Modeling atrial arrhythmias: impact on clinical diagnosis and therapies

Implementation of a Cellular Automaton for efficient simulations of atrial arrhythmias

In silico models offer a promising advancement for studying cardiac arrhythmias and their clinical implications. However, existing detailed mathematical models often suffer from prolonged computational time compared to diagnostic needs. This study introduces a Cellular Automaton (CA) model tailored to replicate atrial electrophysiology in different stages of Atrial Fibrillation (AF), including persistent AF (PsAF). The CA, using a finite set of states, has been trained using biophysical simulations on a reduced domain for a large set of pacing conditions. Fine-tuning included tissue heterogeneity and anisotropic propagation through pacing simulations. Characterized by Action Potential Duration (APD), Diastolic Interval (DI) and Conduction Velocity (CV) for varying levels of electrical remodeling, the biophysical simulations introduced restitution curves or surfaces into the CA. Validation involved a comprehensive comparison with realistic 2D and 3D atrial models, evaluating healthy and pro-arrhythmic behaviors. Comparisons between CA and biophysical solver revealed striking proximity, with a Cycle Length difference of <10 ms in self-sustained re-entry and a 4.66±0.57 ms difference in depolarization times across the complete atrial geometry. Notably, the CA model exhibited a 80% accuracy, 96% specificity and 45% sensitivity in predicting AF inducibility under different pacing sites and substrate conditions. Additionally, the CA allowed for a 64-fold decrease in computing time compared to the biophysical solver. CA emerges as an efficient and valid model for simulation of atrial electrophysiology across different stages of AF, with potential as a general screening tool for rapid tests. While biophysical tests are recommended for investigating specific mechanisms, CA proves valuable in clinical applications for personalized therapy planning through digital twin simulations.

Spiral wave classification using normalized compression distance: Towards atrial tissue spatiotemporal electrophysiological behavior characterization

Analysis of electrical activation patterns such as re-entries during atrial fibrillation (Afib) is crucial in understanding arrhythmic mechanisms and assessment of diagnostic measures. Spiral waves are a phenomena that provide intuitive basis for re-entries occurring in cardiac tissue. Distinct spiral wave behaviors such as stable spiral waves, meandering spiral waves, and spiral wave break-up may have distinct electrogram manifestations on a mapping catheter. Hence, it is desirable to have an automated classification of spiral wave behavior based on catheter recordings for a qualitative characterization of spatiotemporal electrophysiological activity on atrial tissue. In this study, we propose a method for classification of spatiotemporal characteristics of simulated atrial activation patterns in terms of distinct spiral wave behaviors during Afib using two different techniques: normalized compressed distance (NCD) and normalized FFT (NFFTD). We use a phenomenological model for cardiac electrical propagation to produce various simulated spiral wave behaviors on a 2D grid and labeled them as stable, meandering, or breakup. By mimicking commonly used catheter types, a star shaped and a circular shaped both of which do the local readings from atrial wall, monopolar and bipolar intracardiac electrograms are simulated. Virtual catheters are positioned at different locations on the grid. The classification performance for different catheter locations, types and for monopolar or bipolar readings were also compared. We observed that the performance for each case differed slightly. However, we found that NCD performance is superior to NFFTD. Through the simulation study, we showed the theoretical validation of the proposed method. Our findings suggest that a qualitative wavefront activation pattern can be assessed during Afib without the need for highly invasive mapping techniques such as multisite simultaneous electrogram recordings.

Lessons from computer simulations of ablation of atrial fibrillation

This paper reviews the simulations of catheter ablation in computer models of the atria, from the first attempts to the most recent anatomical models. It describes how postulated substrates of atrial fibrillation can be incorporated into mathematical models, how modelling studies can be designed to test ablation strategies, what their current trade-offs and limitations are, and what clinically relevant lessons can be learnt from these simulations. Drawing a parallel between clinical and modelling studies, six ablation targets are considered: pulmonary vein isolation, linear ablation, ectopic foci, complex fractionated atrial electrogram, rotors and ganglionated plexi. The examples presented for each ablation target illustrate a major advantage of computer models, the ability to identify why a therapy is successful or not in a given atrial fibrillation substrate. The integration of pathophysiological data to create detailed models of arrhythmogenic substrates is expected to solidify the understanding of ablation mechanisms and to provide theoretical arguments supporting substrate-specific ablation strategies.

