Sensitivity of reentrant driver localization to electrophysiological parameter variability in image-based computational models of persistent atrial fibrillation sustained by a fibrotic substrate

Perlin noise generation of physiologically realistic cardiac fibrosis

Fibrosis, a pathological increase in extracellular matrix proteins, is a significant health issue that hinders the function of many organs in the body, in some cases fatally. In the heart, fibrosis impacts on electrical propagation in a complex and poorly predictable fashion, potentially serving as a substrate for dangerous arrhythmias. Individual risk depends on the spatial manifestation of fibrotic tissue, and learning the spatial arrangement on the fine scale in order to predict these impacts still relies upon invasive ex vivo procedures. As a result, the effects of spatial variability on the symptomatic impact of cardiac fibrosis remain poorly understood. In this work, we address the issue of availability of such imaging data via a computational methodology for generating new realisations of cardiac fibrosis microstructure. Using the Perlin noise technique from computer graphics, together with an automated calibration process that requires only a single training image, we demonstrate successful capture of collagen texturing in four types of fibrosis microstructure observed in histological sections. We then use this generator to quantitatively analyse the conductive properties of these different types of cardiac fibrosis, as well as produce three-dimensional realisations of histologically-observed patterning. Owing to the generator's flexibility and automated calibration process, we also anticipate that it might be useful in producing additional realisations of other physiological structures.

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

A Review of Personalised Cardiac Computational Modelling Using Electroanatomical Mapping Data

Computational models of cardiac electrophysiology have gradually matured during the past few decades and are now being personalised to provide patient-specific therapy guidance for improving suboptimal treatment outcomes. The predictive features of these personalised electrophysiology models hold the promise of providing optimal treatment planning, which is currently limited in the clinic owing to reliance on a population-based or average patient approach. The generation of a personalised electrophysiology model entails a sequence of steps for which a range of activation mapping, calibration methods and therapy simulation pipelines have been suggested. However, the optimal methods that can potentially constitute a clinically relevant in silico treatment are still being investigated and face limitations, such as uncertainty of electroanatomical data recordings, generation and calibration of models within clinical timelines and requirements to validate or benchmark the recovered tissue parameters. This paper is aimed at reporting techniques on the personalisation of cardiac computational models, with a focus on calibrating cardiac tissue conductivity based on electroanatomical mapping data.

Computational Modeling and Simulation of the Fibrotic Human Atria

Patient-specific modeling of atrial electrical activity enables the execution of simulations that can provide mechanistic insights and provide novel solutions to vexing clinical problems. The geometry and fibrotic remodeling of the heart can be reconstructed from clinical-grade medical scans and used to inform personalized models with detail incorporated at the cell- and tissue-scale to represent changes in image-identified diseased regions. Here, we provide a rubric for the reconstruction of realistic atrial models from pre-segmented 3D renderings of the left atrium with fibrotic tissue regions delineated, which are the output from clinical-grade systems for quantifying fibrosis. We then provide a roadmap for using those models to carry out patient-specific characterization of the fibrotic substrate in terms of its potential to harbor reentrant drivers via cardiac electrophysiology simulations.

Up digital and personal: How heart digital twins can transform heart patient care

Precision medicine is the vision of health care where therapy is tailored to each patient. As part of this vision, digital twinning technology promises to deliver a digital representation of organs or even patients by using tools capable of simulating personal health conditions and predicting patient or disease trajectories on the basis of relationships learned both from data and from biophysics knowledge. Such virtual replicas would update themselves with data from monitoring devices and medical tests and assessments, reflecting dynamically the changes in our health conditions and the responses to treatment. In precision cardiology, the concepts and initial applications of heart digital twins have slowly been gaining popularity and the trust of the clinical community. In this article, we review the advancement in heart digital twinning and its initial translation to the management of heart rhythm disorders.

Patchy fibrosis promotes trigger-substrate interactions that both generate and maintain atrial fibrillation

Fibrosis has been mechanistically linked to arrhythmogenesis in multiple cardiovascular conditions, including atrial fibrillation (AF). Previous studies have demonstrated that fibrosis can create functional barriers to conduction which may promote excitation wavebreak and the generation of re-entry, while also acting to pin re-entrant excitation in stable rotors during AF. However, few studies have investigated the role of fibrosis in the generation of AF triggers in detail. We apply our in-house computational framework to study the impact of fibrosis on the generation of AF triggers and trigger-substrate interactions in two- and three-dimensional atrial tissue models. Our models include a reduced and efficient description of stochastic, spontaneous cellular triggers as well as a simple model of heterogeneous inter-cellular coupling. Our results demonstrate that fibrosis promotes the emergence of focal excitations, primarily through reducing the electrotonic load on individual fibre strands. This enables excitation to robustly initiate within these single strands before spreading to neighbouring strands and inducing a full tissue focal excitation. Enhanced conduction block can allow trigger-substrate interactions that result in the emergence of complex, re-entrant excitation patterns. This study provides new insight into the mechanisms by which fibrosis promotes the triggers and substrate necessary to induce and sustain arrhythmia.

Impact of noise on the instability of spiral waves in stochastic 2D mathematical models of human atrial fibrillation

Sustained spiral waves, also known as rotors, are pivotal mechanisms in persistent atrial fibrillation (AF). Stochasticity is inevitable in nonlinear biological systems such as the heart; however, it is unclear how noise affects the instability of spiral waves in human AF. This study presents a stochastic two-dimensional mathematical model of human AF and explores how Gaussian white noise affects the instability of spiral waves. In homogeneous tissue models, Gaussian white noise may lead to spiral-wave meandering and wavefront break-up. As the noise intensity increases, the spatial dispersion of phase singularity (PS) points increases. This finding indicates the potential AF-protective effects of cardiac system stochasticity by destabilizing the rotors. By contrast, Gaussian white noise is unlikely to affect the spiral-wave instability in the presence of localized scar or fibrosis regions. The PS points are located at the boundary or inside the scar/fibrosis regions. Localized scar or fibrosis may play a pivotal role in stabilizing spiral waves regardless of the presence of noise. This study suggests that fibrosis and scars are essential for stabilizing the rotors in stochastic mathematical models of AF. Further patient-derived realistic modeling studies are required to confirm the role of scar/fibrosis in AF pathophysiology.

Comparing Inducibility of Re-Entrant Arrhythmia in Patient-Specific Computational Models to Clinical Atrial Fibrillation Phenotypes

BACKGROUND

Computational models of fibrosis-mediated, re-entrant left atrial (LA) arrhythmia can identify possible substrate for persistent atrial fibrillation (AF) ablation. Contemporary models use a 1-size-fits-all approach to represent electrophysiological properties, limiting agreement between simulations and patient outcomes.

OBJECTIVES

The goal of this study was to test the hypothesis that conduction velocity (ϴ) modulation in persistent AF models can improve simulation agreement with clinical arrhythmias.

METHODS

Patients with persistent AF (n = 37) underwent ablation and were followed up for ≥2 years to determine post-ablation outcomes: AF, atrial flutter (AFL), or no recurrence. Patient-specific LA models (n = 74) were constructed using pre-ablation and ≥90 days' post-ablation magnetic resonance imaging data. Simulated pacing gauged in silico arrhythmia inducibility due to AF-like rotors or AFL-like macro re-entrant tachycardias. A physiologically plausible range of ϴ values (±10 or 20% vs. baseline) was tested, and model/clinical agreement was assessed.

