Analytical solutions for the mathematical model describing the formation of liver zones via Adomian's method.
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.
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia.
Abdelhalim
A
Ebaid
D003198:Computer Simulation; D006801:Humans; D021621:Imaging, Three-Dimensional; D008099:Liver / Q000033:anatomy & histology* / Q000502:physiology; D008102:Liver Circulation; D055641:Mathematical Concepts; D008953:Models, Anatomic; D017711:Nonlinear Dynamics