Mathematical Models and Numerical Methods for Analysis of Mechanical and Chemical Loading in Articular Cartilage

Richard Schugart
Mathematical Biosciences Institute, The Ohio State University

(October 20, 2005 10:30 AM - 11:30 AM)

Mathematical Models and Numerical Methods for Analysis of Mechanical and Chemical Loading in Articular Cartilage

Abstract

Articular cartilage is the primary load-bearing soft tissue in joints such as the knee, shoulder, and hip. Multiphasic continuum mixture models have been used to describe the relative contribution of effects due to solid, fluid, and ionic phases in cartilage. This research is motivated by the need to quantify differences between the normal and osteoarthritic mechanical and physico-chemical states in the tissue. In this talk, I will present numerical methods and mathematical models pertaining to the cells and extracellular matrix of articular cartilage. Two problems will be described. The first problem is the development of an accelerated numerical method for the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage deformation. The second problem is the formulation and application of a triphasic mechano-chemical model to analyze osmotic loading experiments for the chondron, which is the functional cell-matrix unit in cartilage.