RESULTS

Fifteen (41%) patients had a recurrence with AF and 6 (16%) with AFL. Arrhythmia was induced in 1,078 of 5,550 simulations. Using baseline ϴ, model/clinical agreement was 46% (34 of 74 models), improving to 65% (48 of 74) when any possible ϴ value was used (McNemar's test, P = 0.014). ϴ modulation improved model/clinical agreement in both pre-ablation and post-ablation models. Pre-ablation model/clinical agreement was significantly greater for patients with extensive LA fibrosis (>17.2%) and an elevated body mass index (>32.0 kg/m2).

CONCLUSIONS

Simulations in persistent AF models show a 41% relative improvement in model/clinical agreement when ϴ is modulated. Patient-specific calibration of ϴ values could improve model/clinical agreement and model usefulness, especially in patients with higher body mass index or LA fibrosis burden. This could ultimately facilitate better personalized modeling, with immediate clinical implications.

High-density mapping of the average complex interval helps localizing atrial fibrillation drivers and predicts catheter ablation outcomes

Background

Persistent Atrial Fibrillation (PersAF) electrogram-based ablation is complex, and appropriate identification of atrial substrate is critical. Little is known regarding the value of the Average Complex Interval (ACI) feature for PersAF ablation.

Objective

Using the evolution of AF complexity by sequentially computing AF dominant frequency (DF) along the ablation procedure, we sought to evaluate the value of ACI for discriminating active drivers (AD) from bystander zones (BZ), for predicting AF termination during ablation, and for predicting AF recurrence during follow-up.

Methods

We included PersAF patients undergoing radiofrequency catheter ablation by pulmonary vein isolation and ablation of atrial substrate identified by Spatiotemporal Dispersion or Complex Fractionated Atrial Electrograms (>70% of recording). Operators were blinded to ACI measurement which was sought for each documented atrial substrate area. AF DF was measured by Independent Component Analysis on 1-minute 12-lead ECGs at baseline and after ablation of each atrial zone. AD were differentiated from BZ either by a significant decrease in DF (>10%), or by AF termination. Arrhythmia recurrence was monitored during follow-up.

Results

We analyzed 159 atrial areas (129 treated by radiofrequency during AF) in 29 patients. ACI was shorter in AD than BZ (76.4 ± 13.6 vs. 86.6 ± 20.3 ms; p = 0.0055), and mean ACI of all substrate zones was shorter in patients for whom radiofrequency failed to terminate AF [71.3 (67.5-77.8) vs. 82.4 (74.4-98.5) ms; p = 0.0126]. ACI predicted AD [AUC 0.728 (0.629-0.826)]. An ACI < 70 ms was specific for predicting AD (Sp 0.831, Se 0.526), whereas areas with an ACI > 100 ms had almost no chances of being active in AF maintenance. AF recurrence was associated with more ACI zones with identical shortest value [3.5 (3-4) vs. 1 (0-1) zones; p = 0.021]. In multivariate analysis, ACI < 70 ms predicted AD [OR = 4.02 (1.49-10.84), p = 0.006] and mean ACI > 75 ms predicted AF termination [OR = 9.94 (1.14-86.7), p = 0.038].

Conclusion

ACI helps in identifying AF drivers, and is correlated with AF termination and AF recurrence during follow-up. It can help in establishing an ablation plan, by prioritizing ablation from the shortest to the longest ACI zone.

Explainable Machine Learning to Predict Anchored Reentry Substrate Created by Persistent Atrial Fibrillation Ablation in Computational Models

Background Postablation arrhythmia recurrence occurs in ~40% of patients with persistent atrial fibrillation. Fibrotic remodeling exacerbates arrhythmic activity in persistent atrial fibrillation and can play a key role in reentrant arrhythmia, but emergent interaction between nonconductive ablation-induced scar and native fibrosis (ie, residual fibrosis) is poorly understood. Methods and Results We conducted computational simulations in pre- and postablation left atrial models reconstructed from late gadolinium enhanced magnetic resonance imaging scans to test the hypothesis that ablation in patients with persistent atrial fibrillation creates new substrate conducive to recurrent arrhythmia mediated by anchored reentry. We trained a random forest machine learning classifier to accurately pinpoint specific nonconductive tissue regions (ie, areas of ablation-delivered scar or vein/valve boundaries) with the capacity to serve as substrate for anchored reentry-driven recurrent arrhythmia (area under the curve: 0.91±0.03). Our analysis suggests there is a distinctive nonconductive tissue pattern prone to serving as arrhythmogenic substrate in postablation models, defined by a specific size and proximity to residual fibrosis. Conclusions Overall, this suggests persistent atrial fibrillation ablation transforms substrate that favors functional reentry (ie, rotors meandering in excitable tissue) into an arrhythmogenic milieu more conducive to anchored reentry. Our work also indicates that explainable machine learning and computational simulations can be combined to effectively probe mechanisms of recurrent arrhythmia.

Personalized ablation vs. conventional ablation strategies to terminate atrial fibrillation and prevent recurrence

AIMS

The long-term success rate of ablation therapy is still sub-optimal in patients with persistent atrial fibrillation (AF), mostly due to arrhythmia recurrence originating from arrhythmogenic sites outside the pulmonary veins. Computational modelling provides a framework to integrate and augment clinical data, potentially enabling the patient-specific identification of AF mechanisms and of the optimal ablation sites. We developed a technology to tailor ablations in anatomical and functional digital atrial twins of patients with persistent AF aiming to identify the most successful ablation strategy.

METHODS AND RESULTS

Twenty-nine patient-specific computational models integrating clinical information from tomographic imaging and electro-anatomical activation time and voltage maps were generated. Areas sustaining AF were identified by a personalized induction protocol at multiple locations. State-of-the-art anatomical and substrate ablation strategies were compared with our proposed Personalized Ablation Lines (PersonAL) plan, which consists of iteratively targeting emergent high dominant frequency (HDF) regions, to identify the optimal ablation strategy. Localized ablations were connected to the closest non-conductive barrier to prevent recurrence of AF or atrial tachycardia. The first application of the HDF strategy had a success of >98% and isolated only 5-6% of the left atrial myocardium. In contrast, conventional ablation strategies targeting anatomical or structural substrate resulted in isolation of up to 20% of left atrial myocardium. After a second iteration of the HDF strategy, no further arrhythmia episode could be induced in any of the patient-specific models.

CONCLUSION

The novel PersonAL in silico technology allows to unveil all AF-perpetuating areas and personalize ablation by leveraging atrial digital twins.

Quantifying the impact of shape uncertainty on predicted arrhythmias

BACKGROUND

Personalised computer models are increasingly used to diagnose cardiac arrhythmias and tailor treatment. Patient-specific models of the left atrium are often derived from pre-procedural imaging of anatomy and fibrosis. These images contain noise that can affect simulation predictions. There are few computationally tractable methods for propagating uncertainties from images to clinical predictions.

METHOD

We describe the left atrium anatomy using our Bayesian shape model that captures anatomical uncertainty in medical images and has been validated on 63 independent clinical images. This algorithm describes the left atrium anatomy using Nmodes=15 principal components, capturing 95% of the shape variance and calculated from 70 clinical cardiac magnetic resonance (CMR) images. Latent variables encode shape uncertainty: we evaluate their posterior distribution for each new anatomy. We assume a normally distributed prior. We use the unscented transform to sample from the posterior shape distribution. For each sample, we assign the local material properties of the tissue using the projection of late gadolinium enhancement CMR (LGE-CMR) onto the anatomy to estimate local fibrosis. To test which activation patterns an atrium can sustain, we perform an arrhythmia simulation for each sample. We consider 34 possible outcomes (31 macro-re-entries, functional re-entry, atrial fibrillation, and non-sustained arrhythmia). For each sample, we determine the outcome by comparing pre- and post-ablation activation patterns following a cross-field stimulus.

