Mathematical modeling of the dynamic exchange of solutes during bicarbonate dialysis

Most End-Stage Renal Disease (ESRD) patients receiving dialysis therapy are in a state of constant metabolic acidosis which is associated with high cardiovascular morbidity and mortality. In an attempt to improve the quality and efficacy of ESRD patients suffering from acidosis many experimental approaches have been used to investigate acid–base balance during dialysis sessions. However, these experimental approaches are expensive and time consuming. To reduce acidosis morbidity, a compartmental mathematical model is used in this paper. The model takes into account the exchange of small solutes, bicarbonate (HCO3−) and carbon dioxide, across a non-uniform trans-membrane dialyzer. Blood and dialysate flows are simulated using the Navier–Stokes and Darcy equations respectively. Since the trans-membrane (TM) flux would not be uniform, both blood- and dialysate-side equations are coupled with interfacial conditions calculated by Kedem–Katchalsky equations. Numerical results and clinical data are in close agreement within a satisfactory range, thus confirming that mathematical models can predict dialysis operative parameters with accuracy. Numerical results also confirm that acid–base balance for ESRD patients can be achieved during HCO3− dialysis therapy. Thus, the model quantifies adequate choice of bicarbonate and electrolyte concentrations to help improve acid–base status of ESRD patients suffering from acidosis. As an investigative framework, the model can also provide a clear insight into other small solute exchanges across the dialyzer membrane.