A three-dimensional human atrial model with fiber orientation. Electrograms and arrhythmic activation patterns relationship

Transition mechanisms from atrial flutter to atrial fibrillation during anti-tachycardia pacing therapy

BACKGROUND

Atrial anti-tachycardia pacing (aATP) has been shown to be effective for the termination of atrial tachyarrhythmias, but its success rate is still not high enough.

OBJECTIVE

The main objective of this study was to investigate the mechanisms of atrial flutter (AFL) termination by aATP and the transition from AFL to atrial fibrillation (AF) during aATP.

METHODS

We developed a multi-scale model of the human atrium based on magnetic resonance images and examined the atrial electrophysiology of AFL during aATP with a ramp protocol.

RESULTS

In successful cases of aATP, paced excitation entered the excitable gap and collided with the leading edge of the reentrant wave front. Furthermore, the excitation propagating in the opposite direction collided with the trailing edge of the reentrant wave to terminate AFL. The second collision was made possible by the distribution of the wave propagation velocity in the atria. The detailed analysis revealed that the slowing of propagation velocity occurred at the exit of the sub-Eustachian isthmus, probably due to source-sink mismatch. During the transition from AFL to AF, the excitation collided with the refractory zone of the preceding wave and broke into multiple wave fronts to induce AF. A similar observation was made for the transition from AF to sinus rhythm. In both cases, the complex anatomy of the atria played an essential role.

CONCLUSION

The complex anatomy of atria plays an essential role in the maintenance of stable AFL and its termination by aATP, which were revealed by the realistic three-dimensional simulation model.

Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

Characterization of airborne particulate matter and its toxic and proarrhythmic effects: A case study in Aburrá Valley, Colombia

Particle matter (PM) is a complex mixture of particles suspended in the air, mainly caused by fuel combustion from vehicles and industry, and has been related to pulmonary and cardiovascular diseases. The Metropolitan Area of Aburrá Valley in Colombia is the second most populous urban agglomeration in the country and the third densest in the world, composed of ten municipalities. Examining the physicochemical properties of PM is crucial in comprehending its composition and its effects on human health, as it varies based on the socioeconomic dynamics specific to each city. This study characterized the PM collected from the north, south, and central zones to evaluate its chemical composition and morphology. Different elements such as silicon, carbon, aluminum, potassium, calcium, sodium, iron, magnesium, and copper and the presence of unburned fuel, motor oil, and silicon fibers were identified. In vitro and in silico studies were conducted to evaluate the toxicity of the PM, and it was found that the PM collected from the central zone had the greatest impact on cell viability and caused DNA damage. The in silico study demonstrated that PM has concentration-dependent proarrhythmic effects, reflected in an action potential duration shortening and an increased number of reentries, which may contribute to the development of cardiac arrhythmias. Overall, the results suggest that the size and chemical composition of ambient PM can induce toxicity and play an important role in the generation of arrhythmias.

Contribution of atrial myofiber architecture to atrial fibrillation

BACKGROUND

The role of fiber orientation on a global chamber level in sustaining atrial fibrillation (AF) is unknown. The goal of this study was to correlate the fiber direction derived from Diffusion Tensor Imaging (DTI) with AF inducibility.

METHODS

Transgenic goats with cardiac-specific overexpression of constitutively active TGF-β1 (n = 14) underwent AF inducibility testing by rapid pacing in the left atrium. We chose a minimum of 10 minutes of sustained AF as a cut-off for AF inducibility. Explanted hearts underwent DTI to determine the fiber direction. Using tractography data, we clustered, visualized, and quantified the fiber helix angles in 8 different regions of the left atrial wall using two reference vectors defined based on anatomical landmarks.

RESULTS

Sustained AF was induced in 7 out of 14 goats. The mean helix fiber angles in 7 out of 8 selected regions were statistically different (P-Value < 0.05) in the AF inducible group. The average fractional anisotropy (FA) and the mean diffusivity (MD) were similar in the two groups with FA of 0.32±0.08 and MD of 8.54±1.72 mm2/s in the non-inducible group and FA of 0.31±0.05 (P-value = 0.90) and MD of 8.68±1.60 mm2/s (P-value = 0.88) in the inducible group.

CONCLUSIONS

DTI based fiber direction shows significant variability across subjects with a significant difference between animals that are AF inducible versus animals that are not inducible. Fiber direction might be contributing to the initiation and sustaining of AF, and its role needs to be investigated further.

Cellular heterogeneity and repolarisation across the atria: an in silico study

Mechanisms of atrial fibrillation and the susceptibility to reentries can be impacted by the repolarization across the atria. Studies into atrial fibrillation ignore cell-to-cell heterogeneity due to electrotonic coupling. Recent studies show that cellular variability may have a larger impact on electrophysiological behaviour than assumed. This paper aims to determine the impact of cellular heterogeneity on the repolarization phase across the AF remodelled atria. Using a population of models approach, 10 anatomically identical atrial models were created to include cellular heterogeneity. Atrial models were compared with an equivalent homogenous model. Activation, APD90, and repolarization maps were used to compare models. The impact of electrotonic coupling in the tissue was determined through a comparison of RMP, APD20, APD50, APD90, and triangulation between regional atrial tissue and the single cell populations. After calibration, cellular heterogeneity does not impact atrial depolarization. Repolarization patterns were significantly impacted by cellular heterogeneity, with the APD90 across the LA increasing due to heterogeneity and the reverse occurring in the RA. Electrotonic coupling caused a reduction in variability across all biomarkers but did not fully remove variability. Electrotonic coupling resulted in an increase in APD20 and APD50, and reduced triangulation compared to isolated cell populations. Heterogeneity also caused a reduction in triangulation compared with regionally homogeneous atria.

A meshless fragile points method for rule-based definition of myocardial fiber orientation

BACKGROUND AND OBJECTIVE

Rule-based methods are commonly used to estimate the arrangement of myocardial fibers by solving the Laplace problem with appropriate Dirichlet boundary conditions. Existing algorithms are using the Finite Element Method (FEM) to solve the Laplace-Dirichlet problem. However, meshless methods are under development for cardiac electrophysiology simulation. The objective of this work is to propose a meshless rule based method for the determination of myocardial fiber arrangement without requiring a mesh discretization as it is required by FEM.

