  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.
