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Accurate estimates of left ventricle elastances based on non-invasivemeasurements are required for clinical decision-making during treatment ofvalvular diseases. The present study proposes a parameter discovery approachbased on a lumped parameter model of the cardiovascular system in conjunctionwith optimization and non-invasive, clinical input measurements to approximateimportant cardiac parameters, including left ventricle elastances. A subset ofparameters of a multi-compartment lumped parameter model was estimated using1st order Adam gradient descent and hybrid Adam and 2nd order quasi-Newtonlimited-memory Broyden-Fletcher-Goldfarb-Shanno optimization routines.Forward-mode automatic differentiation was used to estimate the Jacobianmatrices and compared to the common finite differences approach. Synthetic dataof healthy and diseased hearts were generated as proxies for non-invasiveclinical measurements and used to evaluate the algorithm. Twelve parametersincluding left ventricle elastances were selected for optimization based on 99%explained variation in mean left ventricle pressure and volume. The hybridoptimization strategy yielded the best overall results compared to 1st orderoptimization with automatic differentiation and finite difference approaches,with mean absolute percentage errors ranging from 6.67% to 14,14%. Errors inleft ventricle elastance estimates for simulated aortic stenosis and mitralregurgitation were smallest when including synthetic measurements for arterialpressure and valvular flow rate at approximately 2% and degraded to roughly 5%when including volume trends as well. However, the latter resulted in bettertracking of the left ventricle pressure waveforms and may be considered whenthe necessary equipment is available.

Non-invasive estimation of left ventricle elastance using a  multi-compartment lumped parameter model and gradient-based optimization with  forward-mode automatic differentiation