Mechanisms of stochastic onset and termination of atrial fibrillation studied with a cellular automaton model

A Review on Atrial Fibrillation (Computer Simulation and Clinical Perspectives)

Atrial fibrillation (AF), a heart condition, has been a well-researched topic for the past few decades. This multidisciplinary field of study deals with signal processing, finite element analysis, mathematical modeling, optimization, and clinical procedure. This article is focused on a comprehensive review of journal articles published in the field of AF. Topics from the age-old fundamental concepts to specialized modern techniques involved in today’s AF research are discussed. It was found that a lot of research articles have already been published in modeling and simulation of AF. In comparison to that, the diagnosis and post-operative procedures for AF patients have not yet been totally understood or explored by the researchers. The simulation and modeling of AF have been investigated by many researchers in this field. Cellular model, tissue model, and geometric model among others have been used to simulate AF. Due to a very complex nature, the causes of AF have not been fully perceived to date, but the simulated results are validated with real-life patient data. Many algorithms have been proposed to detect the source of AF in human atria. There are many ablation strategies for AF patients, but the search for more efficient ablation strategies is still going on. AF management for patients with different stages of AF has been discussed in the literature as well but is somehow limited mostly to the patients with persistent AF. The authors hope that this study helps to find existing research gaps in the analysis and the diagnosis of AF.

M/M/Infinity Birth-Death Processes - A Quantitative Representational Framework to Summarize and Explain Phase Singularity and Wavelet Dynamics in Atrial Fibrillation

Rationale

A quantitative framework to summarize and explain the quasi-stationary population dynamics of unstable phase singularities (PS) and wavelets in human atrial fibrillation (AF) is at present lacking. Building on recent evidence showing that the formation and destruction of PS and wavelets in AF can be represented as renewal processes, we sought to establish such a quantitative framework, which could also potentially provide insight into the mechanisms of spontaneous AF termination.

Objectives

Here, we hypothesized that the observed number of PS or wavelets in AF could be governed by a common set of renewal rate constants λ _f (for PS or wavelet formation) and λ _d (PS or wavelet destruction), with steady-state population dynamics modeled as an M/M/∞ birth-death process. We further hypothesized that changes to the M/M/∞ birth-death matrix would explain spontaneous AF termination.

Methods and Results

AF was studied in in a multimodality, multispecies study in humans, animal experimental models (rats and sheep) and Ramirez-Nattel-Courtemanche model computer simulations. We demonstrated: (i) that λ _f and λ _d can be combined in a Markov M/M/∞ process to accurately model the observed average number and population distribution of PS and wavelets in all systems at different scales of mapping; and (ii) that slowing of the rate constants λ _f and λ _d is associated with slower mixing rates of the M/M/∞ birth-death matrix, providing an explanation for spontaneous AF termination.

Conclusion

M/M/∞ birth-death processes provide an accurate quantitative representational architecture to characterize PS and wavelet population dynamics in AF, by providing governing equations to understand the regeneration of PS and wavelets during sustained AF, as well as providing insight into the mechanism of spontaneous AF termination.

Understanding the transition from paroxysmal to persistent atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterized by the chaotic motion of electrical wavefronts in the atria. In clinical practice, AF is classified under two primary categories: paroxysmal AF, short intermittent episodes separated by periods of normal electrical activity; and persistent AF, longer uninterrupted episodes of chaotic electrical activity. However, the precise reasons why AF in a given patient is paroxysmal or persistent is poorly understood. Recently, we have introduced the percolation-based Christensen-Manani-Peters (CMP) model of AF which naturally exhibits both paroxysmal and persistent AF, but precisely how these differences emerge in the model is unclear. In this paper, we dissect the CMP model to identify the cause of these different AF classifications. Starting from a mean-field model where we describe AF as a simple birth-death process, we add layers of complexity to the model and show that persistent AF arises from reentrant circuits which exhibit an asymmetry in their probability of activation relative to deactivation. As a result, different simulations generated at identical model parameters can exhibit fibrillatory episodes spanning several orders of magnitude from a few seconds to months. These findings demonstrate that diverse, complex fibrillatory dynamics can emerge from very simple dynamics in models of AF.

Autonomic modulation before and after paroxysmal atrial fibrillation events in patients with ischemic heart disease

BACKGROUND

The autonomic activity plays a critical role in generating paroxysmal atrial fibrillation (PAF). This study aimed to evaluate the changes in the autonomic nerve activity before and after PAF events in patients with and without ischemic heart disease (IHD).

