We develop an alternative view of the heart based on this fact, by considering the heart as a non-Euclidean manifold with a electrophysiological el- metric based on wave velocity. This metric is more natural than the Euclidean metric for studying the electrophysiology of the heart, because el-distances directly encode wave propagation.
We characterize this metric for a particular case of rotational orthotropic anisotropy of cardiac tissue on a small and a large scale. We show that although this metric is locally highly curved and non-Euclidean, its global geometry is close to that of an isotropic metric on the heart. That is, wave arrival times in anisotropic cardiac tissue with principal velocities v_f>v_s>v_n are well-approximated by arrival times in isotropic tissue with velocity v_f in all directions. We illustrate this with numerical simulations of a slab of cardiac tissue and of a model of the ventricles based on DTMRI scans of the canine heart.
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