Application of mathematical modeling to quantify ventricular contribution following durable left ventricular assist device support

Abstract

Ejection Fraction (EF), a measure of the ability of the heart to pump blood, is an important parameter for the diagnosis for heart failure as well as in the monitoring of the therapy provided. The standard method of calculating EF uses the left ventricular volume (LVV) by identifying the end-diastolic and end-systolic volumes. For patients implanted with a continuous flow (CF) left ventricular assist devices (LVADs), there are two pathways for blood ejection, Trans-Aortic Valve Flow (TAVF) which is intermittent and Trans-VAD Flow (TVF) that flows continuously throughout the cardiac cycle. Using the standard method to calculate EF in LVAD patients provides the fraction of the total blood ejected from the ventricle over a cardiac cycle. When monitoring the patient for recovery, it is vital to quantify the precise contribution of the Trans-Aortic Valve path independently from the Trans-VAD contribution. In this paper we demonstrate how this can be accomplished with a mathematical lumped parameter model of the interaction of the cardiovascular system and the LVAD. We introduce the Trans-Aortic Valve Ejection Fraction (TAVEF), which is the measure of the Trans-Aortic Valve contribution to the overall circulation. The dilated failing heart is represented by an unimodal End-Sytolic Pressure Volume Relationship (ESPVR). Our results indicate that TAVEF describes the contribution of the TAVF better as compared to standard EF over the entire range of LVAD speeds, and captures the point of aortic valve closure by becoming 0, whereas the standard EF is non-zero. TAVEF can be a useful, reliable, non-invasive mechanism for monitoring ventricular recovery.