Anisotropic conduction in the myocardium due to fibrosis: the effect of texture on wave propagation

Systematic in-silico evaluation of fibrosis effects on re-entrant wave dynamics in atrial tissue

Despite the key role of fibrosis in atrial fibrillation (AF), the effects of different spatial distributions and textures of fibrosis on wave propagation mechanisms in AF are not fully understood. To clarify these aspects, we performed a systematic computational study to assess fibrosis effects on the characteristics and stability of re-entrant waves in electrically-remodelled atrial tissues. A stochastic algorithm, which generated fibrotic distributions with controlled overall amount, average size, and orientation of fibrosis elements, was implemented on a monolayer spheric atrial model. 245 simulations were run at changing fibrosis parameters. The emerging propagation patterns were quantified in terms of rate, regularity, and coupling by frequency-domain analysis of correspondent synthetic bipolar electrograms. At the increase of fibrosis amount, the rate of reentrant waves significantly decreased and higher levels of regularity and coupling were observed (p < 0.0001). Higher spatial variability and pattern stochasticity over repetitions was observed for larger amount of fibrosis, especially in the presence of patchy and compact fibrosis. Overall, propagation slowing and organization led to higher stability of re-entrant waves. These results strengthen the evidence that the amount and spatial distribution of fibrosis concur in dictating re-entry dynamics in remodeled tissue and represent key factors in AF maintenance.

Homogenisation for the monodomain model in the presence of microscopic fibrotic structures

Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to incorporate structural heterogeneities on small spatial scales, preventing a full understanding of the critical arrhythmogenic effects of conditions such as cardiac fibrosis. In this work, we explore the technique of homogenisation by volume averaging for the inclusion of non-conductive micro-structures into larger-scale cardiac meshes with minor computational overhead. Importantly, our approach is not restricted to periodic patterns, enabling homogenised models to represent, for example, the intricate patterns of collagen deposition present in different types of fibrosis. We first highlight the importance of appropriate boundary condition choice for the closure problems that define the parameters of homogenised models. Then, we demonstrate the technique's ability to correctly upscale the effects of fibrotic patterns with a spatial resolution of 10 µm into much larger numerical mesh sizes of 100- 250 µm . The homogenised models using these coarser meshes correctly predict critical pro-arrhythmic effects of fibrosis, including slowed conduction, source/sink mismatch, and stabilisation of re-entrant activation patterns. As such, this approach to homogenisation represents a significant step towards whole organ simulations that unravel the effects of microscopic cardiac tissue heterogeneities.

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

Multiparametric analysis of geometric features of fibrotic textures leading to cardiac arrhythmias

One of the important questions in cardiac electrophysiology is to characterise the arrhythmogenic substrate; for example, from the texture of the cardiac fibrosis, which is considered one of the major arrhythmogenic conditions. In this paper, we perform an extensive in silico study of the relationships between various local geometric characteristics of fibrosis on the onset of cardiac arrhythmias. In order to define which texture characteristics have better predictive value, we induce arrhythmias by external stimulation, selecting 4363 textures in which arrhythmia can be induced and also selecting 4363 non-arrhythmogenic textures. For each texture, we determine such characteristics as cluster area, solidity, mean distance, local density and zig-zag propagation path, and compare them in arrhythmogenic and non-arrhythmogenic cases. Our study shows that geometrical characteristics, such as cluster area or solidity, turn out to be the most important for prediction of the arrhythmogenic textures. Overall, we were able to achieve an accuracy of 67% for the arrhythmogenic texture-classification problem. However, the accuracy of predictions depends on the size of the region chosen for the analysis. The optimal size for the local areas of the tissue was of the order of 0.28 of the wavelength of the arrhythmia. We discuss further developments and possible applications of this method for characterising the substrate of arrhythmias in fibrotic textures.

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.

