A mesh-less approach for fast estimation of electrical activation time in the ventricular wall

The dynamics of electrophysiological wave propagation in ventricular tissue are the result of a large number of interrelated processes. However there are applications in which a rough estimation of tissue activation time at a set of given points is sufficient. This paper presents a mesh-less method for fast calculation of the activation time at any arbitrary point of the ventricular domain. It is based on estimating the path and the elapse time that an electrophysiological signal would need to travel over two points on a given 3D geometry. Due to the inhomogeneities of the medium and its layer based structure, the ventricular wall is modeled as a multi-layered domain. The travel time of a wave is estimated by finding the trajectory that it would follow in a multilayered region. The performance and accuracy of the method is checked against the Eikonal model in a two layer axisymmetric left ventricule. The comparison shows some benefits from the current approach. This method is useful for the estimation of the electrical activation sequence in a hexahedral mesh during mechanical simulation of the heart, since it removes the need for another refined mesh for the electrophysiological part.