Effect of testosterone treatment on the trabecular bone score in older men with low serum testosterone

The trabecular bone score (TBS) is an indirect measure of vertebral bone microarchitecture. Our objective was to examine the effect of testosterone treatment on TBS. One hundred and ninety-seven hypogonadal men were randomized to testosterone or placebo. After 12 months, there was no difference in the changes in TBS by randomized group.

INTRODUCTION

In the Bone Trial of the Testosterone Trials, testosterone treatment increased trabecular volumetric bone mineral density (vBMD) and increased estimated bone strength as determined by finite element analysis. The trabecular bone score (TBS) is an indirect measure of vertebral bone microarchitecture. TBS predicts fracture independent of lumbar spine areal (a) BMD. The objective of this study was to examine the effect of testosterone treatment on TBS compared to its effects on vBMD and aBMD.

METHODS

Two hundred and eleven men were enrolled in the Bone Trial of the Testosterone Trials. Of these, 197 men had 2 repeat TBS and vBMD measurements; 105 men were allocated to receive testosterone, and 92 men to placebo for 1 year. TBS, aBMD, and vBMD were assessed at baseline and month 12.

RESULTS

There was no difference in the percent change in TBS by randomized group: 1.6% (95% confidence intervals (CI) 0.2-3.9) in the testosterone group and 1.4% (95% CI -0.2, 3.1) in the placebo group. In contrast, vBMD increased by 6% (95% CI 4.5-7.5) in the testosterone group compared to 0.4% (95% CI -1.65-0.88) in the placebo groups.

CONCLUSIONS

TBS is not clinically useful in monitoring the 1-year effect of testosterone treatment on bone structure in older hypogonadal men.

Bone density and strength from thoracic and lumbar CT scans both predict incident vertebral fractures independently of fracture location

In a population-based study, we found that computed tomography (CT)-based bone density and strength measures from the thoracic spine predicted new vertebral fracture as well as measures from the lumbar spine, suggesting that CT scans at either the thorax or abdominal regions are useful to assess vertebral fracture risk.

INTRODUCTION

Prior studies have shown that computed tomography (CT)-based lumbar bone density and strength measurements predict incident vertebral fracture. This study investigated whether CT-based bone density and strength measurements from the thoracic spine predict incident vertebral fracture and compared the performance of thoracic and lumbar bone measurements to predict incident vertebral fracture.

METHODS

This case-control study of community-based men and women (age 74.6 ± 6.6) included 135 cases with incident vertebral fracture at any level and 266 age- and sex-matched controls. We used baseline CT scans to measure integral and trabecular volumetric bone mineral density (vBMD) and vertebral strength (via finite element analysis, FEA) at the T8 and L2 levels. Association between these measurements and vertebral fracture was determined by using conditional logistic regression. Sensitivity and specificity for predicting incident vertebral fracture were determined for lumbar spine and thoracic bone measurements.

RESULTS

Bone measurements from T8 and L2 predicted incident vertebral fracture equally well, regardless of fracture location. Specifically, for predicting vertebral fracture at any level, the odds ratio (per 1-SD decrease) for the vBMD and strength measurements at L2 and T8 ranged from 2.0 to 2.7 (p < 0.0001) and 1.8 to 2.8 (p < 0.0001), respectively. Results were similar when predicting fracture only in the thoracic versus the thoracolumbar spine. Lumbar and thoracic spine bone measurements had similar sensitivity and specificity for predicting incident vertebral fracture.

CONCLUSION

These findings indicated that like those from the lumbar spine, CT-based bone density and strength measurements from the thoracic spine may be useful for identifying individuals at high risk for vertebral fracture.

Biomechanical Computed Tomography analysis (BCT) for clinical assessment of osteoporosis

The surgeon general of the USA defines osteoporosis as "a skeletal disorder characterized by compromised bone strength, predisposing to an increased risk of fracture." Measuring bone strength, Biomechanical Computed Tomography analysis (BCT), namely, finite element analysis of a patient's clinical-resolution computed tomography (CT) scan, is now available in the USA as a Medicare screening benefit for osteoporosis diagnostic testing. Helping to address under-diagnosis of osteoporosis, BCT can be applied "opportunistically" to most existing CT scans that include the spine or hip regions and were previously obtained for an unrelated medical indication. For the BCT test, no modifications are required to standard clinical CT imaging protocols. The analysis provides measurements of bone strength as well as a dual-energy X-ray absorptiometry (DXA)-equivalent bone mineral density (BMD) T-score at the hip and a volumetric BMD of trabecular bone at the spine. Based on both the bone strength and BMD measurements, a physician can identify osteoporosis and assess fracture risk (high, increased, not increased), without needing confirmation by DXA. To help introduce BCT to clinicians and health care professionals, we describe in this review the currently available clinical implementation of the test (VirtuOst), its application for managing patients, and the underlying supporting evidence; we also discuss its main limitations and how its results can be interpreted clinically. Together, this body of evidence supports BCT as an accurate and convenient diagnostic test for osteoporosis in both sexes, particularly when used opportunistically for patients already with CT. Biomechanical Computed Tomography analysis (BCT) uses a patient's CT scan to measure both bone strength and bone mineral density at the hip or spine. Performing at least as well as DXA for both diagnosing osteoporosis and assessing fracture risk, BCT is particularly well-suited to "opportunistic" use for the patient without a recent DXA who is undergoing or has previously undergone CT testing (including hip or spine regions) for an unrelated medical condition.

Treatment of bone loss in proximal femurs of postmenopausal osteoporotic women with AGN1 local osteo-enhancement procedure (LOEP) increases hip bone mineral density and hip strength: a long-term prospective cohort study

This first-in-human study of AGN1 LOEP demonstrated that this minimally-invasive treatment durably increased aBMD in femurs of osteoporotic postmenopausal women. AGN1 resorption was coupled with new bone formation by 12 weeks and that new bone was maintained for at least 5-7 years resulting in substantially increased FEA-estimated femoral strength.

INTRODUCTION

This first-in-human study evaluated feasibility, safety, and in vivo response to treating proximal femurs of postmenopausal osteoporotic women with a minimally-invasive local osteo-enhancement procedure (LOEP) to inject a resorbable triphasic osteoconductive implant material (AGN1).

METHODS

This prospective cohort study enrolled 12 postmenopausal osteoporotic (femoral neck T-score ≤ - 2.5) women aged 56 to 89 years. AGN1 LOEP was performed on left femurs; right femurs were untreated controls. Subjects were followed-up for 5-7 years. Outcomes included adverse events, proximal femur areal bone mineral density (aBMD), AGN1 resorption, and replacement with bone by X-ray and CT, and finite element analysis (FEA) estimated hip strength.

RESULTS

Baseline treated and control femoral neck aBMD was equivalent. Treated femoral neck aBMD increased by 68 ± 22%, 59 ± 24%, and 58 ± 27% over control at 12 and 24 weeks and 5-7 years, respectively (p < 0.001, all time points). Using conservative assumptions, FEA-estimated femoral strength increased by 41%, 37%, and 22% at 12 and 24 weeks and 5-7 years, respectively (p < 0.01, all time points). Qualitative analysis of X-ray and CT scans demonstrated that AGN1 resorption and replacement with bone was nearly complete by 24 weeks. By 5-7 years, AGN1 appeared to be fully resorbed and replaced with bone integrated with surrounding trabecular and cortical bone. No procedure- or device-related serious adverse events (SAEs) occurred.

CONCLUSIONS

Treating femurs of postmenopausal osteoporotic women with AGN1 LOEP results in a rapid, durable increase in aBMD and femoral strength. These results support the use and further clinical study of this approach in osteoporotic patients at high risk of hip fracture.

Prediction of incident vertebral fracture using CT-based finite element analysis

Prior studies show vertebral strength from computed tomography-based finite element analysis may be associated with vertebral fracture risk. We found vertebral strength had a strong association with new vertebral fractures, suggesting that vertebral strength measures identify those at risk for vertebral fracture and may be a useful clinical tool.

