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VF is commonly characterised by two mechanisms, multi wavelet reentry and rotors, but no governing equation exists to explain and predict their population dynamics.
We hypothesized a single equation derived from an M/G/∞ renewal process could explain rotor and wavelet numbers in VF.
Phase singularity (PS) and wavefront (WF) tracking was used to identify wavelets and rotors in epicardial recordings of induced VF during cardiac surgery (n=13 patients). Autocorrelation and distributions of PS and WF lifetimes and inter-formation times were assessed to verify an underlying renewal process. Distributions were fitted using maximum likelihood to calculate formation (λf) and destruction (λd) rates, and combined in an M/G/∞ process to develop a potential governing equation of VF dynamics.
PS and WF inter-event-time distributions were consistent with the Weibull in all 210 epochs (PS: mean Χ2 P=0.23(95%CI,0.18,0.28); WF: mean Χ2 P=0.19(95%CI,0.13,0.27)), with zero autocorrelation at non-zero lags, indicative of an underlying renewal process over all stages (perfusion, ischemia and reflow). The M/G/∞ equation accurately predicted average PS and WF number (R>0.90) and population distribution (Χ2 P>0.05) in all epochs. Differences in λf (term: 0.015/ms (95%CI,0.010,0.020), non-term 0.023/ms (95%CI,0.019,0.027)), and average PS number (term: 1.68 (95%CI, 1.36, 2.00), non-term: (2.00 (95%CI, 1.86, 2.15)) was observed in spontaneous VF termination.
M/G/∞ renewal process provides a governing equation to explain the number of wavelets and rotors in VF, which could be used in mechanistic studies to guide development of new therapies.