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Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 547954, 8 pages
http://dx.doi.org/10.1155/2013/547954
Research Article

Analytical Solutions for the Mathematical Model Describing the Formation of Liver Zones via Adomian’s Method

Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

Received 27 May 2013; Revised 30 June 2013; Accepted 15 July 2013

Academic Editor: Eddie Ng

Copyright © 2013 Abdelhalim Ebaid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The formation of liver zones is modeled by a system of two integropartial differential equations. In this research, we introduce the mathematical formulation of these integro-partial differential equations obtained by Bass et al. in 1987. For better understanding of this mathematical formulation, we present a medical introduction for the liver in order to make the formulation as clear as possible. In applied mathematics, the Adomian decomposition method is an effective procedure to obtain analytic and approximate solutions for different types of operator equations. This Adomian decomposition method is used in this work to solve the proposed model analytically. The stationary solutions (as time tends to infinity) are also obtained through it, which are in full agreement with those obtained by Bass et al. in 1987.