RESULTS

We create patient-specific atrial electrophysiology models of ten patients. We validate the mean and standard deviation maps from the unscented transform with the same statistics obtained with 12,000 Monte Carlo (ground truth) samples. We found discrepancies <3% and <2% for the mean and standard deviation for fibrosis burden and activation time, respectively. For each patient case, we then compare the predicted outcome from a model built on the clinical data (deterministic approach) with the probability distribution obtained from the simulated samples. We found that the deterministic approach did not predict the most likely outcome in 80% of the cases. Finally, we estimate the influence of each source of uncertainty independently. Fixing the anatomy to the posterior mean and maintaining uncertainty in fibrosis reduced the prediction of self-terminating arrhythmias from ≃14% to ≃7%. Keeping the fibrosis fixed to the sample mean while retaining uncertainty in shape decreased the prediction of substrate-driven arrhythmias from ≃33% to ≃18% and increased the prediction of macro-re-entries from ≃54% to ≃68%.

CONCLUSIONS

We presented a novel method for propagating shape uncertainty in atrial models through to uncertainty in numerical simulations. The algorithm takes advantage of the unscented transform to compute the output distribution of the outcomes. We validated the unscented transform as a viable sampling strategy to deal with anatomy uncertainty. We then showed that the prediction computed with a deterministic model does not always coincide with the most likely outcome. Finally, we found that shape uncertainty affects the predictions of macro-re-entries, while fibrosis uncertainty affects the predictions of functional re-entries.

Interpretable machine learning of action potential duration restitution kinetics in single-cell models of atrial cardiomyocytes

Action potential duration (APD) restitution curve and its maximal slope (Smax) reflect single cell-level dynamic instability for inducing chaotic heart rhythms. However, conventional parameter sensitivity analysis often fails to describe nonlinear relationships between ion channel parameters and electrophysiological phenotypes, such as Smax. We explored the parameter-phenotype mapping in a population of 5000 single-cell atrial cell models through interpretable machine learning (ML) approaches. Parameter sensitivity analyses could explain the linear relationships between parameters and electrophysiological phenotypes, including APD₉₀, resting membrane potential, Vmax, refractory period, and APD/calcium alternans threshold, but not for Smax. However, neural network models had better prediction performance for Smax. To interpret the ML model, we evaluated the parameter importance at the global and local levels by computing the permutation feature importance and the local interpretable model-agnostic explanations (LIME) values, respectively. Increases in I_CaL, I_NCX, and I_Kr, and decreases in I_K1, I_b,Cl, I_Kur, I_SERCA, and I_to are correlated with higher Smax values. The LIME algorithm determined that I_NaK plays a significant role in determining Smax as well as I_to and I_Kur. The atrial cardiomyocyte population was hierarchically clustered into three distinct groups based on the LIME values and the single-cell simulation confirmed that perturbations in I_NaK resulted in different behaviors of APD restitution curves in three clusters. Our combined top-down interpretable ML and bottom-up mechanistic simulation approaches uncovered the role of I_NaK in heterogeneous behaviors of Smax in the atrial cardiomyocyte population.

Predicting Atrial Fibrillation Recurrence by Combining Population Data and Virtual Cohorts of Patient-Specific Left Atrial Models

BACKGROUND

Current ablation therapy for atrial fibrillation is suboptimal, and long-term response is challenging to predict. Clinical trials identify bedside properties that provide only modest prediction of long-term response in populations, while patient-specific models in small cohorts primarily explain acute response to ablation. We aimed to predict long-term atrial fibrillation recurrence after ablation in large cohorts, by using machine learning to complement biophysical simulations by encoding more interindividual variability.

METHODS

Patient-specific models were constructed for 100 atrial fibrillation patients (43 paroxysmal, 41 persistent, and 16 long-standing persistent), undergoing first ablation. Patients were followed for 1 year using ambulatory ECG monitoring. Each patient-specific biophysical model combined differing fibrosis patterns, fiber orientation maps, electrical properties, and ablation patterns to capture uncertainty in atrial properties and to test the ability of the tissue to sustain fibrillation. These simulation stress tests of different model variants were postprocessed to calculate atrial fibrillation simulation metrics. Machine learning classifiers were trained to predict atrial fibrillation recurrence using features from the patient history, imaging, and atrial fibrillation simulation metrics.

RESULTS

We performed 1100 atrial fibrillation ablation simulations across 100 patient-specific models. Models based on simulation stress tests alone showed a maximum accuracy of 0.63 for predicting long-term fibrillation recurrence. Classifiers trained to history, imaging, and simulation stress tests (average 10-fold cross-validation area under the curve, 0.85±0.09; recall, 0.80±0.13; precision, 0.74±0.13) outperformed those trained to history and imaging (area under the curve, 0.66±0.17) or history alone (area under the curve, 0.61±0.14).

CONCLUSION

A novel computational pipeline accurately predicted long-term atrial fibrillation recurrence in individual patients by combining outcome data with patient-specific acute simulation response. This technique could help to personalize selection for atrial fibrillation ablation.

Current progress of computational modeling for guiding clinical atrial fibrillation ablation

Atrial fibrillation (AF) is one of the most common arrhythmias, associated with high morbidity, mortality, and healthcare costs, and it places a significant burden on both individuals and society. Anti-arrhythmic drugs are the most commonly used strategy for treating AF. However, drug therapy faces challenges because of its limited efficacy and potential side effects. Catheter ablation is widely used as an alternative treatment for AF. Nevertheless, because the mechanism of AF is not fully understood, the recurrence rate after ablation remains high. In addition, the outcomes of ablation can vary significantly between medical institutions and patients, especially for persistent AF. Therefore, the issue of which ablation strategy is optimal is still far from settled. Computational modeling has the advantages of repeatable operation, low cost, freedom from risk, and complete control, and is a useful tool for not only predicting the results of different ablation strategies on the same model but also finding optimal personalized ablation targets for clinical reference and even guidance. This review summarizes three-dimensional computational modeling simulations of catheter ablation for AF, from the early-stage attempts such as Maze III or circumferential pulmonary vein isolation to the latest advances based on personalized substrate-guided ablation. Finally, we summarize current developments and challenges and provide our perspectives and suggestions for future directions.

Characterizing the arrhythmogenic substrate in personalized models of atrial fibrillation: sensitivity to mesh resolution and pacing protocol in AF models

AIMS

Computationally guided persistent atrial fibrillation (PsAF) ablation has emerged as an alternative to conventional treatment planning. To make this approach scalable, computational cost and the time required to conduct simulations must be minimized while maintaining predictive accuracy. Here, we assess the sensitivity of the process to finite-element mesh resolution. We also compare methods for pacing site distribution used to evaluate inducibility arrhythmia sustained by re-entrant drivers (RDs).

METHODS AND RESULTS

Simulations were conducted in low- and high-resolution models (average edge lengths: 400/350 µm) reconstructed from PsAF patients' late gadolinium enhancement magnetic resonance imaging scans. Pacing was simulated from 80 sites to assess RD inducibility. When pacing from the same site led to different outcomes in low-/high-resolution models, we characterized divergence dynamics by analysing dissimilarity index over time. Pacing site selection schemes prioritizing even spatial distribution and proximity to fibrotic tissue were evaluated. There were no RD sites observed in low-resolution models but not high-resolution models, or vice versa. Dissimilarity index analysis suggested that differences in simulation outcome arising from differences in discretization were the result of isolated conduction block incidents in one model but not the other; this never led to RD sites unique to one mesh resolution. Pacing site selection based on fibrosis proximity led to the best observed trade-off between number of stimulation locations and predictive accuracy.

CONCLUSION

Simulations conducted in meshes with 400 µm average edge length and ∼40 pacing sites proximal to fibrosis are sufficient to reveal the most comprehensive possible list of RD sites, given feasibility constraints.

