Electroanatomical characterization of atrial microfibrosis in a histologically detailed computer model

Late gadolinium enhancement in areas with electrically fractionated potentials during sinus rhythm in patients with atrial fibrillation

The areas with electrically fractionated potentials (AEFP) during sinus rhythm are related to non-pulmonary vein triggers and may serve as substrates of atrial fibrillation (AF) maintenance. However, the histological properties of these compounds remain unclear. Therefore, we aimed to evaluate the late gadolinium enhancement (LGE) properties of AEFP in patients with AF. We enrolled 15 patients with AF who had undergone LGE magnetic resonance imaging before catheter ablation. AEFP in the left atrium was detected using the HD-Grid and NavX systems after pulmonary vein isolation. We compared LGE properties between AEFP and the surrounding non-fractionated areas (non-AEFP). LGE heterogeneity and density were evaluated through entropy (LGE entropy) and the volume ratio of the enhancement voxel (LGE volume ratio), respectively. Thirty-three AEFP were detected in the left atrium. LGE entropy and LGE volume ratio were significantly higher in AEFP than in non-AEFP [LGE entropy: 6.2 (6.1-6.4) vs. 5.9 (5.8-6.0), p ≤ 0.0001; LGE volume ratio: 23.0% (17.2-29.0%) vs. 10.4% (3.4-20.2%), p ≤ 0.0001]. The atrial voltages did not differ [2.4 (1.3-3.7) vs. 2.5 (1.9-3.1) mV, p = 0.96]. AF recurrence was more significantly found in patients with more than three AEFP than in those without it (log-rank test: p = 0.009). AEFP is likely to be distributed in heterogeneous and moderate LGE areas, regardless of the atrial voltage.

Perlin noise generation of physiologically realistic cardiac fibrosis

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

Functional substrate analysis in patients with persistent atrial fibrillation

OBJECTIVES

The aim of this study was to describe the correlation between atrial electrogram duration map (AEDUM), spatiotemporal electrogram dispersion (STED) and low voltage areas (LVA) in patients with persistent atrial fibrillation (PsAF).

BACKGROUND

The degree of left atrial (LA) tissue remodelling and augmented anisotropic conduction is one of the major issues related to PsAF ablation outcome.

METHODS

This study enrolled consecutive patients with PsAF undergoing pulmonary vein isolation. In all patients, voltage, AEDUM and STED maps were created, and the correlation was reported between these three mapping methods.

RESULTS

A total of 40 patients with PsAF were enrolled. The mean age was 62.2 ± 7.4 years, and males were 72.5% (n = 29). The overall bipolar voltage of the LA was 3.06 ± 1.87 mV. All patients had at least one AEDUM area (overall AEDUM area: 21.8 ± 8.2 cm2); the mean longest electrogram (EGMs) duration was 90 ± 19 ms. STED areas with < 120 ms was 46.3 ± 20.2 cm2 which covered 45 ± 22% of the LA surface. AEDUM and STED areas were most frequently reported on the roof, the anterior wall and the septum. The extension of the AEDUM areas was significantly smaller than STED areas with CL < 120 ms (21.8 ± 8.2 vs 46.3 ± 20.2; p-value < 0.0001). In 24 patients (60%), AEDUM areas was entirely included in the STED areas with CL < 120 ms. In the three (7.5%) patients with LVA, no correspondence with STED and AEDUM was noted.

CONCLUSION

AEDUM and STED maps allow to identify areas of conductive dysfunction as a possible atrial substrate even if a normal voltage is detected.

Ablation of persistent atrial fibrillation based on atrial electrogram duration map: methodology and clinical outcomes from the AEDUM pilot study

BACKGROUND

Catheter ablation of persistent atrial fibrillation (PsAF) represents a challenge for the electrophysiologist and there are still divergences regarding the best ablative approach to adopt. Create a new map of the duration of atrial bipolar electrograms (Atrial Electrogram DUration Map, AEDUM) to recognize a functional substrate during sinus rhythm and guide a patient-tailored ablative strategy for PsAF.

