Computational Biomechanics

Finite element simulations in computational biomechanics commonly require the discretization of extremely complicated geometries. Creating meshes for these complex geometries can be very difficult and time consuming using hexahedral elements. Automatic meshing algorithms exist for tetrahedral elements, but these elements often have numerical problems that discourage their use in complex finite element models. To overcome these problems we have implemented a stabilized, nodally-integrated tetrahedral element formulation in FEBio, our in-house developed finite element code, allowing researchers to use linear tetrahedral elements in their models and still obtain accurate solutions. In addition to facilitating automatic mesh generation, this also allows researchers to use mesh refinement algorithms which are fairly well developed for tetrahedral elements but not so much for hexahedral elements. In this document, the implementation of the stabilized, nodallyintegrated, tetrahedral element, named the "UT4 element", is described. Two slightly different variations of the nodally integrated tetrahedral element are considered. In one variation the entire virtual work is stabilized and in the other one the stabilization is only applied to the isochoric part of the virtual work. The implementation of both formulations has been verified and the convergence behavior illustrated using the patch test and three verification problems. Also, a model from our laboratory with very complex geometry is discretized and analyzed using the UT4 element to show its utility for a problem from the biomechanics literature. The convergence behavior of the UT4 element does vary depending on problem, tetrahedral mesh structure and choice of formulation parameters, but the results from the verification problems should assure analysts that a converged solution using the UT4 element can be obtained that is more accurate than the solution from a classical linear tetrahedral formulation.

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software). [DOI: 10.1115/1.4004810]

The anterior-inferior glenohumeral capsule is the primary passive stabilizer to the glenohumeral joint during anterior dislocation. Physical examinations following dislocation are crucial for proper diagnosis of capsule pathology; however,they are not standardized for joint position which may lead to misdiagnoses and poor outcomes. To suggest joint positions for physical examinations where the stability provided by the capsule may be consistent among patients, the objective of this study was to evaluate the distribution of maximum principal strain on the anterior-inferior capsule using two validated subject-specific finite element models of the glenohumeral joint at clinically relevant joint positions. The joint positions with 25 N anterior load applied at 60° of glenohumeral abduction and 10°, 20°, 30° and 40° of external rotation resulted in distributions of strain that were similar between shoulders(r²≥0.7). Furthermore, those positions with 20-40° of external rotation resulted in capsule strains on the glenoid side of the anterior band of the inferior glenohumeral ligament that were significantly greater than in all other capsule regions. These findings suggest that anterior stability provided by the anterior-inferior capsule may be consistent among subjects at joint positions with 60° of glenohumeral abduction and a mid-range (20-40°) of external rotation, and that the glenoid side has the greatest contribution to stability at these joint positions. Therefore, it may be possible to establish standard joint positions for physical examinations that clinicians can use to effectively diagnose pathology in the anterior-inferior capsule following dislocation and lead to improved outcomes.

Instability is a significant concern in total hip arthroplasty (THA), particularly when there is structural compromise of the capsule due to pre-existing pathology or due to necessities of surgical approach. An experimentally grounded fiber-direction-based finite element model of the hip capsule was developed, and was integrated with an established three-dimensional model of impingement/dislocation. Model validity was established by close similarity to results from a cadaveric experiment in a servohydraulic hip simulator. Parametric computational runs explored effects of graded levels of capsule thickness, of regional detachment from the capsule's femoral or acetabular insertions, of surgical incisions of capsule substance, and of capsule defect repairs. Depending strongly upon the specific site, localized capsule defects caused varying degrees of construct stability compromise, with several specific situations involving over 60% decrement in dislocation resistance. Construct stability was returned substantially toward intact-capsule levels following well-conceived repairs, although the suture sites involved were often at substantial risk of failure. These parametric model results underscore the importance of retaining or robustly repairing capsular structures in THA, in order to maximize overall construct stability. © 2011 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 29:1642–1648, 2011

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.