Bioartificial kidney. I. Theoretical analysis of convective flow in hollow fiber modules: application to a...

Analytical expressions describing convective flow in a continuous arteriovenous hollow fiber hemofilter were developed. In the lumen of the hollow fiber membrane, existing analytical expressions were applied to describe velocity profiles and pressure. For flow in the shell (the extracapillary space separating the fibers), analytical expressions for the radial and axial velocity profiles and pressure distribution were derived by first finding the stream function. The expressions are based on a similarity solution. Previous analyses of ultrafiltration have either ignored osmotic pressure or assumed constant shell pressure. In this paper, the axial variation in lumen pressure, shell pressure, and osmotic pressure were accounted for. The predicted filtration rates agree well with the experimental results. This flow model is general enough to describe flow in hollow fiber membrane systems employed as bioreactors (e.g., for cell cultures and as bioartificial organs) and as separators (e.g., ultrafiltration and microfiltration) operating in the open-shell mode. The results were applied to determine the design of an optimally functioning bioartificial hemofilter for use ex vivo or in vivo.