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