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Hemodialysis (HD) is a necessary treatment for end-stage kidney disease (ESKD) patients in order to prevent cardiovascular morbidity and mortality that may be related to the hemodynamic effects of rapid ultrafiltration. Despite significant advances in HD technology, only half of ESKD patients treated with HD survive more than 3 years. Fluid management remains one of the most challenging aspects of HD care, with serious implications for morbidity and mortality. In this paper, we develop a novel algorithm to design real time optimal, robust ultrafiltration rates based on actual HD data to identifying the parameters of a fluid volume model of an individual patient during HD. Our design achieves, if exists, an optimal ultrafiltration profile for the identified nominal model under maximum ultrafiltration and hematocrit constraints and guarantees that these constraints are satisfied over a pre-defined set of parameter uncertainty. We demonstrate the robust performance of our algorithm through a combination of clinical data and simulations.

Chronic dialysis is a necessary treatment for end-stage kidney disease (ESKD) patients in order to increase life span, with hemodialysis (HD) being the dominant modality. Despite significant advances in HD technology, only half of ESKD patients treated with this modality survive more than 3 years. Fluid management remains one of the most challenging aspects of HD care, with serious implications for morbidity and mortality. Ultrafiltration has been associated with intradialytic hypotension, also associated with adverse outcomes. Therefore, removing a specified fluid volume to achieve an adequate balance without negative outcomes remains a critical challenge to improving patient outcomes. Therefore, it has been suggested that in addition to blood pressure information, routine HD treatments should include blood volume monitoring. Sensors integrated in dialysis machines are able to track the concentration of various blood components, such as hematocrit, with high accuracy and resolution and to derive a relative blood volume (RBV) changes. In this paper, we propose a novel algorithm to design an optimal, robust ultrafiltration rate profile based on identifying the parameters of a fluid volume model of an individual patient during HD and RBV sensor. Our design achieves, if exists, an optimal ultrafiltration profile for the identified nominal model under maximum ultrafiltration and hematocrit constraints, and guarantees that these constraints are satisfied over a pre-defined set of parameter uncertainty. We demonstrate the performance of our algorithm through a combination of clinical data and simulations.

This paper investigates the global stability of artificial kidney fluid volume dynamics described by a nonlinear multi-compartment model of extracellular fluid volume exchange during dialysis. Only a few papers in the literature have addressed the stability of similar classes of compartment models. In these papers, the global stability of such models is established using the Lyapunov method; however, their results are not applicable to our model. We developed a new nonlinear Lyapunov function which enables us to prove the stability of a general class of nonlinear multi-compartment models. To examine the oscillatory behavior of the model under external input, we tested our stability results during the short-term of the ultrafiltration process.