METHODS

Forty PsAF subjects were assigned in a 1:1 ratio to either for PVI alone (Group B1) or PVI+AEDUM areas ablation (Group B2). A cohort of 15 patients without AF history undergoing left-sided accessory pathway ablation was used as a control group (Group A). In all patients, voltage and AEDUM maps were created during sinus rhythm. The minimum follow-up was 12 months, with rhythm monitoring via 48-h ECG Holter or by implantable cardiac device.

RESULTS

Electrogram (EGM) duration was higher in Group B than in Group A (49±16.2ms vs 34.2±3.8ms; p-value<0.001). In Group B the mean cumulative AEDUM area was 21.8±8.2cm2; no difference between the two subgroups was observed (22.3±9.1cm2 vs 21.2±7.2cm2; p-value=0.45). The overall bipolar voltage recorded inside the AEDUM areas was lower than in the remaining atrial areas [median: 1.30mV (IQR: 0.71-2.38mV) vs 1.54mV (IQR: 0.79-2.97mV); p-value: <0.001)]. Low voltage areas (<0.5mV) were recorded in three (7.5%) patients in Group B. During the follow-up [median 511 days (376-845days)] patients who underwent PVI-only experienced more AF recurrence than those receiving a tailored approach (65% vs 35%; p-value= 0.04).

CONCLUSIONS

All PsAF patients exhibited AEDUM areas. An ablation approach targeting these areas resulted in a more effective strategy compared with PVI only.

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

Graph-based homogenisation for modelling cardiac fibrosis

Fibrosis, the excess of extracellular matrix, can affect, and even block, propagation of action potential in cardiac tissue. This can result in deleterious effects on heart function, but the nature and severity of these effects depend strongly on the localisation of fibrosis and its by-products in cardiac tissue, such as collagen scar formation. Computer simulation is an important means of understanding the complex effects of fibrosis on activation patterns in the heart, but concerns of computational cost place restrictions on the spatial resolution of these simulations. In this work, we present a novel numerical homogenisation technique that uses both Eikonal and graph approaches to allow fine-scale heterogeneities in conductivity to be incorporated into a coarser mesh. Homogenisation achieves this by deriving effective conductivity tensors so that a coarser mesh can then be used for numerical simulation. By taking a graph-based approach, our homogenisation technique functions naturally on irregular grids and does not rely upon any assumptions of periodicity, even implicitly. We present results of action potential propagation through fibrotic tissue in two dimensions that show the graph-based homogenisation technique is an accurate and effective way to capture fine-scale domain information on coarser meshes in the context of sharp-fronted travelling waves of activation. As test problems, we consider excitation propagation in tissue with diffuse fibrosis and through a tunnel-like structure designed to test homogenisation, interaction of an excitation wave with a scar region, and functional re-entry.

A Review of Healthy and Fibrotic Myocardium Microstructure Modeling and Corresponding Intracardiac Electrograms

Computational simulations of cardiac electrophysiology provide detailed information on the depolarization phenomena at different spatial and temporal scales. With the development of new hardware and software, in silico experiments have gained more importance in cardiac electrophysiology research. For plane waves in healthy tissue, in vivo and in silico electrograms at the surface of the tissue demonstrate symmetric morphology and high peak-to-peak amplitude. Simulations provided insight into the factors that alter the morphology and amplitude of the electrograms. The situation is more complex in remodeled tissue with fibrotic infiltrations. Clinically, different changes including fractionation of the signal, extended duration and reduced amplitude have been described. In silico, numerous approaches have been proposed to represent the pathological changes on different spatial and functional scales. Different modeling approaches can reproduce distinct subsets of the clinically observed electrogram phenomena. This review provides an overview of how different modeling approaches to incorporate fibrotic and structural remodeling affect the electrogram and highlights open challenges to be addressed in future research.

