  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.
