Prediction of Optimal Continuous‐Flow Total Artificial Heart and Vascular Parameters to Maintain Hemodynamic Homeostasis

Abstract

Ventricular‐vascular interaction is very complex, because pulsatile pressures depend on vascular properties and three cardiac parameters—heart rate, ventricular compliance and contractility. There is a growing interest in modeling the interaction of the vasculature and continuous‐flow pumps to optimize the design, control, and pharmacological support of a continuous‐flow total artificial heart. The lack of pulsatility that makes the interaction easier to model, however, also introduces a new constraint: continuous‐flow pumps depend only on two parameters—pump speed and an internal resistance. The purpose of this work is to predict flows and pressures in terms of vascular and pump properties. The vasculature was characterized by parameters for arterial and venous compliances, as well as systemic and pulmonary resistances. Through linearization and simplification, we were able to develop simple algebraic formulas predicting total flow, systemic arterial and venous pressure, pulmonary arterial and venous pressure, as well as pump power. With fewer parameters than a ventricle, a pump does not have enough flexibility to adjust the limited set of pump parameters to independently control pressures while maintaining normal blood volume and vascular resistances. Our algebraic solution, however, suggests that pump and vascular parameter values can be adjusted to optimize hemodynamic homeostasis.