METHODS

The study included 49 patients (71.43 ± 12.24 years old, 26 males) with PAF events lasting more than 30 s during 24-hr ambulatory Holter monitoring. The 20-min intervals before and after PAF events were divided into eight segments of 5 min each. Heart rate variability (HRV) analyses of the time and frequency domains were applied to each time segment.

RESULTS

Patients with IHD had significant increases in the root mean square successive differences (r-MSSD, p = .008) and HF component (p = .04), followed by a significant increase in the LF/HF ratio (p = .02) preceding the onset of PAF. Patients without IHD had only a significant increase in the r-MSSD (p = .045) preceding the onset of PAF. During the termination of PAF events, patients in both the IHD and control groups had a significantly decreased r-MSSD and HF, respectively.

CONCLUSION

Ischemic heart disease causes a sympathovagal imbalance in the initiation of PAF. Decreased parasympathetic activity regulated the termination of PAF in both the IHD and control groups. The modification of the autonomic nervous system (ANS) activity should be individualized due to the autonomic complexity in AF arrhythmogenesis and termination.

Usage of a new mapping algorithm to detect possible critical substrate for continuity of atrial fibrillation: fractionation mapping in preliminary experience

Although treatment of atrial fibrillation (AF) classically focuses on eliminating the pulmonary vein (PV) triggers, isolation of PVs is associated with limited success rates in patients with persistent AF. The role of the left atrial appendage (LAA) as both trigger and driver in arrhythmogenesis of AF was previously demonstrated. In the present case, fractionation mapping software of Ensite system was firstly tested to detect critical substrate during AF. Focusing on the width and continuity of fractionation pattern, the LAA was accepted as main driver for maintenance of AF. Ablation in fractionated electrograms around the LAA caused acute AF termination. After isolation of the LAA, no AF was inducible with atrial stimulation with and without isoproterenol infusion. Fractionation mapping may be used to detect potential importance of the LAA in AF continuity.

Unified mechanism of local drivers in a percolation model of atrial fibrillation

The mechanisms of atrial fibrillation (AF) are poorly understood, resulting in disappointing success rates of ablative treatment. Different mechanisms defined largely by different atrial activation patterns have been proposed and, arguably, this dispute has slowed the progress of AF research. Recent clinical evidence suggests a unifying mechanism of local drivers based on sustained reentrant circuits in the complex atrial architecture. Here, we present a percolation inspired computational model showing spontaneous emergence of AF that strongly supports, and gives a theoretical explanation for, the clinically observed diversity of activation. We show that the difference in surface activation patterns is a direct consequence of the thickness of the discrete network of heart muscle cells through which electrical signals percolate to reach the imaged surface. The model naturally follows the clinical spectrum of AF spanning sinus rhythm, paroxysmal AF, and persistent AF as the decoupling of myocardial cells results in the lattice approaching the percolation threshold. This allows the model to make the prediction that, for paroxysmal AF, reentrant circuits emerge near the endocardium, but in persistent AF they emerge deeper in the bulk of the atrial wall. If experimentally verified, this may go towards explaining the lowering ablation success rate as AF becomes more persistent.

Addressing challenges of quantitative methodologies and event interpretation in the study of atrial fibrillation

Atrial fibrillation (AF) is the commonest arrhythmia, yet the mechanisms of its onset and persistence are incompletely known. Although techniques for quantitative assessment have been investigated, there have been few attempts to integrate this information to advance disease treatment protocols. In this review, key quantitative methods for AF analysis are described, and suggestions are provided for the coordination of the available information, and to develop foci and directions for future research efforts. Quantitative biologists may have an interest in this topic in order to develop machine learning and tools for arrhythmia characterization, but they may perhaps have a minimal background in the clinical methodology and in the types of observed events and mechanistic hypotheses that have thus far been developed. We attempt to address these issues via exploration of the published literature. Although no new data is presented in this review, examples are shown of current lines of investigation, and in particular, how electrogram analysis and whole-chamber quantitative modeling of the left atrium may be useful to characterize fibrillatory patterns of activity, so as to propose avenues for more efficacious acquisition and interpretation of AF data.

A novel IRBF-RVM model for diagnosis of atrial fibrillation

BACKGROUND AND OBJECTIVE

Atrial fibrillation (AF) is one of the common cardiovascular diseases, and electrocardiography (ECG) is a key indicator for the detection and diagnosis of AF and other heart diseases. In this study, an improved machine learning method is proposed for rapid modeling and accurate diagnosis of AF.

