A Computer Simulation Study of Anatomy Induced Drift of Spiral Waves in the Human Atrium

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.

The role of the Cx43/Cx45 gap junction voltage gating on wave propagation and arrhythmogenic activity in cardiac tissue

Gap junctions (GJs) formed of connexin (Cx) protein are the main conduits of electrical signals in the heart. Studies indicate that the transitional zone of the atrioventricular (AV) node contains heterotypic Cx43/Cx45 GJ channels which are highly sensitive to transjunctional voltage (Vj). To investigate the putative role of Vj gating of Cx43/Cx45 channels, we performed electrophysiological recordings in cell cultures and developed a novel mathematical/computational model which, for the first time, combines GJ channel Vj gating with a model of membrane excitability to simulate a spread of electrical pulses in 2D. Our simulation and electrophysiological data show that Vj transients during the spread of cardiac excitation can significantly affect the junctional conductance (gj) of Cx43/Cx45 GJs in a direction- and frequency-dependent manner. Subsequent simulation data indicate that such pulse-rate-dependent regulation of gj may have a physiological role in delaying impulse propagation through the AV node. We have also considered the putative role of the Cx43/Cx45 channel gating during pathological impulse propagation. Our simulation data show that Vj gating-induced changes in gj can cause the drift and subsequent termination of spiral waves of excitation. As a result, the development of fibrillation-like processes was significantly reduced in 2D clusters, which contained Vj-sensitive Cx43/Cx45 channels.

Restitution Slope Affects the Outcome of Dominant Frequency Ablation in Persistent Atrial Fibrillation: CUVIA-AF2 Post-Hoc Analysis Based on Computational Modeling Study

Introduction

Although the dominant frequency (DF) localizes the reentrant drivers and the maximal slope of the action potential duration (APD) restitution curve (Smax) reflects the tendency of the wave-break, their interaction has never been studied. We hypothesized that DF ablation has different effects on atrial fibrillation (AF) depending on Smax.

Methods

We studied the DF and Smax in 25 realistic human persistent AF model samples (68% male, 60 ± 10 years old). Virtual AF was induced by ramp pacing measuring Smax, followed by spatiotemporal DF evaluation for 34 s. We assessed the DF ablation effect depending on Smax in both computational modeling and a previous clinical trial, CUVIA-AF (170 patients with persistent AF, 70.6% male, 60 ± 11 years old).

Results

Mean DF had an inverse relationship with Smax regardless of AF acquisition timing (p < 0.001). Virtual DF ablations increased the defragmentation rate compared to pulmonary vein isolation (PVI) alone (p = 0.015), especially at Smax <1 (61.5 vs. 7.7%, p = 0.011). In post-DF ablation defragmentation episodes, DF was significantly higher (p = 0.002), and Smax was lower (p = 0.003) than in episodes without defragmentation. In the post-hoc analysis of CUVIA-AF2, we replicated the inverse relationship between Smax and DF (r = −0.47, p < 0.001), and we observed better rhythm outcomes of clinical DF ablations in addition to a PVI than of empirical PVI at Smax <1 [hazard ratio 0.45, 95% CI (0.22–0.89), p = 0.022; log-rank p = 0.021] but not at ≥ 1 (log-rank p = 0.177).

Conclusion

We found an inverse relationship between DF and Smax and the outcome of DF ablation after PVI was superior at the condition with Smax <1 in both in-silico and clinical trials.

Drift and termination of spiral waves in optogenetically modified cardiac tissue at sub-threshold illumination

The development of new approaches to control cardiac arrhythmias requires a deep understanding of spiral wave dynamics. Optogenetics offers new possibilities for this. Preliminary experiments show that sub-threshold illumination affects electrical wave propagation in the mouse heart. However, a systematic exploration of these effects is technically challenging. Here, we use state-of-the-art computer models to study the dynamic control of spiral waves in a two-dimensional model of the adult mouse ventricle, using stationary and non-stationary patterns of sub-threshold illumination. Our results indicate a light-intensity-dependent increase in cellular resting membrane potentials, which together with diffusive cell-cell coupling leads to the development of spatial voltage gradients over differently illuminated areas. A spiral wave drifts along the positive gradient. These gradients can be strategically applied to ensure drift-induced termination of a spiral wave, both in optogenetics and in conventional methods of electrical defibrillation.

