Impact of ultrafiltration on back-diffusion in hemodialyzer.

Ultrafiltration of water from blood to dialysate decreases the rate of back-diffusion of solutes from dialysate to blood. Therefore, back-clearance (bK) of hemodialyzers may be expressed as bK = bK0--bTrQu, where bK0 is the diffusive back-clearance, bTr is the "back-"transmittance coefficient, and Qu is the net ultrafiltration rate. A formula for bK was derived from the one-dimensional theory of hemodialyzer, and bTr was described as a function of bK0 and the Staverman reflection coefficient. The transport parameters, bK0 and bTr, for creatinine and vitamin B12 were measured in two types of hemodialyzers with negligible back-filtration, using water solutions, and compared with the transport parameters, K0 and Tr, for the case of both diffusion and ultrafiltration from blood to dialysate. bK0 was in general equal to K0. bTr was not different from Tr for creatinine whereas bTr was lower than Tr for vitamin B12. Experimental values of bTr for vitamin B12 were in general agreement with theoretical predictions. However, experimental values of bTr for creatinine were lower than predicted values. We conclude that the impact of ultrafiltration on back-clearance for slowly diffusing solutes is weaker than on their clearance.

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).