METHODS

This paper presents a novel IRBF-RVM model that combines the integrated radial basis function (IRBF) and relevance vector machine (RVM), which is utilized for the diagnosis of AF. The synchronous 12-lead ECG signals are collected from the human body surface so as to fully reflect the electrical activity of the whole heart. RR intervals of the QRS-waves in ECG signals are obtained by means of the classical Pan-Tompkins algorithm. The RR-features extracted from RR intervals are adopted as the diagnostic features for AF patients. In addition, the conventional RBF-RVM model, support vector machine (SVM) and other machine learning methods are also investigated for the diagnosis of AF so as to reflect the advantage of the proposed IRBF-RVM model. The open MIT-BIH arrhythmia database (MITDB) is also used to evaluate the predictive performance of these state-of-the-art methods.

RESULTS

Altogether 1056 AF patients and 904 healthy people are participated in this study and validate the effectiveness of each channel of the 12-lead ECG signals. Experimental results show that the classification rate of IRBF-RVM can reach up to 98.16% by recurring to Channel II of the 12-lead ECG signals.

CONCLUSIONS

IRBF-RVM absorbs the advantages of IRBF, which makes the kernel parameter of IRBF-RVM have a much larger selectable region than RBF-RVM. In addition, RVM has faster modeling and recognition speed in comparison with SVM. This work lays the foundation for the application of RVM to accurate diagnosis of AF.

Understanding AF Mechanisms Through Computational Modelling and Simulations

AF is a progressive disease of the atria, involving complex mechanisms related to its initiation, maintenance and progression. Computational modelling provides a framework for integration of experimental and clinical findings, and has emerged as an essential part of mechanistic research in AF. The authors summarise recent advancements in development of multi-scale AF models and focus on the mechanistic links between alternations in atrial structure and electrophysiology with AF. Key AF mechanisms that have been explored using atrial modelling are pulmonary vein ectopy; atrial fibrosis and fibrosis distribution; atrial wall thickness heterogeneity; atrial adipose tissue infiltration; development of repolarisation alternans; cardiac ion channel mutations; and atrial stretch with mechano-electrical feedback. They review modelling approaches that capture variability at the cohort level and provide cohort-specific mechanistic insights. The authors conclude with a summary of future perspectives, as envisioned for the contributions of atrial modelling in the mechanistic understanding of AF.

Understanding the Beat-to-Beat Variations of P-Waves Morphologies in AF Patients During Sinus Rhythm: A Scoping Review of the Atrial Simulation Studies

The remarkable advances in high-performance computing and the resulting increase of the computational power have the potential to leverage computational cardiology toward improving our understanding of the pathophysiological mechanisms of arrhythmias, such as Atrial Fibrillation (AF). In AF, a complex interaction between various triggers and the atrial substrate is considered to be the leading cause of AF initiation and perpetuation. In electrocardiography (ECG), P-wave is supposed to reflect atrial depolarization. It has been found that even during sinus rhythm (SR), multiple P-wave morphologies are present in AF patients with a history of AF, suggesting a higher dispersion of the conduction route in this population. In this scoping review, we focused on the mechanisms which modify the electrical substrate of the atria in AF patients, while investigating the existence of computational models that simulate the propagation of the electrical signal through different routes. The adopted review methodology is based on a structured analytical framework which includes the extraction of the keywords based on an initial limited bibliographic search, the extensive literature search and finally the identification of relevant articles based on the reference list of the studies. The leading mechanisms identified were classified according to their scale, spanning from mechanisms in the cell, tissue or organ level, and the produced outputs. The computational modeling approaches for each of the factors that influence the initiation and the perpetuation of AF are presented here to provide a clear overview of the existing literature. Several levels of categorization were adopted while the studies which aim to translate their findings to ECG phenotyping are highlighted. The results denote the availability of multiple models, which are appropriate under specific conditions. However, the consideration of complex scenarios taking into account multiple spatiotemporal scales, personalization of electrophysiological and anatomical models and the reproducibility in terms of ECG phenotyping has only partially been tackled so far.

