One of the parameters determining the efficiency of cleaning the blood in hemodialysis therapy is an effective mass transfer processes of metabolites through the dialyzer, which is defined by the mechanism of molecular diffusion and convection of low and medium weight substances in the blood. The article presents an analysis of modern mass transport models: streaming and kinetic; the analytical expressions of the spatial and temporal distribution of metabolites in the dialyzer. The results of mathematical modeling showed that these models do not reflect the full extent of the entire mechanism of mass transfer and must be supplemented. This is primarily due to the fact that blood is a non-Newtonian fluid. In addition, during hemodialysis, there is a change of the rheological properties of the blood - viscosity aggregated and deformability of erythrocytes, which ultimately affects the dialyzer mass transfer processes, reduces its clearance and thus reduces the efficiency of hemodialysis. The authors consider that the solution to this problem might be to develop a space-time mathematical model of mass transfer (the so-called distributed model of mass transfer), built with the influence of the driving forces behind the transfer of substances through the membrane dialyzer basic parameters and characteristics of fibers and rheological blood properties. In our view, the space-time dependence of the distribution of concentrations of metabolites in the blood and dialysate hemodialyzers allow to predict normalization the concentration of metabolites in the blood, and thus improve the accuracy of assessing the quality of dialysis.

Keywords: hemodialysis, mathematical modeling, spatial distribution, the time dependence, the space-time model