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

Locating regions of arrhythmogenic substrate by analyzing the duration of triggered atrial activities

Catheter ablation is the most widely used minimum invasive technique to cure atrial arrhythmias. However, the success rate of the treatment is still moderate and depends on the experience and expertise of the physicians. The aim of this work is to present a simple and feasible method to identify the arrhythmogenic areas on the atrium based on the duration of atrial activities in the intraatrial electrograms. Depolarization waves are created by giving pacing impulses from coronary sinus (CS). The duration of the activity triggered from sinus node (SN) and pacing sequences are analysed by calculating the duration of the activity to mark regions with long atrial activity waves. The intraatrial electrograms have been analysed on the basis of temporal and spatial information. The region specific study may favour the localization of the critical sites in the patient specific atrial anatomy and aid the physician in ascertaining the efficacy of the cardiac therapies. The identification of suitable markers for critical patterns of the depolarization waves may be crucial to guide an effective ablation treatment. In this work a novel study for point-to-point analysis of the intraatrial electrograms was carried out.

Dynamics of atrial arrhythmias modulated by time-dependent acetylcholine concentration: a simulation study

AIM

The autonomic nervous system modulates atrial activity, notably through acetylcholine (ACh) release. This time-dependent action may alter the dynamics of atrial arrhythmia. Our aim is to investigate in a computer model the changes induced by ACh release and degradation on the dynamical regime of a reentry.

METHODS AND RESULTS

A functional reentry was simulated in a 10 × 5 cm(2) two-dimensional tissue with canine atrial membrane kinetics including an ACh-dependent K(+) current. The local ACh concentration was altered over time in a circular region following a predefined spatiotemporal profile (ACh release and degradation) characterized by its maximum ACh level, time constant of release/degradation, and diameter of the region. Phase singularities were tracked to monitor the complexity of the dynamics. Four scenarios were identified: (i) the original reentry remained stable; (ii) repolarization gradients induced by ACh release caused wavebreaks, resulting in a transient complex dynamics that spontaneously converted to a single stable reentry; (iii) the reentry self-terminated through wavebreaks and wavefront interactions; (4) wavebreaks led to a complex dynamics that converted to two or three reentries that remained stable after ACh degradation. Higher ACh level, short ACh release time constant, larger heterogeneous region, and short distance between the heterogeneous region and the spiral tip were associated with higher occurrence of ACh-induced wavebreaks.

CONCLUSION

Variation of ACh concentration over time may modulate the complexity of atrial arrhythmias.

A brief history of tissue models for cardiac electrophysiology

The last four decades have produced a number of significant advances in the developments of computer models to simulate and investigate the electrical activity of cardiac tissue. The tissue descriptions that underlie these simulations have been built from a combination of clever insight and careful comparison with measured data at multiple scales. Tissue models have not only led to greater insights into the mechanisms of life-threatening arrhythmias but have been used to engineer new therapies to treat the consequences of cardiac disease. This paper is a look back at the early years in the cardiac modeling and the challenges facing the field as models move toward the clinic.

Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach

Under diseased conditions, remodeling of the cardiac tissue properties (“passive properties”) takes place; these are aspects of electrophysiological behavior that are not associated with active ion transport across cell membranes. Remodeling of the passive electrophysiological properties most often results from structural remodeling, such as gap junction down-regulation and lateralization, fibrotic growth infiltrating the myocardium, or the development of an infarct scar. Such structural remodeling renders atrial or ventricular tissue as a major substrate for arrhythmias. The current review focuses on these aspects of cardiac arrhythmogenesis. Due to the inherent complexity of cardiac arrhythmias, computer simulations have provided means to elucidate interactions pertinent to this spatial scale. Here we review the current state-of-the-art in modeling atrial and ventricular arrhythmogenesis as arising from the disease-induced changes in the passive tissue properties, as well as the contributions these modeling studies have made to our understanding of the mechanisms of arrhythmias in the heart. Because of the rapid advance of structural imaging methodologies in cardiac electrophysiology, we chose to present studies that have used such imaging methodologies to construct geometrically realistic models of cardiac tissue, or the organ itself, where the regional remodeling properties of the myocardium can be represented in a realistic way. We emphasize how the acquired knowledge can be used to pave the way for clinical applications of cardiac organ modeling under the conditions of structural remodeling.

