A one-dimensional model of simultaneous hemodialysis and ultrafiltration with highly permeable membranes

A one-dimensional model of combined convective and diffusive mass transfer in a hemodialyser is presented. Solutions and results are given for two regimes of ultrafiltration (UF): at low transmembrane pressures when UF flow is proportional to transmembrane pressure and in the limit of large transmembrane pressures when UF is limited by protein concentration polarization. It is found that the overall clearance is always less than the sum of dialytic and UF clearances due to interaction between convective and diffusive transfers. For a given UF flow the clearance is not sensitive to UF flux distribution along the membrane. Model predictions of urea clearance are in good agreement with measurements obtained in vitro with saline on hemodialysers equipped with a polyacrylonitrile membrane.