METHODS

The proposed method employs the Fragile Points Method (FPM) for the solution of the Laplace-Dirichlet problem. FPM uses simple discontinuous trial functions and single-point exact integration for linear trial functions that set it as a promising alternative to the Finite Element Method. We derive the FPM formulation of the Laplace-Dirichlet and we estimate ventricular and atrial fiber arrangements according to rules based on histology findings for four different geometries. The obtained fiber arrangements from FPM are compared with the ones obtained from FEM by calculating the angle between the fiber vector fields of the two methods for three different directions (i.e., longitudinal, sheet, transverse).

RESULTS

The fiber arrangements that were generated with FPM were in close agreement with the generated arrangements from FEM for all three directions. The mean angle difference between the FPM and FEM vector fields were lower than 0.030^∘ for the ventricular fiber arrangements and lower than 0.036^∘ for the atrial fiber arrangements.

DISCUSSION

The proposed meshless rule-based method was proven to generate myocardial fiber arrangements with very close agreement with FEM while alleviates the requirement for a mesh of the latter. This is of great value for cardiac electrophysiology solvers that are based on meshless methods since they require a well defined myocardial fiber arrangement to simulate accurately the propagation of electrical signals in the heart. Combining a meshless solution for both the determination of the fibers and the electrical signal propagation can allow for solution that do not require the definition of a mesh. To our knowledge, this work is the first one to propose a meshless rule-based method for myocardial fiber arrangement determination.

Rule-based definition of muscle bundles in patient-specific models of the left atrium

Atrial fibrillation (AF) is the most common arrhythmia encountered clinically, and as the population ages, its prevalence is increasing. Although the CHA2DS2- VASc score is the most used risk-stratification system for stroke risk in AF, it lacks personalization. Patient-specific computer models of the atria can facilitate personalized risk assessment and treatment planning. However, a challenge faced in creating such models is the complexity of the atrial muscle arrangement and its influence on the atrial fiber architecture. This work proposes a semi-automated rule-based algorithm to generate the local fiber orientation in the left atrium (LA). We use the solutions of several harmonic equations to decompose the LA anatomy into subregions. Solution gradients define a two-layer fiber field in each subregion. The robustness of our approach is demonstrated by recreating the fiber orientation on nine models of the LA obtained from AF patients who underwent WATCHMAN device implantation. This cohort of patients encompasses a variety of morphology variants of the left atrium, both in terms of the left atrial appendages (LAAs) and the number of pulmonary veins (PVs). We test the fiber construction algorithm by performing electrophysiology (EP) simulations. Furthermore, this study is the first to compare its results with other rule-based algorithms for the LA fiber architecture definition available in the literature. This analysis suggests that a multi-layer fiber architecture is important to capture complex electrical activation patterns. A notable advantage of our approach is the ability to reconstruct the main LA fiber bundles in a variety of morphologies while solving for a small number of harmonic fields, leading to a comparatively straightforward and reproducible approach.

In-silico drug trials for precision medicine in atrial fibrillation: From ionic mechanisms to electrocardiogram-based predictions in structurally-healthy human atria

Atrial fibrillation (AF) inducibility, sustainability and response to pharmacological treatment of individual patients are expected to be determined by their ionic current properties, especially in structurally-healthy atria. Mechanisms underlying AF and optimal cardioversion are however still unclear. In this study, in-silico drug trials were conducted using a population of human structurally-healthy atria models to 1) identify key ionic current properties determining AF inducibility, maintenance and pharmacological cardioversion, and 2) compare the prognostic value for predicting individual AF cardioversion of ionic current properties and electrocardiogram (ECG) metrics. In the population of structurally-healthy atria, 477 AF episodes were induced in ionic current profiles with both steep action potential duration (APD) restitution (eliciting APD alternans), and high excitability (enabling propagation at fast rates that transformed alternans into discordant). High excitability also favored 211 sustained AF episodes, so its decrease, through prolonged refractoriness, explained pharmacological cardioversion. In-silico trials over 200 AF episodes, 100 ionic profiles and 10 antiarrhythmic compounds were consistent with previous clinical trials, and identified optimal treatments for individual electrophysiological properties of the atria. Algorithms trained on 211 simulated AF episodes exhibited >70% accuracy in predictions of cardioversion for individual treatments using either ionic current profiles or ECG metrics. In structurally-healthy atria, AF inducibility and sustainability are enabled by discordant alternans, under high excitability and steep restitution conditions. Successful pharmacological cardioversion is predicted with 70% accuracy from either ionic or ECG properties, and it is optimal for treatments maximizing refractoriness (thus reducing excitability) for the given ionic current profile of the atria.

Atrial fibrosis identification with unipolar electrogram eigenvalue distribution analysis in multi-electrode arrays

Abstract

Atrial fibrosis plays a key role in the initiation and progression of atrial fibrillation (AF). Atrial fibrosis is typically identified by a peak-to-peak amplitude of bipolar electrograms (b-EGMs) lower than 0.5 mV, which may be considered as ablation targets. Nevertheless, this approach disregards signal spatiotemporal information and b-EGM sensitivity to catheter orientation. To overcome these limitations, we propose the dominant-to-remaining eigenvalue dominance ratio (EIGDR) of unipolar electrograms (u-EGMs) within neighbor electrode cliques as a waveform dispersion measure, hypothesizing that it is correlated with the presence of fibrosis. A simulated 2D tissue with a fibrosis patch was used for validation. We computed EIGDR maps from both original and time-aligned u-EGMs, denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}$$\end{document}R and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R}^{\mathcal{A}}$$\end{document}RA, respectively, also mapping the gain in eigenvalue concentration obtained by the alignment, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \mathcal{R}^{\mathcal{A}}$$\end{document}ΔRA. The performance of each map in detecting fibrosis was evaluated in scenarios including noise and variable electrode-tissue distance. Best results were achieved by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R}^{\mathcal{A}}$$\end{document}RA, reaching 94% detection accuracy, versus the 86% of b-EGMs voltage maps. The proposed strategy was also tested in real u-EGMs from fibrotic and non-fibrotic areas over 3D electroanatomical maps, supporting the ability of the EIGDRs as fibrosis markers, encouraging further studies to confirm their translation to clinical settings.