Diversity and complexity of the cavotricuspid isthmus in rabbits: A novel scheme for classification and geometrical transformation of anatomical structures

The aim of this study was to describe the morphology of the cavotricuspid isthmus (CTI) in detail and introduce a comprehensive scheme to describe the topology of this region based on functional considerations. This may lead to a better understanding of isthmus-dependent flutter and fibrillation and to improved intervention strategies. We used images of the cavotricuspid isthmus from 52 rabbits of both sexes with a median weight of 3.40 ± 0.93 kg. The area of the CTI was 124.25 ± 42.14 mm² with 53.28 ± 21.13 mm² covered by pectinate muscles connecting the terminal crest and the vestibule. Isthmus length decreased from inferolateral (13.09 ±2.14 mm) to central (9.85 ± 2.14 mm) to paraseptal (4.88 ± 1.96 mm) resembling the overall human geometry. Ramification sites of pectinate muscles were identified and six levels dividing the CTI from posterior to anterior were introduced. This allowed the classification of pectinate muscle segments based on the connected ramification level. To account for the high inter-individual variations in size and shape, the CTI was projected onto a normalized reference frame using bilinear transformation. Furthermore, two measures of complexity were introduced: (i) the ramification index, which reflects the total number of muscle segments connected to a ramification site and (ii) the complexity index, which reflects the type of ramification (branching or merging site). Topological analysis showed that the complexity of the pectinate muscle network decreases from inferolateral to paraseptal and that the number of electrically uncoupled parallel pathways increases in the central section between the terminal crest and the vestibule which introduces potential reentry pathways.

Etiology-Specific Remodeling in Ventricular Tissue of Heart Failure Patients and Its Implications for Computational Modeling of Electrical Conduction

With an estimated 64.3 million cases worldwide, heart failure (HF) imposes an enormous burden on healthcare systems. Sudden death from arrhythmia is the major cause of mortality in HF patients. Computational modeling of the failing heart provides insights into mechanisms of arrhythmogenesis, risk stratification of patients, and clinical treatment. However, the lack of a clinically informed approach to model cardiac tissues in HF hinders progress in developing patient-specific strategies. Here, we provide a microscopy-based foundation for modeling conduction in HF tissues. We acquired 2D images of left ventricular tissues from HF patients (n = 16) and donors (n = 5). The composition and heterogeneity of fibrosis were quantified at a sub-micrometer resolution over an area of 1 mm². From the images, we constructed computational bidomain models of tissue electrophysiology. We computed local upstroke velocities of the membrane voltage and anisotropic conduction velocities (CV). The non-myocyte volume fraction was higher in HF than donors (39.68 ± 14.23 vs. 22.09 ± 2.72%, p < 0.01), and higher in ischemic (IC) than nonischemic (NIC) cardiomyopathy (47.2 ± 16.18 vs. 32.16 ± 6.55%, p < 0.05). The heterogeneity of fibrosis within each subject was highest for IC (27.1 ± 6.03%) and lowest for donors (7.47 ± 1.37%) with NIC (15.69 ± 5.76%) in between. K-means clustering of this heterogeneity discriminated IC and NIC with an accuracy of 81.25%. The heterogeneity in CV increased from donor to NIC to IC tissues. CV decreased with increasing fibrosis for longitudinal (R ² = 0.28, p < 0.05) and transverse conduction (R ² = 0.46, p < 0.01). The tilt angle of the CV vectors increased 2.1° for longitudinal and 0.91° for transverse conduction per 1% increase in fibrosis. Our study suggests that conduction fundamentally differs in the two etiologies due to the characteristics of fibrosis. Our study highlights the importance of the etiology-specific modeling of HF tissues and integration of medical history into electrophysiology models for personalized risk stratification and treatment planning.

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

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

Assessing the ability of substrate mapping techniques to guide ventricular tachycardia ablation using computational modelling

BACKGROUND

Identification of targets for ablation of post-infarction ventricular tachycardias (VTs) remains challenging, often requiring arrhythmia induction to delineate the reentrant circuit. This carries a risk for the patient and may not be feasible. Substrate mapping has emerged as a safer strategy to uncover arrhythmogenic regions. However, VT recurrence remains common.

GOAL

To use computer simulations to assess the ability of different substrate mapping approaches to identify VT exit sites.

METHODS

A 3D computational model of the porcine post-infarction heart was constructed to simulate VT and paced rhythm. Electroanatomical maps were constructed based on endocardial electrogram features and the reentry vulnerability index (RVI - a metric combining activation (AT) and repolarization timings to identify tissue susceptibility to reentry). Since scar transmurality in our model was not homogeneous, parameters derived from all signals (including dense scar regions) were used in the analysis. Potential ablation targets obtained from each electroanatomical map during pacing were compared to the exit site detected during VT mapping.

