A p-type finite element solution for the simulation of O 2 transport in articular cartilage tissue: heterogeneous and porous media

Abstract

The partial pressure of oxygen (pO₂) is suggested to have a regulatory effect on chondrocyte biosynthetic activities, and its effect during expansion is unknown. The authors hypothesize that oxygen tension due to mechanical deformation or swelling could be as important as direct mechanical effects on cell biosynthetic activities. While there are plenty of studies on measuring and/or modelling pO₂ in articular cartilage (AC) for static (rest) conditions, to the best of the authors’ knowledge there are very few such studies on pO₂ in AC for dynamic conditions such as swelling or tissue deformation. In this study, it is attempted to develop a model to study the dynamics of oxygen transport in AC. A high-precision hybrid element is designed using the p-type finite element method, by which diffusion and convection are incorporated as a single element. A domain decomposition method is used that allows the use of a different type of discretization with independent discretization variables in non-overlapping sub-domains, for a generic three-dimensional approach to elliptic boundary value problems of order 2 or higher. The formulation developed in this study might be used in determining the necessary flow conditions to cultivate tissue constructs in tissue repair and tissue engineering.

Keywords

finite element method oxygen diffusion P-type FEM mass transfer variational calculus

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