INTRODUCTION

We aimed to determine the association between vertebral strength by quantitative computed tomography (CT)-based finite element analysis (FEA) and incident vertebral fracture (VF). In addition, we examined sensitivity and specificity of previously proposed diagnostic thresholds for fragile bone strength and low BMD in predicting VF.

METHODS

In a case-control study, 26 incident VF cases (13 men, 13 women) and 62 age- and sex-matched controls aged 50 to 85 years were selected from the Framingham multi-detector computed tomography cohort. Vertebral compressive strength, integral vBMD, trabecular vBMD, CT-based BMC, and CT-based aBMD were measured from CT scans of the lumbar spine.

RESULTS

Lower vertebral strength at baseline was associated with an increased risk of new or worsening VF after adjusting for age, BMI, and prevalent VF status (odds ratio (OR) = 5.2 per 1 SD decrease, 95% CI 1.3-19.8). Area under receiver operating characteristic (ROC) curve comparisons revealed that vertebral strength better predicted incident VF than CT-based aBMD (AUC = 0.804 vs. 0.715, p = 0.05) but was not better than integral vBMD (AUC = 0.815) or CT-based BMC (AUC = 0.794). Additionally, proposed fragile bone strength thresholds trended toward better sensitivity for identifying VF than that of aBMD-classified osteoporosis (0.46 vs. 0.23, p = 0.09).

CONCLUSION

This study shows an association between vertebral strength measures and incident vertebral fracture in men and women. Though limited by a small sample size, our findings also suggest that bone strength estimates by CT-based FEA provide equivalent or better ability to predict incident vertebral fracture compared to CT-based aBMD. Our study confirms that CT-based estimates of vertebral strength from FEA are useful for identifying patients who are at high risk for vertebral fracture.

Finite element models predict the location of microdamage in cancellous bone following uniaxial loading

High-resolution finite element models derived from micro-computed tomography images are often used to study the effects of trabecular microarchitecture and loading mode on tissue stress, but the degree to which existing finite element methods correctly predict the location of tissue failure is not well characterized. In the current study, we determined the relationship between the location of highly strained tissue, as determined from high-resolution finite element models, and the location of tissue microdamage, as determined from three-dimensional fluoroscopy imaging, which was performed after the microdamage was generated in-vitro by mechanical testing. Fourteen specimens of human vertebral cancellous bone were assessed (8 male donors, 2 female donors, 47-78 years of age). Regions of stained microdamage, were 50-75% more likely to form in highly strained tissue (principal strains exceeding 0.4%) than elsewhere, and generally the locations of the regions of microdamage were significantly correlated (p<0.05) with the locations of highly strained tissue. This spatial correlation was stronger for the largest regions of microdamage (≥1,000,000μm(3) in volume); 87% of large regions of microdamage were located near highly strained tissue. Together, these findings demonstrate that there is a strong correlation between regions of microdamage and regions of high strain in human cancellous bone, particularly for the biomechanically more important large instances of microdamage.

The associations between QCT-based vertebral bone measurements and prevalent vertebral fractures depend on the spinal locations of both bone measurement and fracture

We examined how spinal location affects the relationships between quantitative computed tomography (QCT)-based bone measurements and prevalent vertebral fractures. Upper spine (T4-T10) fractures appear to be more strongly related to bone measures than lower spine (T11-L4) fractures, while lower spine measurements are at least as strongly related to fractures as upper spine measurements.

INTRODUCTION

Vertebral fracture (VF), a common injury in older adults, is most prevalent in the mid-thoracic (T7-T8) and thoracolumbar (T12-L1) areas of the spine. However, measurements of bone mineral density (BMD) are typically made in the lumbar spine. It is not clear how the associations between bone measurements and VFs are affected by the spinal locations of both bone measurements and VF.

METHODS

A community-based case-control study includes 40 cases with moderate or severe prevalent VF and 80 age- and sex-matched controls. Measures of vertebral BMD, strength (estimated by finite element analysis), and factor of risk (load:strength ratio) were determined based on QCT scans at the L3 and T10 vertebrae. Associations were determined between bone measures and prevalent VF occurring at any location, in the upper spine (T4-T10), or in the lower spine (T11-L4).

RESULTS

Prevalent VF at any location was significantly associated with bone measures, with odds ratios (ORs) generally higher for measurements made at L3 (ORs = 1.9-3.9) than at T10 (ORs = 1.5-2.4). Upper spine fracture was associated with these measures at both T10 and L3 (ORs = 1.9-8.2), while lower spine fracture was less strongly associated (ORs = 1.0-2.4) and only reached significance for volumetric BMD measures at L3.

CONCLUSIONS

Closer proximity between the locations of bone measures and prevalent VF does not strengthen associations between bone measures and fracture. Furthermore, VF etiology may vary by region, with VFs in the upper spine more strongly related to skeletal fragility.

A comparison of DXA and CT based methods for estimating the strength of the femoral neck in post-menopausal women

The study goal was to compare simple two-dimensional (2D) analyses of bone strength using dual energy x-ray absorptiometry (DXA) data to more sophisticated three-dimensional (3D) finite element analyses using quantitative computed tomography (QCT) data. DXA- and QCT-derived femoral neck geometry, simple strength indices, and strength estimates were well correlated.

INTRODUCTION

Simple 2D analyses of bone strength can be done with DXA data and applied to large data sets. We compared 2D analyses to 3D finite element analyses (FEA) based on QCT data.

METHODS

Two hundred thirteen women participating in the Study of Women's Health Across the Nation (SWAN) received hip DXA and QCT scans. DXA BMD and femoral neck diameter and axis length were used to estimate geometry for composite bending (BSI) and compressive strength (CSI) indices. These and comparable indices computed by Hip Structure Analysis (HSA) on the same DXA data were compared to indices using QCT geometry. Simple 2D engineering simulations of a fall impacting on the greater trochanter were generated using HSA and QCT femoral neck geometry; these estimates were benchmarked to a 3D FEA of fall impact.

RESULTS

DXA-derived CSI and BSI computed from BMD and by HSA correlated well with each other (R=0.92 and 0.70) and with QCT-derived indices (R=0.83-0.85 and 0.65-0.72). The 2D strength estimate using HSA geometry correlated well with that from QCT (R=0.76) and with the 3D FEA estimate (R=0.56).

CONCLUSIONS

Femoral neck geometry computed by HSA from DXA data corresponds well enough to that from QCT for an analysis of load stress in the larger SWAN data set. Geometry derived from BMD data performed nearly as well. Proximal femur breaking strength estimated from 2D DXA data is not as well correlated with that derived by a 3D FEA using QCT data.

Three-dimensional characterization of resorption cavity size and location in human vertebral trabecular bone

The number and size of resorption cavities in cancellous bone are believed to influence rates of bone loss, local tissue stress and strain and potentially whole bone strength. Traditional two-dimensional approaches to measuring resorption cavities in cancellous bone report the percent of the bone surface covered by cavities or osteoclasts, but cannot measure cavity number or size. Here we use three-dimensional imaging (voxel size 0.7×0.7×5.0 μm) to characterize resorption cavity location, number and size in human vertebral cancellous bone from nine elderly donors (7 male, 2 female, ages 47-80 years). Cavities were 30.10 ± 8.56 μm in maximum depth, 80.60 ± 22.23∗10(3) μm(2) in surface area and 614.16 ± 311.93∗10(3) μm(3) in volume (mean ± SD). The average number of cavities per unit tissue volume (N.Cv/TV) was 1.25 ± 0.77 mm(-3). The ratio of maximum cavity depth to local trabecular thickness was 30.46 ± 7.03% and maximum cavity depth was greater on thicker trabeculae (p<0.05, r(2)=0.14). Half of the resorption cavities were located entirely on nodes (the intersection of two or more trabeculae) within the trabecular structure. Cavities that were not entirely on nodes were predominately on plate-like trabeculae oriented in the cranial-caudal (longitudinal) direction. Cavities on plate-like trabeculae were larger in maximum cavity depth, cavity surface area and cavity volume than cavities on rod-like trabeculae (p<0.05). We conclude from these findings that cavity size and location are related to local trabecular microarchitecture.

