(427d) Anoroxic Region in Tissue by Theory of Krogh in Cartesian Coordinates

A microscopic view of capillaries in tissue indicates a repetitive arrangement of capillaries surrounded by a cylindrical layer of tissue. The residence time of the blood in the capillary is in the order of 1 second. The wave diffusion and relaxation time is comparable in magnitude to the residence time of the blood. Krogh [1919] showed that the cylindrical capilary tissue model can be used to study the supply of oxygen to muscle. The tissue space surrounding the capillary is considered a continuous phase albeit it consists of discrete cells. An effective diffusivity DT can be used to represent the diffusion process in the tissue. The driving force for the diffusion is driven by the consumption of the solute by the cells within the tissue space. The Michaelis-Menten equation can be used to describe the metabolic consumption of the solute in the tissue space. The governing equation for diffusion at steady state was written in cartesian coordinates and the critical distance beyond which no diffusion can be expected was calculated. The quadratric equation in xcritical is then,

AXc^2 + BXc + C = 0 Where,

A = -(Ro/2DAB)

B = + (xc + tm) Ro/DAB

C = C0 + RozAT/VA + K0xc RoAT/2A -(Ro/2DAB)xc + tm)2 + Ro(xc + tm)/DAB

A, B and C are given in terms of the thickness of the capillary, capillary diameter, tissue diameter, binary diffusivity, entrance concentration and area of the tissue. When the solution of the quadratic expression for the critical distance in the tissue are real, and found to be less than the thickness of the tissue then the onset of zero concentration will occur prior to the periphery of the tissue. This zone can be seen as the anaroxic or oxygen depleted regions in the tissue.