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).