Abstract
Oxygen plays an important role in the metabolism of cells inside the human body. The transfer of oxygen from blood to tissue takes place in capillaries through a diffusion process. The capillary-tissue region is usually represented by the so-called Krogh cylinder model, in which the distribution of the oxygen concentration in a tissue region leads to a diffusion equation with oxygen consumption rates following the Michaelis-Menten kinetics. In this paper, we restrict ourselves to the steady state case and solve the equation analytically by means of asymptotic expansion for a particular limit of the oxygen consumption rate. Results show that there exists a critical ratio between supply and consumption of oxygen in the tissue region in order to fulfill the cell’s oxygen requirements. Above from this critical ratio, we also found a critical distance in the tissue region above which the oxygen concentration vanishes. We compared our asymptotic results with numerical simulations, which turned out to be quite in agreement.
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