Numerical modeling of the electrical activity of the atria and the pulmonary veins
Three axes are explored. 1) Derivation of mathematical models. Mathematical methods allow to derive simplified models from three-dimensional complex ones, while controlling approximation errors. We construct a bilayer surface model that allows to simulate three-dimensional phenomena for a bi-dimensional computational load, to investigate 3D atrial patterns such that electrical dissociation or transmural heterogeneities. Those methods are also used to construct a homogenized model that includes the non linear behavior of gap junctions. 2) Triggers of atrial arrhythmia. Proofs of concept of arrhythmogenic mechanisms are given by using numerical models of the pulmonary veins. The first mechanism is based on a unidirectional conduction block triggered by a discontinuity of the fibre distribution. The second one comes from a different propagation pattern during the depolarization and the repolarization when two layer of fibres are superimposed. 3)Atrial arrhythmia perpetuation. We investigate the influence of transmural heterogeneities of the distribution of fibrosis on the perpetuation of atrial arrhythmia. Several ablation protocols are assessed. Finally, a method of personalization of the model is given.