Physics-Informed Neural Networks for Cardiac Activation Mapping

By F. Sahli Costabal, Yibo Yang, Paris Perdikaris, Daniel E. Hurtado, Ellen Kuhl. 2020

A critical procedure in diagnosing atrial fibrillation is the creation of electro-anatomic activation maps. Current methods generate these mappings from interpolation using a few sparse data points recorded inside the atria; they neither include prior knowledge of the underlying physics nor uncertainty of these recordings. Here we propose a physics-informed neural network for cardiac activation mapping that accounts for the underlying wave propagation dynamics and we quantify the epistemic uncertainty associated with these predictions. These uncertainty estimates not only allow us to quantify the predictive error of the neural network, but also help to reduce it by judiciously selecting new informative measurement locations via active learning. We illustrate the potential of our approach using a synthetic benchmark problem and a personalized electrophysiology model of the left atrium. We show that our new method outperforms linear interpolation and Gaussian process regression for the benchmark problem and linear interpolation at clinical densities for the left atrium. In both cases, the active learning algorithm achieves lower error levels than random allocation. Our findings open the door toward physics-based electro-anatomic mapping with the ultimate goals to reduce procedural time and improve diagnostic predictability for patients affected by atrial fibrillation. Open source code is available at https://github.com/fsahli/EikonalNet.

Subfields: AI for Physical Sciences, Medical & Health AI

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Citations in the corpus

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, methodology): “They have been used in many scientific applications, including fluid mechanics modeling (Raissi et al., 2020), cardiac activation mapping (Sahli Costabal et al., 2020), stochastic systems modeling (Yang and Perdikaris, 2019), and discovery of differential equations (Raissi et al., 2018; Raissi,…”
Physics informed deep learning for computational elastodynamics without labeled data (2020, background): “…ﬂuid ﬂows and Navier-Stokes equations [10, 17–21], solving stochastic PDEs [22], ﬂows transport in porous media [23–25], cardiovascular systems [26–28], design of metamaterials [29– 31], metamodeling of nonlinear structural systems [32, 33], and discovery of physical laws [34–36], among others.”
Physics-informed neural networks with hard constraints for inverse design (2021, methodology): “Moreover, PINNs have been successfully employed to solve diverse inverse problems , including in optics [8], ﬂuid mechanics [45, 55], systems biology [60], biomedicine [46, 24], and even inverse problems of stochastic PDEs [62] and fractional PDEs [38].”
Parallel Physics-Informed Neural Networks via Domain Decomposition (2021, background): “Due to their simplicity, PINNs have led to progress in many areas of computational science, see for examples [7, 8, 9, 10, 11, 12, 13, 14, 15].”
Self-adaptive loss balanced Physics-informed neural networks (2021, background): “A series of remarkable results across problems in various fields such as machinery and engineering, including biomedical problems [20], finance [21].”
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets (2021, unknown): “…have found wide applicability across diverse applications including fluid mechanics ( 19 , 20 ), heat transfer ( 21 , 22 ), bioengi-neering ( 23 , 24 ), materials ( 25 – 28 ), and finance ( 29 , 30 ), showcasing the remarkable effectiveness of ML techniques in learning black box functions, even…”
Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture (2020, result): “By incorporating loss functions based on the PDE, initial condition, and boundary condition residual errors, PINNs recover the solution to the PDE without requiring the use of any other model or simulation.”
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems (2021, background): “Its merit and effectiveness has been demonstrated over a plethora of scientific applications in many areas [3–7].”
PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain (2020, methodology): “This weakly-supervised method has been applied to solve various PDEs with limited training data in many scientific problems, including subsurface flows [20], vortex-induced vibrations [21], turbulent flows [22, 23], cardiovascular systems [14, 24–26], metamaterial design [27–29], geostatistical mode”
Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, methodology): “The Eikonal equation describes wave propagation, like the travel time of seismic wave (Waheed et al, 2021; Smith et al, 2021a) or cardiac activation electrical waves (Sahli Costabal et al, 2020; Grandits et al, 2021).”
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems (2021, methodology): “PINNs have been successfully employed to solve diverse problems in diﬀerent ﬁelds, for example in optics [7, 8], ﬂuid mechanics [9], systems biology [10], and biomedicine [11].”
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations (2021, methodology): “…wide range of applications, for example in simulating ﬂuid ﬂow [Raissi et al., 2020, Sun et al., 2020], carrying out cardiac activation mapping [Sahli Costabal et al., 2020], modelling wave physics [Moseley et al., 2020b], and even in predicting the temperature distribution over an espresso cup…”
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks (2020, background): “PINNs in particular, have demonstrated remarkable power in applications including fluid dynamics [12, 13, 14], biomedical engineering [15, 16, 17], meta-material design [18, 19], free boundary problems [20], Bayesian networks and uncertainty quantification [21, 22], high dimensional PDEs [23, 24, 25”
When and why PINNs fail to train: A neural tangent kernel perspective (2020, background): “Thanks to the approximation capabilities of neural networks, physics-informed neural networks (PINNs) have already led to a series of remarkable results across a range of problems in computational science and engineering, including fluids mechanics [1, 2, 4, 5], bio-engineering [6, 7], meta-material”