Eikonal-based initiation of fibrillatory activity in thin-walled cardiac propagation models

Simulation of atrial fibrillation in a non-ohmic propagation model with dynamic gap junctions

Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel-Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100  μm resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.

Personalized Evaluation of Atrial Complexity of Patients Undergoing Atrial Fibrillation Ablation: A Clinical Computational Study

Current clinical guidelines establish Pulmonary Vein (PV) isolation as the indicated treatment for Atrial Fibrillation (AF). However, AF can also be triggered or sustained due to atrial drivers located elsewhere in the atria. We designed a new simulation workflow based on personalized computer simulations to characterize AF complexity of patients undergoing PV ablation, validated with non-invasive electrocardiographic imaging and evaluated at one year after ablation. We included 30 patients using atrial anatomies segmented from MRI and simulated an automata model for the electrical modelling, consisting of three states (resting, excited and refractory). In total, 100 different scenarios were simulated per anatomy varying rotor number and location. The 3 states were calibrated with Koivumaki action potential, entropy maps were obtained from the electrograms and compared with ECGi for each patient to analyze PV isolation outcome. The completion of the workflow indicated that successful AF ablation occurred in patients with rotors mainly located at the PV antrum, while unsuccessful procedures presented greater number of driving sites outside the PV area. The number of rotors attached to the PV was significantly higher in patients with favorable long-term ablation outcome (1-year freedom from AF: 1.61 ± 0.21 vs. AF recurrence: 1.40 ± 0.20; p-value = 0.018). The presented workflow could improve patient stratification for PV ablation by screening the complexity of the atria.

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.

A statistical model of false negative and false positive detection of phase singularities

The complexity of cardiac fibrillation dynamics can be assessed by analyzing the distribution of phase singularities (PSs) observed using mapping systems. Interelectrode distance, however, limits the accuracy of PS detection. To investigate in a theoretical framework the PS false negative and false positive rates in relation to the characteristics of the mapping system and fibrillation dynamics, we propose a statistical model of phase maps with controllable number and locations of PSs. In this model, phase maps are generated from randomly distributed PSs with physiologically-plausible directions of rotation. Noise and distortion of the phase are added. PSs are detected using topological charge contour integrals on regular grids of varying resolutions. Over 100 × 10⁶ realizations of the random field process are used to estimate average false negative and false positive rates using a Monte-Carlo approach. The false detection rates are shown to depend on the average distance between neighboring PSs expressed in units of interelectrode distance, following approximately a power law with exponents in the range of 1.14 to 2 for false negatives and around 2.8 for false positives. In the presence of noise or distortion of phase, false detection rates at high resolution tend to a non-zero noise-dependent lower bound. This model provides an easy-to-implement tool for benchmarking PS detection algorithms over a broad range of configurations with multiple PSs.

Evaluation of a Rapid Anisotropic Model for ECG Simulation

State-of-the-art cardiac electrophysiology models that are able to deliver physiologically motivated activation maps and electrocardiograms (ECGs) can only be solved on high-performance computing architectures. This makes it nearly impossible to adopt such models in clinical practice. ECG imaging tools typically rely on simplified models, but these neglect the anisotropic electric conductivity of the tissue in the forward problem. Moreover, their results are often confined to the heart-torso interface. We propose a forward model that fully accounts for the anisotropic tissue conductivity and produces the standard 12-lead ECG in a few seconds. The activation sequence is approximated with an eikonal model in the 3d myocardium, while the ECG is computed with the lead-field approach. Both solvers were implemented on graphics processing units and massively parallelized. We studied the numerical convergence and scalability of the approach. We also compared the method to the bidomain model in terms of ECGs and activation maps, using a simplified but physiologically motivated geometry and 6 patient-specific anatomies. The proposed methods provided a good approximation of activation maps and ECGs computed with a bidomain model, in only a few seconds. Both solvers scaled very well to high-end hardware. These methods are suitable for use in ECG imaging methods, and may soon become fast enough for use in interactive simulation tools.

Equivalent dipole sources to estimate the influence of extracellular myocardial anisotropy in thin-walled cardiac forward models

The extracellular domain of the heart is anisotropic, which affects volume conduction and therefore body surface potentials. This paper tests the hypothesis that when wall thickness is sufficiently small (such as in the atria), the effect of extracellular anisotropy can be estimated by modifying local dipole current sources. A formula based on the Gabor-Nelson equivalent dipole and on the reciprocity theorem is derived to compute a linear transformation of the dipole sources that approximates in an isotropic volume conductor the far-field of the actual sources in an anisotropic volume conductor. It involves solving three Poisson equation (once for all). The results obtained in an atrial model embedded in a boundary-element torso model suggest that when wall thickness is < 3  mm, simulated P waves are weakly altered by extracellular anisotropy during sinus rhythm: an anisotropy ratio of 4:1 typically reduced the longitudinal component of the dipole sources by < 3%, increased the transverse component by < 5%, and increased the transmural component by ≈ 25% (which may be relevant in case of epicardial-endocardial dissociation). Due to uncertainty on experimental conductivity values, it is proposed that atrial extracellular anisotropy may be neglected when computing P waves.