RESULTS

Simulation data showed that voltage cut-offs applied to bipolar electrograms could delineate the scar, but not the VT circuit. Electrogram fractionation had the highest correlation with scar transmurality. The RVI identified regions closest to VT exit site but was outperformed by AT gradients combined with voltage cut-offs. The performance of all metrics was affected by pacing location.

CONCLUSIONS

Substrate mapping could provide information about the infarct, but the directional dependency on activation should be considered. Activation-repolarization metrics have utility in safely identifying VT targets, even with non-transmural scars.

An Inverse Eikonal Method for Identifying Ventricular Activation Sequences from Epicardial Activation Maps

A key mechanism controlling cardiac function is the electrical activation sequence of the heart's main pumping chambers termed the ventricles. As such, personalization of the ventricular activation sequences is of pivotal importance for the clinical utility of computational models of cardiac electrophysiology. However, a direct observation of the activation sequence throughout the ventricular volume is virtually impossible. In this study, we report on a novel method for identification of activation sequences from activation maps measured at the outer surface of the heart termed the epicardium. Conceptually, the method attempts to identify the key factors governing the ventricular activation sequence - the timing of earliest activation sites (EAS) and the velocity tensor field within the ventricular walls - from sparse and noisy activation maps sampled from the epicardial surface and fits an Eikonal model to the observations. Regularization methods are first investigated to overcome the severe ill-posedness of the inverse problem in a simplified 2D example. These methods are then employed in an anatomically accurate biventricular model with two realistic activation models of varying complexity - a simplified trifascicular model (3F) and a topologically realistic model of the His-Purkinje system (HPS). Using epicardial activation maps at full resolution, we first demonstrate that reconstructing the volumetric activation sequence is, in principle, feasible under the assumption of known location of EAS and later evaluate robustness of the method against noise and reduced spatial resolution of observations. Our results suggest that the FIMIN algorithm is able to robustly recover the full 3D activation sequence using epicardial activation maps at a spatial resolution achievable with current mapping systems and in the presence of noise. Comparing the accuracy achieved in the reconstructed activation maps with clinical data uncertainties suggests that the FIMIN method may be suitable for the patient- specific parameterization of activation models.

Characterizing the clinical implementation of a novel activation-repolarization metric to identify targets for catheter ablation of ventricular tachycardias using computational models

Identification of targets for catheter ablation of ventricular tachycardias (VTs) remains a significant challenge. VTs are often driven by re-entrant circuits resulting from a complex interaction between the front (activation) and tail (repolarization) of the electrical wavefront. Most mapping techniques do not take into account the tissue repolarization which may hinder the detection of ablation targets. The re-entry vulnerability index (RVI), a recently proposed mapping procedure, incorporates both activation and repolarization times to uncover VT circuits. The method showed potential in a series of experiments, but it still requires further development to enable its incorporation into a clinical protocol. Here, in-silico experiments were conducted to thoroughly assess RVI maps constructed under clinically-relevant mapping conditions. Within idealized as well as anatomically realistic infarct models, we show that parameters of the algorithm such as the search radius can significantly alter the specificity and sensitivity of the RVI maps. When constructed on sparse grids obtained following various placements of clinical recording catheters, RVI maps can identify vulnerable regions as long as two electrodes were placed on both sides of the line of block. Moreover, maps computed during pacing without inducing VT can reveal areas of abnormal repolarization and slow conduction but not directly vulnerability. In conclusion, the RVI algorithm can detect re-entrant circuits during VT from low resolution mapping grids resembling the clinical setting. Furthermore, RVI maps may provide information about the underlying tissue electrophysiology to guide catheter ablation without the need of inducing potentially harmful VT during the clinical procedure. Finally, the ability of the RVI maps to identify vulnerable regions with specificity in high resolution computer models could potentially improve the prediction of optimal ablation targets of simulation-based strategies.

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Safe and accurate detection of targets for catheter ablation remains a challenge.

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We conducted a thorough assessment of the Re-entry Vulnerability Index (RVI).

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Parameters of the algorithm can alter the specificity and sensitivity of RVI maps.

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When constructed on sparse grids RVI maps could still detect arrhythmogenic sites.