Fibrotic Remodeling during Persistent Atrial Fibrillation: In Silico Investigation of the Role of Calcium for Human Atrial Myofibroblast Electrophysiology

During atrial fibrillation, cardiac tissue undergoes different remodeling processes at different scales from the molecular level to the tissue level. One central player that contributes to both electrical and structural remodeling is the myofibroblast. Based on recent experimental evidence on myofibroblasts' ability to contract, we extended a biophysical myofibroblast model with Ca²⁺ handling components and studied the effect on cellular and tissue electrophysiology. Using genetic algorithms, we fitted the myofibroblast model parameters to the existing in vitro data. In silico experiments showed that Ca²⁺ currents can explain the experimentally observed variability regarding the myofibroblast resting membrane potential. The presence of an L-type Ca²⁺ current can trigger automaticity in the myofibroblast with a cycle length of 799.9 ms. Myocyte action potentials were prolonged when coupled to myofibroblasts with Ca²⁺ handling machinery. Different spatial myofibroblast distribution patterns increased the vulnerable window to induce arrhythmia from 12 ms in non-fibrotic tissue to 22 ± 2.5 ms and altered the reentry dynamics. Our findings suggest that Ca²⁺ handling can considerably affect myofibroblast electrophysiology and alter the electrical propagation in atrial tissue composed of myocytes coupled with myofibroblasts. These findings can inform experimental validation experiments to further elucidate the role of myofibroblast Ca²⁺ handling in atrial arrhythmogenesis.

Multiparameter optimization of nonuniform passive diffusion properties for creating coarse-grained equivalent models of cardiac propagation

The arrhythmogenic role of discrete cardiac propagation may be assessed by comparing discrete (fine-grained) and equivalent continuous (coarse-grained) models. We aim to develop an optimization algorithm for estimating the smooth conductivity field that best reproduces the diffusion properties of a given discrete model. Our algorithm iteratively adjusts local conductivity of the coarse-grained continuous model by simulating passive diffusion from white noise initial conditions during 3-10 ms and computing the root mean square error with respect to the discrete model. The coarse-grained conductivity field was interpolated from up to 300 evenly spaced control points. We derived an approximate formula for the gradient of the cost function that required (in two dimensions) only two additional simulations per iteration regardless of the number of estimated parameters. Conjugate gradient solver facilitated simultaneous optimization of multiple conductivity parameters. The method was tested in rectangular anisotropic tissues with uniform and nonuniform conductivity (slow regions with sinusoidal profile) and random diffuse fibrosis, as well as in a monolayer interconnected cable model of the left atrium with spatially-varying fibrosis density. Comparison of activation maps served as validation. The results showed that after convergence the errors in activation time were < 1 ms for rectangular geometries and 1-3 ms in the atrial model. Our approach based on the comparison of passive properties (<10 ms simulation) avoids performing active propagation simulations (>100 ms) at each iteration while reproducing activation maps, with possible applications to investigating the impact of microstructure on arrhythmias.

Machine Learning Identification of Pro-arrhythmic Structures in Cardiac Fibrosis

Cardiac fibrosis and other scarring of the heart, arising from conditions ranging from myocardial infarction to ageing, promotes dangerous arrhythmias by blocking the healthy propagation of cardiac excitation. Owing to the complexity of the dynamics of electrical signalling in the heart, however, the connection between different arrangements of blockage and various arrhythmic consequences remains poorly understood. Where a mechanism defies traditional understanding, machine learning can be invaluable for enabling accurate prediction of quantities of interest (measures of arrhythmic risk) in terms of predictor variables (such as the arrangement or pattern of obstructive scarring). In this study, we simulate the propagation of the action potential (AP) in tissue affected by fibrotic changes and hence detect sites that initiate re-entrant activation patterns. By separately considering multiple different stimulus regimes, we directly observe and quantify the sensitivity of re-entry formation to activation sequence in the fibrotic region. Then, by extracting the fibrotic structures around locations that both do and do not initiate re-entries, we use neural networks to determine to what extent re-entry initiation is predictable, and over what spatial scale conduction heterogeneities appear to act to produce this effect. We find that structural information within about 0.5 mm of a given point is sufficient to predict structures that initiate re-entry with more than 90% accuracy.

