ANALYTIC MULTIPLICATIVE SEPARATION AND EXISTENCE INVESTIGATION OF NON-LINEAR OXYGEN TRANSPORT WITH POISEUILLE HEMODYNAMIC FLOW IN A SEMI-GENERALIZED COORDINATE SYSTEM

Abstract

A well known governing nonlinear PDE used to model oxygen transport is formulated in a generalized co-ordinate system where the Laplacian is expressed in metric tensor form. A reduction of the pde to simpler problem, which has never been done before, subject to specific integrability conditions is shown. A specific form of the initial equation to be reduced has been used by Nair and coworkers [1-3] describing the intraluminal problem of oxygen transport in large capillaries or arterioles and more recent work by [4] describing release of ATP in microchannels. In each of these cases, a tube with a central core, rich in red blood cells, and with a thin plasma region near the boundary wall, free of RBCs is considered. A co-ordinate transformation to solve reduced pde in core region is adopted. An extension and modification of the work of Erbe and Wang [5] is derived and existence of positive solutions of an ode obtained in the general formulation is obtained for nonhomogeneous mixed boundary conditions and on general positive interval. Finally a solution method is given to solve a linear equation used by Nair [1-3] in the plasma layer.