An exact analysis for a solute transport, due to simultaneous dialysis and ultrafiltration, in a hollow-fibre artificial kidney

Bulk mass transport limitations during high-flux hemodialysis

Solute clearance during high-flux hemodialysis is determined by the combined effects of solute convection and diffusion in the membrane, blood, and dialysate. Previous studies have focused almost entirely on the membrane transport phenomena, largely ignoring the potential contribution from bulk mass transport across the fluid boundary layers in the blood and dialysate. This study presents a theoretical analysis of the coupled transport equations in the membrane, blood, and dialysate including the contributions from both convective and diffusive transport in each of these regions. The resulting theoretical expression for the solute flux demonstrates that bulk mass transfer limitations can have an important effect on solute transport and, in turn, solute clearance during high-flux hemodialysis.

Alternative descriptions of combined diffusive and convective mass transport in hemodialyzer

Two alternative versions of the mathematical description of the combined diffusive and convective membrane transport in hemodialyzers were compared using the one-dimensional theory of hemodialyzers. The first version is based on the assumption of homogeneity of the membrane. The second version is a widely used "ad hoc" formulation, which can be interpreted as a description of the membrane as tighter at the dialysate side than at the blood side. Theoretical predictions of the increase of dialyzer clearance caused by ultrafiltration, as assessed by transmittance coefficient, were compared to experimental data about transport of small solutes (urea, creatinine, and sodium) as well as middle molecules (vitamin B12) in three types of hollow-fiber hemodialyzer. For one type of dialyzer, the theory assuming the homogeneous membrane yielded the correct predictions for the small solutes. For two other types of dialyzer, the alternative version of the theory was adequate. For vitamin B12, the experimental values of transmittance coefficient were between the values predicted by the two versions of the theory for all three types of hemodialyzer. Thus, the two versions should be considered as a possible adequate description of solute transport in hemodialyzers.

Theoretical basis and experimental verification of the impact of ultrafiltration on dialyzer clearance

Dialyzer clearance K is usually presented as K = K0 + Tr Qu, were Qu is ultrafiltration rate, K0 is clearance for Qu = 0, and Tr is transmittance coefficient. Although a simple and accurate mathematical description of K0 is widely used, only a somewhat inaccurate formula for Tr that predicts a linear relationship between Tr and K0 has been proposed before. In this study the detailed investigation of Tr using a one-dimensional theory of a dialyzer is presented. In general, the application of a one-dimensional theory requires sophisticated numerical methods, but for small and middle molecular weight solutes an analytical formula for K can be derived. Tr predicted by the developed theory in comparison to Tr predicted by the previous linear formula is higher for small molecular weight solutes and lower for middle and large molecular weight solutes. These theoretical results were confirmed in experiments carried out in vitro for hollow-fiber dialyzers and small molecular weight solutes (urea, creatinine, sodium, TcO4) as well as middle molecular weight solutes (vitamin B12).