Intramural wave propagation in cardiac tissue: asymptotic solutions and cusp waves

The cardiac muscle is well known to conduct electric impulses anisotropically, showing a larger conduction velocity along than across fibers. Fiber orientation is not uniform within the cardiac wall, but rotates by as much as 180 degrees throughout the wall thickness. Numerical simulations and experiments have indicated that this rotational anisotropy considerably affects the spread of excitation in cardiac tissue: the wave front shows a complex intramural shape with trailing cusps. The cusps can travel across layers and reach the epicardial and endocardial surfaces where they cause apparent accelerations of propagation. In the present study we provide an analytical description of the asymptotic wave front, as well as of cusp waves. We investigate the motion of cusp waves, based on the assumption that they occur at the intersection of asymptotic solutions, and we show that our theoretical analysis is in close agreement with numerical simulations. The asymptotic solutions are found to be determined purely by the fiber organization within the cardiac wall, independent of the excitable properties of cardiac tissue.