On the analysis of oxygen diffusion and reaction in biological systems

Abstract

An analysis of oxygen diffusion and reaction in multiregion biological systems is presented. This analysis considers a time-dependent flux boundary condition and oxygen consumption governed by Michaelis-Menten kinetics. The mathematical problem is developed in a uniform fashion, so as to include both the single cell and anisotropic systems with distinct regions which are characteristic of either a multicell spheroid or a tumor mass. Both transient and steady-state solutions are obtained, based on orthogonal collocation. Literature results on single-cell analysis are corroborated, and detailed transient solutions are presented for the oxygenation of a multicell spheroid, and for systemic oxygenation of both small and large tumors.