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In absence of arrhythmia, RVI maps revealed abnormal sites, but not vulnerability.

Ectopic beats arise from micro-reentries near infarct regions in simulations of a patient-specific heart model

Ectopic beats are known to be involved in the initiation of a variety of cardiac arrhythmias. Although their location may vary, ectopic excitations have been found to originate from infarct areas, regions of micro-fibrosis and other heterogeneous tissues. However, the underlying mechanisms that link ectopic foci to heterogeneous tissues have yet to be fully understood. In this work, we investigate the mechanism of micro-reentry that leads to the generation of ectopic beats near infarct areas using a patient-specific heart model. The patient-specific geometrical model of the heart, including scar and peri-infarct zones, is obtained through magnetic resonance imaging (MRI). The infarct region is composed of ischemic myocytes and non-conducting cells (fibrosis, for instance). Electrophysiology is captured using an established cardiac myocyte model of the human ventricle modified to describe ischemia. The simulation results clearly reveal that ectopic beats emerge from micro-reentries that are sustained by the heterogeneous structure of the infarct regions. Because microscopic information about the heterogeneous structure of the infarct regions is not available, Monte-Carlo simulations are used to identify the probabilities of an infarct region to behave as an ectopic focus for different levels of ischemia and different percentages of non-conducting cells. From the proposed model, it is observed that ectopic beats are generated when a percentage of non-conducting cells is near a topological metric known as the percolation threshold. Although the mechanism for micro-reentries was proposed half a century ago to be a source of ectopic beats or premature ventricular contractions during myocardial infarction, the present study is the first to reproduce this mechanism in-silico using patient-specific data.

Microheterogeneity-induced conduction slowing and wavefront collisions govern macroscopic conduction behavior: A computational and experimental study

The incidence of cardiac arrhythmias is known to be associated with tissue heterogeneities including fibrosis. However, the impact of microscopic structural heterogeneities on conduction in excitable tissues remains poorly understood. In this study, we investigated how acellular microheterogeneities affect macroscopic conduction under conditions of normal and reduced excitability by utilizing a novel platform of paired in vitro and in silico studies to examine the mechanisms of conduction. Regular patterns of nonconductive micro-obstacles were created in confluent monolayers of the previously described engineered-excitable Ex293 cell line. Increasing the relative ratio of obstacle size to intra-obstacle strand width resulted in significant conduction slowing up to 23.6% and a significant increase in wavefront curvature anisotropy, a measure of spatial variation in wavefront shape. Changes in bulk electrical conductivity and in path tortuosity were insufficient to explain these observed macroscopic changes. Rather, microscale behaviors including local conduction slowing due to microscale branching, and conduction acceleration due to wavefront merging were shown to contribute to macroscopic phenomena. Conditions of reduced excitability led to further conduction slowing and a reversal of wavefront curvature anisotropy due to spatially non-uniform effects on microscopic slowing and acceleration. This unique experimental and computation platform provided critical mechanistic insights in the impact of microscopic heterogeneities on macroscopic conduction, pertinent to settings of fibrotic heart disease.

It is well known that perturbations in the heart structure are associated with the initiation and maintenance of clinically significant cardiac arrhythmia. While previous studies have examined how single structural perturbations affect local electrical conduction, our understanding of how numerous microscopic heterogeneities act in aggregate to alter macroscopic electrical behavior is limited. In this study, we utilized simplified engineered excitable cells that contain the minimal machinery of excitability and can be directly computationally modeled. By pairing experimental and computational studies, we showed that the microscopic branching and collisions of electrical waves slow and speed conduction, respectively, resulting in macroscopic changes in the speed and pattern of electrical activation. These microscale behaviors are significantly altered under reduced excitability, resulting in exaggerated collision effects. Overall, this study helps improve our understanding of how microscopic structural heterogeneities in excitable tissue lead to abnormal action potential propagation, conducive to arrhythmias.

