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

TL;DR

This work tackles the slow turnaround of physics-based circulatory models by introducing a physics-informed neural network (PINN) that enforces the governing ODEs of a closed-loop five-compartment circulatory system embedding the left ventricle. The PINN enables rapid forward predictions and an inverse modeling path to estimate physiologic parameters, including LV contractility indexed by the end-systolic elastance $E_{es}$, from single-beat LV pressure-volume waveforms. Validation on synthetic data shows sub-5% predictive error relative to ODE solutions, while inverse estimation from swine measurements recovers ground-truth values and detects a $E_{es}$ increase from baseline to dobutamine-treated states by 58%–284%. These results suggest the approach could enable real-time, patient-specific estimation of LV contractility and other parameters from single-beat data in the clinical setting.

Abstract

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.

Figures (10)

• Figure 1: The electrical equivalent diagram of the closed-loop blood circulation. lv, left ventricle; ao, aorta; art, peripheral artery; vc, vena cava; la, left atrium; av, aortic valve; mv, mitral valve.
• Figure 2: Model architecture: Input layer size is 22, comprising 12 Fourier terms and 10 input parameters. Four separate neural networks, each characterized by its set of weights and biases represented as $\boldsymbol{\theta}_{i}$.
• Figure 3: Results of the PINN training
• Figure 4: Total order Sobol indices associated with $V_{lv}$ and $P_{lv}$ for each input parameters
• Figure 5: RMAE between the estimated input parameters and their ground truth for the 100.0 synthetic cases