Graphical Abstract

Upper panels: map of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}^{\mathcal {A}}$$\end{document}RA from 3×3 cliques for Ψ= 0^∘ and bipolar voltage map V^b-m, performed assuming a variable electrode-to-tissue distance and noisy u-EGMs (noise level σ_v = 46.4 μV ). Lower panels: detected fibrotic areas (brown), using the thresholds that maximize detection accuracy of each map

The Effects of Fibrotic Cell Type and Its Density on Atrial Fibrillation Dynamics: An In Silico Study

Remodeling in atrial fibrillation (AF) underlines the electrical and structural changes in the atria, where fibrosis is a hallmark of arrhythmogenic structural alterations. Fibrosis is an important feature of the AF substrate and can lead to abnormal conduction and, consequently, mechanical dysfunction. The fibrotic process comprises the presence of fibrotic cells, including fibroblasts, myofibroblasts and fibrocytes, which play an important role during fibrillatory dynamics. This work assesses the effect of the diffuse fibrosis density and the intermingled presence of the three types of fibrotic cells on the dynamics of persistent AF. For this purpose, the three fibrotic cells were electrically coupled to cardiomyocytes in a 3D realistic model of human atria. Low (6.25%) and high (25%) fibrosis densities were implemented in the left atrium according to a diffuse fibrosis representation. We analyze the action potential duration, conduction velocity and fibrillatory conduction patterns. Additionally, frequency analysis was performed in 50 virtual electrograms. The tested fibrosis configurations generated a significant conduction velocity reduction, where the larger effect was observed at high fibrosis density (up to 82% reduction in the fibrocytes configuration). Increasing the fibrosis density intensifies the vulnerability to multiple re-entries, zigzag propagation, and chaotic activity in the fibrillatory conduction. The most complex propagation patterns were observed at high fibrosis densities and the fibrocytes are the cells with the largest proarrhythmic effect. Left-to-right dominant frequency gradients can be observed for all fibrosis configurations, where the fibrocytes configuration at high density generates the most significant gradients (up to 4.5 Hz). These results suggest the important role of different fibrotic cell types and their density in diffuse fibrosis on the chaotic propagation patterns during persistent AF.

Atrial proarrhythmic effect of lead as one of the PM10 metal components of air pollution. An in-silico study

Particulate matter (PM) is considered the most severe environmental pollution problem due to its serious effects on human health associated with an increased risk of cardiovascular morbidity and mortality. In this work, a physicochemical characterization of PM10 from the city of Medellin was developed. The results evince that lead (Pb) is one of the most abundant elements since it is present in all analyzed samples. Therefore, Pb was chosen to perform an in-silico study to assess its effects on atrial arrhythmias generation. For this purpose, we developed a model representing the Pb2+ blocking effect on the L-type calcium channel. This formulation was incorporated in a human atrial cell mathematical model and in 2D and 3D models of human atria. The simulations showed a proarrhythmic effect at high Pb2+ concentrations, through shortening of action potential duration inducing the generation of reentrant activity and atrial flutter. The results contribute to the knowledge about the cardiac physiopathological processes, triggered by lead as one of the main PM10 metal components of air pollution, that yields the generation of arrhythmias.

Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks. In particular, two very important questions are: 1) What determines the potential of a wave break to initiate re-entry? and 2) How do these breaks evolve such that the system is able to maintain spatiotemporally chaotic electrical activity? Here we approach these questions numerically using optogenetics in an in silico model of human atrial tissue that has undergone chronic atrial fibrillation (cAF) remodelling. In the lesser studied sub-threshold illumination régime, we discover a new mechanism of wave break initiation in cardiac tissue that occurs for gentle slopes of the restitution characteristics. This mechanism involves the creation of conduction blocks through a combination of wavefront-waveback interaction, reshaping of the wave profile and heterogeneous recovery from the excitation of the spatially extended medium, leading to the creation of re-excitable windows for sustained re-entry. This finding is an important contribution to cardiac arrhythmia research as it identifies scenarios in which low-energy perturbations to cardiac rhythm can be potentially life-threatening.

Characterization of Atrial Propagation Patterns and Fibrotic Substrate With a Modified Omnipolar Electrogram Strategy in Multi-Electrode Arrays

Introduction: The omnipolar electrogram method was recently proposed to try to generate orientation-independent electrograms. It estimates the electric field from the bipolar electrograms of a clique, under the assumption of locally plane and homogeneous propagation. The local electric field evolution over time describes a loop trajectory from which omnipolar signals in the propagation direction, substrate and propagation features, are derived. In this work, we propose substrate and conduction velocity mapping modalities based on a modified version of the omnipolar electrogram method, which aims to reduce orientation-dependent residual components in the standard approach. Methods: A simulated electrical propagation in 2D, with a tissue including a circular patch of diffuse fibrosis, was used for validation. Unipolar electrograms were calculated in a multi-electrode array, also deriving bipolar electrograms along the two main directions of the grid. Simulated bipolar electrograms were also contaminated with real noise, to assess the robustness of the mapping strategies against noise. The performance of the maps in identifying fibrosis and in reproducing unipolar reference voltage maps was evaluated. Bipolar voltage maps were also considered for performance comparison. Results: Results show that the modified omnipolar mapping strategies are more accurate and robust against noise than bipolar and standard omnipolar maps in fibrosis detection (accuracies higher than 85 vs. 80% and 70%, respectively). They present better correlation with unipolar reference voltage maps than bipolar and original omnipolar maps (Pearson's correlations higher than 0.75 vs. 0.60 and 0.70, respectively). Conclusion: The modified omnipolar method improves fibrosis detection, characterization of substrate and propagation, also reducing the residual sensitivity to directionality over the standard approach and improving robustness against noise. Nevertheless, studies with real electrograms will elucidate its impact in catheter ablation interventions.