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.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Effects of fibrosis on the extracellular potential based on 3D reconstructions from histological sections of heart tissue

Atrial fibrillation is the most common arrhythmia. However, the mechanisms of AF are not completely understood. It is known that fractionated signals are measured in AF but the etiology of fractionated signals is still not clear. The central question is to evaluate the effects of segmented fibrotic areas in histological tissue sections on the extracellular potential in a simulation study. We calculated the transmembrane voltages and extracellular potentials from the excitation wave front around a 3D fibrotic area from mouse hearts that were reconstructed from histological tissue sections. Extracellular potentials resulted in fragmented signals and differed strongly by stimulations from different directions. The transmural angle of the excitation waves had a significantly influence on the signal morphologies. We suggest for future clinical systems to implement the possibility for substrate mapping by stimulations from different directions in sinus rhythm.

Automated Texture Analysis and Determination of Fibre Orientation of Heart Tissue: A Morphometric Study

The human heart has a heterogeneous structure, which is characterized by different cell types and their spatial configurations. The physical structure, especially the fibre orientation and the interstitial fibrosis, determines the electrical excitation and in further consequence the contractility in macroscopic as well as in microscopic areas. Modern image processing methods and parameters could be used to describe the image content and image texture. In most cases the description of the texture is not satisfying because the fibre orientation, detected with common algorithms, is biased by elements such as fibrocytes or endothelial nuclei. The goal of this work is to figure out if cardiac tissue can be analysed and classified on a microscopic level by automated image processing methods with a focus on an accurate detection of the fibre orientation. Quantitative parameters for identification of textures of different complexity or pathological attributes inside the heart were determined. The focus was set on the detection of the fibre orientation, which was calculated on the basis of the cardiomyocytes’ nuclei. It turned out that the orientation of these nuclei corresponded with a high precision to the fibre orientation in the image plane. Additionally, these nuclei also indicated very well the inclination of the fibre.

Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia

Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.

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.

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.

Computational Approaches to Understanding the Role of Fibroblast-Myocyte Interactions in Cardiac Arrhythmogenesis

The adult heart is composed of a dense network of cardiomyocytes surrounded by nonmyocytes, the most abundant of which are cardiac fibroblasts. Several cardiac diseases, such as myocardial infarction or dilated cardiomyopathy, are associated with an increased density of fibroblasts, that is, fibrosis. Fibroblasts play a significant role in the development of electrical and mechanical dysfunction of the heart; however the underlying mechanisms are only partially understood. One widely studied mechanism suggests that fibroblasts produce excess extracellular matrix, resulting in collagenous septa. These collagenous septa slow propagation, cause zig-zag conduction paths, and decouple cardiomyocytes resulting in a substrate for arrhythmia. Another emerging mechanism suggests that fibroblasts promote arrhythmogenesis through direct electrical interactions with cardiomyocytes via gap junctions. Due to the challenges of investigating fibroblast-myocyte coupling in native cardiac tissue, computational modeling and in vitro experiments have facilitated the investigation into the mechanisms underlying fibroblast-mediated changes in cardiomyocyte action potential morphology, conduction velocity, spontaneous excitability, and vulnerability to reentry. In this paper, we summarize the major findings of the existing computational studies investigating the implications of fibroblast-myocyte interactions in the normal and diseased heart. We then present investigations from our group into the potential role of voltage-dependent gap junctions in fibroblast-myocyte interactions.

Role of atrial tissue substrate and electrical activation pattern in fractionation of atrial electrograms: a computational study

Complex fractionated atrial electrograms (CFAEs) are often used as a clinical marker for re-entrant drivers of atrial fibrillation. However, outcomes of clinical ablation procedures based on CFAEs are controversial and the mechanistic links between fractionation, re-entrant activity and the characteristics of the atrial substrate are not completely understood. We explore such links by simulating electrograms arising from both normal and re-entrant electrical activity in atrial tissue models. 2D and 3D tissue geometries with a range of conditions for intracellular coupling and myofiber orientation fields were studied. Electrograms were fractionated in the presence of complex atrial fiber fields and in 3D irregular geometries, due to far-field excitations. The complexity of the local electrical activity was not a strong determinant of the degree of fractionation. These results suggest that electrogram fractionation is more strongly linked to atrial substrate characteristics (including tissue geometry, fiber orientation and degree of intercelullar coupling) than to the electrical activation pattern sustaining atrial fibrillation.

An efficient finite element approach for modeling fibrotic clefts in the heart

Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.