Steve A. Maas

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.

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.

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.

Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios

Experimental measurements of the Poissons ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poissons ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poissons ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress-strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super-helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poissons ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poissons ratios and the nonlinear stress-strain behavior seen experimentally. Parametric studies revealed that the predicted Poissons ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poissons ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress-strain behavior and large Poissons ratios, while fiber crimp alone could only account for the nonlinear stress-strain behavior.

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.

Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding.

This study formulates and implements a finite element contact algorithm for solid-fluid (biphasic) mixtures, accommodating both finite deformation and sliding. The finite element source code is made available to the general public. The algorithm uses a penalty method regularized with an augmented Lagrangian method to enforce the continuity of contact traction and normal component of fluid flux across the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. The accuracy of the implementation is verified using contact problems, for which exact solutions are obtained by alternative analyses. Illustrations are also provided that demonstrate large deformations and sliding under configurations relevant to biomechanical applications such as articular contact. This study addresses an important computational need in the biomechanics of porous-permeable soft tissues. Placing the source code in the public domain provides a useful resource to the biomechanics community.

A new discrete element analysis method for predicting hip joint contact stresses

Quantifying cartilage contact stress is paramount to understanding hip osteoarthritis. Discrete element analysis (DEA) is a computationally efficient method to estimate cartilage contact stresses. Previous applications of DEA have underestimated cartilage stresses and yielded unrealistic contact patterns because they assumed constant cartilage thickness and/or concentric joint geometry. The study objectives were to: (1) develop a DEA model of the hip joint with subject-specific bone and cartilage geometry, (2) validate the DEA model by comparing DEA predictions to those of a validated finite element analysis (FEA) model, and (3) verify both the DEA and FEA models with a linear-elastic boundary value problem. Springs representing cartilage in the DEA model were given lengths equivalent to the sum of acetabular and femoral cartilage thickness and gap distance in the FEA model. Material properties and boundary/loading conditions were equivalent. Walking, descending, and ascending stairs were simulated. Solution times for DEA and FEA models were ~7 s and ~65 min, respectively. Irregular, complex contact patterns predicted by DEA were in excellent agreement with FEA. DEA contact areas were 7.5%, 9.7% and 3.7% less than FEA for walking, descending stairs, and ascending stairs, respectively. DEA models predicted higher peak contact stresses (9.8-13.6 MPa) and average contact stresses (3.0-3.7 MPa) than FEA (6.2-9.8 and 2.0-2.5 MPa, respectively). DEA overestimated stresses due to the absence of the Poissons effect and a direct contact interface between cartilage layers. Nevertheless, DEA predicted realistic contact patterns when subject-specific bone geometry and cartilage thickness were used. This DEA method may have application as an alternative to FEA for pre-operative planning of joint-preserving surgery such as acetabular reorientation during peri-acetabular osteotomy.

Multiphasic Finite Element Framework for Modeling Hydrated Mixtures With Multiple Neutral and Charged Solutes

Computational tools are often needed to model the complex behavior of biological tissues and cells when they are represented as mixtures of multiple neutral or charged constituents. This study presents the formulation of a finite element modeling framework for describing multiphasic materials in the open-source finite element software febio.1 Multiphasic materials may consist of a charged porous solid matrix, a solvent, and any number of neutral or charged solutes. This formulation proposes novel approaches for addressing several challenges posed by the finite element analysis of such complex materials: The exclusion of solutes from a fraction of the pore space due to steric volume and short-range electrostatic effects is modeled by a solubility factor, whose dependence on solid matrix deformation and solute concentrations may be described by user-defined constitutive relations. These solute exclusion mechanisms combine with long-range electrostatic interactions into a partition coefficient for each solute whose value is dependent upon the evaluation of the electric potential from the electroneutrality condition. It is shown that this electroneutrality condition reduces to a polynomial equation with only one valid root for the electric potential, regardless of the number and valence of charged solutes in the mixture. The equation of charge conservation is enforced as a constraint within the equation of mass balance for each solute, producing a natural boundary condition for solute fluxes that facilitates the prescription of electric current density on a boundary. It is also shown that electrical grounding is necessary to produce numerical stability in analyses where all the boundaries of a multiphasic material are impermeable to ions. Several verification problems are presented that demonstrate the ability of the code to reproduce known or newly derived solutions: (1) the Kedem-Katchalsky model for osmotic loading of a cell; (2) Donnan osmotic swelling of a charged hydrated tissue; and (3) current flow in an electrolyte. Furthermore, the code is used to generate novel theoretical predictions of known experimental findings in biological tissues: (1) current-generated stress in articular cartilage and (2) the influence of salt cation charge number on the cartilage creep response. This generalized finite element framework for multiphasic materials makes it possible to model the mechanoelectrochemical behavior of biological tissues and cells and sets the stage for the future analysis of reactive mixtures to account for growth and remodeling.

Accuracy and Feasibility of Dual Fluoroscopy and Model-Based Tracking to Quantify In Vivo Hip Kinematics During Clinical Exams

Accurate measurements of in-vivo hip kinematics may elucidate the mechanisms responsible for impaired function and chondrolabral damage in hips with femoroacetabular impingement (FAI). The objectives of this study were to quantify the accuracy and demonstrate the feasibility of using dual fluoroscopy to measure in-vivo hip kinematics during clinical exams used in the assessment of FAI. Steel beads were implanted into the pelvis and femur of two cadavers. Specimens were imaged under dual fluoroscopy during the impingement exam, FABER test, and rotational profile. Bead locations measured with model-based tracking were compared with those measured using dynamic radiostereometric analysis. Error was quantified by bias and precision, defined as the average and standard deviation of the differences between tracking methods, respectively. A normal male volunteer was also imaged during clinical exams. Bias and precision along a single axis did not exceed 0.17 and 0.21 mm, respectively. Comparing kinematics, positional error was less than 0.48 mm and rotational error was less than 0.58°. For the volunteer, kinematics were reported as joint angles and bone-bone distance. These results demonstrate that dual fluoroscopy and model-based tracking can accurately measure hip kinematics in living subjects during clinical exams of the hip.