A cylindrical-layer domain scaling approach to modeling urea clearance in a hemodialyzer

A hemodialyzer (artificial kidney) typically consists of a cylindrical housing containing about 10,000 parallel hollow fibers that carry blood along the axis of the housing, while the dialyzer fluid (dialysate) flows around the fibers in the opposite direction. Uremic toxins are cleared from the blood by diffusing across the fibers' semipermeable membranes into the dialysate. It is too computationally costly to simulate the flow in the entire dialyzer in three dimensions. As a result, most simulations either extrapolate single-fiber results to the entire flow domain or use a porous medium approach, and miss the interfiber flow details. Here, we employed a domain scaling approach to model urea clearance in hemodialyzer models of increasing complexity. We developed 1-, 7-, 19-, 37-, 61-, 91- and 127-fiber 3D models of a commercial hemodialyzer. We performed simulations using clinically-relevant blood (100-500 mL/min) and dialysate flow rates (200-800 mL/min) and found the urea clearance increased as the dialysate flow rate increased at a constant blood flow rate, similar to known clinical results. This suggests that the cylindrical-layer domain scaling approach may capture sufficient fiber-fiber interactions to accurately model the steady flow physics in a full-scale hemodialyzer.