Characterization of the Electrophysiologic Remodeling of Patients With Ischemic Cardiomyopathy by Clinical Measurements and Computer Simulations Coupled With Machine Learning

Rationale

Patients with ischemic cardiomyopathy (ICMP) are at high risk for malignant arrhythmias, largely due to electrophysiological remodeling of the non-infarcted myocardium. The electrophysiological properties of the non-infarcted myocardium of patients with ICMP remain largely unknown.

Objectives

To assess the pro-arrhythmic behavior of non-infarcted myocardium in ICMP patients and couple computational simulations with machine learning to establish a methodology for the development of disease-specific action potential models based on clinically measured action potential duration restitution (APDR) data.

Methods and Results

We enrolled 22 patients undergoing left-sided ablation (10 ICMP) and compared APDRs between ICMP and structurally normal left ventricles (SNLVs). APDRs were clinically assessed with a decremental pacing protocol. Using genetic algorithms (GAs), we constructed populations of action potential models that incorporate the cohort-specific APDRs. The variability in the populations of ICMP and SNLV models was captured by clustering models based on their similarity using unsupervised machine learning. The pro-arrhythmic potential of ICMP and SNLV models was assessed in cell- and tissue-level simulations. Clinical measurements established that ICMP patients have a steeper APDR slope compared to SNLV (by 38%, p < 0.01). In cell-level simulations, APD alternans were induced in ICMP models at a longer cycle length compared to SNLV models (385–400 vs 355 ms). In tissue-level simulations, ICMP models were more susceptible for sustained functional re-entry compared to SNLV models.

Conclusion

Myocardial remodeling in ICMP patients is manifested as a steeper APDR compared to SNLV, which underlies the greater arrhythmogenic propensity in these patients, as demonstrated by cell- and tissue-level simulations using action potential models developed by GAs from clinical measurements. The methodology presented here captures the uncertainty inherent to GAs model development and provides a blueprint for use in future studies aimed at evaluating electrophysiological remodeling resulting from other cardiac diseases.

A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation

In the context of cardiac electrophysiology, we propose a novel computational approach to highlight and explain the long-debated mechanisms behind atrial fibrillation (AF) and to reliably numerically predict its induction and sustainment. A key role is played, in this respect, by a new way of setting a parametrization of electrophysiological mathematical models based on conduction velocities; these latter are estimated from high-density mapping data, which provide a detailed characterization of patients' electrophysiological substrate during sinus rhythm. We integrate numerically approximated conduction velocities into a mathematical model consisting of a coupled system of partial and ordinary differential equations, formed by the monodomain equation and the Courtemanche-Ramirez-Nattel model. Our new model parametrization is then adopted to predict the formation and self-sustainment of localized reentries characterizing atrial fibrillation, by numerically simulating the onset of ectopic beats from the pulmonary veins. We investigate the paroxysmal and the persistent form of AF starting from electro-anatomical maps of two patients. The model's response to stimulation shows how substrate characteristics play a key role in inducing and sustaining these arrhythmias. Localized reentries are less frequent and less stable in case of paroxysmal AF, while they tend to anchor themselves in areas affected by severe slow conduction in case of persistent AF.

Using Machine Learning to Characterize Atrial Fibrotic Substrate From Intracardiac Signals With a Hybrid in silico and in vivo Dataset

In patients with atrial fibrillation, intracardiac electrogram signal amplitude is known to decrease with increased structural tissue remodeling, referred to as fibrosis. In addition to the isolation of the pulmonary veins, fibrotic sites are considered a suitable target for catheter ablation. However, it remains an open challenge to find fibrotic areas and to differentiate their density and transmurality. This study aims to identify the volume fraction and transmurality of fibrosis in the atrial substrate. Simulated cardiac electrograms, combined with a generalized model of clinical noise, reproduce clinically measured signals. Our hybrid dataset approach combines in silico and clinical electrograms to train a decision tree classifier to characterize the fibrotic atrial substrate. This approach captures different in vivo dynamics of the electrical propagation reflected on healthy electrogram morphology and synergistically combines it with synthetic fibrotic electrograms from in silico experiments. The machine learning algorithm was tested on five patients and compared against clinical voltage maps as a proof of concept, distinguishing non-fibrotic from fibrotic tissue and characterizing the patient's fibrotic tissue in terms of density and transmurality. The proposed approach can be used to overcome a single voltage cut-off value to identify fibrotic tissue and guide ablation targeting fibrotic areas.

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.

Computational modeling identifies embolic stroke of undetermined source patients with potential arrhythmic substrate

Cardiac magnetic resonance imaging (MRI) has revealed fibrosis in embolic stroke of undetermined source (ESUS) patients comparable to levels seen in atrial fibrillation (AFib). We used computational modeling to understand the absence of arrhythmia in ESUS despite the presence of putatively pro-arrhythmic fibrosis. MRI-based atrial models were reconstructed for 45 ESUS and 45 AFib patients. The fibrotic substrate's arrhythmogenic capacity in each patient was assessed computationally. Reentrant drivers were induced in 24/45 (53%) ESUS and 22/45 (49%) AFib models. Inducible models had more fibrosis (16.7 ± 5.45%) than non-inducible models (11.07 ± 3.61%; p<0.0001); however, inducible subsets of ESUS and AFib models had similar fibrosis levels (p=0.90), meaning that the intrinsic pro-arrhythmic substrate properties of fibrosis in ESUS and AFib are indistinguishable. This suggests that some ESUS patients have latent pre-clinical fibrotic substrate that could be a future source of arrhythmogenicity. Thus, our work prompts the hypothesis that ESUS patients with fibrotic atria are spared from AFib due to an absence of arrhythmia triggers.

Atrial fibrosis and substrate based characterization in atrial fibrillation: Time to move forwards

Atrial fibrillation (AF) is the most commonly encountered cardiac arrhythmia in clinical practice. However, current therapeutic interventions for atrial fibrillation have limited clinical efficacy as a consequence of major knowledge gaps in the mechanisms sustaining atrial fibrillation. From a mechanistic perspective, there is increasing evidence that atrial fibrosis plays a central role in the maintenance and perpetuation of atrial fibrillation. Electrophysiologically, atrial fibrosis results in alterations in conduction velocity, cellular refractoriness, and produces conduction block promoting meandering, unstable wavelets and micro-reentrant circuits. Clinically, atrial fibrosis has also linked to poor clinical outcomes including AF-related thromboembolic complications and arrhythmia recurrences post catheter ablation. In this article, we review the pathophysiology behind the formation of fibrosis as AF progresses, the role of fibrosis in arrhythmogenesis, surrogate markers for detection of fibrosis using cardiac magnetic resonance imaging, echocardiography and electroanatomic mapping, along with their respective limitations. We then proceed to review the current evidence behind therapeutic interventions targeting atrial fibrosis, including drugs and substrate-based catheter ablation therapies followed by the potential future use of electro phenotyping for AF characterization to overcome the limitations of contemporary substrate-based methodologies.

Using machine learning to identify local cellular properties that support re-entrant activation in patient-specific models of atrial fibrillation

AIMS

Atrial fibrillation (AF) is sustained by re-entrant activation patterns. Ablation strategies have been proposed that target regions of tissue that may support re-entrant activation patterns. We aimed to characterize the tissue properties associated with regions that tether re-entrant activation patterns in a validated virtual patient cohort.

