Mathematical modeling of cerebral oxygen transport from capillaries to tissue

Abstract

A non-linear model of oxygen transport from a capillary to tissue is considered. The model takes into account the convection of oxygen in the blood, its diffusion transfer through the capillary wall, and the diffusion and consumption of oxygen in tissue. In the current work, a boundary value problem for the oxygen transport model is studied. The existence theorem is proved and a numerical algorithm is constructed and implemented. The numerical experiments studying the effect of low hematocrit and reduced blood flow rate on cerebral hypoxia in preterm infants are conducted.