Mathematical model of substance diffusion in tissue with nonlinear consumption¹

Article type: Research Article

Authors: Zaiko, Valery M. | Sharikov, Alexander N.

Affiliations: Laboratory of Biomechanics, Artificial Heart Division, Institute of Transplantology and Artificial Organs, 2/3 Pehotnaya Street, P.O. 123436, Moscow, U.S.S.R.

Note: [1] The Authors are grateful to Professor Fung’s secretary, Ms. Virginia Stephens, for retyping their manuscript which became necessary. Executive Editorial Office

Note: [] Accepted by: Editor Y.C.B. Fung

Abstract: The process of substance diffusion in tissue with nonlinear consumption of Michaelis-Menten type is described analytically. Formulas are derived describing the substance concentration profile in the capillary and in the tissue on condition that concentration several times exceeds the Michaelis-Menten constant in value. The model takes into consideration the finite substance permeability through the capillary wall and substance diffusion into the tissue only in the radial direction.

DOI: 10.3233/BIR-1979-16607

Journal: Biorheology, vol. 16, no. 6, pp. 429-434, 1979