METHODS AND RESULTS

Atrial fibrillation patient-specific models (seven paroxysmal and three persistent) were generated and validated against local activation time (LAT) measurements during an S1-S2 pacing protocol from the coronary sinus and high right atrium, respectively. Atrial models were stimulated with burst pacing from three locations in the proximity of each pulmonary vein to initiate re-entrant activation patterns. Five atria exhibited sustained activation patterns for at least 80 s. Models with short maximum action potential durations (APDs) were associated with sustained activation. Phase singularities were mapped across the atria sustained activation patterns. Regions with a low maximum conduction velocity (CV) were associated with tethering of phase singularities. A support vector machine (SVM) was trained on maximum local conduction velocity and action potential duration to identify regions that tether phase singularities. The SVM identified regions of tissue that could support tethering with 91% accuracy. This accuracy increased to 95% when the SVM was also trained on surface area.

CONCLUSION

In a virtual patient cohort, local tissue properties, that can be measured (CV) or estimated (APD; using effective refractory period as a surrogate) clinically, identified regions of tissue that tether phase singularities. Combing CV and APD with atrial surface area further improved the accuracy in identifying regions that tether phase singularities.

Translational applications of computational modelling for patients with cardiac arrhythmias

Cardiac arrhythmia is associated with high morbidity, and its underlying mechanisms are poorly understood. Computational modelling and simulation approaches have the potential to improve standard-of-care therapy for these disorders, offering deeper understanding of complex disease processes and sophisticated translational tools for planning clinical procedures. This review provides a clinician-friendly summary of recent advancements in computational cardiology. Organ-scale models automatically generated from clinical-grade imaging data are used to custom tailor our understanding of arrhythmia drivers, estimate future arrhythmogenic risk and personalise treatment plans. Recent mechanistic insights derived from atrial and ventricular arrhythmia simulations are highlighted, and the potential avenues to patient care (eg, by revealing new antiarrhythmic drug targets) are covered. Computational approaches geared towards improving outcomes in resynchronisation therapy have used simulations to elucidate optimal patient selection and lead location. Technology to personalise catheter ablation procedures are also covered, specifically preliminary outcomes form early-stage or pilot clinical studies. To conclude, future developments in computational cardiology are discussed, including improving the representation of patient-specific fibre orientations and fibrotic remodelling characterisation and how these might improve understanding of arrhythmia mechanisms and provide transformative tools for patient-specific therapy.

Using cardiac ionic cell models to interpret clinical data

For over 100 years cardiac electrophysiology has been measured in the clinic. The electrical signals that can be measured span from noninvasive ECG and body surface potentials measurements through to detailed invasive measurements of local tissue electrophysiology. These electrophysiological measurements form a crucial component of patient diagnosis and monitoring; however, it remains challenging to quantitatively link changes in clinical electrophysiology measurements to biophysical cellular function. Multi-scale biophysical computational models represent one solution to this problem. These models provide a formal framework for linking cellular function through to emergent whole organ function and routine clinical diagnostic signals. In this review, we describe recent work on the use of computational models to interpret clinical electrophysiology signals. We review the simulation of human cardiac myocyte electrophysiology in the atria and the ventricles and how these models are being used to link organ scale function to patient disease mechanisms and therapy response in patients receiving implanted defibrillators, \cardiac resynchronisation therapy or suffering from atrial fibrillation and ventricular tachycardia. There is a growing use of multi-scale biophysical models to interpret clinical data. This allows cardiologists to link clinical observations with cellular mechanisms to better understand cardiopathophysiology and identify novel treatment strategies. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Arrhythmogenic propensity of the fibrotic substrate after atrial fibrillation ablation: a longitudinal study using magnetic resonance imaging-based atrial models

AIMS

Inadequate modification of the atrial fibrotic substrate necessary to sustain re-entrant drivers (RDs) may explain atrial fibrillation (AF) recurrence following failed pulmonary vein isolation (PVI). Personalized computational models of the fibrotic atrial substrate derived from late gadolinium enhanced (LGE)-magnetic resonance imaging (MRI) can be used to non-invasively determine the presence of RDs. The objective of this study is to assess the changes of the arrhythmogenic propensity of the fibrotic substrate after PVI.

METHODS AND RESULTS

Pre- and post-ablation individualized left atrial models were constructed from 12 AF patients who underwent pre- and post-PVI LGE-MRI, in six of whom PVI failed. Pre-ablation AF sustained by RDs was induced in 10 models. RDs in the post-ablation models were classified as either preserved or emergent. Pre-ablation models derived from patients for whom the procedure failed exhibited a higher number of RDs and larger areas defined as promoting RD formation when compared with atrial models from patients who had successful ablation, 2.6 ± 0.9 vs. 1.8 ± 0.2 and 18.9 ± 1.6% vs. 13.8 ± 1.5%, respectively. In cases of successful ablation, PVI eliminated completely the RDs sustaining AF. Preserved RDs unaffected by ablation were documented only in post-ablation models of patients who experienced recurrent AF (2/5 models); all of these models had also one or more emergent RDs at locations distinct from those of pre-ablation RDs. Emergent RDs occurred in regions that had the same characteristics of the fibrosis spatial distribution (entropy and density) as regions that harboured RDs in pre-ablation models.

CONCLUSION

Recurrent AF after PVI in the fibrotic atria may be attributable to both preserved RDs that sustain AF pre- and post-ablation, and the emergence of new RDs following ablation. The same levels of fibrosis entropy and density underlie the pro-RD propensity in both pre- and post-ablation substrates.

Preprocedure Application of Machine Learning and Mechanistic Simulations Predicts Likelihood of Paroxysmal Atrial Fibrillation Recurrence Following Pulmonary Vein Isolation

BACKGROUND

Pulmonary vein isolation (PVI) is an effective treatment strategy for patients with atrial fibrillation (AF), but many experience AF recurrence and require repeat ablation procedures. The goal of this study was to develop and evaluate a methodology that combines machine learning (ML) and personalized computational modeling to predict, before PVI, which patients are most likely to experience AF recurrence after PVI.

METHODS

This single-center retrospective proof-of-concept study included 32 patients with documented paroxysmal AF who underwent PVI and had preprocedural late gadolinium enhanced magnetic resonance imaging. For each patient, a personalized computational model of the left atrium simulated AF induction via rapid pacing. Features were derived from pre-PVI late gadolinium enhanced magnetic resonance images and from results of simulations of AF induction. The most predictive features were used as input to a quadratic discriminant analysis ML classifier, which was trained, optimized, and evaluated with 10-fold nested cross-validation to predict the probability of AF recurrence post-PVI.

RESULTS

In our cohort, the ML classifier predicted probability of AF recurrence with an average validation sensitivity and specificity of 82% and 89%, respectively, and a validation area under the curve of 0.82. Dissecting the relative contributions of simulations of AF induction and raw images to the predictive capability of the ML classifier, we found that when only features from simulations of AF induction were used to train the ML classifier, its performance remained similar (validation area under the curve, 0.81). However, when only features extracted from raw images were used for training, the validation area under the curve significantly decreased (0.47).

CONCLUSIONS

ML and personalized computational modeling can be used together to accurately predict, using only pre-PVI late gadolinium enhanced magnetic resonance imaging scans as input, whether a patient is likely to experience AF recurrence following PVI, even when the patient cohort is small.

An audit of uncertainty in multi-scale cardiac electrophysiology models

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Accurate Conduction Velocity Maps and Their Association With Scar Distribution on Magnetic Resonance Imaging in Patients With Postinfarction Ventricular Tachycardias

BACKGROUND

Characterizing myocardial conduction velocity (CV) in patients with ischemic cardiomyopathy (ICM) and ventricular tachycardia (VT) is important for understanding the patient-specific proarrhythmic substrate of VTs and therapeutic planning. The objective of this study is to accurately assess the relation between CV and myocardial fibrosis density on late gadolinium-enhanced cardiac magnetic resonance imaging (LGE-CMR) in patients with ICM.

