A mathematical model for the evolution of solute concentrations in a hemodialysis filter

We consider the process of hemodialysis performed by means of a hollow fiber dialyzer with a special focus on the dynamics of the light solutes (including metabolic waste products) through the porous fibers membrane. The model we illustrate here completes the one formulated in a previous paper in which solutes concentrations in the dialyzate were neglected. Exploiting the large difference between the characteristic time of the processes in the machine and the relaxation time to equilibrium in the body, we confine our study to the case of constant input data in order to emphasize the role of the solute transport mechanisms. Numerical solutions show that diffusion is dominant at the early stage of filtration.