A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: Implications for sudden cardiac death.
Dharmaprani D., Jenkins EV., Quah JX., Lahiri A., Tiver K., Mitchell L., Bradley CP., Hayward M., Paterson DJ., Taggart P., Clayton RH., Nash MP., Ganesan AN.
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.