Finite Element Prediction of Transchondral Stress and Strain in the Human Hip: Effects of Cartilage Constitutive Model

Introduction: Osteoarthritis (OA) may be initiated by abnormal mechanical loading, which can alter both cartilage metabolism and mechanical behavior [1]. OA of the hip affects approximately 10% of the population [2]. Understanding the causes of hip OA is the first step in developing treatment strategies to delay or reverse disease progression. Surface fibrillation is common in early-stage OA, and may be caused by elevated tensile strains at the articular surface [3]. Cartilage delamination at the subchondral plate is a frequent clinical finding in early-stage OA in the pathomorphologic human hip, and may be caused by elevated shear stress at the osteochondral interface [4]. While clinical observation motivates the evaluation of tensile strain and shear stress at the cartilage surfaces and transchondrally (through the cartilage thickness), appropriate modeling strategies for accurately capturing these variables must be determined prior to their prediction in live subjects. Unlike contact stress and contact area, which can be directly validated [5], confidence in predictions of tensile strain and maximum shear stress relies on evaluating and interpreting the sensitivity to modeling assumptions. Therefore, the objectives of this study were to use a population of validated finite element (FE) models of normal human hips to evaluate the mesh resolution required for accurate predictions of cartilage tensile strain and shear stress, to assess the sensitivity of predictions for cartilage tensile strain and shear stress to the choice of cartilage constitutive assumptions, and to determine the patterns of transchondral stress and strain that occur during activities of daily living. Methods: Specimen-specific FE models of five normal cadaveric hips from male donors were generated (40 ± 14 years old, mass 63 ± 14 kg, height 177 ± 9 cm) [5]. Cartilage mesh convergence was evaluated for Green Lagrange first principal strain (E 1) and Cauchy shear stress (τ max) by analyzing FE models with three, four, five and six elements through the cartilage thickness in one specimen. The approximate element Jacobian was consistently maintained across meshes. The nearly-incompressible hyperelastic behavior of cartilage under physiological loading rates was fit to three constitutive models: neo-Hookean (nH), Veronda Westmann (VW) and ellipsoidal fiber distribution with a neo-Hookean matrix (EFD) [6]. To determine material coefficients for these constitutive models, experimental data from unconfined compression testing [5] was fit to analytical solutions. Incompressibility was justified based on the loading rate of the simulated activities [7]. FE models were analyzed using all three constitutive models. E 1 …