Mechanical failure begins preferentially near resorption cavities in human vertebral cancellous bone under compression

The amount of bone turnover in the body has been implicated as a factor that can influence fracture risk and bone strength. Here we test the idea that remodeling cavities promote local tissue failure by determining if microscopic tissue damage (microdamage) caused by controlled loading in vitro is more likely to form near resorption cavities. Specimens of human vertebral cancellous bone (L4, 7 male and 2 female, age 70±10, mean±SD) were loaded in compression to the yield point, stained for microscopic tissue damage and submitted to three-dimensional fluorescent imaging using serial milling (image voxel size 0.7×0.7×5.0 μm). We found the resulting damage volume per bone volume (DV/BV) was correlated with percent eroded surface (p<0.01, r(2)=0.65), demonstrating that whole specimen measures of resorption cavities and microdamage are related. Locations of microdamage were more than two times as likely to have a neighboring resorption cavity than randomly selected sites without microdamage (relative risk 2.39, 95% confidence interval of relative risk: 2.09-2.73), indicating a spatial association between resorption cavities and microdamage at the local level. Individual microdamage sites were 48,700 (40,100; 62,700) μm(3) in size (median, 25th and 75th percentiles). That microdamage was associated with resorption cavities when measured at the whole specimen level as well as at the local level provides strong evidence that resorption cavities play a role in mechanical failure processes of cancellous bone and therefore have the potential to influence resistance to clinical fracture.

Validity of serial milling-based imaging system for microdamage quantification

Understanding the three-dimensional distribution of microdamage within trabecular bone may help provide a better understanding of the mechanisms of bone failure. Toward that end, a novel serial milling-based fluorescent imaging system was developed for quantifying microscopic damage in three dimensions throughout cores of trabecular bone. The overall goal for this study was to compare two-dimensional (2D), surface-based measures of microdamage extracted from this new imaging system against those from more conventional histological section analyses. Human vertebral trabecular cores were isolated, stained en bloc with a series of chelating fluorochromes, monotonically loaded, and underwent microdamage quantification via the two methods. Bone area fraction measured by the new system was significantly correlated to that measured by histological point counting (p<0.001, R(2)=0.80). Additionally, the new system produced statistically equivalent (p=0.021) measures of damage fraction (mean+/-SD), Dx.AF=0.047+/-0.021, to that obtained from stereological point counting, Dx.AF=0.048+/-0.017, at a 10% difference level. These results demonstrate that this serial milling-based fluorescent imaging system provides a destructive yet practical alternative to more conventional histologic section analysis in addition to its ability to provide a better understanding of the three-dimensional nature of microdamage.

Automated high-resolution three-dimensional fluorescence imaging of large biological specimens

We describe a novel automated technique for visualizing the three-dimensional distribution of fluorochrome-labelled components, in which image resolution is uncoupled from specimen size. This method is based on computer numerically controlled milling technology and combines an arrayed imaging technique with fluorescence capabilities. Fluorescent signals are segmented by emission spectra such that multiple fluorochromes present within a single specimen may be reconstructed and visualized individually or as a group. The automated nature of the system minimizes the workload and time involved in image capture and volume reconstruction. As an application, the system was used to image zones of fluorochrome-labelled microdamage within an 8-mm diameter cylinder of trabecular bone at a voxel size of 3 x 3 x 8 microm3. Our reconstruction of this specimen provides a visual map and quantitative measures of the volume of damage present throughout the cylinder, clearly demonstrating the interpretive power afforded by three-dimensional visualization. The three-dimensional nature of this highly automated and adaptable system has the potential to facilitate new diagnostic tools and techniques with application to a wide range of biological and medical research fields.

A biomechanical perspective on bone quality

Observations that dual-energy X-ray absorptiometry (DXA) measures of areal bone mineral density cannot completely explain fracture incidence after anti-resorptive treatment have led to renewed interest in bone quality. Bone quality is a vague term but generally refers to the effects of skeletal factors that contribute to bone strength but are not accounted for by measures of bone mass. Because a clinical fracture is ultimately a mechanical event, it follows then that any clinically relevant modification of bone quality must change bone biomechanical performance relative to bone mass. In this perspective, we discuss a framework for assessing the clinically relevant effects of bone quality based on two general concepts: (1) the biomechanical effects of bone quality can be quantified from analysis of the relationship between bone mechanical performance and bone density; and (2) because of its hierarchical nature, biomechanical testing of bone at different physical scales (<1 mm, 1 mm, 1 cm, etc.) can be used to isolate the scale at which the most clinically relevant changes in bone quality occur. As an example, we review data regarding the relationship between the strength and density in excised specimens of trabecular bone and highlight the fact that it is not yet clear how this relationship changes during aging, osteoporosis development, and anti-resorptive treatment. Further study of new and existing data using this framework should provide insight into the role of bone quality in osteoporotic fracture risk.

bFGF administration lowers the phosphate threshold for mineralization in bone marrow stromal cells

Basic fibroblast growth factor (bFGF) is a potent mitogen and acts as an autocrine/paracrine factor for osteoblasts. Long-term administration of bFGF in vivo increases osteoblast number and stimulates matrix formation, but induces hypophosphatemia and impairs matrix mineralization. The goal of this study was to examine the interaction between bFGF and low levels of organic phosphate in an effort to better understand the possible long-term therapeutic effects of bFGF. These data show that in vitro administration of bFGF accelerates the calcification process and lowers the phosphate threshold needed for successful bone nodule formation. This correlates well with the observed upregulation of mRNA production for alkaline phosphatase and osteocalcin at day 7. These findings help elucidate the mechanisms of bFGF action on bone marrow stromal cell differentiation and mineralization and indicate that the delay in mineralization observed in vivo may not be caused by decreased phosphate availability alone.

Mechanical and chemical characteristics of mineral produced by basic fibroblast growth factor-treated bone marrow stromal cells in vitro

It has been shown that various organ and cell cultures exhibit increased mineral formation with the addition of basic fibroblast growth factor (bFGF) and phosphate ions in the medium. However, to date there has been no attempt to relate the chemical composition of mineral formed in vitro to a measure of its mechanical properties. This information is important for understanding the in vivo mineralization process, the development of in vitro models, and the design of tissue-engineered bone substitutes. In this study we examined the reduced modulus; hardness; and mineral-to-matrix, crystallinity, carbonate-to-mineral, and calcium-to-phosphorus ratios of mineral formed by bFGF-treated rat-derived bone marrow stromal cells in vitro. The cells were treated with 1 or 3 mM beta-glycerophosphate for 3 and 4 weeks. Both mechanical parameters, reduced modulus and hardness, increased with increasing beta-glycerophosphate concentration. The only chemical measure of the mineral composition that exhibited the same dependency was the mineral-to-matrix ratio. The values of crystallinity and carbonate fraction were similar to those for intact cortical bone, but the calcium-to-phosphorus ratio was substantially lower than that of normal bone. These data indicate that the mineral formed by bFGF-treated bone cells is mechanically and chemically different from naturally formed lamellar bone tissue after 4 weeks in culture. These results can be used to improve in vitro models of mineral formation as well as enhance the design of tissue-engineered bone substitutes.

Architecture and trabecular bone - toward an improved understanding of the biomechanical effects of age, sex and osteoporosis

From an engineering perspective, trabecular bone is a highly complex material, being anisotropic with different strengths in tension, compression, and shear and with mechanical properties that vary widely across anatomic sites, and with aging and disease. While mechanical properties depend very much on volume fraction, the role of architecture and tissue material properties remain uncertain. In the context of osteoporosis, there is wide interest in the biomechanical role of architecture since this should lead to improved understanding of the disease and ultimately better diagnosis and drug treatment assessment. This study reviews what is known about architectural changes in trabecular bone associated with age, gender and osteoporosis and the role of these changes in the mechanical properties of bone. Recent development of three-dimensional high-resolution imaging technologies has provided more accurate measures of quantitative metrics of architecture, thereby providing new data and raising questions about earlier conclusions. Focusing on the hip and spine, this literature is synthesized and outstanding issues are identified. In addition, the changing paradigm of biomechanical research on trabecular architecture is addressed. Because of the complexity of the trabecular micromechanics, the prevailing approach to date can be classified as an inverse one, whereby candidate metrics of architecture are developed and tested for efficacy in an empirical trial-and-error fashion. In this approach, the biomechanics is treated only as an assay since it is not used to guide development of the candidate metrics. By contrast, a more forward approach is to study the associated micromechanics using engineering analysis and from that identify the metrics that in theory most affect mechanical properties. The latter approach, facilitated by the new high-resolution imaging techniques and increased computational power, is discussed in an attempt to direct attention to new types of architectural metrics that are independent of bone density and that should improve the ability to explain how age, gender and osteoporosis affect the mechanical properties of trabecular bone.

