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.

翻译：基于控制方程数值求解的物理计算机模型通常无法进行快速预测，这限制了它们在临床中的应用。为解决此问题，我们开发了一种物理信息神经网络（PINN）模型，该模型编码了嵌入左心室（LV）的闭环血液循环系统的物理规律。PINN模型经过训练，能够满足与循环系统集总参数描述相关的常微分方程组（ODEs）。与数值求解ODEs获得的结果相比，模型预测的最大误差小于5%。我们还利用PINN模型开发了一种逆向建模方法，可从单搏LV压力和容积波形中快速估计模型参数（约需3分钟）。通过使用PINN模型生成的不同参数值的合成LV压力和容积波形，我们证明逆向建模方法能够恢复相应的真实值，这表明模型参数具有唯一性。随后，将PINN逆向建模方法应用于估计以收缩末期弹性模量$E_{es}$为指标的LV收缩力，所用波形来自11个猪模型，其中包括3个动物在给予多巴酚丁胺（一种正性肌力药物）前后的波形。与未使用多巴酚丁胺的数据相比，使用多巴酚丁胺相关数据估计的$E_{es}$高出约58%至284%，这表明该方法可以利用单搏测量估计LV收缩力。PINN逆向建模有望在临床中通过单搏测量同时估计LV收缩力及其他生理参数。