Heart Rhythm Insights Into Structural Remodeling in Atrial Tissue: Timed Automata Approach

The heart rhythm of a person following heart transplantation (HTX) is assumed to display an intrinsic cardiac rhythm because it is significantly less influenced by the autonomic nervous system-the main source of heart rate variability in healthy people. Therefore, such a rhythm provides evidence for arrhythmogenic processes developing, usually silently, in the cardiac tissue. A model is proposed to simulate alterations in the cardiac tissue and to observe the effects of these changes on the resulting heart rhythm. The hybrid automata framework used makes it possible to represent reliably and simulate efficiently both the electrophysiology of a cardiac cell and the tissue organization. The curve fitting method used in the design of the hybrid automaton cycle follows the well-recognized physiological phases of the atrial myocyte membrane excitation. Moreover, knowledge of the complex architecture of the right atrium, the ability of the almost free design of intercellular connections makes the automata approach the only one possible. Two particular aspects are investigated: impairment of the impulse transmission between cells and structural changes in intercellular connections. The first aspect models the observed fatigue of cells due to specific cardiac tissue diseases. The second aspect simulates the increase in collagen deposition with aging. Finally, heart rhythms arising from the model are validated with the sinus heart rhythms recorded in HTX patients. The modulation in the impairment of the impulse transmission between cells reveals qualitatively the abnormally high heart rate variability observed in patients living long after HTX.

Is human atrial fibrillation stochastic or deterministic?-Insights from missing ordinal patterns and causal entropy-complexity plane analysis

The mechanism of atrial fibrillation (AF) maintenance in humans is yet to be determined. It remains controversial whether cardiac fibrillatory dynamics are the result of a deterministic or a stochastic process. Traditional methods to differentiate deterministic from stochastic processes have several limitations and are not reliably applied to short and noisy data obtained during clinical studies. The appearance of missing ordinal patterns (MOPs) using the Bandt-Pompe (BP) symbolization is indicative of deterministic dynamics and is robust to brief time series and experimental noise. Our aim was to evaluate whether human AF dynamics is the result of a stochastic or a deterministic process. We used 38 intracardiac atrial electrograms during AF from the coronary sinus of 10 patients undergoing catheter ablation of AF. We extracted the intervals between consecutive atrial depolarizations (AA interval) and converted the AA interval time series to their BP symbolic representation (embedding dimension 5, time delay 1). We generated 40 iterative amplitude-adjusted, Fourier-transform (IAAFT) surrogate data for each of the AA time series. IAAFT surrogates have the same frequency spectrum, autocorrelation, and probability distribution with the original time series. Using the BP symbolization, we compared the number of MOPs and the rate of MOP decay in the first 1000 timepoints of the original time series with that of the surrogate data. We calculated permutation entropy and permutation statistical complexity and represented each time series on the causal entropy-complexity plane. We demonstrated that (a) the number of MOPs in human AF is significantly higher compared to the surrogate data (2.7 ± 1.18 vs. 0.39 ± 0.28, p < 0.001); (b) the median rate of MOP decay in human AF was significantly lower compared with the surrogate data (6.58 × 10^-3 vs. 7.79 × 10^-3, p < 0.001); and (c) 81.6% of the individual recordings had a rate of decay lower than the 95% confidence intervals of their corresponding surrogates. On the causal entropy-complexity plane, human AF lay on the deterministic part of the plane that was located above the trajectory of fractional Brownian motion with different Hurst exponents on the plane. This analysis demonstrates that human AF dynamics does not arise from a rescaled linear stochastic process or a fractional noise, but either a deterministic or a nonlinear stochastic process. Our results justify the development and application of mathematical analysis and modeling tools to enable predictive control of human AF.

Machine learning methods for locating re-entrant drivers from electrograms in a model of atrial fibrillation

Mapping resolution has recently been identified as a key limitation in successfully locating the drivers of atrial fibrillation (AF). Using a simple cellular automata model of AF, we demonstrate a method by which re-entrant drivers can be located quickly and accurately using a collection of indirect electrogram measurements. The method proposed employs simple, out-of-the-box machine learning algorithms to correlate characteristic electrogram gradients with the displacement of an electrogram recording from a re-entrant driver. Such a method is less sensitive to local fluctuations in electrical activity. As a result, the method successfully locates 95.4% of drivers in tissues containing a single driver, and 95.1% (92.6%) for the first (second) driver in tissues containing two drivers of AF. Additionally, we demonstrate how the technique can be applied to tissues with an arbitrary number of drivers. In its current form, the techniques presented are not refined enough for a clinical setting. However, the methods proposed offer a promising path for future investigations aimed at improving targeted ablation for AF.