Kal Renganathan Sharma
On the Explicit Expression for Plasma Layer Thickness
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ABSTRACT. The marginal zone theory is used to account for the observed Fahreus Linquist effect when the viscoity of blood changes with the diameter of the capillary. An attributable cause is the axial accumulation of cells. The discharge rate from Hagen Poiseulle law at steady state was derived by Haynes (1960) for the core and plasma layer and a total discharge rate was expressed as a function of the pressure drop along the capillary, quartic dependence on the radius of the capillary and quartic dependence on the dimensionless marginal zone thickness. The apparent of viscosity of the blood is expressed as a function of the ratio of the core layer viscosity and the plasma layer viscosity. In order to back out a marginal zone thickness from a given set of information, the Charm and Kurland expression (1974) for the viscosity and hematocrit variation and the temperature dependence parameter of the hematocrit alpha can be used to develop two transcendental equations and two unknowns. This is the recommended procedure used currently and the equations are quartic in sigma, the dimensionless ratio of marginal zone thickness with the radius of the capillary. In this study an alternate procedure is developed for solving for the marginal zone thickness explicitly. On examination of the temperature variation parameter, alpha, for a given temperature, the transcendental equation is linear zed by a linear regression between alpha*H and H the hematocrit. The slope and intercept values are used in the expression of sigma = sqrt(alpha (c)/alpha(t)) and the hematocrit expression H(t) = H(c)*sigma^2. The resulting quadratic in simga^2 can be solved for and the sigma values obtained explicitly.