A multiscale approach to modeling transport processes in the whole hemodialyzer: A step towards optimal design

Hemodialyzers, or artificial kidneys, consist of cylindrical modules housing about 10^4 hollow fibers carrying blood. Uremic toxins are cleared from the blood by diffusing and convecting through the fibers' semipermeable membranes into a dialysate solution surrounding the fibers flowing in a countercurrent manner. Experimental studies reveal a dialysate flow channeling phenomenon that is correlated with decreased dialyzer clearance efficiency. To understand the mechanics of dialysate channeling we developed a multiscale computational dialyzer model that divides the dialyzer cross-section into three annular rings. The model captures both the module- and fiber-scale flow physics and is able to predict, for the first time, the toxin concentration profile across the dialyzer cross section. For a high-flux commercial hemodialyzer (the Baxter CT190G) we found peak dialysate axial velocity values at the periphery of the dialyzer module and peak dialysate toxin concentrations upstream of the dialysate outlet, consistent with previous "in vitro" and numerical studies. The detailed model revealed that outlet blood urea concentration remained as high as 80% of the inlet values in fibers near the centerline of the dialyzer and fell to almost zero at the inner ring periphery. These results provide a clear link between dialysate channeling and dialyzer clearance performance and suggest that annular multiscale models can be used to resolve outstanding issues in dialyzer design and performance.