A mathematical model the for hollow fibers dialyzers is presented.  The model describes the phenomena occurring in the machine and also the redistribution of chemicals in the patient's body. The scheme for the cross flow is derived referring to a single fiber, starting from the basic laws of fluid dynamics and exploiting the smallness of the ratio between the fiber radius and the fiber length to obtain significant simplifications. The mathematical problem is a system of integral and partial differential equations in which the input data are in principle unknown, since the blood composition is considerably altered while going through the fibers dialyzers. Indeed the body’s patient reacts redistributing urea, sodium ions, etc. between intra- and extracellular compartments with its own dynamics, thus updating the various concentrations at the dialyzer inlet. Hence the model which describes purification process occurring in the dialyzer is coupled which a compartments model accounting for the body response. We present numerical simulations, showing a reasonable agreement with the data for a specific patient taken from the literature.

dialysis, hollow fibers, blood filtration, compartments model