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

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 fibre structure. We recently proposed Fibernet, a method for the automatic identification of the anisotropic conduction - and thus fibres - 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 fibre 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 fibre 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 fibre orientation error in eight different atrial anatomies. Currently our approach can estimate the fibre orientation and conduction velocities in under 7 min with quantified uncertainty, which opens the door to its application in clinical practice. We hope the proposed methodology will enable further personalisation of cardiac digital twins for precision medicine. KEY POINTS: The direction of heart muscle fibres strongly affects how electrical signals travel, but current imaging methods cannot measure these fibres inside the living atria. We improved our previous method (Fibernet) by introducing $\Delta$ -Fibernet, which is more accurate and can estimate uncertainty in the results. $\Delta$ -Fibernet works directly on the surface of the heart and includes a new approach to select the most reliable fibre direction. The method produces results in under 7 min and could support personalised treatment planning for heart rhythm disorders.