Biomechanics of trabecular bone

Trabecular bone is a complex material with substantial heterogeneity. Its elastic and strength properties vary widely across anatomic sites, and with aging and disease. Although these properties depend very much on density, the role of architecture and tissue material properties remain uncertain. It is interesting that the strains at which the bone fails are almost independent of density. Current work addresses the underlying structure-function relations for such behavior, as well as more complex mechanical behavior, such as multiaxial loading, time-dependent failure, and damage accumulation. A unique tool for studying such behavior is the microstructural class of finite element models, particularly the "high-resolution" models. It is expected that with continued progress in this field, substantial insight will be gained into such important problems as osteoporosis, bone fracture, bone remodeling, and design/analysis of bone-implant systems. This article reviews the state of the art in trabecular bone biomechanics, focusing on the mechanical aspects, and attempts to identify important areas of current and future research.

Relative roles of microdamage and microfracture in the mechanical behavior of trabecular bone

Compared to trabecular microfracture, the biomechanical consequences of the morphologically more subtle trabecular microdamage are unclear but potentially important because of its higher incidence. A generic three-dimensional finite element model of the trabecular bone microstructure was used to investigate the relative biomechanical roles of these damage categories on reloading elastic modulus after simulated overloads to various strain levels. Microfractures of individual trabeculae were modeled using a maximum fracture strain criterion, for three values of fracture strain (2%, 8%, and 35%). Microdamage within the trabeculae was modeled using a strain-based modulus reduction rule based on cortical bone behavior. When combining the effects of both microdamage and microfracture, the model predicted reductions in apparent modulus upon reloading of over 60% at an applied apparent strain of 2%, in excellent agreement with previously reported experimental data. According to the model, up to 80% of the trabeculae developed microdamage at 2% apparent strain, and between 2% and 10% of the trabeculae were fractured, depending on which fracture strain was assumed. If microdamage could not occur but microfracture could, good agreement with the experimental data only resulted if the trabecular hard tissue had a fracture strain of 2%. However, a high number of fractures (10% of the trabeculae) would need to occur for this case, and this has not been observed in published damage morphology studies. We conclude therefore that if the damage behavior of trabecular hard tissue is similar to that of cortical bone, then extensive microdamage is primarily responsible for the large loss in apparent mechanical properties that can occur with overloading of trabecular bone.

Trabecular eccentricity and bone adaptation

It is well established that bones functionally adapt by mechanisms that control tissue density, whole bone geometry, and trabecular orientation. In this study, we propose the existence of another such powerful mechanism, namely, trabecular eccentricity, i.e. non-central placement of trabecular bone within a cortical envelope. In the human femoral neck, trabecular eccentricity results in a thicker cortical shell on the inferior than superior aspect. In an overall context of expanding understanding of bone adaptation, the goal of this study was to demonstrate the biomechanical significance of, and provide a mechanistic explanation for, the relationship between trabecular eccentricity and stresses in the human femoral neck. Using composite beam theory, we showed that the biomechanical effects of eccentricity during a habitual loading situation were to increase the stress at the superior aspect of the neck and decrease the stress at the inferior aspect, resulting in an overall protective effect. Further, increasing eccentricity had a stress-reducing effect equivalent to that of increasing cortical thickness or increasing trabecular modulus. We conclude that an asymmetric placement of trabecular bone within a cortical bone envelope represents yet another mechanism by which whole bones can adapt to mechanical demands.

Effects of bone cement volume and distribution on vertebral stiffness after vertebroplasty

STUDY DESIGN

The biomechanical behavior of a single lumbar vertebral body after various surgical treatments with acrylic vertebroplasty was parametrically studied using finite-element analysis.

OBJECTIVES

To provide a theoretical framework for understanding and optimizing the biomechanics of vertebroplasty. Specifically, to investigate the effects of volume and distribution of bone cement on stiffness recovery of the vertebral body.

SUMMARY OF BACKGROUND DATA

Vertebroplasty is a treatment that stabilizes a fractured vertebra by addition of bone cement. However, there is currently no information available on the optimal volume and distribution of the filler material in terms of stiffness recovery of the damaged vertebral body.

METHODS

An experimentally calibrated, anatomically accurate finite-element model of an elderly L1 vertebral body was developed. Damage was simulated in each element based on empirical measurements in response to a uniform compressive load. After virtual vertebroplasty (bone cement filling range of 1-7 cm3) on the damaged model, the resulting compressive stiffness of the vertebral body was computed for various spatial distributions of the filling material and different loading conditions.

RESULTS

Vertebral stiffness recovery after vertebroplasty was strongly influenced by the volume fraction of the implanted cement. Only a small amount of bone cement (14% fill or 3.5 cm3) was necessary to restore stiffness of the damaged vertebral body to the predamaged value. Use of a 30% fill increased stiffness by more than 50% compared with the predamaged value. Whereas the unipedicular distributions exhibited a comparative stiffness to the bipedicular or posterolateral cases, it showed a medial-lateral bending motion ("toggle") toward the untreated side when a uniform compressive pressure load was applied.

CONCLUSION

Only a small amount of bone cement ( approximately 15% volume fraction) is needed to restore stiffness to predamage levels, and greater filling can result in substantial increase in stiffness well beyond the intact level. Such overfilling also renders the system more sensitive to the placement of the cement because asymmetric distributions with large fills can promote single-sided load transfer and thus toggle. These results suggest that large fill volumes may not be the most biomechanically optimal configuration, and an improvement might be achieved by use of lower cement volume with symmetric placement.

Dependence of yield strain of human trabecular bone on anatomic site

Understanding the dependence of human trabecular bone strength behavior on anatomic site provides insight into structure-function relationships and is essential to the increased success of site-specific finite element models of whole bones. To investigate the hypothesis that the yield strains of human trabecular bone depend on anatomic site, the uniaxial tensile and compressive yield properties were compared for cylindrical specimens from the vertebra (n=61), proximal tibia (n=31), femoral greater trochanter (n=23), and femoral neck (n=27) taken from 61 donors (67+/-15years). Test protocols were used that minimized end artifacts and loaded specimens along the main trabecular orientation. Yield strains by site (mean+/-S.D.) ranged from 0.70+/-0.05% for the trochanter to 0.85+/-0.10% for the femoral neck in compression, from 0.61+/-0.05% for the trochanter to 0.70+/-0.05% for the vertebra in tension, and were always higher in compression than tension (p<0.001). The compressive yield strain was higher for the femoral neck than for all other sites (p<0.001), as was the tensile yield strain for the vertebra (p<0.007). Analysis of covariance, with apparent density as the covariate, indicated that inter-site differences existed in yield stress even after adjusting statistically for density (p<0.035). Coefficients of variation in yield strain within each site ranged from only 5-12%, consistent with the strong linear correlations (r(2)=0.94-0.98) found between yield stress and modulus. These results establish that the yield strains of human trabecular bone can differ across sites, but that yield strain may be considered uniform within a given site despite substantial variation in elastic modulus and yield stress.

