Electrocardiogram (ECG) signals provide essential information about the heart's condition and are widely used for diagnosing cardiovascular diseases. The morphology of a single heartbeat over the available leads is a primary biosignal for monitoring cardiac conditions. However, analyzing heartbeat morphology can be challenging due to noise and artifacts, missing leads, and a lack of annotated data. Generative models, such as denoising diffusion generative models (DDMs), have proven successful in generating complex data. We introduce $\texttt{BeatDiff}$, a light-weight DDM tailored for the morphology of multiple leads heartbeats. We then show that many important ECG downstream tasks can be formulated as conditional generation methods in a Bayesian inverse problem framework using $\texttt{BeatDiff}$ as priors. We propose $\texttt{EM-BeatDiff}$, an Expectation-Maximization algorithm, to solve this conditional generation tasks without fine-tuning. We illustrate our results with several tasks, such as removal of ECG noise and artifacts (baseline wander, electrode motion), reconstruction of a 12-lead ECG from a single lead (useful for ECG reconstruction of smartwatch experiments), and unsupervised explainable anomaly detection. Numerical experiments show that the combination of $\texttt{BeatDiff}$ and $\texttt{EM-BeatDiff}$ outperforms SOTA methods for the problems considered in this work.

Reliable patient-specific ventricular repolarization times (RTs) can identify regions of functional block or afterdepolarizations, indicating arrhythmogenic cardiac tissue and the risk of sudden cardiac death. Unipolar electrograms (UEs) record electric potentials, and the Wyatt method has been shown to be accurate for estimating RT from a UE. High-pass filtering is an important step in processing UEs, however, it is known to distort the T-wave phase of the UE, which may compromise the accuracy of the Wyatt method. The aim of this study was to examine the effects of high-pass filtering, and improve RT estimates derived from filtered UEs. We first generated a comprehensive set of UEs, corresponding to early and late activation and repolarization, that were then high-pass filtered with settings that mimicked the CARTO filter. We trained a deep neural network (DNN) to output a probabilistic estimation of RT and a measure of confidence, using the filtered synthetic UEs and their true RTs. Unfiltered ex-vivo human UEs were also filtered and the trained DNN used to estimate RT. Even a modest 2 Hz high-pass filter imposes a significant error on RT estimation using the Wyatt method. The DNN outperformed the Wyatt method in 62.75% of cases, and produced a significantly lower absolute error (p=8.99E-13), with a median of 16.91 ms, on 102 ex-vivo UEs. We also applied the DNN to patient UEs from CARTO, from which an RT map was computed. In conclusion, DNNs trained on synthetic UEs improve the RT estimation from filtered UEs, which leads to more reliable repolarization maps that help to identify patient-specific repolarization abnormalities.

The Purkinje system is a heart structure responsible for transmitting electrical impulses through the ventricles in a fast and coordinated way to trigger mechanical contraction. Estimating a patient-specific compatible Purkinje Network from an electro-anatomical map is a challenging task, that could help to improve models for electrophysiology simulations or provide aid in therapy planning, such as radiofrequency ablation. In this study, we present a methodology to inversely estimate a Purkinje network from a patient's electro-anatomical map. First, we carry out a simulation study to assess the accuracy of the method for different synthetic Purkinje network morphologies and myocardial junction densities. Second, we estimate the Purkinje network from a set of 28 electro-anatomical maps from patients, obtaining an optimal conduction velocity in the Purkinje network of 1.95 ± 0.25 m/s, together with the location of their Purkinje-myocardial junctions, and Purkinje network structure. Our results showed an average local activation time error of 6.8±2.2 ms in the endocardium. Finally, using the personalized Purkinje network, we obtained correlations higher than 0.85 between simulated and clinical 12-lead ECGs.