Computational biomechanical models for the pericellular matrix of articular cartilage

Articular cartilage is a resilient biological soft tissue that serves to support load in diarthrodial joints such as the knee, shoulder and hip. Cartilage can be idealized as a biphasic mixture that is comprised of a solid extracellular matrix (ECM) saturated by interstitial fluid. Cartilage ECM is maintained by a sparse population of cells called chondrocytes, which are surrounded by a narrow layer called the pericellular matrix (PCM). Together, the chondrocyte and its surrounding PCM are termed the chondron. Since cartilage is avascular and aneural, cell metabolic activity is highly dependent upon the mechanical characteristics of the local extracellular environment. However, the relationships between microscopic and macroscopic biphasic mechanical variables are not well understood. This research is motivated by the need to quantify these relationships. Two computational models were developed pertaining to mechanical interactions between the cells, the PCM and the ECM of articular cartilage.;In the first study, a transient finite element model (FEM) was developed for linear biphasic mechanics in the microscopic environment of a single cell within a cartilage layer under cyclic loading in confined compression. The microscopic domain was modeled as a micron-scale cylinder of ECM with a spherical inclusion arising from the presence of a single cell and its encapsulating PCM. Boundary conditions for the three-zone microscale model were generated using an analytical solution for macroscopic cyclic confined compressive loading of a cartilage layer. To perform these simulations, an axisymmetric displacement- velocity penalty biphasic FEM was implemented as a weak formulation in the software package Comsol Multiphysics. Accuracy of the implementation was verified against known analytical solutions for cyclic compressive loading of a biphasic layer, and dynamic radial deformation of a layered biphasic sphere. The microscale biphasic FEM was employed to analyze the effects of frequency on biphasic mechanical variables in the cellular microenvironment under macroscopic cyclic confined compressive loading at 1% engineering strain, and in the frequency range 0.01-1 Hz.;The second investigation consisted of the formulation, implementation and application of a multiscale axisymmetric elastic boundary element method (BEM) for simulating in situ chondron deformation in states of mechanical equilibrium within a cartilage explant under equilibrated unconfined compression. The microscopic domain was modeled as a micron-scale sphere of ECM with an ellipsoidal inclusion, representing the chondron. Boundary conditions for this microscale model were generated using a known analytical solution for unconfined compression of a cartilage layer. Accuracy of the three-zone BEM was evaluated and compared to analytical solutions and finite element solutions. The BEM was then integrated with a nonlinear optimization technique (Nelder-Mead) to determine PCM elastic properties in situ within the ECM of the cartilage explant by solving an inverse problem associated with the experimental data.