Generative modeling and inverse imaging of cardiac transmembrane potential

Noninvasive reconstruction of cardiac transmembrane potential (TMP) from surface electrocardiograms (ECG) involves an ill-posed inverse problem. Model-constrained regularization is powerful for incorporating rich physiological knowledge about spatiotemporal TMP dynamics. These models are controlled by high-dimensional physical parameters which, if fixed, can introduce model errors and reduce the accuracy of TMP reconstruction. Simultaneous adaptation of these parameters during TMP reconstruction, however, is difficult due to their high dimensionality. We introduce a novel model-constrained inference framework that replaces conventional physiological models with a deep generative model trained to generate TMP sequences from low-dimensional generative factors. Using a variational auto-encoder (VAE) with long short-term memory (LSTM) networks, we train the VAE decoder to learn the conditional likelihood of TMP, while the encoder learns the prior distribution of generative factors. These two components allow us to develop an efficient algorithm to simultaneously infer the generative factors and TMP signals from ECG data. Synthetic and real-data experiments demonstrate that the presented method significantly improve the accuracy of TMP reconstruction compared with methods constrained by conventional physiological models or without physiological constraints.