Mathematical model of calcium exchange during hemodialysis using a citrate containing dialysate

Abstract

International audienceIn this paper we propose a mathematical model for the calcium exchange during hemodialysis. This model combines a first part describing the flows of two fluids, blood and dialysate, in a dialyser fiber to a second part which tackle the chemical reactions between several chemical species present in these fluids. The model governing the fluid flows is obtained by asymptotic analysis and takes into account the anisotropy of the fibers forming a dialyzer. We complete this partial differential equations system by standard boundary conditions, the specificity of our study being that we optimize the values of input and output pressures such that the blood and dialysate flow rates match the values measured on clinical dialyzers. In order to to highlight the differences in the flow, several rheologies for blood are proposed. The fluid velocity field drives the convective part in the reaction–diffusion system, modelling the exchange of five chemical species present in blood and dialysate. Finally, several numerical experiments illustrate this model emphasizing the calcium balance for citrate containing dialysates