confirming that the least rigid segment of the specimen identified as that with the BV/TVMIN accounted for most of the mechanical behavior of the entire specimen. Addition of ρTISSUE to the regression model did not make a significant contribution to the predictive power of the models for E or σY. Therefore, regression models where vBMD = ρTISSUE · BV/TVAVG was the independent variable were not different from regression models where only BV/TVMIN was the independent variable (P = 0.23 for E and P = 0.78 for σY)

https://static-content.springer.com/image/art%3A10.1007%2Fs00223-008-9174-x/MediaObjects/223_2008_9174_Fig3_HTML.gif
Fig. 3

Linear regression models illustrating that (a) modulus of elasticity and (b) yield strength of noncancer (normal and osteoporotic) and metastatic cancer cancellous bone specimens are functions of BV/TVMIN regardless of the underlying pathology. Linear regression models illustrating that (c) modulus of elasticity and (d) yield strength of noncancer (normal and osteoporotic) and metastatic cancer cancellous bone specimens are functions of vBMD regardless of the underlying pathology. Specimen groups: cancer (CA, red), noncancer (green), cancer and noncancer combined (black)

Using Fisher’s Z-transformation test, the coefficients of determination for the linear regressions where E and σY were dependent variables and BV/TVMIN was the independent variable were significantly better than the linear regressions where BV/TVAVG for the entire specimen was the independent variable (< 0.01) (Table 3). This implies that the least rigid segment through the bone specimen where most of the deformation occurs is identified by that cross section through the specimen with the minimum bone volume fraction. However, BV/TVAVG is correlated with BV/TVMIN for all specimens (R2 = 0.94, < 0.01).

vBMD, calculated as the product of ρTISSUE and BV/TVAVG, explained 85% of the variation in E (Fig. 3c) and 84% of the variation in σY (Fig. 3d) for all specimens combined regardless of pathology or skeletal site. Additionally, for the linear regressions fit separately to the cancer and noncancer specimens, the slopes and y-intercepts were not statistically different between the specimen groups for any of the independent variables evaluated—BV/TVAVG, P = 0.27; BV/TVMIN, P = 0.69; and vBMD, P = 0.44—supporting the hypothesis that the compressive mechanical properties of normal and pathologic bone affected by osteoporosis and/or metastatic cancer are well represented by a single analytic function that reflects the trabecular microstructure. The least rigid cross section through the bone specimen with the minimum BV/TV dictates the mechanical behavior of the entire bone specimen independent of skeletal site or bone pathology. Even though metastatic cancer affects the mineralization, hardness, and stiffness of cancellous bone tissue, this effect is evident primarily at the material level and has less impact on the macroscopic mechanical properties of the entire bone specimen.

Discussion

Osteoporosis and metastatic cancer affect millions of patients (often both in the same patient), and pathologic fracture is a common complication. Modeling human cancellous bone as rigid porous foam, we demonstrated that the cross section through the bone with the minimum bone volume fraction governed the mechanical behavior of the entire specimen for normal, osteoporotic, and metastatic cancer to bone. Surprisingly, bone tissue mineral density alone was not a strong indicator of the macroscopic mechanical behavior of cancellous bone. This result supports the hypothesis that the strength and stiffness of normal and pathologic cancellous bone affected by osteoporosis or metastatic cancer can be predicted using a unified relationship where vBMD or BV/TV measured by QCT is the independent variable. This work establishes the supremacy of bone structure over tissue-level material properties when accounting for the macroscopic, continuum-level behavior of cancellous bone. The unified relationships derived in this work suggest that the net response of cells responsible for making and destroying bone to modifiers of their activity are reflected by changes in the trabecular structure and bone volume fraction.

Since the cells that form and destroy bone are responsible for altering the bone structural and material properties, we hypothesized that, using measures of bone tissue mineralization and trabecular structure, a unified relationship could be derived that predicts the mechanical properties of normal and pathologic bone affected by osteoporosis and/or metastatic cancer. As noted by previous authors [45, 46], the inter- and intraspecimen variability in BMD and trabecular structure can be quite large depending on anatomic site and underlying bone pathology. Since the cancellous bone specimens were structurally heterogeneous, we drew an analogy with Castigliano’s second theorem for structures and postulated that the least rigid transaxial subregion through the specimen accounted for most of the specimen deformation and therefore dictated the mechanical behavior of the entire specimen. In the present study, the intraspecimen variation for BV/TV ranged 4–63%, with a mean of 24%. While the strength and stiffness of normal and pathologic bone specimens of similar BV/TV were variable, this variation was more than bracketed by the range of intra- and interspecimen variation in BV/TV for all the specimens. In particular, the variation in BV/TVMIN accounted for 84% of the variation in the compressive strength and modulus for all cancellous bone specimens independent of skeletal site or bone pathology, suggesting that the transaxial subregion through the specimen with the minimum BV/TV corresponded to the weakest subregion throughout the specimen with the least axial rigidity.

