  The eikonal equation has become an indispensable tool for modeling cardiac
electrical activation accurately and efficiently. In principle, by matching
clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible
to build patient-specific models of cardiac electrophysiology in a purely
non-invasive manner. Nonetheless, the fitting procedure remains a challenging
task. The present study introduces a novel method, Geodesic-BP, to solve the
inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine
learning frameworks, allowing us to optimize the parameters of the eikonal
equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a
simulated cardiac activation with high accuracy in a synthetic test case, even
in the presence of modeling inaccuracies. Furthermore, we apply our algorithm
to a publicly available dataset of a biventricular rabbit model, with promising
results. Given the future shift towards personalized medicine, Geodesic-BP has
the potential to help in future functionalizations of cardiac models meeting
clinical time constraints while maintaining the physiological accuracy of
state-of-the-art cardiac models.
