Nonlinear Stability Analysis for Artificial Kidney Multi-compartmental Models

This paper addresses a new global stability analysis for a specific class of nonlinear multi-compartment models with non-positive flows and whose balances are described by equilibrium sets. We apply the stability analysis to our physiological-based model of extracellular fluid used during dialysis therapy in end-stage kidney disease patients. To gain an in-depth understanding of the risk associated with fluid removal by the artificial kidney during the short time (3-5hrs) of the dialysis therapy, we use the stability results to analyze the solutions behavior of our model under standard ultrafiltration and patient-specific ultrafiltration profiles. Therefore, the standard ultrafiltration profiles do not guarantee optimal outcomes, and we highly recommend incorporating physiological insights into the ultrafiltration profiles to improve outcomes.