Electrophysiological Characterization of Human Atria: The Understated Role of Temperature

Ambient temperature has a profound influence on cellular electrophysiology through direct control over the gating mechanisms of different ion channels. In the heart, low temperature is known to favor prolongation of the action potential. However, not much is known about the influence of temperature on other important characterization parameters such as the resting membrane potential (RMP), excitability, morphology and characteristics of the action potential (AP), restitution properties, conduction velocity (CV) of signal propagation, etc. Here we present the first, detailed, systematic in silico study of the electrophysiological characterization of cardiomyocytes from different regions of the normal human atria, based on the effects of ambient temperature (5-50°C). We observe that RMP decreases with increasing temperature. At ~ 48°C, the cells lose their excitability. Our studies show that different parts of the atria react differently to the same changes in temperature. In tissue simulations a drop in temperature correlated positively with a decrease in CV, but the decrease was region-dependent, as expected. In this article we show how this heterogeneous response can provide an explanation for the development of a proarrhythmic substrate during mild hypothermia. We use the above concept to propose a treatment strategy for atrial fibrillation that involves severe hypothermia in specific regions of the heart for a duration of only ~ 200 ms.

Classification of sinus rhythm single potential morphology in patients with mitral valve disease

Aims

The morphology of unipolar single potentials (SPs) contains information on intra-atrial conduction disorders and possibly the substrate underlying atrial fibrillation (AF). This study examined the impact of AF episodes on features of SP morphology during sinus rhythm (SR) in patients with mitral valve disease.

Methods and results

Intraoperative epicardial mapping (interelectrode distance 2 mm) of the right and left atrium (RA, LA), Bachmann’s bundle (BB), and pulmonary vein area (PVA) was performed in 67 patients (27 male, 67 ± 11 years) with or without a history of paroxysmal AF (PAF). Unipolar SPs were classified according to their differences in relative R- and S-wave amplitude ratios. A clear predominance of S-waves was observed at BB and the RA in both the no AF and PAF groups (BB 88.8% vs. 85.9%, RA 92.1% vs. 85.1%, respectively). Potential voltages at the RA, BB, and PVA were significantly lower in the PAF group (P < 0.001 for each) and were mainly determined by the size of the S-waves amplitudes. The largest difference in S-wave amplitudes was found at BB; the S-wave amplitude was lower in the PAF group [4.08 (2.45–6.13) mV vs. 2.94 (1.40–4.75) mV; P < 0.001]. In addition, conduction velocity (CV) at BB was lower as well [0.97 (0.70–1.21) m/s vs. 0.89 (0.62–1.16) m/s, P < 0.001].

Conclusion

Though excitation of the atria during SR is heterogeneously disrupted, a history of AF is characterized by decreased SP amplitudes at BB due to loss of S-wave amplitudes and decreased CV. This suggests that SP morphology could provide additional information on wavefront propagation.

Immuno-Electrophysiological Mechanisms of Functional Electrical Connections Between Recipient and Donor Heart in Patients With Orthotopic Heart Transplantation Presenting With Atrial Arrhythmias

[Figure: see text].

Cardiac computational modelling

Cardiovascular diseases currently have a major social and economic impact, constituting one of the leading causes of mortality and morbidity. Personalized computational models of the heart are demonstrating their usefulness both to help understand the mechanisms underlying cardiac disease, and to optimize their treatment and predict the patient's response. Within this framework, the Spanish Research Network for Cardiac Computational Modelling (VHeart-SN) has been launched. The general objective of the VHeart-SN network is the development of an integrated, modular and multiscale multiphysical computational model of the heart. This general objective is addressed through the following specific objectives: a) to integrate the different numerical methods and models taking into account the specificity of patients; b) to assist in advancing knowledge of the mechanisms associated with cardiac and vascular diseases; and c) to support the application of different personalized therapies. This article presents the current state of cardiac computational modelling and different scientific works conducted by the members of the network to gain greater understanding of the characteristics and usefulness of these models.

Advances in the Fabrication of Biomaterials for Gradient Tissue Engineering

Natural tissues and organs exhibit an array of spatial gradients, from the polarized neural tube during embryonic development to the osteochondral interface present at articulating joints. The strong structure-function relationships in these heterogeneous tissues have sparked intensive research into the development of methods that can replicate physiological gradients in engineered tissues. In this Review, we consider different gradients present in natural tissues and discuss their critical importance in functional tissue engineering. Using this basis, we consolidate the existing fabrication methods into four categories: additive manufacturing, component redistribution, controlled phase changes, and postmodification. We have illustrated this with recent examples, highlighted prominent trends in the field, and outlined a set of criteria and perspectives for gradient fabrication.

Sensitivity and Uncertainty Analysis of Two Human Atrial Cardiac Cell Models Using Gaussian Process Emulators

Biophysically detailed cardiac cell models reconstruct the action potential and calcium dynamics of cardiac myocytes. They aim to capture the biophysics of current flow through ion channels, pumps, and exchangers in the cell membrane, and are highly detailed. However, the relationship between model parameters and model outputs is difficult to establish because the models are both complex and non-linear. The consequences of uncertainty and variability in model parameters are therefore difficult to determine without undertaking large numbers of model evaluations. The aim of the present study was to demonstrate how sensitivity and uncertainty analysis using Gaussian process emulators can be used for a systematic and quantitive analysis of biophysically detailed cardiac cell models. We selected the Courtemanche and Maleckar models of the human atrial action potential for analysis because these models describe a similar set of currents, with different formulations. In our approach Gaussian processes emulate the main features of the action potential and calcium transient. The emulators were trained with a set of design data comprising samples from parameter space and corresponding model outputs, initially obtained from 300 model evaluations. Variance based sensitivity indices were calculated using the emulators, and first order and total effect indices were calculated for each combination of parameter and output. The differences between the first order and total effect indices indicated that the effect of interactions between parameters was small. A second set of emulators were then trained using a new set of design data with a subset of the model parameters with a sensitivity index of more than 0.1 (10%). This second stage analysis enabled comparison of mechanisms in the two models. The second stage sensitivity indices enabled the relationship between the L-type Ca 2+ current and the action potential plateau to be quantified in each model. Our quantitative analysis predicted that changes in maximum conductance of the ultra-rapid K + channel I Kur would have opposite effects on action potential duration in the two models, and this prediction was confirmed by additional simulations. This study has demonstrated that Gaussian process emulators are an effective tool for sensitivity and uncertainty analysis of biophysically detailed cardiac cell models.

