A two-layer model for studying the effect of plasma layer on the delivery of oxygen to tissue using a finite element method
type: Item
instance of: scholarly article
title: A two-layer model for studying the effect of plasma layer on the delivery of oxygen to tissue using a finite element method
zbMATH Open document ID: 0890.76100
DOI: 10.1016/S0307-904X(97)00035-8
author: Maithili Sharan
author: Balbir Singh
author: Pawan Kumar
published in: Applied Mathematical Modelling
publication date: 1998-07-01T00:00:00Z
review text: The authors present a mathematical model for the transport of oxygen in the system capillaries and in the surrounding tissue. The model can find applications when one studies the molecular diffusion, the convective effect of the blood, the nonlinear effects of oxyhaemoglobin and the consumption of oxygen in the metabolic process. A two-layer model for the blood consisting of a core of erythrocytes surrounded by a cell-free plasma layer is proposed. The resulting nonlinear convective diffusion equations with the physiologically relevant boundary conditions are solved by a finite element methods, and a fixed point iterative technique is used to tackle the nonlinear terms. The authors report that partial pressure of oxygen in the tissue increases when the core-to-capillary diameter ratio increases. This conclusion follows from the fact that the plasma layer obstructs the transport of oxygen from the blood to the tissue. The effects of capillary diameters and core radii on the delivery of oxygen to tissue are also examined.
Mathematics Subject Classification ID: 76Z05
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 92C10
zbMATH DE Number: 1062739
zbMATH Keywords: capillaries
zbMATH Keywords: core of erythrocytes
zbMATH Keywords: cell-free plasma layer
zbMATH Keywords: nonlinear convective diffusion equations
zbMATH Keywords: fixed point iterative technique
zbMATH Keywords: core-to-capillary diameter ratio
MaRDI profile type: Publication
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full work available at URL: s0307-904x(97)00035-8
OpenAlex ID: W1966724686
description: scientific article; zbMATH DE number 1062739