Mathematical model to characterize internal filtration

Convective-diffusive dialysis techniques have recently gained considerable favor. Indeed, convective fluxes through dialyzer membranes have been demonstrated to play a role in enhancing the clearance of middle-molecular-weight solutes. An interesting opportunity is given by exploiting the internal filtration (IF)/back filtration mechanism that occurs spontaneously in high-flux dialyzers, but is difficult to quantify. In view of overcoming this drawback, a semi-empirical, lumped-parameter mathematical model for characterization of IF phenomena was developed. The model considers a dialyzer as composed by N adjacent axial blocks. For each block, hydrodynamics in the blood and dialysate compartments are determined considering hydraulic resistance and calculating local filtration. Blood viscosity and oncotic pressure are calculated locally based on hematocrit and protein concentration. Resistance parameters were determined experimentally for the BS-UL (Toray Industries Inc., Tokyo, Japan) dialyzers. The set of equations describing the model, implemented into a software program, is solved using a numerical method. Simulations allow highlighting the role of device-, treatment- and patient-dependent parameters in affecting IF. Provided an extensive validation is carried out, the use of a mathematical model could be the key to make IF more understandable and its use reliable in clinical practice.