The Antimalarial Chloroquine Reduces the Burden of Persistent Atrial Fibrillation

In clinical practice, reducing the burden of persistent atrial fibrillation by pharmacological means is challenging. We explored if blocking the background and the acetylcholine-activated inward rectifier potassium currents (I_K1 and I_KACh) could be antiarrhythmic in persistent atrial fibrillation. We thus tested the hypothesis that blocking I_K1 and I_KACh with chloroquine decreases the burden of persistent atrial fibrillation. We used patch clamp to determine the IC₅₀ of I_K1 and I_KACh block by chloroquine and molecular modeling to simulate the interaction between chloroquine and Kir2.1 and Kir3.1, the molecular correlates of I_K1 and I_KACh. We then tested, as a proof of concept, if oral chloroquine administration to a patient with persistent atrial fibrillation can decrease the arrhythmia burden. We also simulated the effects of chloroquine in a 3D model of human atria with persistent atrial fibrillation. In patch clamp the IC₅₀ of I_K1 block by chloroquine was similar to that of I_KACh. A 14-day regimen of oral chloroquine significantly decreased the burden of persistent atrial fibrillation in a patient. Mathematical simulations of persistent atrial fibrillation in a 3D model of human atria suggested that chloroquine prolonged the action potential duration, leading to failure of reentrant excitation, and the subsequent termination of the arrhythmia. The combined block of I_K1 and I_KACh can be a targeted therapeutic strategy for persistent atrial fibrillation.

Identifying Potential Re-Entrant Circuit Locations From Atrial Fibre Maps

Re-entrant circuits have been identified as potential drivers of atrial fibrillation (AF). In this paper, we develop a novel computational framework for finding the locations of re-entrant circuits from high resolution fibre orientation data. The technique follows a statistical approach whereby we generate continuous fibre tracts across the tissue and couple adjacent fibres stochastically if they are within a given distance of each other. By varying the connection distance, we identify which regions are most susceptible to forming re-entrant circuits if muscle fibres are uncoupled, through the action of fibrosis or otherwise. Our results highlight the sleeves of the pulmonary veins, the posterior left atrium and the left atrial appendage as the regions most susceptible to re-entrant circuit formation. This is consistent with known risk locations in clinical AF. If the model can be personalised for individual patients undergoing ablation, future versions may be able to suggest suitable ablation targets.

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.

The effect of complex intramural microstructure caused by structural remodeling on the stability of atrial fibrillation: Insights from a three-dimensional multi-layer modeling study

BACKGROUND

Recent researches have suggested that the complex three-dimensional structures caused by structural remodeling play a key role in atrial fibrillation (AF) substrates. Here we aimed to investigate this hypothesis using a multi-layer model representing intramural microstructural features.

METHODS

The proposed multi-layer model was composed of the endocardium, connection wall, and epicardium. In the connection wall, intramural fibrosis was simulated using fibrotic patches randomly scattered in the myocardial tissue of fibrotic layers, while endo-epicardial dissociation was simulated using myocardial patches randomly scattered in the fibrotic tissue of isolation layers. Multiple simulation groups were generated to quantitatively analyze the effects of endo-epicardial dissociation and intramural fibrosis on AF stability, including a stochastic group, interrelated groups, fibrosis-degree-controlled groups, and dissociation-degree-controlled groups.

RESULTS

1. Stable intramural re-entries were observed to move along complete re-entrant circuits inside the transmural wall in four of 65 simulations in the stochastic group. 2. About 21 of 23 stable simulations in the stochastic group were distributed in the areas with high endo-epicardial dissociation and intramural fibrosis. 3. The difference between fibrosis-degree-controlled groups and dissociation-degree-controlled groups suggested that some distributions of connection areas may affect AF episodes despite low intramural fibrosis and endo-epicardial dissociation. 4. The overview of tracking phase singularities revealed that endo-epicardial dissociation played a visible role in AF substrates.

CONCLUSION

The complex intramural microstructure is positively correlated with critical components of AF maintenance mechanisms. The occurrence of intramural re-entry further indicates the complexity of AF wave-dynamics.

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.

Personalized computational modeling of left atrial geometry and transmural myofiber architecture

Atrial fibrillation (AF) is a supraventricular tachyarrhythmia characterized by complete absence of coordinated atrial contraction and is associated with an increased morbidity and mortality. Personalized computational modeling provides a novel framework for integrating and interpreting the role of atrial electrophysiology (EP) including the underlying anatomy and microstructure in the development and sustenance of AF. Coronary computed tomography angiography data were segmented using a statistics-based approach and the smoothed voxel representations were discretized into high-resolution tetrahedral finite element (FE) meshes. To estimate the complex left atrial myofiber architecture, individual fiber fields were generated according to morphological data on the endo- and epicardial surfaces based on local solutions of Laplace’s equation and transmurally interpolated to tetrahedral elements. The influence of variable transmural microstructures was quantified through EP simulations on 3 patients using 5 different fiber interpolation functions. Personalized geometrical models included the heterogeneous thickness distribution of the left atrial myocardium and subsequent discretization led to high-fidelity tetrahedral FE meshes. The novel algorithm for automated incorporation of the left atrial fiber architecture provided a realistic estimate of the atrial microstructure and was able to qualitatively capture all important fiber bundles. Consistent maximum local activation times were predicted in EP simulations using individual transmural fiber interpolation functions for each patient suggesting a negligible effect of the transmural myofiber architecture on EP. The established modeling pipeline provides a robust framework for the rapid development of personalized model cohorts accounting for detailed anatomy and microstructure and facilitates simulations of atrial EP.

