Modeling Arterial Hypotension During Hemodialysis

A mathematical model of the hemodynamic response to hemodialysis is presented. This model includes the dynamics of sodium, urea, and potassium in the intracellular and extracellular pools; fluid balance equations for the intracellular, interstitial, and plasma volumes; systemic and pulmonary hemodynamics; and the action of several short-term arterial pressure control mechanisms. The control mechanisms are triggered by information coming from both arterial and cardiopulmonary pressoreceptors, and they work on systemic arterial resistance, heart rate, and systemic venous unstressed volume. Moreover, the model hypothesizes that decreasing left atrial pressure below a given threshold causes a paradoxical withdrawal of the sympathetic drive and a consequent vasodepressor syncope. The model is used to simulate the pattern of the main hemodynamic quantities (systemic arterial pressure, heart rate, total systemic resistance, and cardiac output) during hemodialysis in several groups of patients (both hypotension resistant and hypotension prone) whose data were drawn from the clinical literature. The simulation results point out that the model is able to reproduce a variety of different conditions, including no hypotension, moderate hypotension, and severe hypotension with ultimate vasodepressor syncope, by adjusting a few parameters with clear physiological meanings. Hypotension is principally imputed to a loss of the sympathetic mechanisms working on systemic resistance and to an impairment of vascular refilling at the capillary wall. The results suggest that hypotension during hemodialysis is a complex phenomenon that depends on the superimposition of several concomitant factors working together that can lead to a variety of distinct individual patterns.