Inverse ESPVR Estimation with Singularity Avoidance via Constrained EDPVR Parameter Optimization

Left ventricular end-systolic elastance E
es
, as an index of cardiac contractility, can play a key role in continuous patient monitoring during cardiac treatment scenarios such as drug therapies. The clinical feasibility of E
es
estimation remains challenging because most techniques have been built on left ventricular pressure and volume, which are difficult to measure or estimate in the regular ICU/CCU setting. The purpose of this paper is to propose and validate a novel approach to estimate E
es
, which is independent of left ventricular pressure and volume. Our methods first derive an analytical representation of E
es
as the inverse function of the gradient of the Frank-Starling Curve based on cardiac mechanics. Second, elucidating the mechanism of singularities in the inverse function, we derive multiple conditions in both end-systolic pressure-volume relationship (ESPVR) and end-diastolic pressure-volume relationship (EDPVR) parameters to avoid these singularities analytically. Third, we formulate a constrained nonlinear least squares problem to optimize both ESPVR and EDPVR parameters simultaneously to avoid singularities. The effectiveness of the proposed method in avoiding singularities was evaluated in an animal experiment. Compared to the conventional E
es
estimation by linear regression, our proposed method reproduced in-vivo hemodynamics more accurately when simulating the estimated E
es
variation during drug administration. Our method can be applied using the available data in the regular ICU/CCU setting. The improved clinical feasibility can support not only physicians’ decision-making, including adjusting drug dosages in current clinical treatment, but also a closed-loop hemodynamic control system requiring accurate continuous E
es
estimation.