Anti-arrhythmic strategies for atrial fibrillation: The role of computational modeling in discovery, development, and optimization

Atrial fibrillation (AF), the most common cardiac arrhythmia, is associated with increased risk of cerebrovascular stroke, and with several other pathologies, including heart failure. Current therapies for AF are targeted at reducing risk of stroke (anticoagulation) and tachycardia-induced cardiomyopathy (rate or rhythm control). Rate control, typically achieved by atrioventricular nodal blocking drugs, is often insufficient to alleviate symptoms. Rhythm control approaches include antiarrhythmic drugs, electrical cardioversion, and ablation strategies. Here, we offer several examples of how computational modeling can provide a quantitative framework for integrating multiscale data to: (a) gain insight into multiscale mechanisms of AF; (b) identify and test pharmacological and electrical therapy and interventions; and (c) support clinical decisions. We review how modeling approaches have evolved and contributed to the research pipeline and preclinical development and discuss future directions and challenges in the field.

Lessons from computer simulations of ablation of atrial fibrillation

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

Modeling left and right atrial contributions to the ECG: A dipole-current source approach

This paper presents the mathematical formulation, the numerical validation and several illustrations of a forward-modeling approach based on dipole-current sources to compute the contribution of a part of the heart to the electrocardiogram (ECG). Clinically relevant applications include identifying in the ECG the contributions from the right and the left atrium. In a Courtemanche-based monodomain computer model of the atria and torso, 1000 dipoles distributed throughout the atrial mid-myocardium are found to be sufficient to reproduce body surface potential maps with a relative error <1% during both sinus rhythm and atrial fibrillation. When the boundary element method is applied to solve the forward problem, this approach enables fast offline computation of the ECG contribution of any anatomical part of the atria by applying the principle of superposition to the dipole sources. In the presence of a right-left activation delay (sinus rhythm), pulmonary vein isolation (sinus rhythm) or left-right differences in refractory period (atrial fibrillation), the decomposition of the ECG is shown to help interpret ECG morphology in relation to the atrial substrate. These tools provide a theoretical basis for a deeper understanding of the genesis of the P wave or fibrillatory waves in normal and pathological cases.

Influence of atrial substrate on local capture induced by rapid pacing of atrial fibrillation

AIMS

Preliminary studies showed that the septum area was the only location allowing local capture of both the atria during rapid pacing of atrial fibrillation (AF) from a single site. The present model-based study investigated the influence of atrial substrate on the ability to capture AF when pacing the septum.

METHODS AND RESULTS

Three biophysical models of AF with an identical anatomy from human atria but with different AF substrates were used: (i) AF based on multiple wavelets, (ii) AF based on heterogeneities in vagal activation, (iii) AF based on heterogeneities in repolarization. A fourth anatomical model without Bachmann's bundle (BB) was also implemented. Rapid pacing was applied from the septum at pacing cycle lengths in the range of 50-100% of AF cycle length. Local capture was automatically assessed with 24 pairs of electrodes evenly distributed on the atrial surface. The results were averaged over 16 AF simulations. In the homogeneous substrate, AF capture could reach 80% of the atrial surface. Heterogeneities degraded the ability to capture during AF. In the vagal substrate, the capture tended to be more regular and the degradation of the capture was not directly related to the spatial extent of the heterogeneities. In the third substrate, heterogeneities induced wave anchorings and wavebreaks even in areas close to the pacing site, with a more dramatic effect on AF capture. Finally, BB did not significantly affect the ability to capture.

CONCLUSION

Atrial fibrillation substrate had a significant effect on rapid pacing outcomes. The response to therapeutic pacing may therefore be specific to each patient.

Geometrical measurement of cardiac wavelength in reaction-diffusion models

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

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

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

Fully automated initiation of simulated episodes of atrial arrhythmias

AIMS

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

METHODS AND RESULTS

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

CONCLUSION

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

Reconstruction of phase maps from the configuration of phase singularities in two-dimensional manifolds

Phase singularity analysis provides a quantitative description of spiral wave patterns observed in chemical or biological excitable media. The configuration of phase singularities (locations and directions of rotation) is easily derived from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase map with a given configuration of phase singularities. The existence of such a phase map is guaranteed provided that the phase singularity configuration satisfies a certain constraint associated with the topology of the supporting medium. This paper presents a constructive mathematical approach to numerically solve this problem in the plane and on the sphere as well as in more general geometries relevant to atrial anatomy including holes and a septal wall. This tool can notably be used to create initial conditions with a controllable spiral wave configuration for cardiac propagation models and thus help in the design of computer experiments in atrial electrophysiology.