Factors affecting basket catheter detection of real and phantom rotors in the atria: A computational study

Anatomically based procedures to ablate atrial fibrillation (AF) are often successful in terminating paroxysmal AF. However, the ability to terminate persistent AF remains disappointing. New mechanistic approaches use multiple-electrode basket catheter mapping to localize and target AF drivers in the form of rotors but significant concerns remain about their accuracy. We aimed to evaluate how electrode-endocardium distance, far-field sources and inter-electrode distance affect the accuracy of localizing rotors. Sustained rotor activation of the atria was simulated numerically and mapped using a virtual basket catheter with varying electrode densities placed at different positions within the atrial cavity. Unipolar electrograms were calculated on the entire endocardial surface and at each of the electrodes. Rotors were tracked on the interpolated basket phase maps and compared with the respective atrial voltage and endocardial phase maps, which served as references. Rotor detection by the basket maps varied between 35-94% of the simulation time, depending on the basket's position and the electrode-to-endocardial wall distance. However, two different types of phantom rotors appeared also on the basket maps. The first type was due to the far-field sources and the second type was due to interpolation between the electrodes; increasing electrode density decreased the incidence of the second but not the first type of phantom rotors. In the simulations study, basket catheter-based phase mapping detected rotors even when the basket was not in full contact with the endocardial wall, but always generated a number of phantom rotors in the presence of only a single real rotor, which would be the desired ablation target. Phantom rotors may mislead and contribute to failure in AF ablation procedures.

Influence of atrial contraction dynamics on cardiac function

In recent years, there has been a move from monoventricular or biventricular models of the heart, to more complex models that incorporate the electromechanical function in all 4 chambers. However, the biophysical foundation is still underdeveloped, with most work in atrial cellular models having focused on electrophysiological properties. Here, we present a biophysical model of human atrial contraction at body temperature and use it to study the effects of atrial contraction on whole organ function and a study of the effects of remodelling due to atrial fibrillation on atrial and ventricular function.

Non-invasive localization of atrial ectopic beats by using simulated body surface P-wave integral maps

Non-invasive localization of continuous atrial ectopic beats remains a cornerstone for the treatment of atrial arrhythmias. The lack of accurate tools to guide electrophysiologists leads to an increase in the recurrence rate of ablation procedures. Existing approaches are based on the analysis of the P-waves main characteristics and the forward body surface potential maps (BSPMs) or on the inverse estimation of the electric activity of the heart from those BSPMs. These methods have not provided an efficient and systematic tool to localize ectopic triggers. In this work, we propose the use of machine learning techniques to spatially cluster and classify ectopic atrial foci into clearly differentiated atrial regions by using the body surface P-wave integral map (BSPiM) as a biomarker. Our simulated results show that ectopic foci with similar BSPiM naturally cluster into differentiated non-intersected atrial regions and that new patterns could be correctly classified with an accuracy of 97% when considering 2 clusters and 96% for 4 clusters. Our results also suggest that an increase in the number of clusters is feasible at the cost of decreasing accuracy.

Arrhythmia Mechanism and Scaling Effect on the Spectral Properties of Electroanatomical Maps With Manifold Harmonics

INTRODUCTION

Spatial and temporal processing of intracardiac electrograms provides relevant information to support the arrhythmia ablation during electrophysiological studies. Current cardiac navigation systems (CNS) and electrocardiographic imaging (ECGI) build detailed 3-D electroanatomical maps (EAM), which represent the spatial anatomical distribution of bioelectrical features, such as activation time or voltage.

OBJECTIVE

We present a principled methodology for spectral analysis of both EAM geometry and bioelectrical feature in CNS or ECGI, including their spectral representation, cutoff frequency, or spatial sampling rate (SSR).

METHODS

Existing manifold harmonic techniques for spectral mesh analysis are adapted to account for a fourth dimension, corresponding to the EAM bioelectrical feature. Appropriate scaling is required to address different magnitudes and units.

RESULTS

With our approach, simulated and real EAM showed strong SSR dependence on both the arrhythmia mechanism and the cardiac anatomical shape. For instance, high frequencies increased significantly the SSR because of the "early-meets-late" in flutter EAM, compared with the sinus rhythm. Besides, higher frequency components were obtained for the left atrium (more complex anatomy) than for the right atrium in sinus rhythm.

CONCLUSION

The proposed manifold harmonics methodology opens the field toward new signal processing tools for principled EAM spatiofeature analysis in CNS and ECGI, and to an improved knowledge on arrhythmia mechanisms.

Atrial Fibrillation Dynamics and Ionic Block Effects in Six Heterogeneous Human 3D Virtual Atria with Distinct Repolarization Dynamics

Atrial fibrillation (AF) usually manifests as reentrant circuits propagating through the whole atria creating chaotic activation patterns. Little is yet known about how differences in electrophysiological and ionic properties between patients modulate reentrant patterns in AF. The goal of this study is to quantify how variability in action potential duration (APD) at different stages of repolarization determines AF dynamics and their modulation by ionic block using a set of virtual whole-atria human models. Six human whole-atria models are constructed based on the same anatomical structure and fiber orientation, but with different electrophysiological phenotypes. Membrane kinetics for each whole-atria model are selected with distinct APD characteristics at 20, 50, and 90% repolarization, from an experimentally calibrated population of human atrial action potential models, including AF remodeling and acetylcholine parasympathetic effects. Our simulations show that in all whole-atria models, reentrant circuits tend to organize around the pulmonary veins and the right atrial appendage, thus leading to higher dominant frequency (DF) and more organized activation in the left atrium than in the right atrium. Differences in APD in all phases of repolarization (not only APD₉₀) yielded quantitative differences in fibrillation patterns with long APD associated with slower and more regular dynamics. Long APD₅₀ and APD₂₀ were associated with increased interatrial conduction block and interatrial differences in DF and organization index, creating reentry instability and self-termination in some cases. Specific inhibitions of I_K1, I_NaK, or I_Na reduce DF and organization of the arrhythmia by enlarging wave meandering, reducing the number of secondary wavelets, and promoting interatrial block in all six virtual patients, especially for the phenotypes with short APD at 20, 50, and/or 90% repolarization. This suggests that therapies aiming at prolonging the early phase of repolarization might constitute effective antiarrhythmic strategies for the pharmacological management of AF. In summary, simulations report significant differences in atrial fibrillatory dynamics resulting from differences in APD at all phases of repolarization.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

Reentry and Ectopic Pacemakers Emerge in a Three-Dimensional Model for a Slab of Cardiac Tissue with Diffuse Microfibrosis near the Percolation Threshold

