DOI Number : 10.5614/itbj.sci.2012.44.2.6
Hits : 2

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

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.

Download Article
Bahasa Indonesia | English


Begin on 10 October 2014 this website is no longer activated for article process in Journal of Mathematical and Fundamental Sciences, Journal of Engineering and Technological Sciences, Journal of ICT Research and Applications and Journal of Visual Art and Design. The next process will be proceeded under new website at

For detail information please contact us to:

       ITB Journal Visitor Number #14981690       
       Jl. Tamansari 64, Bandung 40116, Indonesia Visitor IP Address #       
       Tel : +62-22-250 1759 ext. 121 © 2011 Institut Teknologi Bandung       
       Fax : +62-22-250 4010, +62-22-251 1215 XHTML + CSS + RSS       
       E-mail : or Developed by AVE