Elucidating the relationship between arrhythmia and ischemic heterogeneity: an in silico study

Dialysis causes blood flow defects in the heart that may augment electrophysiological heterogeneity in the form of increased number of ischemic zones in the human left ventricle. We computationally tested whether a larger number of ischemic zones aggravate arrhythmia using a 2D electrophysiological model of the human ventricle.A human ventricle cardiomyocyte model capable of simulating ischemic action potentials was adapted in this study. The cell model was incorporated into a spatial 2D model consisting of known number of ischemic zones. Inter-cellular gap junction coupling within ischemic zones was reduced to simulate slow conduction. Arrhythmia severity was assessed by inducing a re-entry, and quantifying the ensuing breakup and tissue pacing rates.Ischemia elevated the isolated cardiomyocyte's resting potential and reduced its action potential duration. In the absence of ischemic zones, the propensity in the 2D model to induce multiple re-entrant waves was low. The inclusion of ischemic zones provided the substrate for initiation of re-entrant waves leading to fibrillation. Dominant frequency, which measured the highest rate of pacing in the tissue, increased drastically with the inclusion of multiple ischemic zones. Re-entrant wave tip maximum numbers increased from 1 tip (no ischemic zone) to 34 tips when a large number (20) of ischemic zones were included. Computational limiting factors of our platform were identified using software profiling.Clinical significance. Dialysis may promote deleterious arrhythmias by increasing tissue level action potential dispersion.

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.

Chaotic tip trajectories of a single spiral wave in the presence of heterogeneities

Spiral waves have been observed in a variety of physical, chemical, and biological systems. They play a major role in cardiac arrhythmias, including fibrillation, where the observed irregular activation patterns are generally thought to arise from the continuous breakup of multiple unstable spiral waves. Using spatially extended simulations of different electrophysiological models of cardiac tissue, we show that a single spiral wave in the presence of heterogeneities can display chaotic tip trajectories, consistent with fibrillation. We also show that the simulated spiral tip dynamics, including chaotic trajectories, can be captured by a simple particle model which only describes the dynamics of the spiral tip. This shows that spiral wave breakup, or interactions with other waves, are not necessary to initiate chaos in spiral waves.

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.

Pro-Arrhythmogenic Effects of Heterogeneous Tissue Curvature - A Suggestion for Role of Left Atrial Appendage in Atrial Fibrillation

BACKGROUND

The arrhythmogenic role of complex atrial morphology has not yet been clearly elucidated. We hypothesized that bumpy tissue geometry can induce action potential duration (APD) dispersion and wavebreak in atrial fibrillation (AF).

METHODS AND RESULTS

We simulated a 2D-bumpy atrial model by varying the degree of bumpiness, and 3D-left atrial (LA) models integrated by LA computed tomographic (CT) images taken from 14 patients with persistent AF. We also analyzed wave-dynamic parameters with bipolar electrograms during AF and compared them with LA-CT geometry in 30 patients with persistent AF. In the 2D-bumpy model, APD dispersion increased (P<0.001) and wavebreak occurred spontaneously when the surface bumpiness was greater, showing phase transition-like behavior (P<0.001). The bumpiness gradient 2D-model showed that spiral wave drifted in the direction of higher bumpiness, and phase singularity (PS) points were mostly located in areas with higher bumpiness. In the 3D-LA model, PS density was higher in the LA appendage (LAA) compared with other parts of the LA (P<0.05). In 30 persistent-AF patients, the surface bumpiness of LAA was 5.8-fold that of other LA parts (P<0.001), and exceeded critical bumpiness to induce wavebreak. Wave dynamics complexity parameters were consistently dominant in the LAA (P<0.001).

CONCLUSIONS

Bumpy tissue geometry promoted APD dispersion, wavebreak, and spiral wave drift in in-silico human atrial tissue, and corresponded to clinical electroanatomical maps.

