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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.
Objective
We hypothesized a single equation derived from an M/G/∞ renewal process could explain rotor and wavelet numbers in VF.
Methodsmaterials-methods
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.
Results
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.
Conclusion
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.
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