Electrocardiographic imaging (ECGi) solves a highly ill-posed problem to estimate electric sources inside the heart from electrocardiograms (ECGs). Among different prior knowledge used to constrain the solution space, physiological models describing cardiac transmembrane potential (TMP) propagation have been found to be powerful regularizer. However, because these models are controlled by a large number of parameters, they are difficult to be customized to patient-specific ECG data, which may negatively impact the accuracy of ECGi. This paper presents a machine learning approach to learn a prior distribution of TMP signals throughout the myocardial wall, which is sufficiently complex and efficiently adaptable to ECG data. The prior distribution is obtained in the form of a generative model with low dimensional generative factors that may provide an effective way to adapt the prior physiological knowledge to patient-specific ECG data.
Method: We use a sequential Variational Autoencoder (VAE) to learn a low dimensional latent factor Z as well as a conditional distribution of TMP signals conditioned on those latent factors. Both the encoder and decoder consist of LSTM networks preserving temporal relation while the spatial dimension (vector length) decreases from TMP to latent variable Z and again increases from Z to TMP. Using simulated 3D TMP sequence VAE is trained by maximizing the evidence lower bound (ELBO).
Result and Analysis: The VAE is trained in two heart models, each with approximately 850 simulated TMP signals considering 50 different origins of ventricular activation and 17 different tissue property configurations. The trained model is able to reconstruct TMP signals with an average normalized mean squared error of 0.045 during training. Additional analyses are performed to investigate the relationship between different components within the latent space and the physical generative factors that control different aspects of TMP signals including repolarization, depolarization, sites of excitation, and tissue properties.