Geometrical measurement of cardiac wavelength in reaction-diffusion models

The dynamics of reentrant arrhythmias often consists in multiple wavelets propagating throughout an excitable medium. An arrhythmia can be sustained only if these reentrant waves have a sufficiently short wavelength defined as the distance traveled by the excitation wave during its refractory period. In a uniform medium, wavelength may be estimated as the product of propagation velocity and refractory period (electrophysiological wavelength). In order to accurately measure wavelength in more general substrates relevant to atrial arrhythmias (heterogeneous and anisotropic), we developed a mathematical framework to define geometrical wavelength at each time instant based on the length of streamlines following the propagation velocity field within refractory regions. Two computational methods were implemented: a Lagrangian approach in which a set of streamlines were integrated, and an Eulerian approach in which wavelength was the solution of a partial differential equation. These methods were compared in 1D/2D tissues and in a model of the left atrium. An advantage of geometrical definition of wavelength is that the wavelength of a wavelet can be tracked over time with high temporal resolution and smaller temporal variability in an anisotropic and heterogeneous medium. The results showed that the average electrophysiological wavelength was consistent with geometrical measurements of wavelength. Wavelets were however often shorter than the electrophysiological wavelength due to interactions with boundaries and other wavelets. These tools may help to assess more accurately the relation between substrate properties and wavelet dynamics in computer models.

Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This article aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention.

Simultaneous epicardial and noncontact endocardial mapping of the canine right atrium: simulation and experiment

Epicardial high-density electrical mapping is a well-established experimental instrument to monitor in vivo the activity of the atria in response to modulations of the autonomic nervous system in sinus rhythm. In regions that are not accessible by epicardial mapping, noncontact endocardial mapping performed through a balloon catheter may provide a more comprehensive description of atrial activity. We developed a computer model of the canine right atrium to compare epicardial and noncontact endocardial mapping. The model was derived from an experiment in which electroanatomical reconstruction, epicardial mapping (103 electrodes), noncontact endocardial mapping (2048 virtual electrodes computed from a 64-channel balloon catheter), and direct-contact endocardial catheter recordings were simultaneously performed in a dog. The recording system was simulated in the computer model. For simulations and experiments (after atrio-ventricular node suppression), activation maps were computed during sinus rhythm. Repolarization was assessed by measuring the area under the atrial T wave (ATa), a marker of repolarization gradients. Results showed an epicardial-endocardial correlation coefficients of 0.80 and 0.63 (two dog experiments) and 0.96 (simulation) between activation times, and a correlation coefficients of 0.57 and 0.46 (two dog experiments) and 0.92 (simulation) between ATa values. Despite distance (balloon-atrial wall) and dimension reduction (64 electrodes), some information about atrial repolarization remained present in noncontact signals.

Modeling atrial pacing

We present a model-based study of a therapeutical approach to atrial fibrillation based on pacing. After a systematic evaluation of different atrial pacing sites, we selected pacing from the septum area and designed a novel septum pacing protocol for atrial fibrillation termination. We then evaluated the performance of septum pacing in different models of atrial fibrillation and investigated the effect atrial substrate (cellular properties, anisotropy and heterogeneities) on the ability to capture during pacing. This study highlights the need for the development of patient-specific algorithms for atrial therapies.

In-silico modeling of atrial repolarization in normal and atrial fibrillation remodeled state

Atrial fibrillation (AF) is the most common cardiac arrhythmia, and the total number of AF patients is constantly increasing. The mechanisms leading to and sustaining AF are not completely understood yet. Heterogeneities in atrial electrophysiology seem to play an important role in this context. Although some heterogeneities have been used in in-silico human atrial modeling studies, they have not been thoroughly investigated. In this study, the original electrophysiological (EP) models of Courtemanche et al., Nygren et al. and Maleckar et al. were adjusted to reproduce action potentials in 13 atrial regions. The parameter sets were validated against experimental action potential duration data and ECG data from patients with AV block. The use of the heterogeneous EP model led to a more synchronized repolarization sequence in a variety of 3D atrial anatomical models. Combination of the heterogeneous EP model with a model of persistent AF-remodeled electrophysiology led to a drastic change in cell electrophysiology. Simulated Ta-waves were significantly shorter under the remodeling. The heterogeneities in cell electrophysiology explain the previously observed Ta-wave effects. The results mark an important step toward the reliable simulation of the atrial repolarization sequence, give a deeper understanding of the mechanism of atrial repolarization and enable further clinical investigations.

