Biomechanical effects of simulated resorption cavities in cancellous bone across a wide range of bone volume fractions.

Resorption cavities formed during bone remodeling may act as "stress risers" and impair cancellous bone strength, but biomechanical analyses of the effects of stress risers have been limited. To provide further insight, we assessed the theoretical biomechanical effects of virtually-added resorption cavities in cancellous bone specimens spanning a wide range of bone volume fraction (BV/TV = 0.05-0.36) and across different anatomic sites (hip and spine) and species (human and canine). Micro-CT scans of 40 cubes of cancellous bone were converted into nonlinear finite element models (voxel element size ∼ 20 µm) for strength assessment. In each model, uniform trench-like resorption cavities with nominal dimensions 500 µm (length) × 200 µm (width) × 40 µm (depth), were virtually added either at random locations throughout the specimen, or, preferentially at locations of high tissue-level strain. We found that cancellous bone strength (p < 0.0001) and its relation with BV/TV (p < 0.001) were both altered by the virtual addition of the resorption cavities. When the resorption cavities were added at random locations throughout the specimen, the reduction in strength did not depend on BV/TV or anatomic site or species. When the resorption cavities were instead added preferentially at locations of high tissue-level strain, the effect was accentuated and was greatest in low-BV/TV bone. We conclude that, in theory, uniform-sized resorption cavities can reduce cancellous bone strength over the full range of BV/TV and across species, and the effect is larger if the cavities occur at highly strained locations in low-BV/TV bone.

Contribution of the intra-specimen variations in tissue mineralization to PTH- and raloxifene-induced changes in stiffness of rat vertebrae.

The intra-specimen spatial variation in mineralization of bone tissue can be changed by drug treatments that alter bone remodeling. However, the contribution of such changes to the overall biomechanical effect of a treatment on bone strength is not known. To provide insight into this issue, we used a rat model to determine the effects of ovariectomy, parathyroid hormone, and raloxifene (vs. sham) on the contribution of spatial variations in mineralization to treatment-induced changes in vertebral stiffness. Mineral density was measured from 6-microm voxel-sized quantitative micro-CT scans. Whole-vertebral and trabecular stiffness values were estimated using finite element analysis of these micro-CT scans, first including all intra-specimen variations in mineral density in the model and then excluding such variations by using a specimen-specific average density throughout each specimen. As expected, we found appreciable effects of treatment on overall bone stiffness, the effect being greater for the trabecular compartment (up to 52% reduction vs. sham, p<0.0001) than the whole vertebra (p=0.055). Intra-specimen mean mineralization was not changed with treatment but the intra-specimen variation in mineralization was, although the effect was small (4%). Intra-specimen spatial variations in mineralization accounted for 10-12% and 5-6% of overall stiffness of the trabecular compartment and whole vertebral body, respectively. However, after accounting for all treatment effects on bone geometry and trabecular microstructure, any treatment effects due to changes in mineralization were negligible (<2%), although statistically detectable (p<0.02). We conclude that, despite a role in the general biomechanical behavior of bone, the spatial variations in tissue mineralization, as measured by quantitative micro-CT, did not appreciably contribute to ovariectomy-, PTH-, or raloxifene-induced changes in stiffness of the whole bone or the trabecular compartment in these rat vertebrae.

Side-artifact errors in yield strength and elastic modulus for human trabecular bone and their dependence on bone volume fraction and anatomic site.

In the context of reconciling the mechanical properties of trabecular bone measured from in vitro mechanical testing with the true in situ behavior, recent attention has focused on the "side-artifact" which results from interruption of the trabecular network along the sides of machined specimens. The objective of this study was to compare the magnitude of the side-artifact error for measurements of elastic modulus vs. yield stress and to determine the dependence of these errors on anatomic site and trabecular micro-architecture. Using a series of parametric variations on micro-CT-based finite element models of trabecular bone from the human vertebral body (n=24) and femoral neck (n=10), side-artifact correction factors were quantified as the ratio of the side-artifact-free apparent mechanical property to the corresponding property measured in a typical experiment. The mean (+/-SD) correction factors for yield stress were 1.32+/-0.17 vs. 1.20+/-0.11 for the vertebral body and femoral neck (p<0.05), respectively, and the corresponding factors for modulus were 1.24+/-0.09 vs. 1.10+/-0.04 (p<0.0001). Correction factors were greater for yield stress than modulus (p<0.003), but no anatomic site effect was detected (p>0.29) after accounting for variations in bone volume fraction (BV/TV). Approximately 30-55% of the variation in the correction factors for modulus and yield stress could be accounted for by BV/TV or micro-architecture, representing an appreciable systematic component of the error. Although some scatter in the correction factor-BV/TV relationships may confound accurate correction of modulus and yield stress for individual specimens, side-artifact correction is nonetheless essential for obtaining accurate mean estimates of modulus and yield stress for a cohort of specimens. We conclude that appreciation and correction for the differential effects of the side-artifact in modulus vs. yield stress and their dependence on BV/TV may improve the interpretation of measured elastic and failure properties for trabecular bone.

Finite element-based probabilistic analysis tool for orthopaedic applications.

Orthopaedic implants, as well as other physical systems, contain inherent variability in geometry, material properties, component alignment, and loading conditions. While complex, deterministic finite element (FE) models do not account for the potential impact of variability on performance, probabilistic studies have typically predicted behavior from simplified FE models to achieve practical solution times. The objective of this research was to develop an efficient and versatile probabilistic FE tool to quantify the effect of uncertainty in the design variables on the performance of orthopaedic components under relevant conditions. Key aspects of the computational tool developed include parametric and automated FE model creation for changes in dimensional variables, efficient solution using the advanced mean-value (AMV) reliability method, and identification of the most significant design variables. Two orthopaedic applications are presented to demonstrate the ability of the computational tool to efficiently and accurately represent component performance.

Comparison of deformable and elastic foundation finite element simulations for predicting knee replacement mechanics.

Rigid body total knee replacement (TKR) models with tibiofemoral contact based on elastic foundation (EF) theory utilize simple contact pressure-surface overclosure relationships to estimate joint mechanics, and require significantly less computational time than corresponding deformable finite element (FE) methods. However, potential differences in predicted kinematics between these representations are currently not well understood, and it is unclear if the estimates of contact area and pressure are acceptable. Therefore, the objectives of the current study were to develop rigid EF and deformable FE models of tibiofemoral contact, and to compare predicted kinematics and contact mechanics from both representations during gait loading conditions with three different implant designs. Linear and nonlinear contact pressure-surface overclosure relationships based on polyethylene material properties were developed using EF theory. All other variables being equal, rigid body FE models accurately estimated kinematics predicted by fully deformable FE models and required only 2% of the analysis time. As expected, the linear EF contact model sufficiently approximated trends for peak contact pressures, but overestimated the deformable results by up to 30%. The nonlinear EF contact model more accurately reproduced trends and magnitudes of the deformable analysis, with maximum differences of approximately 15% at the peak pressures during the gait cycle. All contact area predictions agreed in trend and magnitude. Using rigid models, edge-loading conditions resulted in substantial overestimation of peak pressure. Optimal nonlinear EF contact relationships were developed for specific TKR designs for use in parametric or repetitive analyses where computational time is paramount. The explicit FE analysis method utilized here provides a unique approach in that both rigid and deformable analyses can be run from the same input file, thus enabling simple selection of the most appropriate representation for the analysis of interest.