Numerical simulation of the effect of sodium profile on cardiovascular response to hemodialysis

PURPOSE: We developed a numerical model that predicts cardiovascular system response to hemodialysis, focusing on the effect of sodium profile during treatment. MATERIALS AND METHODS: The model consists of a 2-compartment solute kinetics model, 3-compartment body fluid model, and 12-lumped-parameter representation of the cardiovascular circulation model connected to set-point models of the arterial baroreflexes. The solute kinetics model includes the dynamics of solutes in the intracellular and extracellular pools and a fluid balance model for the intracellular, interstitial, and plasma volumes. Perturbation due to hemodialysis treatment induces a pressure change in the blood vessels and the arterial baroreceptors then trigger control mechanisms (autoregulation system). These in turn alter heart rate, systemic arterial resistance, and cardiac contractility. The model parameters are based largely on the reported values. RESULTS: We present the results obtained by numerical simulations of cardiovascular response during hemodialysis with 3 different dialysate sodium concentration profiles. In each case, dialysate sodium concentration profile was first calculated using an inverse algorithm according to plasma sodium concentration profiles, and then the percentage changes in each compartment pressure, heart rate, and systolic ventricular compliance and systemic arterial resistance during hemodialysis were determined. A plasma concentration with an upward convex curve profile produced a cardiovascular response more stable than linear or downward convex curves. CONCLUSION: By conducting numerical tests of dialysis/cardiovascular models for various treatment profiles and creating a database from the results, it should be possible to estimate an optimal sodium profile for each patient.