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An Asymptotic Study for the Steady Model of Oxygen Diffusion in Tissue Region
Kartika Yulianti1 & Agus Y. Gunawan2
1Department of Mathematics Education, Indonesia University of Education (UPI), Bandung 40154, Indonesia
2Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
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Abstract. Oxygen plays an important role in cell metabolism inside a human's body. The transfer of oxygen from blood to tissues takes place in capillaries through the diffusion process. A capillary-tissue region is usually represented by so called the Krogh Cylinder arrangement 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 consider the steady case and solve the equation analytically, by means of the asymptotic expansions, for a particular limit of the oxygen consumption rate. Results show that there exists a critical ratio between supply and consumption of oxygen in tissue region in order to fulfill cellís oxygen requirements. Above this critical ratio, we also find a critical distance in the tissue region above which the oxygen concentration vanishes. We also compare our asymptotic results with numerical simulations which are both quite in agreement.
Keywords: Asymptotic expansions; Diffusion Process; Krogh Cylinder.