Reconceptualising Atrial Fibrillation Using Renewal Theory: A Novel Approach to the Assessment of Atrial Fibrillation Dynamics

Abstract

Despite a century of research, the mechanisms of AF remain unresolved. A universal motif within AF research has been unstable re-entry, but this remains poorly characterised, with competing key conceptual paradigms of multiple wavelets and more driving rotors. Understanding the mechanisms of AF is clinically relevant, especially with regard to treatment and ablation of the more persistent forms of AF. Here, the authors outline the surprising but reproducible finding that unstable re-entrant circuits are born and destroyed at quasi-stationary rates, a finding based on a branch of mathematics known as renewal theory. Renewal theory may be a way to potentially unify the multiple wavelet and rotor theories. The renewal rate constants are potentially attractive because they are temporally stable parameters of a defined probability distribution (the exponential distribution) and can be estimated with precision and accuracy due to the principles of renewal theory. In this perspective review, this new representational architecture for AF is explained and placed into context, and the clinical and mechanistic implications are discussed.

The inspection paradox: An important consideration in the evaluation of rotor lifetimes in cardiac fibrillation

“…We have recently investigated spiral vortex regeneration population dynamics in AF and VF ( Dharmaprani et al, 2019b ; Dharmaprani et al, 2021 ; Dharmaprani et al, 2022 ). These studies have shown in cardiac fibrillation, similar to other natural systems, PS inter-formation times and lifetimes fit with an exponential distribution, consistent with the notion that PS creation and annihilation may be characterised as renewal processes ( Dharmaprani et al, 2019b ; Dharmaprani et al, 2021 ; Quah et al, 2021 ). By combining the renewal rate constants for PS formation (λf—pronounced ‘lambda-f’) and destruction (λd), we have shown that it is possible to explain the Poisson distribution of PS that is observed in both AF and VF ( Dharmaprani et al, 2019b ; Dharmaprani et al, 2021 ; Quah et al, 2021 ) ( Jenkins et al, 2022 ).…”

“…A surprising finding is that the population dynamics of PS in these diverse systems appear to be governed by common statistical laws ( Davidsen et al, 2008 ; Tan et al, 2020 ). Specifically, theoretical studies have predicted that due to the effective statistically independent nature of spiral nucleation and annihilation processes under conditions of spatiotemporal turbulence, PS populations should follow Poisson distributions ( Gil et al, 1990 ; Wang, 2004 ), with the corollary being that PS lifetimes should be exponentially distributed ( Tan et al, 2020 ; Quah et al, 2021 ). These statistical properties have empirically been subsequently demonstrated to apply to spiral vortex regeneration in fluid mechanics ( Ecke and Hu, 1997 ; Egolf et al, 2000 ), chemical reactions ( Beta et al, 2006 ), quantum fluids ( Abo-Shaeer et al, 2002 ; Tan et al, 2020 ), as well as biologically in the brain ( Huang et al, 2010 ) and cell membranes of living cells ( Tan et al, 2020 ).…”

Vomiting, electrolyte disturbance, and medications; the perfect storm for acquired long QT syndrome and cardiac arrest: a case report

“…In self-terminating epochs, it appears that the rate of reentrant rotor formation and destruction is much slower compared with more sustained arrhythmia epochs. We have developed a novel statistical framework based on renewal theory to characterize these differences [ 25 – 27 ]. It would be of significant interest to extend these approaches to the clinical scenario of TdP, which would allow us to gain insight into the optimal prophylactic and treatment strategies for this form of arrhythmia.…”

Role of interatrial conduction in atrial fibrillation: Mechanistic insights from renewal theory–based fibrillatory dynamic analysis

“… 20 , 23 In the context of fibrillation, exponential-type distributions have consistently been observed for phase singularity (PS) formation, as well as PS lifetimes in multiple laboratories. 18 , 19 , 27 , 28 , 29 In computational, animal, and human models of cardiac fibrillation, using the renewal theory approach, 9 , 10 , 11 , 12 , 30 we confirmed these observations and demonstrated it could allow for accurate quantification of rates of PS formation (λ f , pronounced as “lambda f”) and destruction of PS (λ d , pronounced as “lambda d”) 9 , 11 , 12 , 30 ( Figure 1 ). We found that although the renewal rate constants scaled with catheter size, 30 the renewal equations for population distribution remained internally consistent, 30 in line with theoretical predictions about the effect of noise 31 and 3-dimensional character of cardiac turbulence.…”

“…8 In this study, we sought to extend previous research by systematic evaluation of interatrial conduction during AF in humans using a renewal theory approach. Renewal theory provides a way to measure the continuous formation and destruction of unstable reentrant circuits in AF [9][10][11][12] and ventricular fibrillation. 9 Unstable reentrant circuits, at present believed to be spiral vortices, 13,14 have been consistently observed in AF research.…”