Osteoblasts respond to pulsatile fluid flow with short-term increases in PGE(2) but no change in mineralization

Although there is no consensus as to the precise nature of the mechanostimulatory signals imparted to the bone cells during remodeling, it has been postulated that deformation-induced fluid flow plays a role in the mechanotransduction pathway. In vitro, osteoblasts respond to fluid shear stress with an increase in PGE(2) production; however, the long-term effects of fluid shear stress on cell proliferation and differentiation have not been examined. The goal of this study was to apply continuous pulsatile fluid shear stresses to osteoblasts and determine whether the initial production of PGE(2) is associated with long-term biochemical changes. The acute response of bone cells to a pulsatile fluid shear stress (0.6 +/- 0.5 Pa, 3.0 Hz) was characterized by a transient fourfold increase in PGE(2) production. After 7 days of static culture (0 dyn/cm(2)) or low (0.06 +/- 0.05 Pa, 0.3 Hz) or high (0.6 +/- 0.5 Pa, 3.0 Hz) levels of pulsatile fluid shear stress, the bone cells responded with an 83% average increase in cell number, but no statistical difference (P > 0.53) between the groups was observed. Alkaline phosphatase activity per cell decreased in the static cultures but not in the low- or high-flow groups. Mineralization was also unaffected by the different levels of applied shear stress. Our results indicate that short-term changes in PGE(2) levels caused by pulsatile fluid flow are not associated with long-term changes in proliferation or mineralization of bone cells.

Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.

Nonlinear behavior of trabecular bone at small strains

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress-strain nonlinearity, that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean +/- SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07+/- 3.24 percent in compression and 13.8 +/- 4.79 percent in tension. At 0.40 percent strain, these values were 23.5 +/- 5.71 and 35.7+/- 7.10 percent, respectively. The magnitude of the nonlineari't depended on both anatomic site (p < 0.001) and loading mode (p < 0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p < 0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress-strain behavior more thoroughly.

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure-function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean+/-S.D.) 18.7+/-3.4GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.

Biomechanical consequences of an isolated overload on the human vertebral body

The biomechanical consequences of an isolated overload to the vertebral body may play a role in the etiology of vertebral fracture. In this context, we quantified residual strains and reductions in stiffness and ultimate load when vertebral bodies were loaded to various levels beyond the elastic regimen and related these properties to the externally applied strain and bone density. Twenty-three vertebral bodies (T11-L4, from 23 cadavers aged 20-90 years) were loaded once in compression to a randomized nominal strain level between 0.37 and 4.5%, unloaded, and then reloaded to 10% strain. Residual strains of up to 1.36% developed on unloading and depended on the applied strain (r2=0.85) but not on density (p = 0.25). Percentage reductions in stiffness and ultimate load of up to 83.7 and 52.5%, respectively, depended on both applied strain (r2 = 0.90 and r2 = 0.32, respectively) and density (r2 = 0.23 and r2 = 0.22, respectively). Development of residual strains is indicative of permanent deformations, whereas percentage reductions in stiffness are direct measures of effective mechanical damage. These results therefore demonstrate that substantial mechanical damage-which is not visible from radiographs-can develop in the vertebral body after isolated overloads, as well as subtle but significant permanent deformations. This behavior is similar to that observed previously for cylindrical cores of trabecular bone. Taken together, these findings indicate that the damage behavior of the lumbar and lower thoracic vertebral body is dominated by the trabecular bone and may be an important factor in the etiology of vertebral fracture.

Localized damage in vertebral bone is most detrimental in regions of high strain energy density

It was hypothesized that damage to bone tissue would be most detrimental to the structural integrity of the vertebral body if it occurred in regions with high strain energy density, and not necessarily in regions of high or low trabecular bone apparent density, or in a particular anatomic location. The reduction in stiffness due to localized damage was computed in 16 finite element models of 10-mm-thick human vertebral sections. Statistical analyses were performed to determine which characteristic at the damage location--strain energy density, apparent density, or anatomic location--best predicted the corresponding stiffness reduction. There was a strong positive correlation between regional strain energy density and structural stiffness reduction in all 16 vertebral sections for damage in the trabecular centrum (p < 0.05, r2 = 0.43-0.93). By contrast, regional apparent density showed a significant negative correlation to stiffness reduction in only four of the sixteen bones (p < 0.05, r2 = 0.47-0.58). While damage in different anatomic locations did lead to different reductions in stiffness (p < 0.0001, ANOVA), no single location was consistently the most critical location for damage. Thus, knowledge of the characteristics of bone that determine strain energy density distributions can provide an understanding of how damage reduces whole bone mechanical properties. A patient-specific finite element model displaying a map of strain energy density can help optimize surgical planning and reinforcement of bone in individuals with high fracture risk.

Heterogeneity of the mechanical properties of demineralized bone

Knowledge of the mechanical properties of the collagenous component of bone is required for composite modeling of bone tissue and for understanding the age- and disease-related reductions in the ductility and strength of bone. The overall goal of this study was to investigate the heterogeneity of the mechanical properties of demineralized bone which remains unexplained and may be due to differences in the collagen structure or organization or in experimental protocols. Uniaxial tension tests were conducted to measure the elastic and failure properties of demineralized human femoral (n = 10) and tibial (n = 13) and bovine humeral (n = 8) and tibial (n = 8) cortical bone. Elastic modulus differed between groups (p = 0.02), varying from 275 +/- 94 MPa (mean +/- SD) to 450 + 50 MPa. Similarly, ultimate stress varied across groups from 15 + 4.2 to 26 + 4.7 MPa (p = 0.03). No significant differences in strain-to-failure were observed between any groups in this study (pooled mean of 8.4 +/- 1.6%; p = 0.42). However, Bowman et al. (1996) reported an average ultimate strain of 12.3 +/- 0.5% for demineralized bovine humeral bone, nearly 40% higher than our value. Taken together, it follows that all the monotonic mechanical properties of demineralized bone can display substantial heterogeneity. Future studies directed at explaining such differences may therefore provide insight into aging and disease of bone tissue.

Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.

Structure-function relationships for coralline hydroxyapatite bone substitute

To improve the understanding of the functional requirements of trabecular bone substitutes, the structure-function relationships of coralline hydroxyapatite were determined and compared to those of trabecular bone from a variety of anatomic sites. Mechanical properties and permeability of cylindrical coralline hydroxyapatite specimens were measured and related to various morphological parameters that were obtained from analysis of high-resolution (20 microm) computer reconstructions of each specimen. Results indicated the average (+/-SD) Young's modulus (2900 +/- 1290 MPa, n = 20) and permeability (0.50 +/- 0.19 x 10(-9) m2, n = 21) of the coralline hydroxyapatite were within the range of values exhibited by high density trabecular bone; ultimate stress (5.87 +/- 1.92 MPa, n = 13), while in the range of mid-density trabecular bone, was low considering its high volume fraction (31.3 +/- 1.9%, n = 49); and ultimate strain (0.22 +/- 0.03%, n = 13) was much lower than that of trabecular bone from any anatomic site. The only correlation found between mechanical and morphological parameters was between Young's modulus and "fabric" (a scalar measure of architecture that combined the degree of microstructural anisotropy with orientation). These results provide insight into the in vivo performance of this implant, as well as the biomechanical requirements for successful trabecular bone substitutes in general.

Biomechanical effects of intraspecimen variations in trabecular architecture: a three-dimensional finite element study

Trabecular architecture is considered important in osteoporosis and has been quantified by a variety of mean parameters characteristic of a whole specimen. Variations within a specimen, however, have been mostly ignored. In this study, the theoretical effects of these intraspecimen variations in architecture on predicted mechanical properties were investigated through a three-dimensional finite element parameter study that simulated variations in trabecular thickness in a controlled manner. An irregularly spaced lattice of different sized rods was used to simulate trabecular bone in three distinct volume fraction ranges, representing young, middle-aged, and elderly vertebral bone. Beta distributions (a type of non-normal distribution) of trabecular thickness with coefficients of variation of either 25%, 40%, or 55% were applied to the rods in each model, and 225 simulations of uniaxial compression tests were performed to obtain modulus values. Percent modulus reductions of 22% and 43% were predicted when the intraspecimen coefficient of variation in trabecular thickness was increased from 25% to 40% and from 25% to 55%, respectively, for models of equal volume fraction. Furthermore, this trend was predicted to be independent of volume fraction. We conclude, therefore, that consideration of the intraspecimen trabecular thickness variation in conjunction with volume fraction may improve the ability to predict trabecular modulus compared with use of volume fraction alone. Further, the model suggests that if age, disease, or drug treatments increase trabecular thickness variation, this may be detrimental to mechanical properties.