METHODS

We enrolled 6 patients with ICM undergoing VT ablation and 5 with structurally normal left ventricles (controls) undergoing premature ventricular contraction or VT ablation. All patients underwent LGE-CMR and electroanatomic mapping (EAM) in sinus rhythm (2960 electroanatomic mapping points analyzed). We estimated CV from electroanatomic mapping local activation time using the triangulation method that provides an accurate estimate of CV as it accounts for the direction of wavefront propagation. We evaluated the association between LGE-CMR intensity and CV with multilevel linear mixed models.

RESULTS

Median CV in patients with ICM and controls was 0.41 m/s and 0.65 m/s, respectively. In patients with ICM, CV in areas with no visible fibrosis was 0.81 m/s (95% CI, 0.59-1.12 m/s). For each 25% increase in normalized LGE intensity, CV decreased by 1.34-fold (95% CI, 1.25-1.43). Dense scar areas have, on average, 1.97- to 2.66-fold slower CV compared with areas without dense scar. Ablation lesions that terminated VTs were localized in areas of slow conduction on CV maps.

CONCLUSIONS

CV is inversely associated with LGE-CMR fibrosis density in patients with ICM. Noninvasive derivation of CV maps from LGE-CMR is feasible. Integration of noninvasive CV maps with electroanatomic mapping during substrate mapping has the potential to improve procedural planning and outcomes. Visual Overview: A visual overview is available for this article.

Time resolution for wavefront and phase singularity tracking using activation maps in cardiac propagation models

The dynamics of cardiac fibrillation can be described by the number, the trajectory, the stability, and the lifespan of phase singularities (PSs). Accurate PS tracking is straightforward in simple uniform tissues but becomes more challenging as fibrosis, structural heterogeneity, and strong anisotropy are combined. In this paper, we derive a mathematical formulation for PS tracking in two-dimensional reaction-diffusion models. The method simultaneously tracks wavefronts and PS based on activation maps at full spatiotemporal resolution. PS tracking is formulated as a linear assignment problem solved by the Hungarian algorithm. The cost matrix incorporates information about distances between PS, chirality, and wavefronts. A graph of PS trajectories is generated to represent the creations and annihilations of PS pairs. Structure-preserving graph transformations are applied to provide a simplified description at longer observation time scales. The approach is validated in 180 simulations of fibrillation in four different types of substrates featuring, respectively, wavebreaks, ionic heterogeneities, fibrosis, and breakthrough patterns. The time step of PS tracking is studied in the range from 0.1 to 10 ms. The results show the benefits of improving time resolution from 1 to 0.1 ms. The tracking error rate decreases by an order of magnitude because the occurrence of simultaneous events becomes less likely. As observed on PS survival curves, the graph-based analysis facilitates the identification of macroscopically stable rotors despite wavefront fragmentation by fibrosis.

Arrhythmia dynamics in computational models of the atria following virtual ablation of re-entrant drivers

Aims

Efforts to improve ablation success rates in persistent atrial fibrillation (AF) patients by targeting re-entrant driver (RD) sites have been hindered by weak mechanistic understanding regarding emergent RDs localization following initial fibrotic substrate modification. This study aimed to systematically assess arrhythmia dynamics after virtual ablation of RD sites in computational models.

Methods and results

Simulations were conducted in 12 patient-specific atrial models reconstructed from pre-procedure late gadolinium-enhanced magnetic resonance imaging scans. In a previous study involving these same models, we comprehensively characterized pre-ablation RDs in simulations conducted with either 'average human AF'-based electrophysiology (i.e. EPavg) or ±10% action potential duration or conduction velocity (i.e. EPvar). Re-entrant drivers seen under the EPavg condition were virtually ablated and the AF initiation protocol was re-applied. Twenty-one emergent RDs were observed in 9/12 atrial models (1.75 ± 1.35 emergent RDs per model); these dynamically localized to boundary regions between fibrotic and non-fibrotic tissue. Most emergent RD locations (15/21, 71.4%) were within 0.1 cm of sites where RDs were seen pre-ablation in simulations under EPvar conditions. Importantly, this suggests that the level of uncertainty in our models' ability to predict patient-specific ablation targets can be substantially mitigated by running additional simulations that include virtual ablation of RDs. In 7/12 atrial models, at least one episode of macro-reentry around ablation lesion(s) was observed.

Conclusion

Arrhythmia episodes after virtual RD ablation are perpetuated by both emergent RDs and by macro-reentrant circuits formed around lesions. Custom-tailoring of ablation procedures based on models should take steps to mitigate these sources of AF recurrence.

Computationally guided personalized targeted ablation of persistent atrial fibrillation

Atrial fibrillation (AF) — the most common arrhythmia — significantly increases the risk of stroke and heart failure. Although catheter ablation can restore normal heart rhythms, patients with persistent AF who develop atrial fibrosis often undergo multiple failed ablations and thus increased procedural risks. Here, we present personalized computational modelling for the reliable predetermination of ablation targets, which are then used to guide the ablation procedure in patients with persistent AF and atrial fibrosis. We first show that a computational model of the atria of patients identifies fibrotic tissue that if ablated will not sustain AF. We then integrated the target-ablation sites in a clinical-mapping system, and tested its feasibility in 10 patients with persistent AF. The computational prediction of ablation targets avoids lengthy electrical mapping and could improve the accuracy and efficacy of targeted AF ablation in patients whilst eliminating the need for repeat procedures.

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.

A comprehensive, multiscale framework for evaluation of arrhythmias arising from cell therapy in the whole post-myocardial infarcted heart

Direct remuscularization approaches to cell-based heart repair seek to restore ventricular contractility following myocardial infarction (MI) by introducing new cardiomyocytes (CMs) to replace lost or injured ones. However, despite promising improvements in cardiac function, high incidences of ventricular arrhythmias have been observed in animal models of MI injected with pluripotent stem cell-derived cardiomyocytes (PSC-CMs). The mechanisms of arrhythmogenesis remain unclear. Here, we present a comprehensive framework for computational modeling of direct remuscularization approaches to cell therapy. Our multiscale 3D whole-heart modeling framework integrates realistic representations of cell delivery and transdifferentiation therapy modalities as well as representation of spatial distributions of engrafted cells, enabling simulation of clinical therapy and the prediction of emergent electrophysiological behavior and arrhythmogenensis. We employ this framework to explore how varying parameters of cell delivery and transdifferentiation could result in three mechanisms of arrhythmogenesis: focal ectopy, heart block, and reentry.

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.

Sensitivity of Ablation Targets Prediction to Electrophysiological Parameter Variability in Image-Based Computational Models of Ventricular Tachycardia in Post-infarction Patients

Ventricular tachycardia (VT), which could lead to sudden cardiac death, occurs frequently in patients with myocardial infarction. Computational modeling has emerged as a powerful platform for the non-invasive investigation of lethal heart rhythm disorders in post-infarction patients and for guiding patient VT ablation. However, it remains unclear how VT dynamics and predicted ablation targets are influenced by inter-patient variability in action potential duration (APD) and conduction velocity (CV). The goal of this study was to systematically assess the effect of changes in the electrophysiological parameters on the induced VTs and predicted ablation targets in personalized models of post-infarction hearts. Simulations were conducted in 5 patient-specific left ventricular models reconstructed from late gadolinium-enhanced magnetic resonance imaging scans. We comprehensively characterized all possible pre-ablation and post-ablation VTs in simulations conducted with either an “average human VT”-based electrophysiological representation (i.e., EP_avg) or with ±10% APD or CV (i.e., EP_var); additional simulations were also executed in some models for an extended range of these parameters. The results showed that: (1) a subset of reentries (76.2–100%, depending on EP parameter set) conducted with ±10% APD/CV was observed in approximately the same locations as reentries observed in EP_avg cases; (2) emergent VTs could be induced sometimes after ablation in EP_avg models, and these emergent VTs often corresponded to the pre-ablation reentries in simulations with EP_var parameter sets. These findings demonstrate that the VT ablation target uncertainty in patient-specific ventricular models with an average representation of VT-remodeled electrophysiology is relatively low and the ablation targets stable, as the localization of the induced VTs was primarily driven by the remodeled structural substrate. Thus, personalized ventricular modeling with an average representation of infarct-remodeled electrophysiology may uncover most targets for VT ablation.

