The interaction between transmural fluid exchange and blood viscosity in narrow blood vessels

Abstract

This work is a theoretical study of the viscosity changes due to transmural fluid exchange in permeable blood vessels and their influence on the filtration rate. Two effects are considered: (i) Variation of the tube hematocrit along the vessel axis which leads to a concomitant variation of the suspension viscosity. (ii) Variation of the total plasma protein concentration along the capillary axis which changes the plasma viscosity. For the first effect, experimental data of Barbee and Cokelet for tube diameters of 29–221 μm are used for the theoretical model. For capillaries of smaller diameters, the “stacked-coins model” is used to simulate the single-file flow of the red cells. A fictitious reservoir approach is proposed to determine the Fåhraeus and Fåhraeus–Lindqvist effects for permeable blood vessels. Results for the rat glomerulus show that the blood viscosity increases along the capillaries due to filtration by as much as 60%. However, this fluid mechanical change affects the filtration fraction be less than 2%, compared with results for earlier models which use the assumption of constant blood viscosity.