Even though the metastatic CA specimens were hypomineralized in comparison to the normal and osteoporotic specimens, bone tissue density accounted for <15% of the variation in stiffness and strength of the specimens; the addition of ρTISSUE explained little additional variation in stiffness or strength not explained by BV/TV alone. For both osteoporosis and metastatic cancer, osteoclast-mediated bone resorption results in a net loss of bone mass and a concomitant change in trabecular structure [47, 48]. Once osteoclasts have resorbed enough bone tissue to create a discontinuity in a trabecular element, that element can no longer support load. As the cross-struts between longitudinally oriented trabeculae become discontinuous, the remaining trabeculae become relatively longer (Fig. 4). Since buckling and bending are the predominant modes of trabecular deformation and failure [49, 50], these changes in trabecular structure influence the mechanical behavior of cancellous bone in disproportion to the corresponding change in mineral mass [40, 51, 52]. The buckling load for a trabecular column is proportional to EA/(l/r)2, where E is the modulus of elasticity of the bone tissue comprising the trabeculae, A is the cross-sectional area of the trabeculae, and l/r is the slenderness ratio, measured as the effective length to width ratio of the trabeculae. We evaluated the extent that trabecular microstructure accounted for the variation in BV/TV and strength by expressing both BV/TV and σY as a function of the inverse square root of the mean trabecular slenderness ratio. Overall, 77% of the variation in BV/TVAVG and nearly 70% of the variation in σY was explained by the mean slenderness ratio for cancer and noncancer specimens combined (Fig. 5a, b). The slope and y-intercept for the noncancer group were not statistically different from the combined data (P = 0.27); however, the slope and y-intercept for the cancer group was statistically different from the combined data (P < 0.001). This is partially due to the presence of local lesion in the cancer data where the slenderness ratio of the trabecular network is directly affected in specific areas. As a result, the changes in trabecular structure as a result of unbalanced bone remodeling pose a triple threat to the mechanical stability of the cancellous network that is disproportionate to the change in mass since not only are there fewer trabeculae but the remaining trabeculae have become thinner and longer, decreasing their stability to bending and buckling in a nonlinear fashion.
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Fig. 4

For both osteoporosis and metastatic cancer, osteoclast-mediated bone resorption results in a net loss of bone mass and a concomitant change in trabecular structure. This example illustrates how changes to the trabecular structure influence the mechanical behavior of cancellous bone in disproportion to the corresponding change in mineral mass. Cancellous bone is comprised of a network of trabecular struts. During unbalanced remodeling, osteoclasts along the surfaces of the trabeculae (red highlight) resorb bone. Once an osteoclast has resorbed enough bone tissue to create a discontinuity, that trabecula can no longer support load. As the transverse trabeculae forming cross-struts between the longitudinally oriented trabeculae become discontinuous, the remaining trabeculae become “functionally” longer. In this example there is a 27% decrease in bone mass but BV/TV has decreased by nearly 50% and the slenderness ratio (l/r) has increased by 56%. These changes in trabecular structure pose a triple threat to the mechanical stability of the cancellous network: Not only are there fewer trabeculae but the remaining trabeculae have become thinner and longer, thereby decreasing their stability to bending and buckling, the primary modes of trabecular failure at the microstructural level, and establishing the supremacy of trabecular structure over mineral mass