The role of personalized atrial modeling in understanding atrial fibrillation mechanisms and improving treatment

Atrial fibrillation is the most common arrhythmia in humans and is associated with high morbidity, mortality and health-related expenses. Computational approaches have been increasingly utilized in atrial electrophysiology. In this review we summarize the recent advancements in atrial fibrillation modeling at the organ scale. Multi-scale atrial models now incorporate high level detail of atrial anatomy, tissue ultrastructure and fibrosis distribution. We provide the state-of-the art methodologies in developing personalized atrial fibrillation models with realistic geometry and tissue properties. We then focus on the use of multi-scale atrial models to gain mechanistic insights in AF. Simulations using atrial models have provided important insight in the mechanisms underlying AF, showing the importance of the atrial fibrotic substrate and altered atrial electrophysiology in initiation and maintenance of AF. Last, we summarize the translational evidence that supports incorporation of computational modeling in clinical practice for development of personalized treatment strategies for patients with AF. In early-stages clinical studies, AF models successfully identify patients where pulmonary vein isolation alone is not adequate for treatment of AF and suggest novel targets for ablation. We conclude with a summary of the future developments envisioned for the field of atrial computational electrophysiology.

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.

Patient-Specific Identification of Atrial Flutter Vulnerability-A Computational Approach to Reveal Latent Reentry Pathways

Atypical atrial flutter (AFlut) is a reentrant arrhythmia which patients frequently develop after ablation for atrial fibrillation (AF). Indeed, substrate modifications during AF ablation can increase the likelihood to develop AFlut and it is clinically not feasible to reliably and sensitively test if a patient is vulnerable to AFlut. Here, we present a novel method based on personalized computational models to identify pathways along which AFlut can be sustained in an individual patient. We build a personalized model of atrial excitation propagation considering the anatomy as well as the spatial distribution of anisotropic conduction velocity and repolarization characteristics based on a combination of a priori knowledge on the population level and information derived from measurements performed in the individual patient. The fast marching scheme is employed to compute activation times for stimuli from all parts of the atria. Potential flutter pathways are then identified by tracing loops from wave front collision sites and constricting them using a geometric snake approach under consideration of the heterogeneous wavelength condition. In this way, all pathways along which AFlut can be sustained are identified. Flutter pathways can be instantiated by using an eikonal-diffusion phase extrapolation approach and a dynamic multifront fast marching simulation. In these dynamic simulations, the initial pattern eventually turns into the one driven by the dominant pathway, which is the only pathway that can be observed clinically. We assessed the sensitivity of the flutter pathway maps with respect to conduction velocity and its anisotropy. Moreover, we demonstrate the application of tailored models considering disease-specific repolarization properties (healthy, AF-remodeled, potassium channel mutations) as well as applicabiltiy on a clinical dataset. Finally, we tested how AFlut vulnerability of these substrates is modulated by exemplary antiarrhythmic drugs (amiodarone, dronedarone). Our novel method allows to assess the vulnerability of an individual patient to develop AFlut based on the personal anatomical, electrophysiological, and pharmacological characteristics. In contrast to clinical electrophysiological studies, our computational approach provides the means to identify all possible AFlut pathways and not just the currently dominant one. This allows to consider all relevant AFlut pathways when tailoring clinical ablation therapy in order to reduce the development and recurrence of AFlut.

Optimal contrast-enhanced MRI image thresholding for accurate prediction of ventricular tachycardia using ex-vivo high resolution models

Patient specific models created from contrast-enhanced (i.e. late-gadolinium, LGE) MRI images can be used for prediction of reentry location and clinical ablation planning. However, there is still a need for direct and systematic comparison between characteristics of ventricular tachycardia (VT) morphologies predicted in computational models and those acquired in clinical or experimental protocols. In this study, we aimed to: 1) assess the differences in VT morphologies predicted by modeling and recorded in experiments in terms of patterns and location of reentries, earliest and latest activation sites, and cycle lengths; and 2) define the optimal range of infarct tissue threshold values which provide best match between simulation and experimental results. To achieve these goals, we utilized LGE-MRI images from 4 swine hearts with inducible monomorphic VT. The images were segmented to identify non-infarcted myocardium, semi viable gray zone (GZ), and core scar based on pixel intensity. Several models were reconstructed from each LGE-MRI scan, with voxels of intensity between that of non-infarcted myocardium and 20-50% of the maximum intensity (in 10% increments) in the infarct region classified as GZ. VT induction was simulated in each model. Our simulation results showed that using GZ intensity thresholds of 20% or 30% resulted in the best match of simulated propagation patterns and reentry locations with those from the experiment. Overall, we matched 70% (7/10) morphologies for all the hearts. Our simulation shows that MRI-based computational models of hearts with myocardial infarction can accurately reproduce the majority of experimentally recorded post-infarction VTs.

Wavelength and Fibrosis Affect Phase Singularity Locations During Atrial Fibrillation

The mechanisms underlying atrial fibrillation (AF), the most common sustained cardiac rhythm disturbance, remain elusive. Atrial fibrosis plays an important role in the development of AF and rotor dynamics. Both electrical wavelength (WL) and the degree of atrial fibrosis change as AF progresses. However, their combined effect on rotor core location remains unknown. The aim of this study was to analyze the effects of WL change on rotor core location in both fibrotic and non-fibrotic atria. Three patient specific fibrosis distributions (total fibrosis content: 16.6, 22.8, and 19.2%) obtained from clinical imaging data of persistent AF patients were incorporated in a bilayer atrial computational model. Fibrotic effects were modeled as myocyte-fibroblast coupling + conductivity remodeling; structural remodeling; ionic current changes + conductivity remodeling; and combinations of these methods. To change WL, action potential duration (APD) was varied from 120 to 240ms, representing the range of clinically observed AF cycle length, by modifying the inward rectifier potassium current (IK1) conductance between 80 and 140% of the original value. Phase singularities (PSs) were computed to identify rotor core locations. Our results show that IK1 conductance variation resulted in a decrease of APD and WL across the atria. For large WL in the absence of fibrosis, PSs anchored to regions with high APD gradient at the center of the left atrium (LA) anterior wall and near the junctions of the inferior pulmonary veins (PVs) with the LA. Decreasing the WL induced more PSs, whose distribution became less clustered. With fibrosis, PS locations depended on the fibrosis distribution and the fibrosis implementation method. The proportion of PSs in fibrotic areas and along the borders varied with both WL and fibrosis modeling method: for patient one, this was 4.2-14.9% as IK1 varied for the structural remodeling representation, but 12.3-88.4% using the combination of structural remodeling with myocyte-fibroblast coupling. The degree and distribution of fibrosis and the choice of implementation technique had a larger effect on PS locations than the WL variation. Thus, distinguishing the fibrotic mechanisms present in a patient is important for interpreting clinical fibrosis maps to create personalized models.

