Renewal Theory as a Universal Quantitative Framework to Characterize Phase Singularity Regeneration in Mammalian Cardiac Fibrillation

Abstract

Background: Despite a century of research, no clear quantitative framework exists to model the fundamental processes responsible for the continuous formation and destruction of phase singularities (PS) in cardiac fibrillation. We hypothesized PS formation/destruction in fibrillation could be modeled as self-regenerating Poisson renewal processes, producing exponential distributions of interevent times governed by constant rate parameters defined by the prevailing properties of each system. Methods: PS formation/destruction were studied in 5 systems: (1) human persistent atrial fibrillation (n=20), (2) tachypaced sheep atrial fibrillation (n=5), (3) rat atrial fibrillation (n=4), (5) rat ventricular fibrillation (n=11), and (5) computer-simulated fibrillation. PS time-to-event data were fitted by exponential probability distribution functions computed using maximum entropy theory, and rates of PS formation and destruction (λ f /λ d ) determined. A systematic review was conducted to cross-validate with source data from literature. Results: In all systems, PS lifetime and interformation times were consistent with underlying Poisson renewal processes (human: λ f , 4.2%/ms±1.1 [95% CI, 4.0–5.0], λ d , 4.6%/ms±1.5 [95% CI, 4.3–4.9]; sheep: λ f , 4.4%/ms [95% CI, 4.1–4.7], λ d , 4.6%/ms±1.4 [95% CI, 4.3–4.8]; rat atrial fibrillation: λ f , 33%/ms±8.8 [95% CI, 11–55], λ d , 38%/ms [95% CI, 22–55]; rat ventricular fibrillation: λ f , 38%/ms±24 [95% CI, 22–55], λ f , 46%/ms±21 [95% CI, 31–60]; simulated fibrillation λ d , 6.6–8.97%/ms [95% CI, 4.1–6.7]; R 2 ≥0.90 in all cases). All PS distributions identified through systematic review were also consistent with an underlying Poisson renewal process. Conclusions: Poisson renewal theory provides an evolutionarily preserved universal framework to quantify formation and destruction of rotational events in cardiac fibrillation.

Prospective cross‐sectional study using Poisson renewal theory to study phase singularity formation and destruction rates in atrial fibrillation (RENEWAL‐AF): Study design

“…Recently, we have shown that an exponential distribution of rotor phase singularity lifetimes is a conserved feature of human and experimental atrial fibrillation and ventricular fibrillation, validated with multiple modalities including electrogram‐based and optical mapping 8 . The exponential distribution is significant because it is the statistical signature of a Poisson stochastic renewal process 9 .…”

“…For over a century, the presence of unstable reentrant circuits has been a defining characteristic of atrial fibrillation 15‐20 . Recently, we described a new approach based on renewal theory to enable measurement of rotor formation and destruction rates 8 …”

“…Using a lookup table, computation of the histograms for phase singularity lifetimes and interformation event times will be performed. For each epoch, observed phase singularity lifetime data will be fitted using maximum likelihood and/or nonlinear least‐squares regression and the phase singularity formation rate, λ f , and destruction rate, λ d , as previously described 8 …”

“…Recently, we have demonstrated that rotational event formation and destruction rates can be accurately determined through characterization of the distributions of interformation event times and rotor lifetimes 8 . In human and experimental models of cardiac fibrillation, we have shown that these consistently show exponential distributions.…”

“…In that study, we demonstrated the feasibility of measuring rotor formation and destruction rates by fitting the distributions of phase singularity interformation event times and phase singularity lifetimes 8 . We demonstrated these consistently followed exponential distributions in human atrial fibrillation, sheep atrial fibrillation and rat atrial fibrillation, 8 and in an extension systematic review published with our study, we demonstrated that this has been a consistent finding observable in the published data of leading investigators in the field of atrial fibrillation and ventricular fibrillation research 8 . The key implication of the exponential distribution identified in our study is that the formation and destruction of rotors occurs at relatively temporally stable rates, and in that study we demonstrated the feasibility of measuring this in both clinical and preclinical data.…”