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Agus Y. Gunawan
2Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10 Bandung, Jawa Barat 40132, Indonesia
Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

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An Asymptotic Study of the Steady State Model of Oxygen Diffusion in Tissue Regions Kartika Yulianti; Agus Y. Gunawan
Journal of Mathematical and Fundamental Sciences Vol. 44 No. 2 (2012)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/itbj.sci.2012.44.2.6

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.
Co-Authors Kartika Yulianti