Temporal stability and specificity of high bipolar electrogram entropy regions in sustained atrial fibrillation: Implications for mapping

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

Background and Objective: Renewal theory is a statistical approach to model the formation and destruction of phase singularities (PS), which occur at the pivots of spiral waves. A common issue arising during observation of renewal processes is an inspection paradox, due to oversampling of longer events. The objective of this study was to characterise the effect of a potential inspection paradox on the perception of PS lifetimes in cardiac fibrillation. Methods: A multisystem, multi-modality study was performed, examining computational simulations (Aliev-Panfilov (APV) model, Courtmanche-Nattel model), experimentally acquired optical mapping Atrial and Ventricular Fibrillation (AF/VF) data, and clinically acquired human AF and VF. Distributions of all PS lifetimes across full epochs of AF, VF, or computational simulations, were compared with distributions formed from lifetimes of PS existing at 10,000 simulated commencement timepoints. Results: In all systems, an inspection paradox led towards oversampling of PS with longer lifetimes. In APV computational simulations there was a mean PS lifetime shift of +84.9% (95% CI, ± 0.3%) (p < 0.001 for observed vs overall), in Courtmanche-Nattel simulations of AF +692.9% (95% CI, ±57.7%) (p < 0.001), in optically mapped rat AF +374.6% (95% CI, ± 88.5%) (p = 0.052), in human AF mapped with basket catheters +129.2% (95% CI, ±4.1%) (p < 0.05), human AF-HD grid catheters 150.8% (95% CI, ± 9.0%) (p < 0.001), in optically mapped rat VF +171.3% (95% CI, ±15.6%) (p < 0.001), in human epicardial VF 153.5% (95% CI, ±15.7%) (p < 0.001). Conclusion: Visual inspection of phase movies has the potential to systematically oversample longer lasting PS, due to an inspection paradox. An inspection paradox is minimised by consideration of the overall distribution of PS lifetimes.

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

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.

Spatial concentration and distribution of phase singularities in human atrial fibrillation: Insights for the AF mechanism

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.

Challenges Associated with Interpreting Mechanisms of AF

Determining optimal treatment strategies for complex arrhythmogenesis in AF is confounded by the lack of consensus regarding the mechanisms causing AF. Studies report different mechanisms for AF, ranging from hierarchical drivers to anarchical multiple activation wavelets. Differences in the assessment of AF mechanisms are likely due to AF being recorded across diverse models using different investigational tools, spatial scales and clinical populations. The authors review different AF mechanisms, including anatomical and functional re-entry, hierarchical drivers and anarchical multiple wavelets. They then describe different cardiac mapping techniques and analysis tools, including activation mapping, phase mapping and fibrosis identification. They explain and review different data challenges, including differences between recording devices in spatial and temporal resolutions, spatial coverage and recording surface, and report clinical outcomes using different data modalities. They suggest future research directions for investigating the mechanisms underlying human AF.

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

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]; R²≥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.