On sampling bones for microcracks.

This paper addresses the problem of designing experiments to measure microcrack density in cortical bone. Microcracks are relatively scarce in bone cross-sections, and their size requires microscope settings having small fields of view. Thus, substantial time is required to count cracks in each cross-section. Consequently, most studies evaluate a relatively small cross-sectional area from each specimen, the chance of finding a crack in any given field is small, and there is a significant chance of not finding even one crack in the specimens representing a particular subject. Therefore, a statistical model for microcrack counting was created to develop guidelines for sampling bones for microcracks. Three questions were addressed. 1) What are the relationships of sample size to variability in microcrack density results and the probability of crackless specimens? 2) How can sample size be chosen a priori so as to reduce the probability of crackless specimens and the associated variability in the data to an acceptable level? 3) What are the confidence intervals for the mean density of microcracks measured using microscopic counting? Using a Poisson model for the distribution of microcracks within microscope fields the total area (mm(2)) that should be examined for each specimen is given by A(s)=-ln(F)/Cr.Dn, where Cr.Dn is the expected microcrack density for an individual sample and F is the desired probability (expressed as a fraction) that the individual sample will contain no microcracks. This equation is validated against 8 results from three different experiments.

Do microcracks decrease or increase fatigue resistance in cortical bone?

Fatigue of cortical bone produces microcracks; it has been hypothesized that these cracks are analogous to those occurring in engineered composite materials and constitute a similar mechanism for fatigue resistance. However, the numbers of these linear microcracks increase substantially with age, suggesting that they contribute to increased fracture incidence among the elderly. To test these opposing hypotheses, we fatigued 20 beams of femoral cortical bone from elderly men and women in load-controlled four point bending having initial strain ranges of 3000 or 5000 microstrain. Loading was stopped at fracture or 10(6) cycles, whichever occurred first, and microcrack density and length were measured in the loaded region and in a control region that was not loaded. We studied the dependence of fatigue life and induced microdamage on initial microdamage, cortical region, subject gender and age, and several other variables. When the effect of modulus variability was controlled, longer fatigue life was associated with higher rather than lower initial crack density, particularly in the medial cortex. The increase in crack density following fatigue loading was greater in specimens from older individuals and those initially having longer microcracks. Crack density increased as much in specimens fatigued short of the failure point as in those that fractured, and microcracks were, on average, shorter in specimens with greater numbers of resorption spaces, a measure of remodeling rate.

Osteon pullout in the equine third metacarpal bone: effects of ex vivo fatigue.

An important concept in bone mechanics is that osteons influence mechanical properties in several ways, including contributing to toughness and fatigue strength by debonding from the interstitial matrix so as to "bridge" developing cracks. Observations of "pulled out" osteons on fracture surfaces are thought to be indicative of such behavior. We tested the hypothesis that osteon pullout varies with mode of loading (fatigue vs. monotonic), cortical region, elastic modulus, and fatigue life. Mid-diaphseal beams from the dorsal, medial, and lateral regions of the equine third metacarpal bone were fractured in four point bending by monotonic loading to failure under deflection control, with or without 10(5) cycles of previous fatigue loading producing 5000 microstrain (15-20% of the expected failure strain) on the first cycle; or sinusoidal fatigue loading to failure, under load or deflection control, with the initial cycle producing 10,000 microstrain (30-40% of the expected failure strain). Using scanning electron microscopy, percent fracture surface area exhibiting osteon pullout (%OP.Ar) was measured. Monotonically loaded specimens and the compression side of fatigue fracture surfaces exhibited no osteon pullout. In load-controlled fatigue, pullout was present on the tension side of fracture surfaces, was regionally dependent (occurring to a greater amount dorsally), and was correlated negatively with elastic modulus and positively with fatigue life. Regional variation in %OP.Ar was also significant for the pooled (load and deflection controlled) fatigue specimens. %OP.Ar was nearly significantly greater in deflection controlled fatigue specimens than in load-controlled specimens (p=0.059). The data suggest that tensile fatigue loading of cortical bone eventually introduces damage that results in osteonal debonding and pullout, which is also associated with increased fatigue life via mechanisms that are not yet clear.

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.

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.

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.

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.