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.

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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.

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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 non-linear 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 bone volume fraction (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 bone volume fraction 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.