Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev–Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions

Constructing bilayer and volumetric atrial models at scale.

To enable large in silico trials and personalized model predictions on clinical timescales, it is imperative that models can be constructed quickly and reproducibly. First, we aimed to overcome the challenges of constructing cardiac models at scale through developing a robust, open-source pipeline for bilayer and volumetric atrial models. Second, we aimed to investigate the effects of fibres, fibrosis and model representation on fibrillatory dynamics. To construct bilayer and volumetric models, we extended our previously developed coordinate system to incorporate transmurality, atrial regions and fibres (rule-based or data driven diffusion tensor magnetic resonance imaging (MRI)). We created a cohort of 1000 biatrial bilayer and volumetric models derived from computed tomography (CT) data, as well as models from MRI, and electroanatomical mapping. Fibrillatory dynamics diverged between bilayer and volumetric simulations across the CT cohort (correlation coefficient for phase singularity maps: left atrial (LA) 0.27 ± 0.19, right atrial (RA) 0.41 ± 0.14). Adding fibrotic remodelling stabilized re-entries and reduced the impact of model type (LA: 0.52 ± 0.20, RA: 0.36 ± 0.18). The choice of fibre field has a small effect on paced activation data (less than 12 ms), but a larger effect on fibrillatory dynamics. Overall, we developed an open-source user-friendly pipeline for generating atrial models from imaging or electroanatomical mapping data enabling in silico clinical trials at scale (https://github.com/pcmlab/atrialmtk)

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

Information Theory and Atrial Fibrillation (AF): A Review

Atrial Fibrillation (AF) is the most common cardiac rhythm disorder seen in hospitals and in general practice, accounting for up to a third of arrhythmia related hospitalizations. Unfortunately, AF treatment is in practice complicated by the lack of understanding of the fundamental mechanisms underlying the arrhythmia, which makes detection of effective ablation targets particularly difficult. Various approaches to AF mapping have been explored in the hopes of better pinpointing these effective targets, such as Dominant Frequency (DF) analysis, complex fractionated electrograms (CFAE) and unipolar reconstruction (FIRM), but many of these methods have produced conflicting results or require further investigation. Exploration of AF using information theoretic-based approaches may have the potential to provide new insights into the complex system dynamics of AF, whilst also providing the benefit of being less reliant on empirically derived definitions in comparison to alternate mapping approaches. This work provides an overview of information theory and reviews its applications in AF analysis, with particular focus on AF mapping. The works discussed in this review demonstrate how understanding AF from a signal property perspective can provide new insights into the arrhythmic phenomena, which may have valuable clinical implications for AF mapping and ablation in the future

Understanding the origins of the basic equations of statistical fibrillatory dynamics

The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with con- servative 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 pat- tern 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.Evan V. Jenkins, Dhani Dharmaprani, Madeline Schopp, Jing Xian Quah, Kathryn Tiver, Lewis Mitchell, Kenneth Pope, and Anand N. Ganesa

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

Background: The potential utility of entropy (En) for atrial fibrillation (AF) mapping has been demonstrated in previous studies by multiple groups, where an association between high bipolar electrogram (EGM) entropy and the pivot of rotors has been shown. Though En is potentially attractive new approach to ablation, no studies have examined its temporal stability and specificity, which are critical to the application of entropy to clinical ablation. In the current study, we sought to objectively measure the temporal stability and specificity of bipolar EGM entropy in medium to long term recordings using three studies: i) a human basket catheter AF study, ii) a tachypaced sheep AF study and iii) a computer simulation study. Objective: To characterize the temporal dynamics and specificity of Approximate, Sample and Shannon entropy (ApEn/SampEn/ShEn) in human (H), sheep (S), and computer simulated AF. Methods: 64-electrode basket bi-atria sustained AF recordings (H:15 min; S:40 min) were separated into 5 s segments. ShEn/ApEn/SampEn were computed, and co-registered with NavX 3D maps. Temporal stability was determined in terms of: (i) global pattern stability of En and (ii) the relative stability the top 10% of En regions. To provide mechanistic insights into underlying mechanisms, stability characteristics were compared to models depicting various propagation patterns. To verify these results, cross-validation was performed across multiple En algorithms, across species, and compared with dominant frequency (DF) temporal characteristics. The specificity of En was also determined by looking at the association of En to rotors and areas of wave cross propagation. Results: Episodes of AF were analysed (H:26 epochs, 6040 s; S:15 epochs, 14,160 s). The global pattern of En was temporally unstable (CV- H:13.42% ± 4.58%; S:14.13% ± 8.13%; Friedman- H: p > 0.001; S: p > 0.001). However, within this dynamic flux, the top 10% of ApEn/SampEn/ShEn regions were relatively temporally stable (Kappa >0.6) whilst the top 10% of DF regions were unstable (Kappa <0.06). In simulated AF scenarios, the experimental data were optimally reproduced in the context of an AF pattern with stable rotating waves surrounded by wavelet breakup (Kappa: 0.610; p < 0.0001). Conclusion: En shows global temporal instability, however within this dynamic flux, the top 10% regions exhibited relative temporal stability. This suggests that high En regions may be an appealing ablation target. Despite this, high En was associated with not just the pivot of rotors but also with areas of cross propagation, which suggests the need for future work before clinical application is possible

A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: Implications for sudden cardiac death

Ventricular fibrillation (VF) is characterized by multiple wavelets and rotors. No equation to predict the number of rotors and wavelets observed during fibrillation has been validated in human VF. Objective The purpose of this study was to test the hypothesis that a single equation derived from a Markov M/M/∞ birth-death process could predict the number of rotors and wavelets occurring in human clinical VF. Methods Epicardial induced VF (256-electrode) recordings obtained from patients undergoing cardiac surgery were studied (12 patients; 62 epochs). Rate constants for phase singularity (PS) (which occur at the pivot points of rotors) and wavefront (WF) formation and destruction were derived by fitting distributions to PS and WF interformation and lifetimes. These rate constants were combined in an M/M/∞ governing equation to predict the number of PS and WF in VF episodes. Observed distributions were compared to those predicted by the M/M/∞ equation. Results The M/M/∞ equation accurately predicted average PS and WF number and population distribution, demonstrated in all epochs. Self-terminating episodes of VF were distinguished from VF episodes requiring termination by a trend toward slower PS destruction, slower rates of PS formation, and a slower mixing rate of the VF process, indicated by larger values of the second largest eigenvalue modulus of the M/M/∞ birth-death matrix. The longest-lasting PS (associated with rotors) had shorter interactivation time intervals compared to shorter-lasting PS lasting <150 ms (∼1 PS rotation in human VF). Conclusion The M/M/∞ equation explains the number of wavelets and rotors observed, supporting a paradigm of VF based on statistical fibrillatory dynamics

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 (λf/λd) 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: λf, 4.2%/ms±1.1 [95% CI, 4.0-5.0], λd, 4.6%/ms±1.5 [95% CI, 4.3-4.9]; sheep: λf, 4.4%/ms [95% CI, 4.1-4.7], λd, 4.6%/ms±1.4 [95% CI, 4.3-4.8]; rat atrial fibrillation: λf, 33%/ms±8.8 [95% CI, 11-55], λd, 38%/ms [95% CI, 22-55]; rat ventricular fibrillation: λf, 38%/ms±24 [95% CI, 22-55], λf, 46%/ms±21 [95% CI, 31-60]; simulated fibrillation λd, 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.Dhani Dharmaprani, Madeline Schopp, Pawel Kuklik, Darius Chapman, Anandaroop Lahiri ... Lewis Mitchell ... et al

PO-616-05 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