A cellular solid criterion for predicting the axial-shear failure properties of bovine trabecular bone

In a long-term effort to develop a complete multi-axial failure criterion for human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai-Wu, Principal Strain, and von Mises phenomenological criteria--all normalized to minimize effects of interspecimen heterogeneity of strength--to predict the on-axis axial-shear failure properties of bovine trabecular bone. The Cellular Solid criterion that was developed here assumed that vertical trabeculae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, respectively. Twenty-seven bovine tibial trabecular bone specimens were destructively tested on-axis without end artifacts, loaded either in combined tension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6). For compression-shear, the mean (+/- S.D.) percentage errors between measured values and criterion predictions were 7.7 +/- 12.6 percent, 19.7 +/- 23.2 percent, 22.8 +/- 18.9 percent, and 82.4 +/- 64.5 percent for the Cellular Solid, Tsai-Wu, Principal Strain, and von Mises criteria, respectively; corresponding mean errors for tension-shear were -5.2 +/- 11.8 percent, 14.3 +/- 12.5 percent, 6.9 +/- 7.6 percent, and 57.7 +/- 46.3 percent. Statistical analysis indicated that the Cellular Solid criterion was the best performer for compression-shear, and performed as well as the Principal Strain criterion for tension-shear. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More importantly, the results firmly establish the importance of cellular solid analysis for understanding and predicting the multiaxial failure behavior of trabecular bone.

Measurement of intraspecimen variations in vertebral cancellous bone architecture

A three-dimensional technique was developed for the quantification of the number and cross-sectional geometry of individual trabeculae oriented along a given direction. As an example application, the number of vertical and horizontal trabeculae and their respective cross-sectional geometry were determined for a set of six vertebral cancellous bone specimens (L3-L4 female vertebral bodies; age range 39-63 years). Three-dimensional optical images at a spatial resolution of 20 microm were obtained using an automated serial milling technique. The thickness distributions were generally right skewed. The mean true thickness for both the vertically and horizontally oriented trabeculae showed a strong relationship with volume fraction (vertical: r2 = 0.86; p < 0.05; horizontal: r2 = 0.80; p < 0.05), and mean trabecular thickness (Tb.Th.) (vertical: r2 = 0.81; p < 0.05; horizontal: r2 = 0.72; p < 0.05). The horizontal trabeculae were greater in number and were thinner than the vertical trabeculae. The coefficient of variation of the intraspecimen vertical trabecular thicknesses ranged from 25% to 42%, and showed a weak, albeit insignificant, positive correlation with volume fraction (r2 = 0.46). The findings demonstrated substantial intraspecimen variations exist in trabecular thickness that are not related to volume fraction. Further studies are recommended to determine the potential role of such intraspecimen variations in architecture on biomechanical properties.

Uniaxial yield strains for bovine trabecular bone are isotropic and asymmetric

Although evidence suggests that yield strains for trabecular bone are isotropic, i.e., independent of loading direction, decisive support for this hypothesis has remained elusive. To explicitly test whether yield strains for trabecular bone are isotropic, compressive and tensile yield strains of 51 specimens of bovine tibial trabecular bone (0.41 +/- 0.08 g/cm3 [mean apparent density +/- SD]) were measured without end artifacts in on-axis (along the principal trabecular orientation) and off-axis (30-40 degrees oblique to on-axis) orientations. Yield strains for the on-axis and off-axis orientations were similar in tension (0.80 +/- 0.03% compared with 0.85 +/- 0.04%, p = 0.21) and compression (0.97 +/- 0.05% compared with 0.96 +/- 0.07%, p > 0.99); as expected, modulus and strength depended on loading direction. When considered with an ancillary experiment on bovine tibial trabecular bone that showed yield strains to be similar between on-axis and 90 degrees off-axis bone, these results firmly establish the isotropy of uniaxial yield strains for bovine tibial trabecular bone. This bone is of high density and has a strong, plate-type, anisotropic architecture. Therefore, yield strains for uniaxial loading are expected to be isotropic, or nearly so, for other types of dense trabecular bone, although further work is required to confirm this and to establish this behavior for bone of lower density.

Dependence of intertrabecular permeability on flow direction and anatomic site

The structure-function relationships for the permeability of trabecular bone may have relevance for tissue engineering, total joint replacements, and whole bone mechanics. To investigate such relationships, we used a constant flow rate permeameter to determine the intrinsic permeability of trabecular bone specimens, oriented longitudinally or transversely to the principal trabecular orientation, from the human vertebral body (n=20), human proximal femur (n=12), and bovine proximal tibia (n=24). Overall, the intertrabecular permeability ranged from 2.68 x 10(-11) to 2.00 x 10(-8) m2. Significant negative nonlinear relations between intertrabecular permeability and volume fraction were found for each group except the longitudinal bovine proximal tibial specimens (r2=0.34-0.80). The average permeability ratio, a measure of the anisotropy, was 2.05, 6.60, and 23.3 for the human vertebral body, bovine tibia, and human femur, respectively. The permeability depended strongly on flow direction relative to the principal trabecular orientation (p<0.0001) and anatomic site (p <0.0001). In addition to providing a comprehensive description of intertrabecular permeability as a function of anatomic site and flow direction, these data provide substantial insight into the underlying structure-function relationships.

Characterization of the mechanical and ultrastructural properties of heat-treated cortical bone for use as a bone substitute

Heat-treated bovine cortical bone has been proposed as an alternative to bone grafts and synthetic bone substitutes because it may combine the advantages of allografts (high stiffness and strength) and synthetic materials (abundant supply, reduced risk of rejection and disease transfer). Its mechanical properties and ultrastructure, however, are not well characterized. To address this, we compared the compressive (n = 20, bovine bone) and tensile (n = 26, bovine bone) mechanical properties and the ultrastructure (n = 12, human bone) of intact versus 350 degrees C heat-treated cortical bone. The 350 degrees C heat-treated bone had a mean +/- SD elastic modulus similar to the intact bone for both compression (16.3 +/- 2.2 GPa, pooled; p = 0.68) and tension (16.3 +/- 3.7 GPa, pooled; p = 0.95). It also maintained 63% of the intact strength in compression but only 9% in tension (p < 0.001). Infrared scans and X-ray diffraction patterns showed no differences between the 350 degrees C heat-treated and intact bone but large differences between ashed (700 degrees C) and intact bone. Similarly, heat-treated bone previously has been shown to be biocompatible and osteoconductive. We conclude, therefore, that 350 degrees C heat-treated cortical bone may be an excellent load-bearing bone substitute provided that it is loaded in compression only in vivo and is shown by future work to have acceptable fatigue properties.

Mechanical behavior of human trabecular bone after overloading

With the etiology of osteoporotic fractures as motivation, the goal of this study was to characterize the mechanical behavior of human trabecular bone after overloading. Specifically, we quantified the reductions in modulus and strength and the development of residual deformations and determined the dependence of these parameters on the applied strain and apparent density. Forty cylindrical specimens of human L1 vertebral trabecular bone were destructively loaded in compression at 0.5% strain per second to strains of up to 3.0% and then immediately unloaded to zero stress and reloaded. (An ancillary experiment on more readily available bovine bone had been performed previously to develop this testing protocol.) In general, the reloading stress-strain curve had a short initial nonlinear region with a tangent modulus similar to Young's modulus. This was followed by an approximately linear region spanning to 0.7% strain, with a reduced residual modulus. The reloading curve always approached the extrapolated envelope of the original loading curve. Percent modulus reduction (between Young's and residual), a quantitative measure of mechanical damage, ranged from 5.2 to 91.0% across the specimens. It increased with increasing plastic strain (r2 = 0.97) but was not related to modulus or apparent density. Percent strength reduction, in the range of 3.6-63.8%, increased with increasing plastic strain (r2 = 0.61) and decreasing apparent density (r2 = 0.23). The residual strains of up to 1.05% depended strongly on applied strain (r2 = 0.96). Statistical comparisons with previous data for bovine tibial bone lend substantial generality to these trends and provide an envelope of expected behavior for other sites. In addition to providing a basis for biomechanical analysis of the effects of damage in trabecular bone at the organ level, these findings support the concept that occasional overloads may increase the risk of fracture by substantially degrading the mechanical properties of the underlying trabecular bone.

