Application of the second-order fluid model to estimate factors affecting clearance of small and middle uremic molecules using combined ultrafiltration and diffusion processes

Uremic solute transport in a hollow fiber dialyzer is investigated theoretically with combined ultrafiltration and diffusion with the assumption of uniform ultrafiltration velocity and other standard assumptions. A numerical solution for concentration profiles in the blood compartment is obtained by using an implicit finite difference scheme implemented with MATLAB R2018a. The resulting system of linear equations is solved using another Matlab script implementing the Gauss–Seidel method. Uremic clearance of three solutes viz. urea, creatinine, and vitamin B-12 are considered. Different factors affecting Cl were observed and discussed in detail. Those factors include operating conditions (inlet blood flow rate, ultrafiltration velocity, etc.), dialyzer geometry (length, radius, number of fibers), and fluid parameters. The solute clearance can be maximized for a suitable set of values of these parameters.