A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: implications for sudden cardiac death

Abstract

BACKGROUND: Ventricular fibrillation (VF) is characterised by multiple wavelets and rotors. No equation to predict the number of rotors and wavelets observed during fibrillation has been validated in human VF. OBJECTIVE: We hypothesized a single equation derived from a Markov M/M/∞ birth-death process, could predict the number of rotors and wavelets occurring in human clinical VF. METHODS: Epicardial induced VF (256-electrodes) recordings obtained from patients undergoing cardiac surgery were studied (n=12 patients, n=62 epochs). Rate constants for phase singularity (PS, which occur at the pivot points of rotors) and wavefront (WF) formation and destruction were derived by fitting distributions to PS and WF inter-formation and lifetimes. These rate-constants were combined in an M/M/∞ governing equation to predict the number of PS and WF in VF episodes. Observed distributions were compared to those predicted by the M/M/∞ equation. RESULTS: The M/M/∞ equation accurately predicted average PS and WF number and population distribution, demonstrated in all epochs. Self-terminating episodes of VF were distinguished from VF episodes requiring termination by a trend towards slower PS destruction, and slower rates of PS formation, and a slower mixing rate of the VF process, indicated by larger values of the second-largest eigenvalue modulus (SLEM) of the M/M/∞ birth-death matrix. The longest-lasting PS (associated with rotors) had shorter inter-activation time intervals compared to shorter lasting PS lasting <150 ms (∼1 PS rotation in human VF). CONCLUSIONS: The M/M/∞ equation explains the number of wavelets and rotors observed, supporting a paradigm of VF based on statistical fibrillatory dynamics.