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Fig. 5

BV/TV (a) and σY (b) plotted as a function of the inverse square root of the slenderness ratio of trabecular elements for each specimen. Specimen groups: cancer (CA, red), noncancer (green), cancer and noncancer combined (black). Overall, 77% of the variation in BV/TV is accounted for by the variation in the inverse square root of the slenderness ratio of the trabeculae. However, for the noncancer specimens, 96% of the variation in BV/TV is explained by the variation in the inverse square root of the slenderness ratio of the trabeculae, but for the cancer specimens only 46% of the variation in BV/TV is explained by the variation in the inverse square root of the slenderness ratio of the trabeculae. This is partially due to the presence of specimens from patients with prostate cancer (with mostly osteoblastic lesions), where for a given bone volume fraction the trabeculae are thicker and shorter than specimens from mostly osteolytic lesions. For the noncancer bone, remodeling is slower and remains coupled under systemic control and the mean changes in trabecular thickness and length are representative of the changes in trabecular microstructure throughout the specimen. In metastatic cancer, malignant cells produce local factors that stimulate osteoclasts to aggressively resorb bone, creating lytic lesions. The bone remodeling process becomes uncoupled; bone formation is suppressed and the lesion cannot be repaired [83]. Unlike osteoporosis, the focal and localized resorption of trabeculae induced by metastatic breast cancer is not captured by the mean changes in trabecular thickness to length measured over the entire specimen

Due to the fragility of the metastatic cancer bone specimens, we were unable to test these specimens in tension or torsion. While compression is a common mode of failure, especially in the spine [53, 54], the skeleton is subjected to complex loads that induce tensile, compressive, and shear stresses in bone. Mechanical testing of normal human and bovine cancellous bone specimens has demonstrated that, similar to compression, the shear and tensile properties of cancellous bone depend on BMD [55, 56]. None of these studies compared the influence of ρTISSUE relative to BV/TV.

Considerable work has been undertaken to understand how alterations in bone density [13], trabecular microstructure [49, 57, 58], bone tissue mineralization [57, 59], organic matrix collagen composition [60, 61], and microcrack propagation [58, 62] affect the micro- and macroscopic mechanical properties of cancellous bone as a result of aging [63, 64] and metabolic bone diseases [65]. Several studies have evaluated bone strength as a function of mineral density [12, 14, 6668], bone volume fraction [11, 18, 6769], trabecular microstructure [70, 71], or a combination of these material and microstructural parameters [51, 72, 73] for normal and osteoporotic bone. Even though cancer metastatic to the skeleton affects millions of patients, few studies have measured the mechanical properties of bone tissue affected by metastatic cancer [6, 74]. Kaneko et al. [6] studied the mechanical properties of femora affected by metastatic cancer. They correlated the compressive strength and stiffness of cancer and noncancer specimens extracted from distal femora containing osteolytic lesions with vBMD measured by peripheral QCT. Similar to our study, they found that vBMD accounted for >77% of the mechanical behavior of the cancer and noncancer specimens combined.

The clinical implications of this work are important for developing noninvasive in vivo fracture risk predictions for bones affected by metastatic cancer, osteoporosis, or both using sequential, transaxial CT [4, 9, 75, 76] or magnetic resonance [7779] images of the involved bones. We have previously applied composite beam theory and structural engineering analysis to sequential, transaxial CT images of bones affected by benign and malignant neoplasms to calculate the load-carrying capacity of the bones and to predict the fracture risk in vivo for children with benign skeletal neoplasms and for women with metastatic breast cancer to the spine [3, 9]. Fracture risk assessments based on composite beam theory or patient-specific finite element models developed from 3D CT data sets [80] require constitutive data for each element of the model. The analytic relationships derived in this work provide these data: E and σY can be calculated from vBMD derived from the CT-based X-ray attenuation coefficient corresponding to each element of the model for normal, osteoporotic, or metastatic cancer cancellous bone.

Acknowledgements

This study was funded by National Institutes of Health grant CA40211 (to B. D. S.), Susan G. Komen grant BCTR0403271 (to B. D. S.), Swiss National Science Foundation grants FP 620–58097.99 and PP-104317/1 (to R. M.), and a Fulbright Full Grant for Graduate Study and Research Abroad (to A. N.). The authors acknowledge Dr. Marc Grynpas for BSE microscopy imaging, Dr. Zaifeng Fan for nanoindentation, Dr. Andrew Rosenberg for providing histological confirmation of skeletal metastasis in bone specimens, and Dr. Martin Stauber for assistance in image visualization. Additionally, they acknowledge Dr. Evan Snyder from Burnham Institute for Medical Research for reviewing the manuscript and providing helpful comments.

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© Springer Science+Business Media, LLC 2008