Modeling left ventricular dynamics using a switched system approach based on a modified atrioventricular piston unit

Abstract

The contribution of the longitudinal atrioventricular plane displacement to ventricular pumping has drawn more and more attentions. In this paper, differential equations of the left ventricle (LV) are derived via the atrioventricular piston concept. The contribution of left ventricular radial function to blood flow was converted to an equivalent coefficient. A systemic circulatory model incorporating the modified atrioventricular piston unit was developed on a switched system form by adding some state-dependent switching planes. Simulation results prove that the end-systolic pressure volume relationship of the model with a changing systemic arterial resistance is approximately linear and insensitive to perturbations in afterload. Then the LV model was validated using a data fitting method. A pressure-volume loop from a patient undergoing routine diagnostic cardiac catheterization with LV angiography was used as measurements. Model parameters and the trapezoidal profile of contraction forces were adjusted by a trial method. The root mean squared error between the measured and estimated LV pressure is 2.99 mmHg. The LV compliance is 0.34 ml/mmHg. The ratio between left ventricular and left atrial cross-section is 1.8. Therefore, parameter values used in the modified LV model match physiological data. The model can reproduce the realistic pressure-flow relationship in the LV chamber.

Keywords: Atrioventricular plane displacement; End-systolic pressure volume relationship; Lumped-element ventricular model; Switched system; Ventricular compliance.