A MATHEMATICAL COUPLED MODEL OF OXYGEN TRANSPORT IN THE MICROCIRCULATION: THE EFFECT OF CONVECTION–DIFFUSION ON OXYGEN TRANSPORT

Abstract

This paper is aimed at examining the effect of convection–diffusion on oxygen transport at the micro-level. A coupled model of the convection–diffusion and molecular diffusion of oxygen is developed, and the solid deformation resulting from capillary fluctuations and the seepage of tissue fluid are incorporated into this model. The results indicate that (1) the oxygen concentration calculated from this coupled model is higher than that given by molecular diffusion models, both within the capillaries and tissue (maximum difference of 16%); (2) convection–diffusion has the greatest effect in tissue surrounding the middle of the capillary, and enhances the amount of oxygen transported to cells far from the oxygen source; (3) larger permeability coefficients or smaller diffusion coefficients produce a more obvious convection–diffusion effect; (4) a counter-current flow occurs near the inlet and outlet ends of the capillary. This model also provides a foundation for the study of how oxygen affects tumor growth.