Mathematical Analysis of Landis-Type Experiments on the Transport of Fluid Across the Walls of Capillary Blood Vessels

摘要

A simplified model of the fluid transport phenomena across the wall of a capillary blood vessel is studied. An analytical method is presented to study the significance of Starling's law in the motion of the plasma in an occluded capillary blood vessel. In this study, the hydrostatic and osmotic pressures in the surrounding tissues are supposed to be unchanged by the occlusion and remain the same at the equilibrium values of the system before the occlusion. Thus the mass flow across the capillary wall, according to Starling's law, is simply proportional to the changed hydrostatic pressure difference across the wall. The red blood cells are ignored. The steady state flow of the plasma in the occluded capillary blood vessel is determined. The result shows that when the permeability exceeds a certain value, the flow across the capillary wall is more or less independent of the permeability of the wall. In that case, the axial flow far upstream governs the fluid motion. When the permeability is small, the flow across the wall became dependent on the permeability. For permeability values pertinent to the mesentery of the rabbit, the flow across the wall of the capillary blood vessel is directly proportional to the permeability. (Author)