A Stochastic Individual-Based Model of the Progression of Atrial Fibrillation in Individuals and Populations

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.

Computational models of atrial fibrillation: achievements, challenges, and perspectives for improving clinical care

Despite significant advances in its detection, understanding and management, atrial fibrillation (AF) remains a highly prevalent cardiac arrhythmia with a major impact on morbidity and mortality of millions of patients. AF results from complex, dynamic interactions between risk factors and comorbidities that induce diverse atrial remodelling processes. Atrial remodelling increases AF vulnerability and persistence, while promoting disease progression. The variability in presentation and wide range of mechanisms involved in initiation, maintenance and progression of AF, as well as its associated adverse outcomes, make the early identification of causal factors modifiable with therapeutic interventions challenging, likely contributing to suboptimal efficacy of current AF management. Computational modelling facilitates the multilevel integration of multiple datasets and offers new opportunities for mechanistic understanding, risk prediction and personalized therapy. Mathematical simulations of cardiac electrophysiology have been around for 60 years and are being increasingly used to improve our understanding of AF mechanisms and guide AF therapy. This narrative review focuses on the emerging and future applications of computational modelling in AF management. We summarize clinical challenges that may benefit from computational modelling, provide an overview of the different in silico approaches that are available together with their notable achievements, and discuss the major limitations that hinder the routine clinical application of these approaches. Finally, future perspectives are addressed. With the rapid progress in electronic technologies including computing, clinical applications of computational modelling are advancing rapidly. We expect that their application will progressively increase in prominence, especially if their added value can be demonstrated in clinical trials.

Modeling and Estimation of Temporal Episode Patterns in Paroxysmal Atrial Fibrillation

OBJECTIVE

The present study proposes a model-based, statistical approach to characterizing episode patterns in paroxysmal atrial fibrillation (AF). Thanks to the rapid advancement of noninvasive monitoring technology, the proposed approach should become increasingly relevant in clinical practice.

METHODS

History-dependent point process modeling is employed to characterize AF episode patterns, using a novel alternating, bivariate Hawkes self-exciting model. In addition, a modified version of a recently proposed statistical model to simulate AF progression throughout a lifetime is considered, involving non-Markovian rhythm switching and survival functions. For each model, the maximum likelihood estimator is derived and used to find the model parameters from observed data.

RESULTS

Using three databases with a total of 59 long-term ECG recordings, the goodness-of-fit analysis demonstrates that the proposed alternating, bivariate Hawkes model fits SR-to-AF transitions in 40 recordings and AF-to-SR transitions in 51; the corresponding numbers for the AF model with non-Markovian rhythm switching are 40 and 11, respectively. Moreover, the results indicate that the model parameters related to AF episode clustering, i.e., aggregation of temporal AF episodes, provide information complementary to the well-known clinical parameter AF burden.

CONCLUSION

Point process modeling provides a detailed characterization of the occurrence pattern of AF episodes that may improve the understanding of arrhythmia progression.

Computational modeling: What does it tell us about atrial fibrillation therapy?

Atrial fibrillation (AF) is a complex cardiac arrhythmia with diverse etiology that negatively affects morbidity and mortality of millions of patients. Technological and experimental advances have provided a wealth of information on the pathogenesis of AF, highlighting a multitude of mechanisms involved in arrhythmia initiation and maintenance, and disease progression. However, it remains challenging to identify the predominant mechanisms for specific subgroups of AF patients, which, together with an incomplete understanding of the pleiotropic effects of antiarrhythmic therapies, likely contributes to the suboptimal efficacy of current antiarrhythmic approaches. Computer modeling of cardiac electrophysiology has advanced in parallel to experimental research and provides an integrative framework to attempt to overcome some of these challenges. Multi-scale cardiac modeling and simulation integrate structural and functional data from experimental and clinical work with knowledge of atrial electrophysiological mechanisms and dynamics, thereby improving our understanding of AF mechanisms and therapy. In this review, we describe recent advances in our quantitative understanding of AF through mathematical models. We discuss computational modeling of AF mechanisms and therapy using detailed, mechanistic cell/tissue-level models, including approaches to incorporate variability in patient populations. We also highlight efforts using whole-atria models to improve catheter ablation therapies. Finally, we describe recent efforts and suggest future extensions to model clinical concepts of AF using patient-level models.

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.

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

Mathematical models of cardiac electrical excitation are increasingly complex, with multiscale models seeking to represent and bridge physiological behaviours across temporal and spatial scales. The increasing complexity of these models makes it computationally expensive to both evaluate long term (more than 60 s) behaviour and determine sensitivity of model outputs to inputs. This is particularly relevant in models of atrial fibrillation (AF), where individual episodes last from seconds to days, and interepisode waiting times can be minutes to months. Potential mechanisms of transition between sinus rhythm and AF have been identified but are not well understood, and it is difficult to simulate AF for long periods of time using state-of-the-art models. In this study, we implemented a Moe-type cellular automaton on a novel, topologically equivalent surface geometry of the left atrium. We used the model to simulate stochastic initiation and spontaneous termination of AF, arising from bursts of spontaneous activation near pulmonary veins. The simplified representation of atrial electrical activity reduced computational cost, and so permitted us to investigate AF mechanisms in a probabilistic setting. We computed large numbers (approx. 10⁵) of sample paths of the model, to infer stochastic initiation and termination rates of AF episodes using different model parameters. By generating statistical distributions of model outputs, we demonstrated how to propagate uncertainties of inputs within our microscopic level model up to a macroscopic level. Lastly, we investigated spontaneous termination in the model and found a complex dependence on its past AF trajectory, the mechanism of which merits future investigation.

Myocardial architecture and patient variability in clinical patterns of atrial fibrillation

Atrial fibrillation (AF) increases the risk of stroke by a factor of 4-5 and is the most common abnormal heart rhythm. The progression of AF with age, from short self-terminating episodes to persistence, varies between individuals and is poorly understood. An inability to understand and predict variation in AF progression has resulted in less patient-specific therapy. Likewise, it has been a challenge to relate the microstructural features of heart muscle tissue (myocardial architecture) with the emergent temporal clinical patterns of AF. We use a simple model of activation wave-front propagation on an anisotropic structure, mimicking heart muscle tissue, to show how variation in AF behavior arises naturally from microstructural differences between individuals. We show that the stochastic nature of progressive transversal uncoupling of muscle strands (e.g., due to fibrosis or gap junctional remodeling), as occurs with age, results in variability in AF episode onset time, frequency, duration, burden, and progression between individuals. This is consistent with clinical observations. The uncoupling of muscle strands can cause critical architectural patterns in the myocardium. These critical patterns anchor microreentrant wave fronts and thereby trigger AF. It is the number of local critical patterns of uncoupling as opposed to global uncoupling that determines AF progression. This insight may eventually lead to patient-specific therapy when it becomes possible to observe the cellular structure of a patient's heart.