A new look at atrial fibrillation: lessons learned from drugs, pacing, and ablation therapies

Atrial fibrillation (AF) is the most common arrhythmia and among the leading causes of stroke and heart failure in Western populations. Despite the increasing size of clinical trials assessing the efficacy and safety of AF therapies, achieved outcomes have not always matched expectations. Considering that AF is a symptom of many possible underlying diseases, clinical research for this arrhythmia should take into account their respective pathophysiology. Accordingly, the definition of the study populations to be included should rely on the established as well as on the new classifications of AF and take advantage from a differentiated look at the AF-electrocardiogram and from increasingly large spectrum of biomarkers. Such an integrated approach could bring researchers and treating physicians one step closer to the ultimate vision of personalized therapy, which, in this case, means an AF therapy based on refined diagnostic elements in accordance with scientific evidence gathered from clinical trials. By applying clear-cut patient inclusion criteria, future studies will be of smaller size and thus of lower cost. In addition, the findings from such studies will be of greater predictive value at the individual patient level, allowing for pinpointed therapeutic decisions in daily practice.

Fully automated initiation of simulated episodes of atrial arrhythmias

AIMS

To develop computational tools for automatically initiating a large number of independent episodes of atrial arrhythmias in electro-anatomical computer models of the atria and therefore facilitating the design of in silico experiments.

METHODS AND RESULTS

A biophysical model of the atria was constructed from segmented medical images of the human atria of a patient with atrial fibrillation (AF). A set of 40 initial conditions were generated based on a priori knowledge about wavefront propagation and the number and location of reentries (1-6 randomly distributed over the atrial epicardium). Simulations were run from each of these initial conditions in three substrates representing different forms of AF dynamics (stable rotors; multiple unstable meandering wavelets; and wavelets broken by repolarization heterogeneities). To demonstrate the applicability of the initiation method for testing clinical of therapeutic interventions, the channel I(Kr) was blocked after 2 s of simulation and its effect on the number of functional reentries was documented. The use of pre-computed initial conditions enabled to successfully generate episodes of simulated AF in each substrate. Blockade of I(Kr) channel prolonged action potential duration, resulting in a reduction of the number of functional reentries. In the substrate with unstable spiral waves, the effect was sufficiently large to terminate AF in about two-thirds of the cases. In the two other substrates, the effect was minor.

CONCLUSION

These new simulation tools may help investigate in computer models therapeutic interventions in different substrates in order to identify substrate-specific optimal therapy.

A three-dimensional finite element model of human atrial anatomy: new methods for cubic Hermite meshes with extraordinary vertices

High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology.

Personalization of atrial anatomy and electrophysiology as a basis for clinical modeling of radio-frequency ablation of atrial fibrillation

Multiscale cardiac modeling has made great advances over the last decade. Highly detailed atrial models were created and used for the investigation of initiation and perpetuation of atrial fibrillation. The next challenge is the use of personalized atrial models in clinical practice. In this study, a framework of simple and robust tools is presented, which enables the generation and validation of patient-specific anatomical and electrophysiological atrial models. Introduction of rule-based atrial fiber orientation produced a realistic excitation sequence and a better correlation to the measured electrocardiograms. Personalization of the global conduction velocity lead to a precise match of the measured P-wave duration. The use of a virtual cohort of nine patient and volunteer models averaged out possible model-specific errors. Intra-atrial excitation conduction was personalized manually from left atrial local activation time maps. Inclusion of LE-MRI data into the simulations revealed possible gaps in ablation lesions. A fast marching level set approach to compute atrial depolarization was extended to incorporate anisotropy and conduction velocity heterogeneities and reproduced the monodomain solution. The presented chain of tools is an important step towards the use of atrial models for the patient-specific AF diagnosis and ablation therapy planing.

An eikonal-diffusion solver and its application to the interpolation and the simulation of reentrant cardiac activations

Electrical propagation of the cardiac impulse in the myocardium can be described by the eikonal-diffusion equation. This equation governs the field of activation times in a domain where conduction properties are specified. This approach has been applied to knowledge-based interpolation of sparse measurements of activation times and to the creation of initial conditions for detailed ionic models of cardiac propagation. This paper presents the mathematical basis, matrix formulation, and compact Matlab implementation of an iterative finite-element solver (triangular meshes) for the eikonal-diffusion equation extended to reentrant activations, which automatically identifies the period of reentry and computes the resulting isochrones. An iterative algorithm is designed to perform Laplacian interpolation of reentrant activation maps to be used as initial estimate for the eikonal-diffusion solver. The performance of the algorithm is analyzed in test-case geometries (ventricular slice and simplified atrial surface model).

