Benjamin J. Ellis

FEBio: finite elements for biomechanics.

In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics.

Validation of finite element predictions of cartilage contact pressure in the human hip joint.

Methods to predict contact stresses in the hip can provide an improved understanding of load distribution in the normal and pathologic joint. The objectives of this study were to develop and validate a three-dimensional finite element (FE) model for predicting cartilage contact stresses in the human hip using subject-specific geometry from computed tomography image data, and to assess the sensitivity of model predictions to boundary conditions, cartilage geometry, and cartilage material properties. Loads based on in vivo data were applied to a cadaveric hip joint to simulate walking, descending stairs, and stair-climbing. Contact pressures and areas were measured using pressure sensitive film. CT image data were segmented and discretized into FE meshes of bone and cartilage. FE boundary and loading conditions mimicked the experimental testing. Fair to good qualitative correspondence was obtained between FE predictions and experimental measurements for simulated walking and descending stairs, while excellent agreement was obtained for stair-climbing. Experimental peak pressures, average pressures, and contact areas were 10.0 MPa (limit of film detection), 4.4-5.0 MPa, and 321.9-425.1 mm(2), respectively, while FE-predicted peak pressures, average pressures, and contact areas were 10.8-12.7 MPa, 5.1-6.2 MPa, and 304.2-366.1 mm(2), respectively. Misalignment errors, determined as the difference in root mean squared error before and after alignment of FE results, were less than 10%. Magnitude errors, determined as the residual error following alignment, were approximately 30% but decreased to 10-15% when the regions of highest pressure were compared. Alterations to the cartilage shear modulus, bulk modulus, or thickness resulted in +/-25% change in peak pressures, while changes in average pressures and contact areas were minor (+/-10%). When the pelvis and proximal femur were represented as rigid, there were large changes, but the effect depended on the particular loading scenario. Overall, the subject-specific FE predictions compared favorably with pressure film measurements and were in good agreement with published experimental data. The validated modeling framework provides a foundation for development of patient-specific FE models to investigate the mechanics of normal and pathological hips.

Verification, validation and sensitivity studies in computational biomechanics

Computational techniques and software for the analysis of problems in mechanics have naturally moved from their origins in the traditional engineering disciplines to the study of cell, tissue and organ biomechanics. Increasingly complex models have been developed to describe and predict the mechanical behavior of such biological systems. While the availability of advanced computational tools has led to exciting research advances in the field, the utility of these models is often the subject of criticism due to inadequate model verification and validation (V&V). The objective of this review is to present the concepts of verification, validation and sensitivity studies with regard to the construction, analysis and interpretation of models in computational biomechanics. Specific examples from the field are discussed. It is hoped that this review will serve as a guide to the use of V&V principles in the field of computational biomechanics, thereby improving the peer acceptance of studies that use computational modeling techniques.

Effects of Idealized Joint Geometry on Finite Element Predictions of Cartilage Contact Stresses in the Hip

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error approximately 0.5mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.

Role of the acetabular labrum in load support across the hip joint

The relatively high incidence of labral tears among patients presenting with hip pain suggests that the acetabular labrum is often subjected to injurious loading in vivo. However, it is unclear whether the labrum participates in load transfer across the joint during activities of daily living. This study examined the role of the acetabular labrum in load transfer for hips with normal acetabular geometry and acetabular dysplasia using subject-specific finite element analysis. Models were generated from volumetric CT data and analyzed with and without the labrum during activities of daily living. The labrum in the dysplastic model supported 4-11% of the total load transferred across the joint, while the labrum in the normal model supported only 1-2% of the total load. Despite the increased load transferred to the acetabular cartilage in simulations without the labrum, there were minimal differences in cartilage contact stresses. This was because the load supported by the cartilage correlated with the cartilage contact area. A higher percentage of load was transferred to the labrum in the dysplastic model because the femoral head achieved equilibrium near the lateral edge of the acetabulum. The results of this study suggest that the labrum plays a larger role in load transfer and joint stability in hips with acetabular dysplasia than in hips with normal acetabular geometry.

Effect of Lateral Meniscal Allograft Sizing on Contact Mechanics of the Lateral Tibial Plateau An Experimental Study in Human Cadaveric Knee Joints

Background A mismatch of the original lateral meniscus and a lateral meniscus allograft by inaccurate preoperative radiographic sizing can have significant consequences on ultimate function. Hypothesis The size of a lateral meniscal allograft affects the contact mechanics of the femoral condyle on the tibial plateau. Study Design Controlled laboratory study. Methods Four right and 2 left knees were tested as intact joints, after meniscectomy, and after replantation with the original menisci and 16 right or 9 left human, fresh-frozen lateral meniscal allografts, respectively. The allografts were allocated into 7 groups according to their outer and inner anteroposterior and mediolateral diameters. Biomechanical testing was performed as compressive loadings with constrained motions in extension and 30° of flexion. Measurements were done with Fuji pressure-sensitive films for contact parameters of the direct femorotibial and meniscotibial contact. Results Oversized lateral meniscal allografts led to greater forces across the articular cartilage, whereas undersized allografts resulted in normal forces across the articular cartilage but greater forces across the meniscus. Two undersized transplants failed. Most of the contact parameters of allografts 10% smaller or larger than the original menisci were in the range of the intact knees. The knees after meniscectomy showed greater forces of the direct femorotibial contact areas than did the intact knees and the knees with the replanted original menisci. The contact mechanics of the knees with the replanted original menisci were close to normal. Conclusion The size of a lateral meniscal allograft has a significant effect on the contact mechanics of the tibial plateau. Clinical Relevance Preoperative radiographic sizing needs to be performed precisely to identify a suitable lateral meniscal allograft. A mismatch may be the reason for failure of the allograft or subsequent development of degenerative changes. A mismatch on graft selection of less than 10% of the size of the original meniscus may be acceptable.

