Rapid Estimation of Left Ventricular Contractility with a Physics-Informed Neural Network Inverse Modeling Approach

Physics-based computer models based on numerical solution of the governing equations generally cannot make rapid predictions, which in turn, limits their applications in the clinic. To address this issue, we developed a physics-informed neural network (PINN) model that encodes the physics of a closed-loop blood circulation system embedding a left ventricle (LV). The PINN model is trained to satisfy a system of ordinary differential equations (ODEs) associated with a lumped parameter description of the circulatory system. The model predictions have a maximum error of less than 5% when compared to those obtained by solving the ODEs numerically. An inverse modeling approach using the PINN model is also developed to rapidly estimate model parameters (in $\sim$ 3 mins) from single-beat LV pressure and volume waveforms. Using synthetic LV pressure and volume waveforms generated by the PINN model with different model parameter values, we show that the inverse modeling approach can recover the corresponding ground truth values, which suggests that the model parameters are unique. The PINN inverse modeling approach is then applied to estimate LV contractility indexed by the end-systolic elastance $E_{es}$ using waveforms acquired from 11 swine models, including waveforms acquired before and after administration of dobutamine (an inotropic agent) in 3 animals. The estimated $E_{es}$ is about 58% to 284% higher for the data associated with dobutamine compared to those without, which implies that this approach can be used to estimate LV contractility using single-beat measurements. The PINN inverse modeling can potentially be used in the clinic to simultaneously estimate LV contractility and other physiological parameters from single-beat measurements.