Diffusion Equation Model for Determining the Concentration of Urea in Artificial Kidney

In medicine, dialysis is primarily used to provide an artificial replacement for lost kidney function (renal replacement therapy) due to renal failure. Dialysis may be used for very sick patients, who have suddenly but temporarily lost their kidney function (acute renal failure) or for quite stable patients who have permanently lost their kidney function. We present a model, which consist of partial differential equation defining the process of diffusion in artificial kidney and finally get the solution of this equation in the form of concentration of urea in blood by using the finite difference approach. The graph drawn between concentration and radial distance shows the variation between these two quantity. Dialysis treatments replace some of these functions through diffusion (waste removal) and ultrafiltration (fluid removal).