Ensemble learning of the atrial fiber orientation with physics-informed neural networks

TL;DR

This work extends Fibernet to cope with the uncertainty in the estimated fiber field and introduces a methodology to select the best fiber orientation members and define the input of the neural networks directly on the atrial surface.

Abstract

The anisotropic structure of the myocardium is a key determinant of the cardiac function. To date, there is no imaging modality to assess in-vivo the cardiac fiber structure. We recently proposed Fibernet, a method for the automatic identification of the anisotropic conduction -- and thus fibers -- in the atria from local electrical recordings. Fibernet uses cardiac activation as recorded during electroanatomical mappings to infer local conduction properties using physics-informed neural networks. In this work, we extend Fibernet to cope with the uncertainty in the estimated fiber field. Specifically, we use an ensemble of neural networks to produce multiple samples, all fitting the observed data, and compute posterior statistics. We also introduce a methodology to select the best fiber orientation members and define the input of the neural networks directly on the atrial surface. With these improvements, we outperform the previous methodology in terms of fiber orientation error in 8 different atrial anatomies. Currently, our approach can estimate the fiber orientation and conduction velocities in under 7 minutes with quantified uncertainty, which opens the door to its application in clinical practice. We hope the proposed methodology will enable further personalization of cardiac digital twins for precision medicine.

Figures (8)

• Figure 1: Schematic highlighting the difference between the input of $\Delta$-Fibernet and Fibernet, and the uncertainty quantification of the ensemble results.
• Figure 2: Left: Schematic of the fiber angle $\alpha(\hbox{\boldmath $x$}{})$ with respect to the orthonormal basis $\mathcal{B}(\hbox{\boldmath $x$}{})$ indicating. Right: Diagram of different behaviour of the fibers selected by Mean Tensor and Medoid approaches.
• Figure 3: Effects of ensemble size on execution time and loss minimization, for $\Delta$-Fibernet, in blue, and Fibernet, in magenta. The left graph presents the execution time for the first iteration and for 10.000 following iterations. In the right, the resulting $\mathcal{L}_{\text{data}}$ and $\mathcal{L}_{\text{eiko}}$ after 10.001 iterations is reported.
• Figure 4: Effect of noise on the prediction of the activation maps for both, $\Delta$-Fibernet and Fibernet. The solid line present the median result, with the filled area presenting the area between the best case and the worst.
• Figure 5: The first and second columns, present the effect of noise on the prediction of the orientation fibers maps for both, $\Delta$-Fibernet and Fibernet respectively. The solid line present the median result, with the filled area presenting the area between the best case and the worst. Meanwhile, on the third and fourth columns, the cumulative error for each model in the ensemble for $\Delta$-Fibernet and Fibernet respectively, for the case with 1 [ms] of noise. For all columns, the red dotted line presents the Mean Tensor fibers and the black dotted line the Medoid fibers.