Atrial Rotor Dynamics Under Complex Fractional Order Diffusion

The mechanisms of atrial fibrillation (AF) are a challenging research topic. The rotor hypothesis states that the AF is sustained by a reentrant wave that propagates around an unexcited core. Cardiac tissue heterogeneities, both structural and cellular, play an important role during fibrillatory dynamics, so that the ionic characteristics of the currents, their spatial distribution and their structural heterogeneity determine the meandering of the rotor. Several studies about rotor dynamics implement the standard diffusion equation. However, this mathematical scheme carries some limitations. It assumes the myocardium as a continuous medium, ignoring, therefore, its discrete and heterogeneous aspects. A computational model integrating both, electrical and structural properties could complement experimental and clinical results. A new mathematical model of the action potential propagation, based on complex fractional order derivatives is presented. The complex derivative order appears of considering the myocardium as discrete-scale invariant fractal. The main aim is to study the role of a myocardial, with fractal characteristics, on atrial fibrillatory dynamics. For this purpose, the degree of structural heterogeneity is described through derivatives of complex order γ = α + jβ. A set of variations for γ is tested. The real part α takes values ranging from 1.1 to 2 and the imaginary part β from 0 to 0.28. Under this scheme, the standard diffusion is recovered when α = 2 and β = 0. The effect of γ on the action potential propagation over an atrial strand is investigated. Rotors are generated in a 2D model of atrial tissue under electrical remodeling due to chronic AF. The results show that the degree of structural heterogeneity, given by γ, modulates the electrophysiological properties and the dynamics of rotor-type reentrant mechanisms. The spatial stability of the rotor and the area of its unexcited core are modulated. As the real part decreases and the imaginary part increases, simulating a higher structural heterogeneity, the vulnerable window to reentrant is increased, as the total meandering of the rotor tip. This in silico study suggests that structural heterogeneity, described by means of complex order derivatives, modulates the stability of rotors and that a wide range of rotor dynamics can be generated.

Variability in pulmonary vein electrophysiology and fibrosis determines arrhythmia susceptibility and dynamics

Success rates for catheter ablation of persistent atrial fibrillation patients are currently low; however, there is a subset of patients for whom electrical isolation of the pulmonary veins alone is a successful treatment strategy. It is difficult to identify these patients because there are a multitude of factors affecting arrhythmia susceptibility and maintenance, and the individual contributions of these factors are difficult to determine clinically. We hypothesised that the combination of pulmonary vein (PV) electrophysiology and atrial body fibrosis determine driver location and effectiveness of pulmonary vein isolation (PVI). We used bilayer biatrial computer models based on patient geometries to investigate the effects of PV properties and atrial fibrosis on arrhythmia inducibility, maintenance mechanisms, and the outcome of PVI. Short PV action potential duration (APD) increased arrhythmia susceptibility, while longer PV APD was found to be protective. Arrhythmia inducibility increased with slower conduction velocity (CV) at the LA/PV junction, but not for cases with homogeneous CV changes or slower CV at the distal PV. Phase singularity (PS) density in the PV region for cases with PV fibrosis was increased. Arrhythmia dynamics depend on both PV properties and fibrosis distribution, varying from meandering rotors to PV reentry (in cases with baseline or long APD), to stable rotors at regions of high fibrosis density. Measurement of fibrosis and PV properties may indicate patient specific susceptibility to AF initiation and maintenance. PV PS density before PVI was higher for cases in which AF terminated or converted to a macroreentry; thus, high PV PS density may indicate likelihood of PVI success.

Atrial fibrillation is the most commonly encountered cardiac arrhythmia, affecting a significant portion of the population. Currently, ablation is the most effective treatment but success rates are less than optimal, being 70% one-year post-treatment. There is a large effort to find better ablation strategies to permanently cure the condition. Pulmonary vein isolation by ablation is more or less the standard of care, but many questions remain since pulmonary vein ectopy by itself does not explain all of the clinical successes or failures. We used computer simulations to investigate how electrophysiological properties of the pulmonary veins can affect rotor formation and maintenance in patients suffering from atrial fibrillation. We used complex, biophysical representations of cellular electrophysiology in highly detailed geometries constructed from patient scans. We heterogeneously varied electrophysiological and structural properties to see their effects on rotor initiation and maintenance. Our study suggests a metric for indicating the likelihood of success of pulmonary vein isolation. Thus either measuring this clinically, or running patient-specific simulations to estimate this metric may suggest whether ablation in addition to pulmonary vein isolation should be performed. Our study provides motivation for a retrospective clinical study or experimental study into this metric.

