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.

The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with conservative system dynamics. Renewal theory has recently been suggested as a statistical formulation with governing equations to quantify the formation and destruction of wavelets and rotors in fibrillatory dynamics. In this perspective Review, we aim to explain the origin of the renewal theory paradigm in spatiotemporal chaos. The ergodic nature of pattern formation in spatiotemporal chaos is demonstrated through the use of three chaotic systems: two classical systems and a simulation of cardiac fibrillation. The logistic map and the baker's transformation are used to demonstrate how the apparently random appearance of patterns in classical chaotic systems has macroscopic parameters that are predictable in a statistical sense. We demonstrate that the renewal theory approach developed for cardiac fibrillation statistically predicts pattern formation in these classical chaotic systems. Renewal theory provides governing equations to describe the apparently random formation and destruction of wavelets and rotors in atrial fibrillation (AF) and ventricular fibrillation (VF). This statistical framework for fibrillatory dynamics provides a holistic understanding of observed rotor and wavelet dynamics and is of conceptual significance in informing the clinical and mechanistic research of the rotor and multiple-wavelet mechanisms of AF and VF.

Background Unstable functional reentrant circuits known as rotors have been consistently observed in atrial fibrillation and are mechanistically believed critical to the maintenance of the arrhythmia. Recently, using a Poisson renewal theory‐based quantitative framework, we have demonstrated that rotor formation (λf) and destruction rates (λd) can be measured using in vivo electrophysiologic data. However, the association of λf and λd with clinical, electrical, and structural markers of atrial fibrillation phenotype is unknown. Methods RENEWAL‐AF is a multicenter prospective cross‐sectional study recruiting adult patients with paroxysmal or persistent atrial fibrillation undergoing clinically indicated catheter ablation. Patients will undergo intraprocedural electrophysiologic atrial fibrillation mapping, with λf and λd to be determined from 2‐minute unipolar electrogram recordings acquired before ablation. The primary objective will be to determine the association of λf and λd as markers of fibrillatory dynamics with clinical, electrical, and structural markers of atrial fibrillation clinical phenotype, measured by preablation transthoracic echocardiogram and cardiac magnetic resonance imaging. An exploratory objective is the noninvasive assessment of λf and λd using surface ECG characteristics via a machine learning approach. Results Not applicable. Conclusion This pilot study will provide insight into the correlation between λf/λd with clinical, electrophysiological, and structural markers of atrial fibrillation phenotype and provide a foundation for the development of noninvasive assessment of λf/λd using surface ECG characteristics will help expand the use of λf/λd in clinical practice.

Background: Cardiac fibrillation is thought to be maintained by rotational activity, with pivoting regions called phase singularities (PSs). Despite a century of research, no clear quantitative framework exists to model the fundamental processes responsible for the continuous formation and destruction of rotors in fibrillation. Objective:We conducted a multi-modality, multi-species study of AF/VF under the hypothesis that PS formation/destruction in fibrillation can be modelled as self-regenerating renewal processes, producing exponential distributions of inter-event times governed by constant rateparameters defined by the prevailing properties of the system.Methods: PS formation/destruction was studied and cross-validated in 5 models, using basket recordings and optical mapping from: i) human persistent AF (n = 20), ii) tachypaced sheep AF (n = 5), iii) rat AF (n = 4), iv) rat VF (n = 11) and v) computer simulated AF (SIM). Hilbert phase maps were constructed. PS lifetime data were fitted by exponential probability distribution functions (PDFs) computed using maximum entropy theory, and the rate parameter ( ) determined. A systematic review was conducted to cross-validate with source data from literature. Results:PS destruction/formation distributions showed good fits to an exponential in all systems (R 2 ≥ 0.90). In humans, = 4.6%/ms (95%CI,4.3,4.9)), sheep 4.4%/ms (95%CI,4.1,4.7)), rat AF 38%/ms (95%CI,22,55), rat VF 46%/ms (95%CI,31.2,60.2) and SIM 5.4%/ms (95%CI,4.1,6.7). All PS distributions identified through systematic review were exponential with comparable to experimental data. Conclusion:These results provide a universal quantitative framework to explain rotor formation and destruction in AF/VF, and a platform for therapeutic advances in cardiac fibrillation.

Background Atrial fibrillation (AF) is characterized by the repetitive regeneration of unstable rotational events, the pivot of which are known as phase singularities (PSs). The spatial concentration and distribution of PSs have not been systematically investigated using quantitative statistical approaches. Objectives We utilized a geospatial statistical approach to determine the presence of local spatial concentration and global clustering of PSs in biatrial human AF recordings. Methods 64‐electrode conventional basket (~5 min, n = 18 patients, persistent AF) recordings were studied. Phase maps were produced using a Hilbert‐transform based approach. PSs were characterized spatially using the following approaches: (i) local “hotspots” of high phase singularity (PS) concentration using Getis‐Ord Gi* (Z ≥ 1.96, P ≤ .05) and (ii) global spatial clustering using Moran's I (inverse distance matrix). Results Episodes of AF were analyzed from basket catheter recordings (H: 41 epochs, 120 000 s, n = 18 patients). The Getis‐Ord Gi* statistic showed local PS hotspots in 12/41 basket recordings. As a metric of spatial clustering, Moran's I showed an overall mean of 0.033 (95% CI: 0.0003‐0.065), consistent with the notion of complete spatial randomness. Conclusion Using a systematic, quantitative geospatial statistical approach, evidence for the existence of spatial concentrations (“hotspots”) of PSs were detectable in human AF, along with evidence of spatial clustering. Geospatial statistical approaches offer a new approach to map and ablate PS clusters using substrate‐based approaches.