Quantitative assessment of steady and pulsatile flow fields in a parallel plate flow chamber

Steady and pulsatile flows were imaged and quantified in a parallel plate flow chamber that was designed to allow constant variation of the volumetric flow rate and to minimize pressure gradients across the width of the flow field. Results indicated that both the steady and pulsatile flow fields were uniform across the width of the flow chamber as shown by linear regression analysis. Further, the dynamic effects of the fluid pulse were transmitted almost instantaneously across the length of the flow field. These findings verify that parallel plate devices designed in this manner are suitable for delivering uniform steady and pulsatile shear stress to adherent cell populations in vitro.

Application of the Tsai-Wu quadratic multiaxial failure criterion to bovine trabecular bone

As a first step toward development of a multiaxial failure criterion for human trabecular bone, the Tsai-Wu quadratic failure criterion was modified as a function of apparent density and applied to bovine tibial trabecular bone. Previous data from uniaxial compressive, tensile, and torsion tests (n = 139 total) were combined with those from new triaxial tests (n = 17) to calibrate and then verify the criterion. Combinations of axial compression and radial pressure were used to produce the triaxial compressive stress states. All tests were performed with minimal end artifacts in the principal material coordinate system of the trabecular network. Results indicated that the stress interaction term F12 exhibited a strong nonlinear dependence on apparent density (r2 > 0.99), ranging from -0.126 MPa-2 at low densities (0.29 g/cm3) to 0.005 MPa-2 at high densities (0.63 g/cm3). After calibration and when used to predict behavior of new-specimens without any curve-fitting, the Tsai-Wu criterion had a mean (+/- SD) error of -32.6 +/- 10.6 percent. Except for the highest density triaxial specimens, most (15/17 specimens) failed at axial stresses close to their predicted uniaxial values, and some reinforcement for transverse loading was observed. We conclude that the Tsai-Wu quadratic criterion, as formulated here, is at best only a reasonable predictor of the multiaxial failure behavior of trabecular bone, and further work is required before it can be confidently applied to human bone.

Creep contributes to the fatigue behavior of bovine trabecular bone

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53 degrees C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.

Yield strain behavior of trabecular bone

If bone adapts to maintain constant strains and if on-axis yield strains in trabecular bone are independent of apparent density, adaptive remodeling in trabecular bone should maintain a constant safety factor (yield strain/functional strain) during habitual loading. To test the hypothesis that yield strains are indeed independent of density, compressive (n = 22) and tensile (n = 22) yield strains were measured without end-artifacts for low density (0.18 +/- 0.04 g cm(-3)) human vertebral trabecular bone specimens. Loads were applied in the superior-inferior direction along the principal trabecular orientation. These 'on-axis' yield strains were compared to those measured previously for high-density (0.51 +/- 0.06 g cm(-3)) bovine tibial trabecular bone (n = 44). Mean (+/- S.D.) yield strains for the human bone were 0.78 +/- 0.04% in tension and 0.84 +/- 0.06% in compression; corresponding values for the bovine bone were 0.78 +/- 0.04 and 1.09 +/- 0.12%, respectively. Tensile yield strains were independent of the apparent density across the entire density range (human p = 0.40, bovine p = 0.64, pooled p = 0.97). By contrast, compressive yield strains were linearly correlated with apparent density for the human bone (p < 0.001) and the pooled data (p < 0.001), and a suggestive trend existed for the bovine data (p = 0.06). These results refute the hypothesis that on-axis yield strains for trabecular bone are independent of density for compressive loading, although values may appear constant over a narrow density range. On-axis tensile yield strains appear to be independent of both apparent density and anatomic site.

Computed tomography-based finite element analysis predicts failure loads and fracture patterns for vertebral sections

Computed tomography-based finite element analysis represents a powerful research tool for investigating the mechanics of skeletal fractures. To provide evidence that this technique can be used to predict failure loads and fracture patterns for bone structures, we compared the observed and predicted failure behaviors of 18 midsagittal sections, 10 mm thick, cut from human vertebral bodies. The specimens were scanned by computed tomography, and finite element models were generated with use of empirically determined density-property relations to assign element-specific material properties. The specimens were loaded to failure in uniaxial compression, and the models were analyzed under matching conditions. The models provided predictions of yield load that were strongly correlated with experimentally measured values (r2 > 0.86) and were typically within 25% of measured values. Predicted stiffness values were moderately correlated with measured values, but large absolute differences existed between them. Comparisons between regions of observed fracture and of high predicted strain indicated that strain was an accurate indicator of the pattern of local fracture in more than two-thirds of the bone specimens. In addition, strain contour plots provided better indicators of local fracture than did stress plots in these heterogeneous bone structures. We conclude that computed tomography-based finite element analysis can be used successfully to predict both global and local failure behavior of simplified skeletal structures.

Impact of spatial resolution on the prediction of trabecular architecture parameters

Although the efficacy of various measures for the assessment of trabecular bone architecture has been widely studied, the impact of spatial resolution on the estimation of these measures has remained relatively unexplored. In this study, ten cubes each of human trabecular bone from the femur and vertebral bodies were obtained from nine cadavers (four males and five females), aged 23-67 years (mean 42.3 years). These specimens were serially milled and imaged at a resolution of 40 microm to produce three-dimensional digitizations from which traditional morphometric and structural anisotropy measures could be computed based on a three-dimensional approach. The cubes were then artificially degraded to an in-plane resolution of 100 microm and an out-of-plane (slice) resolution of 100-1000 microm. These resolutions mimicked in vivo resolutions as seen using magnetic resonance (MR) imaging. All images, original and degraded, were individually segmented using a thresholding algorithm, and both the traditional morphometric and structural anisotropy measures were recomputed. The choice of slice direction was varied along the superior-inferior (axial), anterior-posterior (coronal), and medial-lateral (sagittal) directions to minimize the impact of the lower slice resolution on the architectural measures. It was found that traditional morphometric measures such as trabecular spacing and trabecular number showed weak resolution dependency; measures such as trabecular thickness, however, showed strong resolution dependency and required very high resolutions for precise measurement. In the case of the femur specimens, both structural anisotropy as well as the preferred orientation showed a strong resolution dependency. The resolution dependency of these parameters could be minimized for the femur and the vertebral body specimens if the slice direction was taken along the superior-inferior direction.

Three-dimensional imaging of trabecular bone using the computer numerically controlled milling technique

Although various techniques exist for high-resolution, three-dimensional imaging of trabecular bone, a common limitation is that resolution depends on specimen size. Most techniques also have limited availability due to their expense and complexity. We therefore developed a simple, accurate technique that has a resolution that is independent of specimen size. Thin layers are serially removed from an embedded bone specimen using a computer numerically controlled (CNC) milling machine, and each exposed cross section is imaged using a low-magnification digital camera. Precise positioning of the specimen under the camera is achieved using the programmable feature of the CNC milling machine. Large specimens are imaged without loss of resolution by moving the specimen under the camera such that an array of field-of-views spans the full cross section. The images from each field-of-view are easily assembled and registered in the postprocessing. High-contrast sections are achieved by staining the bone black with silver nitrate and embedding it in whitened methylmethacrylate. Due to the high contrast nature and high resolution of the images, thresholding at a single value yielded excellent predictions of morphological parameters such as bone volume fraction (mean +/- SD percent error = 0.70 +/- 4.28%). The main limitations of this fully automated "CNC milling technique" are that the specimen is destroyed and the process is relatively slow. However, because of its accuracy, independence of image resolution from specimen size, and ease of implementation, this new technique is an excellent method for ex situ imaging of trabecular architecture, particularly when high resolution is required.

