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Abstract
In cardiac electrophysiology, it is important to predict the necessary conditions
for conduction failure, the failure of the cardiac excitation propagation even in
the presence of normal excitable tissue, in high-dimensional anisotropic space because
these conditions may provide feasible mechanisms for abnormal excitation propagations
such as atrial re-entry and, subsequently, atrial fibrillation even without taking
into account the time-dependent refractory region. Some conditions of conduction failure
have been studied for anisotropy or simple curved surfaces, but the general conditions
on anisotropic curved surfaces (anisotropic and curved surface) remain unknown. To
predict and analyze conduction failure on anisotropic curved surfaces, a new analytic
approach is proposed, called the relative acceleration approach borrowed from spacetime
physics. Motivated by a discrete model of cardiac excitation propagation, this approach
is based on the hypothesis that a large relative acceleration can translate to a dramatic
increase in the curvature of the wavefront and, subsequently, to conduction failure.
For simple anisotropic surfaces, the relative acceleration approach is validated by
computational simulations or the previously known results from the kinematics approach.
As a practical application, this approach is proposed to provide theoretical explanations
of the mechanism of cardiac excitation propagation around the pulmonary vein with
anatomically observed anisotropy.