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

Ventricular fibrillation (VF) is characterized 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

The purpose of this study was to test the hypothesis that 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-electrode) recordings obtained from patients undergoing cardiac surgery were studied (12 patients; 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 interformation 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 toward slower PS destruction, slower rates of PS formation, and a slower mixing rate of the VF process, indicated by larger values of the second largest eigenvalue modulus of the M/M/∞ birth-death matrix. The longest-lasting PS (associated with rotors) had shorter interactivation time intervals compared to shorter-lasting PS lasting <150 ms (∼1 PS rotation in human VF).

Conclusion

The M/M/∞ equation explains the number of wavelets and rotors observed, supporting a paradigm of VF based on statistical fibrillatory dynamics.