Termination of spiral waves during cardiac fibrillation via shock-induced phase resetting

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.defibrillation ͉ phase resetting curve M any systems in nature exhibit incredibly varied spatiotemporal patterns such as traveling waves, spiral waves, and Turing patterns (1-7). Spiral waves rotate around phase singularities (PSs) and often do not remain stationary and can even break up into a state of defect-mediated turbulence (7,8). During ventricular fibrillation (VF), PS pairs of opposite chirality are mutually annihilated if the phase gradient between them is sufficiently large to halt propagation (9). The probability of all PSs extinguishing at the same time, and thus resulting in spontaneous termination of VF, varies with the size of the heart (10). In humans, VF almost never terminates spontaneously, and electrical defibrillators are necessary to stop VF and restore the normal rhythm.Normally, the human heart beats about once per second; a pacemaker region periodically generates an electrical wave that propagates rapidly through the heart, triggering nearly synchronous contraction. Like many oscillators, this pacemaker region can be reset by an advance or a delay that depends on the time and strength of the stimulus (11, 12). Typically, periodic systems are characterized as limit cycle oscillators (similar to the minute hand moving around a clock) and the stimulus-induced perturbations are described by using phase-resetting curves (PRC...

Phase Mapping of Cardiac Fibrillation

“…In other words, time-encoding of phase in not reliable in studying cardiac fibrillation, and an alternate approach is needed where each cycle is coded to 0 to 2 radians irrespective of its cycle length. 3 Hence, for studying the spatial distribution of phase during cardiac fibrillation, a 2-variable state-space approach is used. In the state-space encoding approach, the scalar electrograms recorded at an electrode location during cardiac fibrillation is treated as an output of a nonlinear dynamical system.…”

“…The development of this phase mapping tool has led to better understanding of fibrillation dynamics as evidenced by the use of phase mapping in detecting PS and their role in demonstrating organization during VF. Some of these works and their findings are (1) PS colocalize with anatomic heterogeneities, and their spatial meandering is modulated by these heterogeneities, 6 (2) PS correlates with the locations of wave breaks, 7 (3) in myopathic human hearts, phase maps were used to show that the organization of electric activity were characterized by wave fronts emanating from a few rotors, 8 and (4) phase mapping technique has also been applied to investigate the mechanism of fibrillation. [7][8][9] Clinical electrophysiologists innovating therapies for both AF and VF are commonly not aware of phase mapping.…”

“…This time-encoding technique deals with a scenario where the activation periods are the same over the surface being mapped. To deal with the scenario of varying activation period over the mapped surface (common in animal and human fibrillation models), Gray et al 2,3 introduced the state-space encoding concept from nonlinear dynamics.…”

Reentrant spiral waves of spreading depression cause macular degeneration in hypoglycemic chicken retina

“…In neocortex in vivo, spiral waves occurred during pharmacologically induced oscillations, activity mediated synaptically rather than by SD (23). Spiral waves have been documented in the heart, where they are based on propagation of sodium-dependent action potentials that become reentrant through gap junctions; in humans, spiral waves are a possible basis of ventricular arrhythmia (24)(25)(26). In an earlier study of chicken retina under control conditions, anodal or cathodal polarization applied during the falling phase of an SD wave could induce a spiral wave that continued for ∼30 min (27).…”

Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes

“…Phase mapping is an analysis technique used to depict the spatiotemporal changes in activation during cardiac fibrillation (15,16). Phase is a variable that describes the progression through the action potential in a specific region of myocardium through a cycle between Ϫ and ϩ.…”