Arrhythmias in cardiac tissue are generally associated with irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. Recently, it was shown in simulations of two-dimensional (2D) discrete models of cardiac tissue that a wave crossing a fibrotic, heterogeneous region may produce reentry and transient or persistent ectopic activity provided the fraction of conducting connections is just above the percolation threshold. Here, we investigate the occurrence of these phenomena in three-dimensions by simulations of a discrete model representing a thin slab of cardiac tissue. This is motivated (i) by the necessity to study the relevance and properties of the percolation-related mechanism for the emergence of microreentries in three dimensions and (ii) by the fact that atrial tissue is quite thin in comparison with ventricular tissue. Here, we simplify the model by neglecting details of tissue anatomy, e. g. geometries of atria or ventricles and the anisotropy in the conductivity. Hence, our modeling study is confined to the investigation of the effect of the tissue thickness as well as to the comparison of the dynamics of electrical excitation in a 2D layer with the one in a 3D slab. Our results indicate a strong and non-trivial effect of the thickness even for thin tissue slabs on the probability of microreentries and ectopic beat generation. The strong correlation of the occurrence of microreentry with the percolation threshold reported earlier in 2D layers persists in 3D slabs. Finally, a qualitative agreement of 3D simulated electrograms in the fibrotic region with the experimentally observed complex fractional atrial electrograms (CFAE) as well as strong difference between simulated electrograms in 2D and 3D were found for the cases where reentry and ectopic activity were triggered by the micro-fibrotic region.

Mechanisms of arrhythmogenesis related to calcium-driven alternans in a model of human atrial fibrillation

The occurrence of atrial fibrillation (AF) is associated with progressive changes in the calcium handling system of atrial myocytes. Calcium cycling instability has been implicated as an underlying mechanism of electrical alternans observed in patients who experience AF. However, the extent to which calcium-induced alternation of electrical activity in the atria contributes to arrhythmogenesis is unknown. In this study, we investigated the effects of calcium-driven alternans (CDA) on arrhythmia susceptibility in a biophysically detailed, 3D computer model of the human atria representing electrical and structural remodeling secondary to chronic AF. We found that elevated propensity to CDA rendered the atria vulnerable to ectopy-induced arrhythmia. It also increased the complexity and persistence of arrhythmias induced by fast pacing, with unstable scroll waves meandering and frequently breaking up to produce multiple wavelets. Our results suggest that calcium-induced electrical instability may increase arrhythmia vulnerability and promote increasing disorganization of arrhythmias in the chronic AF-remodeled atria, thus playing an important role in the progression of the disease.

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.

Computational simulations of the effects of the G229D KCNQ1 mutation on human atrial fibrillation

Atrial fibrillation (AF) is related to mutations at the genetic level. This includes mutations in genes that encode KCNQ1, a subunit of the I Ks channel. Here, we investigate the mechanism of gain-of-function in I Ks towards the occurrence of AF. We used the Courtemanche-Ramirez-Nattel (CRN) human atrial cell model (Am J Physiol Heart Circ Physiol 275:H301-H321, 1998) and applied the modification proposed by Hasegawa et al. (Heart Rhythm 11:67-75, 2014) to fit the behavior of I Ks due to the G229D mutation in KCNQ1 under a heterozygous mutant form. This was incorporated into two-(2D) and three-dimensional (3D) tissue models, where the mutation sustained a reentrant wave. However, under the wild-type condition, the reentrant wave terminated before the end of our simulations (in 2D, the spiral wave terminated before 10 s, while in 3D, the spiral wave terminated before 13 s). Sustained reentry under the mutation conditions also resulted in a spiral wave breakup in the 3D model, which was sustained until the end of the simulation (20 s), indicating AF.

Fractionated electrograms and rotors detection in chronic atrial fibrillation using model-based clustering

The identification of atrial fibrillation (AF) substrates is needed to improve ablation therapy guided by electrograms, although mechanisms that sustain AF are not fully understood. Detection of complex fractionated atrial electrograms (CFAE) is used for this purpose. Nonetheless, efficacy of this method is inadequate in the case of chronic AF. Recent hypothesis proposes the rotors as fibrillatory substrate. Novel approaches seek to relate CFAE with rotor; nevertheless, such methods are not able to identify the associated substrate. Furthermore, the patterns that characterize CFAE generated by rotors remain unknown. Thus, tracking of rotors is an unsolved issue. In this paper, we propose a non-supervised method to find patterns associated with fibrillatory substrates in chronic AF. We extracted two features based on local activation wave detection and one feature based on non-linear dynamics. Gaussian mixture model-based clustering was used to discriminate CFAE patterns. Resulting clusters are visualized in an electroanatomic map. We assessed the proposed method in a real database labeled according to the level of fractionation and in a simulated episode of chronic AF in which a rotor was detected. Our results indicate that the method proposed can separate different levels of fractionation in CFAE, and provide evidence that clustering can be used to locate the vortex of the rotors. Provided approach can support ablation therapy procedures by means of CFAE patterns discrimination.

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

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

Detailed Anatomical and Electrophysiological Models of Human Atria and Torso for the Simulation of Atrial Activation

Atrial arrhythmias, and specifically atrial fibrillation (AF), induce rapid and irregular activation patterns that appear on the torso surface as abnormal P-waves in electrocardiograms and body surface potential maps (BSPM). In recent years both P-waves and the BSPM have been used to identify the mechanisms underlying AF, such as localizing ectopic foci or high-frequency rotors. However, the relationship between the activation of the different areas of the atria and the characteristics of the BSPM and P-wave signals are still far from being completely understood. In this work we developed a multi-scale framework, which combines a highly-detailed 3D atrial model and a torso model to study the relationship between atrial activation and surface signals in sinus rhythm. Using this multi scale model, it was revealed that the best places for recording P-waves are the frontal upper right and the frontal and rear left quadrants of the torso. Our results also suggest that only nine regions (of the twenty-one structures in which the atrial surface was divided) make a significant contribution to the BSPM and determine the main P-wave characteristics.