Finite element prediction of cartilage contact stresses in normal human hips

Our objectives were to determine cartilage contact stress during walking, stair climbing, and descending stairs in a well‐defined group of normal volunteers and to assess variations in contact stress and area among subjects and across loading scenarios. Ten volunteers without history of hip pain or disease with normal lateral center‐edge angle and acetabular index were selected. Computed tomography imaging with contrast was performed on one hip. Bone and cartilage surfaces were segmented from volumetric image data, and subject‐specific finite element models were constructed and analyzed using a validated protocol. Acetabular contact stress and area were determined for seven activities. Peak stress ranged from 7.52 ± 2.11 MPa for heel‐strike during walking (233% BW) to 8.66 ± 3.01 MPa for heel‐strike during descending stairs (261% BW). Average contact area across all activities was 34% of the surface area of the acetabular cartilage. The distribution of contact stress was highly non‐uniform, and more variability occurred among subjects for a given activity than among activities for a single subject. The magnitude and area of contact stress were consistent between activities, although inter‐activity shifts in contact pattern were found as the direction of loading changed. Relatively small incongruencies between the femoral and acetabular cartilage had a large effect on the contact stresses. These effects tended to persist across all simulated activities. These results demonstrate the diversity and trends in cartilage contact stress in healthy hips during activities of daily living and provide a basis for future comparisons between normal and pathologic hips.

Effect of mechanical boundary conditions on orientation of angiogenic microvessels

AIM Mechanical forces are important regulators of cell and tissue phenotype. We hypothesized that mechanical loading and boundary conditions would influence neovessel activity during angiogenesis. METHODS AND RESULTS Using an in vitro model of angiogenesis sprouting and a mechanical loading system, we evaluated the effects of boundary conditions and applied loading. The model consisted of rat microvessel fragments cultured in a 3D collagen gel, previously shown to recapitulate angiogenic sprouting observed in vivo. We examined changes in neovascular growth in response to four different mechanical conditions. Neovessel density, diameter, length and orientation were measured from volumetric confocal images of cultures exposed to no external load (free-floating shape control), intrinsic loads (fixed ends, no stretch), static external load (static stretch), or cyclic external load (cyclic stretch). Neovessels sprouted and grew by the third day of culture and continued to do so during the next 3 days of loading. The numbers of neovessels and branch points were significantly increased in the static stretch group when compared with the free-floating shape control group. In all mechanically loaded cultures, neovessel diameter and length distributions were heterogeneous, whereas they were homogeneous in shape control cultures. Neovessels were significantly more oriented along the direction of mechanical loading than those in the shape controls. Interestingly, collagen fibrils were organized parallel and adjacent to growing neovessels. CONCLUSION Externally applied boundary conditions regulate neovessel sprouting and elongation during angiogenesis, affecting both neovessel growth characteristics and network morphometry. Furthermore, neovessels align parallel to the direction of stress/strain or internally generated traction, and this may be because of collagen fibril alignment induced by the growing neovessels themselves.

Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltat<<Delta(2) / //parallelC(4)//K//, where Delta is a characteristic dimension, C(4) is the elasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.

Patient-specific Analysis of Cartilage and Labrum Mechanics in Human Hips with Acetabular Dysplasia

BACKGROUND Acetabular dysplasia is a major predisposing factor for development of hip osteoarthritis (OA), and may result from alterations to chondrolabral loading. Subject-specific finite element (FE) modeling can be used to evaluate chondrolabral mechanics in the dysplastic hip, thereby providing insight into mechanics that precede OA. OBJECTIVE To evaluate chondrolabral contact mechanics and congruency in dysplastic hips and normal hips using a validated approach to subject-specific FE modeling. METHODS FE models of ten subjects with normal acetabula and ten subjects with dysplasia were constructed using a previously validated protocol. Labrum load support, and labrum and acetabular cartilage contact stress and contact area were compared between groups. Local congruency was determined at the articular surface for two simulated activities. RESULTS The labrum in dysplastic hips supported 2.8-4.0 times more of the load transferred across the joint than in normal hips. Dysplastic hips did not have significantly different congruency in the primary load-bearing regions than normal hips, but were less congruent in some unloaded regions. Normal hips had larger cartilage contact stress than dysplastic hips in the few regions that had significant differences. CONCLUSIONS The labrum in dysplastic hips has a far more significant role in hip mechanics than it does in normal hips. The dysplastic hip is neither less congruent than the normal hip, nor subjected to elevated cartilage contact stresses. This study supports the concept of an outside-in pathogenesis of OA in dysplastic hips and that the labrum in dysplastic hips should be preserved during surgery.