Computational Modeling of Electrophysiology and Pharmacotherapy of Atrial Fibrillation: Recent Advances and Future Challenges

The pathophysiology of atrial fibrillation (AF) is broad, with components related to the unique and diverse cellular electrophysiology of atrial myocytes, structural complexity, and heterogeneity of atrial tissue, and pronounced disease-associated remodeling of both cells and tissue. A major challenge for rational design of AF therapy, particularly pharmacotherapy, is integrating these multiscale characteristics to identify approaches that are both efficacious and independent of ventricular contraindications. Computational modeling has long been touted as a basis for achieving such integration in a rapid, economical, and scalable manner. However, computational pipelines for AF-specific drug screening are in their infancy, and while the field is progressing quite rapidly, major challenges remain before computational approaches can fill the role of workhorse in rational design of AF pharmacotherapies. In this review, we briefly detail the unique aspects of AF pathophysiology that determine requirements for compounds targeting AF rhythm control, with emphasis on delimiting mechanisms that promote AF triggers from those providing substrate or supporting reentry. We then describe modeling approaches that have been used to assess the outcomes of drugs acting on established AF targets, as well as on novel promising targets including the ultra-rapidly activating delayed rectifier potassium current, the acetylcholine-activated potassium current and the small conductance calcium-activated potassium channel. Finally, we describe how heterogeneity and variability are being incorporated into AF-specific models, and how these approaches are yielding novel insights into the basic physiology of disease, as well as aiding identification of the important molecular players in the complex AF etiology.

The Fibrotic Substrate in Persistent Atrial Fibrillation Patients: Comparison Between Predictions From Computational Modeling and Measurements From Focal Impulse and Rotor Mapping

Focal impulse and rotor mapping (FIRM) involves intracardiac detection and catheter ablation of re-entrant drivers (RDs), some of which may contribute to arrhythmia perpetuation in persistent atrial fibrillation (PsAF). Patient-specific computational models derived from late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) has the potential to non-invasively identify all areas of the fibrotic substrate where RDs could potentially be sustained, including locations where RDs may not manifest during mapped AF episodes. The objective of this study was to carry out multi-modal assessment of the arrhythmogenic propensity of the fibrotic substrate in PsAF patients by comparing locations of RD-harboring regions found in simulations and detected by FIRM (RD_sim and RD_FIRM) and analyze implications for ablation strategies predicated on targeting RDs. For 11 PsAF patients who underwent pre-procedure LGE-MRI and FIRM-guided ablation, we retrospectively simulated AF in individualized atrial models, with geometry and fibrosis distribution reconstructed from pre-ablation LGE-MRI scans, and identified RD_sim sites. Regions harboring RD_sim and RD_FIRM were compared. RD_sim were found in 38 atrial regions (median [inter-quartile range (IQR)] = 4 [3; 4] per model). RD_FIRM were identified and subsequently ablated in 24 atrial regions (2 [1; 3] per patient), which was significantly fewer than the number of RD_sim-harboring regions in corresponding models (p < 0.05). Computational modeling predicted RD_sim in 20 of 24 (83%) atrial regions identified as RD_FIRM-harboring during clinical mapping. In a large number of cases, we uncovered RD_sim-harboring regions in which RD_FIRM were never observed (18/22 regions that differed between the two modalities; 82%); we termed such cases “latent” RD_sim sites. During follow-up (230 [180; 326] days), AF recurrence occurred in 7/11 (64%) individuals. Interestingly, latent RD_sim sites were observed in all seven computational models corresponding to patients who experienced recurrent AF (2 [2; 2] per patient); in contrast, latent RD_sim sites were only discovered in two of four patients who were free from AF during follow-up (0.5 [0; 1.5] per patient; p < 0.05 vs. patients with AF recurrence). We conclude that substrate-based ablation based on computational modeling could improve outcomes.

Dispersion of Recovery and Vulnerability to Re-entry in a Model of Human Atrial Tissue With Simulated Diffuse and Focal Patterns of Fibrosis

Fibrosis in atrial tissue can act as a substrate for persistent atrial fibrillation, and can be focal or diffuse. Regions of fibrosis are associated with slowed or blocked conduction, and several approaches have been used to model these effects. In this study a computational model of 2D atrial tissue was used to investigate how the spatial scale of regions of simulated fibrosis influenced the dispersion of action potential duration (APD) and vulnerability to re-entry in simulated normal human atrial tissue, and human tissue that has undergone remodeling as a result of persistent atrial fibrillation. Electrical activity was simulated in a 10 × 10 cm square 2D domain, with a spatially varying diffusion coefficient as described below. Cellular electrophysiology was represented by the Courtemanche model for human atrial cells, with the model parameters set for normal and remodeled cells. The effect of fibrosis was modeled with a smoothly varying diffusion coefficient, obtained from sampling a Gaussian random field (GRF) with length scales of between 1.25 and 10.0 mm. Twenty samples were drawn from each field, and used to allocate a value of diffusion coefficient between 0.05 and 0.2 mm²/ms. Dispersion of APD was assessed in each sample by pacing at a cycle length of 1,000 ms, followed by a premature beat with a coupling interval of 400 ms. Vulnerability to re-entry was assessed with an aggressive pacing protocol with pacing cycle lengths decreasing from 450 to 250 ms in 25 ms intervals for normal tissue and 300–150 ms for remodeled tissue. Simulated fibrosis at smaller spatial scales tended to lengthen APD, increase APD dispersion, and increase vulnerability to sustained re-entry relative to fibrosis at larger spatial scales. This study shows that when fibrosis is represented by smoothly varying tissue diffusion, the spatial scale of fibrosis has important effects on both dispersion of recovery and vulnerability to re-entry.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

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.

Comparing Reentrant Drivers Predicted by Image-Based Computational Modeling and Mapped by Electrocardiographic Imaging in Persistent Atrial Fibrillation

Electrocardiographic mapping (ECGI) detects reentrant drivers (RDs) that perpetuate arrhythmia in persistent AF (PsAF). Patient-specific computational models derived from late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) identify all latent sites in the fibrotic substrate that could potentially sustain RDs, not just those manifested during mapped AF. The objective of this study was to compare RDs from simulations and ECGI (RD_sim/RD_ECGI) and analyze implications for ablation. We considered 12 PsAF patients who underwent RD_ECGI ablation. For the same cohort, we simulated AF and identified RD_sim sites in patient-specific models with geometry and fibrosis distribution from pre-ablation LGE-MRI. RD_sim- and RD_ECGI-harboring regions were compared, and the extent of agreement between macroscopic locations of RDs identified by simulations and ECGI was assessed. Effects of ablating RD_ECGI/RD_sim were analyzed. RD_sim were predicted in 28 atrial regions (median [inter-quartile range (IQR)] = 3.0 [1.0; 3.0] per model). ECGI detected 42 RD_ECGI-harboring regions (4.0 [2.0; 5.0] per patient). The number of regions with RD_sim and RD_ECGI per individual was not significantly correlated (R = 0.46, P = ns). The overall rate of regional agreement was fair (modified Cohen's κ₀ statistic = 0.11), as expected, based on the different mechanistic underpinning of RD_sim- and RD_ECGI. nineteen regions were found to harbor both RD_sim and RD_ECGI, suggesting that a subset of clinically observed RDs was fibrosis-mediated. The most frequent source of differences (23/32 regions) between the two modalities was the presence of RD_ECGI perpetuated by mechanisms other than the fibrotic substrate. In 6/12 patients, there was at least one region where a latent RD was observed in simulations but was not manifested during clinical mapping. Ablation of fibrosis-mediated RD_ECGI (i.e., targets in regions that also harbored RD_sim) trended toward a higher rate of positive response compared to ablation of other RD_ECGI targets (57 vs. 41%, P = ns). Our analysis suggests that RDs in human PsAF are at least partially fibrosis-mediated. Substrate-based ablation combining simulations with ECGI could improve outcomes.