Computational assessment of the functional role of sinoatrial node exit pathways in the human heart

AIM

The human right atrium and sinoatrial node (SAN) anatomy is complex. Optical mapping experiments suggest that the SAN is functionally insulated from atrial tissue except at discrete SAN-atrial electrical junctions called SAN exit pathways, SEPs. Additionally, histological imaging suggests the presence of a secondary pacemaker close to the SAN. We hypothesise that a) an insulating border-SEP anatomical configuration is related to SAN arrhythmia; and b) a secondary pacemaker, the paranodal area, is an alternate pacemaker but accentuates tachycardia. A 3D electro-anatomical computational model was used to test these hypotheses.

METHODS

A detailed 3D human SAN electro-anatomical mathematical model was developed based on our previous anatomical reconstruction. Electrical activity was simulated using tissue specific variants of the Fenton-Karma action potential equations. Simulation experiments were designed to deploy this complex electro-anatomical system to assess the roles of border-SEPs and paranodal area by mimicking experimentally observed SAN arrhythmia. Robust and accurate numerical algorithms were implemented for solving the mono domain reaction-diffusion equation implicitly, calculating 3D filament traces, and computing dominant frequency among other quantitative measurements.

RESULTS

A centre to periphery gradient of increasing diffusion was sufficient to permit initiation of pacemaking at the centre of the 3D SAN. Re-entry within the SAN, micro re-entry, was possible by imposing significant SAN fibrosis in the presence of the insulating border. SEPs promoted the micro re-entry to generate more complex SAN-atrial tachycardia. Simulation of macro re-entry, i.e. re-entry around the SAN, was possible by inclusion of atrial fibrosis in the presence of the insulating border. The border shielded the SAN from atrial tachycardia. However, SAN micro-structure intercellular gap junctional coupling and the paranodal area contributed to prolonged atrial fibrillation. Finally, the micro-structure was found to be sufficient to explain shifts of leading pacemaker site location.

CONCLUSIONS

The simulations establish a relationship between anatomy and SAN electrical function. Microstructure, in the form of intercellular gap junction coupling, was found to regulate SAN function and arrhythmia.

BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.

Optimization of catheter ablation of atrial fibrillation: insights gained from clinically-derived computer models

Atrial fibrillation (AF) is the most common heart rhythm disturbance, and its treatment is an increasing economic burden on the health care system. Despite recent intense clinical, experimental and basic research activity, the treatment of AF with current antiarrhythmic drugs and catheter/surgical therapies remains limited. Radiofrequency catheter ablation (RFCA) is widely used to treat patients with AF. Current clinical ablation strategies are largely based on atrial anatomy and/or substrate detected using different approaches, and they vary from one clinical center to another. The nature of clinical ablation leads to ambiguity regarding the optimal patient personalization of the therapy partly due to the fact that each empirical configuration of ablation lines made in a patient is irreversible during one ablation procedure. To investigate optimized ablation lesion line sets, in silico experimentation is an ideal solution. 3D computer models give us a unique advantage to plan and assess the effectiveness of different ablation strategies before and during RFCA. Reliability of in silico assessment is ensured by inclusion of accurate 3D atrial geometry, realistic fiber orientation, accurate fibrosis distribution and cellular kinetics; however, most of this detailed information in the current computer models is extrapolated from animal models and not from the human heart. The predictive power of computer models will increase as they are validated with human experimental and clinical data. To make the most from a computer model, one needs to develop 3D computer models based on the same functionally and structurally mapped intact human atria with high spatial resolution. The purpose of this review paper is to summarize recent developments in clinically-derived computer models and the clinical insights they provide for catheter ablation.