Simulation of Ectopic Pacemakers in the Heart: Multiple Ectopic Beats Generated by Reentry inside Fibrotic Regions

The inclusion of nonconducting media, mimicking cardiac fibrosis, in two models of cardiac tissue produces the formation of ectopic beats. The fraction of nonconducting media in comparison with the fraction of healthy myocytes and the topological distribution of cells determines the probability of ectopic beat generation. First, a detailed subcellular microscopic model that accounts for the microstructure of the cardiac tissue is constructed and employed for the numerical simulation of action potential propagation. Next, an equivalent discrete model is implemented, which permits a faster integration of the equations. This discrete model is a simplified version of the microscopic model that maintains the distribution of connections between cells. Both models produce similar results when describing action potential propagation in homogeneous tissue; however, they slightly differ in the generation of ectopic beats in heterogeneous tissue. Nevertheless, both models present the generation of reentry inside fibrotic tissues. This kind of reentry restricted to microfibrosis regions can result in the formation of ectopic pacemakers, that is, regions that will generate a series of ectopic stimulus at a fast pacing rate. In turn, such activity has been related to trigger fibrillation in the atria and in the ventricles in clinical and animal studies.

Assessing the atrial electromechanical coupling during atrial focal tachycardia, flutter, and fibrillation using electromechanical wave imaging in humans

Minimally-invasive treatments of cardiac arrhythmias such as radio-frequency ablation are gradually gaining importance in clinical practice but still lack a noninvasive imaging modality which provides insight into the source or focus of an arrhythmia. Cardiac deformations imaged at high temporal and spatial resolution can be used to elucidate the electrical activation sequence in normal and paced human subjects non-invasively and could potentially aid to better plan and monitor ablation-based arrhythmia treatments. In this study, a novel ultrasound-based method is presented that can be used to quantitatively characterize focal and reentrant arrhythmias. Spatio-temporal maps of the full-view of the atrial and ventricular mechanics were obtained in a single heartbeat, revealing with otherwise unobtainable detail the electromechanical patterns of atrial flutter, fibrillation, and tachycardia in humans. During focal arrhythmias such as premature ventricular complex and focal atrial tachycardia, the previously developed electromechanical wave imaging methodology is hereby shown capable of identifying the location of the focal zone and the subsequent propagation of cardiac activation. During reentrant arrhythmias such as atrial flutter and fibrillation, Fourier analysis of the strains revealed highly correlated mechanical and electrical cycle lengths and propagation patterns. High frame rate ultrasound imaging of the heart can be used non-invasively and in real time, to characterize the lesser-known mechanical aspects of atrial and ventricular arrhythmias, also potentially assisting treatment planning for intraoperative and longitudinal monitoring of arrhythmias.

Rotor mapping and ablation to treat atrial fibrillation

PURPOSE OF REVIEW

Rotors have long been postulated to drive atrial fibrillation, but evidence has been limited to animal models. This changed recently with the demonstration using focal impulse and rotor modulation (FIRM) mapping that rotors act as human atrial fibrillation sources. This mechanistic approach to diagnosing the causes of atrial fibrillation in individual patients has been supported by substantially improved outcomes from FIRM-guided ablation, resulting in increased attention to rotors as therapeutic targets.

RECENT FINDINGS

In this review, we outline the pathophysiology of rotors in animal and in-silico studies of fibrillation, and how this motivated FIRM mapping in humans. We highlight the characteristics of rotors in human atrial fibrillation, now validated by several techniques, with discussion on similar and discrepant findings between techniques. The interventional approaches to eliminate atrial fibrillation rotors are explained and the ablation results in latest studies using FIRM are discussed.

SUMMARY

We propose that mapping localized sources for human atrial fibrillation, specifically rotors, is moving the field towards a unifying hypothesis that explains several otherwise contradictory observations in atrial fibrillation management. We conclude by suggesting areas of potential research that may reveal more about these critical sites and how these may lead to better and novel treatments for atrial fibrillation.

Structural contributions to fibrillatory rotors in a patient-derived computational model of the atria

AIMS

The aim of this study was to investigate structural contributions to the maintenance of rotors in human atrial fibrillation (AF) and possible mechanisms of termination.

METHODS AND RESULTS

A three-dimensional human biatrial finite element model based on patient-derived computed tomography and arrhythmia observed at electrophysiology study was used to study AF. With normal physiological electrical conductivity and effective refractory periods (ERPs), wave break failed to sustain reentrant activity or electrical rotors. With depressed excitability, decreased conduction anisotropy, and shorter ERP characteristic of AF, reentrant rotors were readily maintained. Rotors were transiently or permanently trapped by fibre discontinuities on the lateral wall of the right atrium near the tricuspid valve orifice and adjacent to the crista terminalis, both known sites of right atrial arrhythmias. Modelling inexcitable regions near the rotor tip to simulate fibrosis anchored the rotors, converting the arrhythmia to macro-reentry. Accordingly, increasing the spatial core of inexcitable tissue decreased the frequency of rotation, widened the excitable gap, and enabled an external wave to impinge on the rotor core and displace the source.

CONCLUSION

These model findings highlight the importance of structural features in rotor dynamics and suggest that regions of fibrosis may anchor fibrillatory rotors. Increasing extent of fibrosis and scar may eventually convert fibrillation to excitable gap reentry. Such macro-reentry can then be eliminated by extending the obstacle or by external stimuli that penetrate the excitable gap.

Three-dimensional cardiac computational modelling: methods, features and applications

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

A two layers monodomain model of cardiac electrophysiology of the atria

Numerical simulations of the cardiac electrophysiology in the atria are often based on the standard bidomain or monodomain equations stated on a two-dimensional manifold. These simulations take advantage of the thinness of the atrial tissue, and their computational cost is reduced, as compared to three-dimensional simulations. However, these models do not take into account the heterogeneities located in the thickness of the tissue, like discontinuities of the fiber direction, although they can be a substrate for atrial arrhythmia (Hocini et al., Circulation 105(20):2442-2448, 2002; Ho et al., Cardiovasc Res 54(2):325-336, 2002; Nattel, Nature 415(6868):219-226, 2002). We investigate a two-dimensional model with two coupled, superimposed layers that allows to introduce three-dimensional heterogeneities, but retains a reasonable computational cost. We introduce the mathematical derivation of this model and error estimates with respect to the three-dimensional model. We give some numerical illustrations of its interest: we numerically show its convergence for vanishing thickness, introduce an optimization process of the coupling coefficient and assess its validity on physiologically relevant geometries. Our model would be an efficient tool to test the influence of three-dimensional fiber direction heterogeneities in reentries or atrial arrhythmia without using three-dimensional models.

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.