# Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks

arXiv: https://arxiv.org/abs/2102.10863 · HTML: https://mlsanity.com/paper/2102.10863/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 22 Feb 2021.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)
- [Gaussian Process Manifold Interpolation for Probabilistic Atrial Activation Maps and Uncertain Conduction Velocity](https://mlsanity.com/paper/2004.10586/) (2020)
- [PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps](https://mlsanity.com/paper/2008.10724/) (2020)

## Built on by (most cited first, 8 of 8)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps](https://mlsanity.com/paper/2201.12362/) (2022)
- [Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical Models](https://mlsanity.com/paper/2312.09787/) (2023)
- [Med-Real2Sim: Non-Invasive Medical Digital Twins using Physics-Informed Self-Supervised Learning](https://mlsanity.com/paper/2403.00177/) (2024)
- [Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds](https://mlsanity.com/paper/2203.06222/) (2022)
- [Estimation of fibre architecture and scar in myocardial tissue using electrograms: an in-silico study](https://mlsanity.com/paper/2212.03012/) (2022)
- [HyperSBINN: A Hypernetwork-Enhanced Systems Biology-Informed Neural Network for Efficient Drug Cardiosafety Assessment](https://mlsanity.com/paper/2408.14266/) (2024)
- [Ensemble learning of the atrial fiber orientation with physics-informed neural networks](https://mlsanity.com/paper/2410.23388/) (2024)

## Abstract (arXiv)

Electroanatomical maps are a key tool in the diagnosis and treatment of atrial fibrillation. Current approaches focus on the activation times recorded. However, more information can be extracted from the available data. The fibers in cardiac tissue conduct the electrical wave faster, and their direction could be inferred from activation times. In this work, we employ a recently developed approach, called physics informed neural networks, to learn the fiber orientations from electroanatomical maps, taking into account the physics of the electrical wave propagation. In particular, we train the neural network to weakly satisfy the anisotropic eikonal equation and to predict the measured activation times. We use a local basis for the anisotropic conductivity tensor, which encodes the fiber orientation. The methodology is tested both in a synthetic example and for patient data. Our approach shows good agreement in both cases, with an RMSE of 2.2ms on the in-silico data and outperforming a state of the art method on the patient data. The results show a first step towards learning the fiber orientations from electroanatomical maps with physics-informed neural networks.