Abstract
Multiple unstable spiral waves rotating around phase singularities (PSs) in the heart, i.e., ventricular fibrillation (VF), is the leading cause of death in the industrialized world. Spiral waves are ubiquitous in nature and have been extensively studied by physiologists, mathematicians, chemists, and biologists, with particular emphasis on their movement and stability. Spiral waves are not easy to terminate because of the difficulty of "breaking" the continuous spatial progression of phase around the PSs. The only means to stop VF (i.e., cardiac defibrillation) is to deliver a strong electric shock to the heart. Here, we use the similarities between spiral wave dynamics and limit cycle oscillators to characterize the spatio-temporal dynamics of VF and defibrillation via phase-resetting curves. During VF, only PSs, including their formation and termination, were associated with large phase changes. At low shock strengths, phase-resetting curves exhibited characteristics of weak (type 1) resetting. As shock strength increased, the number of postshock PSs decreased to zero coincident with a transition to strong (type 0) resetting. Our results indicate that shock-induced spiral wave termination in the heart is caused by altering the phase around the PSs, such that, depending on the preshock phase, sites are either excited by membrane depolarization (phase advanced) or exhibit slowed membrane repolarization (phase delay). Strong shocks that defibrillate break the continuity of phase around PSs by forcing the state of all sites to the fast portion of state space, thus quickly leading to a "homogeneity of state," subsequent global repolarization and spiral wave termination.