# Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach

arXiv: https://arxiv.org/abs/2308.08410 · HTML: https://mlsanity.com/paper/2308.08410/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 16 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps](https://mlsanity.com/paper/2201.12362/) (2022)
- [Deep Computational Model for the Inference of Ventricular Activation Properties](https://mlsanity.com/paper/2208.04028/) (2022)
- [Inference of ventricular activation properties from non-invasive electrocardiography](https://mlsanity.com/paper/2010.15214/) (2020)
- [GEASI: Geodesic-based Earliest Activation Sites Identification in cardiac models](https://mlsanity.com/paper/2102.09962/) (2021)
- [Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds](https://mlsanity.com/paper/2203.06222/) (2022)
- [PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps](https://mlsanity.com/paper/2008.10724/) (2020)

## Built on by (most cited first, 5 of 5)

- [Solving the Inverse Problem of Electrocardiography for Cardiac Digital Twins: A Survey](https://mlsanity.com/paper/2406.11445/) (2024)
- [Probabilistic learning of the Purkinje network from the electrocardiogram](https://mlsanity.com/paper/2312.09887/) (2023)
- [Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging](https://mlsanity.com/paper/2408.11573/) (2024)
- [Ensemble learning of the atrial fiber orientation with physics-informed neural networks](https://mlsanity.com/paper/2410.23388/) (2024)
- [Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging](https://mlsanity.com/paper/2602.07466/) (2026)

## Abstract (arXiv)

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.