Towards personalized clinical in-silico modeling of atrial anatomy and electrophysiology

Computational atrial models aid the understanding of pathological mechanisms and therapeutic measures in basic research. The use of biophysical models in a clinical environment requires methods to personalize the anatomy and electrophysiology (EP). Strategies for the automation of model generation and for evaluation are needed. In this manuscript, the current efforts of clinical atrial modeling in the euHeart project are summarized within the context of recent publications in this field. Model-based segmentation methods allow for the automatic generation of ready-to-simulate patient-specific anatomical models. EP models can be adapted to patient groups based on a-priori knowledge and to the individual without significant further data acquisition. ECG and intracardiac data build the basis for excitation personalization. Information from late enhancement (LE) MRI can be used to evaluate the success of radio-frequency ablation (RFA) procedures and interactive virtual atria pave the way for RFA planning. Atrial modeling is currently in a transition from the sole use in basic research to future clinical applications. The proposed methods build the framework for model-based diagnosis and therapy evaluation and planning. Complex models allow to understand biophysical mechanisms and enable the development of simplified models for clinical applications.

A framework for personalization of computational models of the human atria

A framework for step-by-step personalization of a computational model of human atria is presented. Beginning with anatomical modeling based on CT or MRI data, next fiber structure is superimposed using a rule-based method. If available, late-enhancement-MRI images can be considered in order to mark fibrotic tissue. A first estimate of individual electrophysiology is gained from BSPM data solving the inverse problem of ECG. A final adjustment of electrophysiology is realized using intracardiac measurements. The framework is applied using several patient data. First clinical application will be computer assisted planning of RF-ablation for treatment of atrial flutter and atrial fibrillation.

Computational modeling of the human atrial anatomy and electrophysiology

This review article gives a comprehensive survey of the progress made in computational modeling of the human atria during the last 10 years. Modeling the anatomy has emerged from simple "peanut"-like structures to very detailed models including atrial wall and fiber direction. Electrophysiological models started with just two cellular models in 1998. Today, five models exist considering e.g. details of intracellular compartments and atrial heterogeneity. On the pathological side, modeling atrial remodeling and fibrotic tissue are the other important aspects. The bridge to data that are measured in the catheter laboratory and on the body surface (ECG) is under construction. Every measurement can be used either for model personalization or for validation. Potential clinical applications are briefly outlined and future research perspectives are suggested.

Effects of electrical and structural remodeling on atrial fibrillation maintenance: a simulation study

Atrial fibrillation, a common cardiac arrhythmia, often progresses unfavourably: in patients with long-term atrial fibrillation, fibrillatory episodes are typically of increased duration and frequency of occurrence relative to healthy controls. This is due to electrical, structural, and contractile remodeling processes. We investigated mechanisms of how electrical and structural remodeling contribute to perpetuation of simulated atrial fibrillation, using a mathematical model of the human atrial action potential incorporated into an anatomically realistic three-dimensional structural model of the human atria. Electrical and structural remodeling both shortened the atrial wavelength--electrical remodeling primarily through a decrease in action potential duration, while structural remodeling primarily slowed conduction. The decrease in wavelength correlates with an increase in the average duration of atrial fibrillation/flutter episodes. The dependence of reentry duration on wavelength was the same for electrical vs. structural remodeling. However, the dynamics during atrial reentry varied between electrical, structural, and combined electrical and structural remodeling in several ways, including: (i) with structural remodeling there were more occurrences of fragmented wavefronts and hence more filaments than during electrical remodeling; (ii) dominant waves anchored around different anatomical obstacles in electrical vs. structural remodeling; (iii) dominant waves were often not anchored in combined electrical and structural remodeling. We conclude that, in simulated atrial fibrillation, the wavelength dependence of reentry duration is similar for electrical and structural remodeling, despite major differences in overall dynamics, including maximal number of filaments, wave fragmentation, restitution properties, and whether dominant waves are anchored to anatomical obstacles or spiralling freely.

euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling

The loss of cardiac pump function accounts for a significant increase in both mortality and morbidity in Western society, where there is currently a one in four lifetime risk, and costs associated with acute and long-term hospital treatments are accelerating. The significance of cardiac disease has motivated the application of state-of-the-art clinical imaging techniques and functional signal analysis to aid diagnosis and clinical planning. Measurements of cardiac function currently provide high-resolution datasets for characterizing cardiac patients. However, the clinical practice of using population-based metrics derived from separate image or signal-based datasets often indicates contradictory treatments plans owing to inter-individual variability in pathophysiology. To address this issue, the goal of our work, demonstrated in this study through four specific clinical applications, is to integrate multiple types of functional data into a consistent framework using multi-scale computational modelling.