An analytical study of ultrafiltration in a hollow fiber artificial kidney

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Abstract
A theoretical investigation of ultrafiltration through hollow fibers used in artificial kidney applications is presented. The hollow fibers are considered to be cylindrical tubes with ideally selective semipermeable walls which retain cellular particles (red and white cells, platelets) and plasma proteins in the blood perfusing the fibers. In contrast, water and species of low and medium molecular weight can freely permeate the membranes. The assumption is made that secondary flows avoid the formation of concentration boundary layers at the wall. Proper nondimensionalization of the equations for axial and radial transport results in the identification of parameters which are important in the characterization of the ultrafiltration through semipermeable tubes. Perturbation analyses for small values of these parameters lead to sets of differential equations which were solved analytically. These closed form solutions demonstrate the influence of hydraulic conductivity of the fiber walls, geometry, and axial and transmembrane pressure drop on the efficiency of hollow fiber artificial kidneys.