Dependence of trabecular damage on mechanical strain

Trabecular damage may play a role in hip fracture, bone remodeling, and prosthesis loosening. We hypothesized that when trabecular bone is loaded beyond its elastic range, both the type and the amount of damage depend on the applied strains. Thirty specimens of trabecular bone from the bovine tibia underwent compression tests to one of three levels of strain (0.4. 1.0. and 2.5%) (n = 10 per group). The 0.4% level was a mechanically nondestructive control group that accounted for any systematic errors. Optical microscopy at magnifications as high as x200 was then used to quantify the trabecular damage for each group. The amount of damage in the yield group (1.0% strain) did not differ from that in the control group (p = 0.66), whereas damage in the post-ultimate strain group (2.5% strain) increased more than 3-fold (p < 0.0008). Four types of damage were observed: transverse cracks, shear bands, parallel cracks, and complete fractures, of which the first two were dominant. These findings therefore indicate that damage occurs within trabeculae at yield. By comparison with our previous work, it can also be concluded that substantial modulus reductions in trabecular bone (as much as 60%) are caused by damage primarily within trabeculae. The ability to detect such damage clinically may improve in vivo estimates of whole-bone strength by identifying regions of densitometrically normal but mechanically compromised trabecular bone.

Load sharing between the shell and centrum in the lumbar vertebral body

STUDY DESIGN

A finite element parametric analysis to investigate the relative load carrying roles of the shell and centrum in the lumbar vertebral body.

OBJECTIVE

To address the issue of the structural role of the vertebral shell and clarify some of the contradictions raised by previous studies.

SUMMARY OF BACKGROUND DATA

A number of experimental and finite element studies have attempted to quantify the relative structural roles of the shell and centrum, but these studies support no consensus on the relative contribution of the shell to vertebral body strength.

METHODS

The authors developed finite element models to predict the fraction of the total compressive force acting on the lumbar vertebral body that is carried by the shell. Parametric variations were investigated to determine how the fraction of shell force was affected by changes in shell thickness, shell and centrum modulus, centrum anistropy, and loading conditions.

RESULTS

The fraction of compressive force carried by the shell increased from approximately 0 at the endplate to approximately 0.2 at the mid-transverse plane for a typical case. The shell force was highly sensitive to the degree of anisotropy of the trabecular centrum but was relatively insensitive to changes in shell thickness and the ratio of shell-to-centrum elastic modulus.

CONCLUSIONS

The conflicting conclusions of previous studies about the structural roles of the vertebral shell and centrum can be explained by differences in their methods. Our findings support the claims that the shell accounts for only approximately 10% of vertebral strength in vivo and that the trabecular centrum is the dominant structural component of the vertebral body.

Systematic and random errors in compression testing of trabecular bone

We sought to quantify the systematic and random errors associated with end-artifacts in the platens compression test for trabecular bone. Our hypothesis was that while errors may depend on anatomic site, they do not depend on apparent density and therefore have substantial random components. Trabecular bone specimens were first tested nondestructively using newly developed accurate protocols and then were tested again using the platens compression test. Percentage differences in modulus between the techniques (bovine proximal tibia [n = 18] and humerus [n = 17] and human lumbar spine, [n = 9]) were in the range of 4-86%. These differences did not depend on anatomic site (p = 0.21) and were only weakly dependent on apparent density and specimen aspect ratio (r2 < 0.10). The mean percentage difference in modulus was 32.6%, representing the systematic component of the end-artifact error. Neglecting the minor variations explained by density and specimen size (approximately 10%), an upper bound on the random error from end-artifacts in this experiment was taken as the SD of the modulus difference (+/-18.2%). Based on a synthesis of data taken from this study and from the literature, we concluded that the systematic underestimation error in the platens compression test can be only approximated and is in the range of 20-40%; the substantial random error (+/-12.5%) confounds correction, particularly when the sample size is small. These errors should be considered when interpreting results from the platens test, and more accurate testing techniques should be used when such errors are not acceptable.

The dependence of shear failure properties of trabecular bone on apparent density and trabecular orientation

The shear properties of trabecular bone, in particular the shear failure strains, are not well understood despite their potential importance in age-related fractures and prosthesis loosening. We hypothesized that shear failure strains (yield and ultimate) are independent of apparent density and trabecular orientation, i.e. are homogeneous and isotropic. We measured the shear failure properties of bovine tibial trabecular bone, where specimens were loaded to failure in torsion longitudinally (n = 25) or transversely (n = 23) relative to the primary trabecular orientation. We found that although failure stresses depended strongly on apparent density (r2 = 0.61 - 0.80), failure strains were independent of apparent density for both trabecular orientations. Although the mean (+/-S.D.) yield strain in the longitudinal group (1.46 +/- 0.19%) was 10% higher (p = 0.01) than in the transverse group (1.33 +/- 0.15%), indicating a slight anisotropy of shear yield strains, the mean ultimate strains did not depend on trabecular orientation (longitudinal group 4.60 +/- 0.77% vs transverse group 4.24 +/- 1.25%, p = 0.20). These findings indicate that shear failure strains are homogeneous and largely isotropic. By combining our shear data with compressive data from a previous experiment, we also predicted that trabecular bone can fail in shear when subjected to compressive loads that are not aligned with the principal trabecular orientation. If this prediction holds for human bone, shear may be a dominant failure mode during off-axis loading of trabecular bone in vivo, such as during falls on the hip.

The effect of impact direction on the structural capacity of the proximal femur during falls

As with any structure, the structural capacity of the proximal femur depends on the applied loads and these can vary as a function of impact direction during a fall. However, despite its potential importance in hip fracture risk assessment, the relative importance of impact direction is unknown. To investigate the role of impact direction in hip fracture, we developed a detailed finite element model of the proximal femur. We analyzed four loading configurations that represent a range of possible falls on the greater trochanter. Our results indicate that a change in the angle between the line of action of the applied force and the axis of the femoral neck from 0 degrees (representing a direct lateral impact) to 45 degrees (representing a posterolateral impact) reduced structural capacity by 26%. This weakening of the femur with changes in impact direction is comparable to the weakening associated with 2-3 decades of age-related bone loss. Our result elucidates the independent contribution of fall mechanics to hip fracture risk by identifying an aspect of the fall (the direction of impact) that is an important determinant of fall severity. The results can also be incorporated into a refined clinical method for assessment of hip fracture risk that accounts for the complex interactions between fall severity and bone fragility.

Mechanical consequences of bone ingrowth in a hip prosthesis inserted without cement

Long-term biomechanical problems associated with the use of sintered porous coating on prosthetic femoral stems inserted without cement include proximal loss of bone and a risk of fatigue fracture of the prosthesis. We sought to identify groups of patients in whom these problems are accentuated and in whom the use of porous coating may thus jeopardize the success of the arthroplasty. We attempted to develop clinical guidelines for the use of sintered porous coating by investigating the long-term biomechanical effects of bone growth into partially (two-thirds) porous-coated anatomic medullary locking hip prostheses that fit well. More specifically, we used a detailed finite element analysis and a composite beam theory to determine the dependence of proximal loading of the bone and maximum stresses on the stem on the development of clinically observed patterns of bone ingrowth and the dependence of the risk of fatigue fracture of the stem on the diameter of the stem, the diameter of the periosteal bone, and the material from which the prosthesis was made. We found that bone ingrowth per se substantially reduced proximal loading of the bone. With typical bone ingrowth, axial and torsional loads acting on the proximal end of the bone were reduced aa much as twofold compared with when there was no ingrowth; bending loads on the proximal end of the bone were also reduced. The risk of fatigue fracture of the stem was insensitive to the development of bone ingrowth. However, the risk of fatigue fracture of the stem increased with decreased diameters of the stem and the periosteal bone and with increased modulus of the stem. The maximum risk of fracture was found in active patients in whom a cobalt-chromium-alloy stem with a small diameter had been implanted in a bone with a small diameter.