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Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps

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Abstract

We propose FiberNet, a method to estimate in-vivo the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electro-mechanical function of the heart, yet they are difficult to determine in-vivo, and hence rarely truly patient-specific in existing cardiac models. FiberNet learns the fiber arrangement by solving an inverse problem with physics-informed neural networks. The inverse problem amounts to identifying the conduction velocity tensor of a cardiac propagation model from a set of sparse activation maps. The use of multiple maps enables the simultaneous identification of all the components of the conduction velocity tensor, including the local fiber angle. We extensively test FiberNet on synthetic 2-D and 3-D examples, diffusion tensor fibers, and a patient-specific case. We show that 3 maps are sufficient to accurately capture the fibers, also in the presence of noise. With fewer maps, the role of regularization becomes prominent. Moreover, we show that the fitted model can robustly reproduce unseen activation maps. We envision that FiberNet will help the creation of patient-specific models for personalized medicine. The full code is available at http://github.com/fsahli/FiberNet.

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Acknowledgements

This work was funded by an Open Seed Fund CORFO 14ENi2-26862 to CRH and FSC, the ANID—Millennium Science Initiative Program—NCN19-161 to FSC. We also acknowledge the School of Engineering computing cluster at Pontificia Universidad Católica de Chile for providing the computational resources for this study. SP and FSC acknowledge the financial support of the Leading House for Latin American Region (Grant Agreement No. RPG 2117). This work was also financially supported by the Theo Rossi di Montelera Foundation, the Metis Foundation Sergio Mantegazza, the Fidinam Foundation, the Horten Foundation to the Center for Computational Medicine in Cardiology. SP also acknowledges the CSCS-Swiss National Supercomputing Centre (Production Grant No. s1074) and the Swiss Heart Foundation (No. FF20042). Finally, we are very grateful to Prof. Angelo Auricchio and Dr. Giulio Conte from Instituto Cardiocentro Ticino, EOC (Lugano, Switzerland) for providing the patient-specific data.

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Correspondence to Francisco Sahli Costabal.

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The authors have no relevant financial or non-financial interests to disclose. The clinical data used in this study were obtained with oral and written informed consent for the investigation. The study has been performed in compliance with the Declaration of Helsinki.

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Appendices

Appendix 1: Smooth basis

When defining a conduction velocity tensor through its eigencomponents, as was done in Sect. 3.1, any two non-coinciding (preferably orthonormal) vectors of the tangent space \({\mathcal {S}}\) may be a feasible choice. Computationally, this 2D basis could be chosen locally, e.g. on a per-triangle basis. However, as the chosen Huber-norm regularization in (8) penalizes variation of the parameter vector \(\varvec{d}{}\), it is greatly beneficial to define a smooth basis.

To this end, we computed the first basis \(\varvec{v}{}_1\) of the tangent space using the vector heat method [42]. The vector heat method quickly computes parallel transport of a chosen vector on the whole manifold by shortly diffusing a given initial vector field using the heat equation with the connection Laplacian \(\Delta ^{\nabla } = -\nabla _C^* \nabla _C\) for \(\nabla _C\) being the Levi-Civita connection of the manifold. The rescaled diffused vectors then closely approximate the parallel transport of the initial vector field (for numerical and qualitative comparisons, we refer to the original paper [42]).

The initial vector to be transported across the manifold is manually selected for each manifold, such that the discontinuities of the vector field are minimal. Discontinuities might arise at the cut-locus, i.e. regions equidistant from the given vector, as there are multiple possible parallel transports at such locations.

Fig. 11
figure 11

Result of transporting a single vector on the anterior wall of the atria across the entire manifold. The resulting vector field is smooth except for parts of high curvature such as the left atrial appendage or pulmonary veins

Figure 11 shows such a computed parallel transport from the anterior wall of the atria. The resulting vector field is smooth in most parts, exhibiting a very low overall variation. Such a basis was chosen manually for all meshes.

Appendix 2: DT-MR imaging errors

See Table 2.

Table 2 Fiber errors for the 7 fiber distributions obtained from DT-MR imaging

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Ruiz Herrera , C., Grandits, T., Plank, G. et al. Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps. Engineering with Computers 38, 3957–3973 (2022). https://doi.org/10.1007/s00366-022-01709-3

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