Minimal Functional Clusters Predict the Probability of Reentry in Cardiac Fibrotic Tissue

Cardiac fibrosis is a well-known arrhythmogenic condition which can lead to sudden cardiac death. Physically, fibrosis can be viewed as a large number of small obstacles in an excitable medium, which may create nonlinear wave turbulence or reentry. The relation between the specific texture of fibrosis and the onset of reentry is of great theoretical and practical importance. Here, we present a conceptual framework which combines functional aspects of propagation manifested as conduction blocks, with reentry wavelength and geometrical clusters of fibrosis. We formulate them into the single concept of minimal functional cluster and through extensive simulations show that it characterizes the path of reexcitation accurately, and importantly its size distribution quantitatively predicts the reentry probability for different fibrosis densities and tissue excitabilities.

Simulation of diffuse and stringy fibrosis in a bilayer interconnected cable model of the left atrium

AIMS

The aim of this study is to design a computer model of the left atrium for investigating fibre-orientation-dependent microstructure such as stringy fibrosis.

METHODS AND RESULTS

We developed an approach for automatic construction of bilayer interconnected cable models from left atrial geometry and epi- and endocardial fibre orientation. The model consisted of two layers (epi- and endocardium) of longitudinal and transverse cables intertwined-like fabric threads, with a spatial discretization of 100 µm. Model validation was performed by comparison with cubic volumetric models in normal conditions. Then, diffuse (n = 2904), stringy (n = 3600), and mixed fibrosis patterns (n = 6840) were randomly generated by uncoupling longitudinal and transverse connections in the interconnected cable model. Fibrosis density was varied from 0% to 40% and mean stringy obstacle length from 0.1 to 2 mm. Total activation time, apparent anisotropy ratio, and local activation time jitter were computed during normal rhythm in each pattern. Non-linear regression formulas were identified for expressing measured propagation parameters as a function of fibrosis density and obstacle length (stringy and mixed patterns). Longer obstacles (even below tissue space constant) were independently associated with prolonged activation times, increased anisotropy, and local fluctuations in activation times. This effect was increased by endo-epicardial dissociation and mitigated when fibrosis was limited to the epicardium.

CONCLUSION

Interconnected cable models enable the study of microstructure in organ-size models despite limitations in the description of transmural structures.

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.

Percolation and tortuosity in heart-like cells

In the last several years, quite a few papers on the joint question of transport, tortuosity and percolation have appeared in the literature, dealing with passage of miscellaneous liquids or electrical currents in different media. However, these methods have not been applied to the passage of action potential in heart fibrosis (HF), which is crucial for problems of heart arrhythmia, especially of atrial tachycardia and fibrillation. In this work we address the HF problem from these aspects. A cellular automaton model is used to analyze percolation and transport of a distributed-fibrosis inflicted heart-like tissue. Although based on a rather simple mathematical model, it leads to several important outcomes: (1) It is shown that, for a single wave front (as the one emanated by the heart's sinus node), the percolation of heart-like matrices is exactly similar to the forest fire case. (2) It is shown that, on the average, the shape of the transport (a question not dealt with in relation to forest fire, and deals with the delay of action potential when passing a fibrotic tissue) behaves like a Gaussian. (3) Moreover, it is shown that close to the percolation threshold the parameters of this Gaussian behave in a critical way. From the physical point of view, these three results are an important contribution to the general percolation investigation. The relevance of our results to cardiological issues, specifically to the question of reentry initiation, are discussed and it is shown that: (A) Without an ectopic source and under a mere sinus node operation, no arrhythmia is generated, and (B) A sufficiently high refractory period could prevent some reentry mechanisms, even in partially fibrotic heart tissue.

Imaging Techniques for the Study of Fibrosis in Atrial Fibrillation Ablation: From Molecular Mechanisms to Therapeutical Perspectives

Atrial fibrillation (AF) is the most prevalent form of cardiac arrhythmia. It is often related to diverse pathological conditions affecting the atria and leading to remodeling processes including collagen accumulation, fatty infiltration, and amyloid deposition. All these events generate atrial fibrosis, which contribute to beget AF. In this scenario, cardiac imaging appears as a promising noninvasive tool for monitoring the presence and degree of LA fibrosis and remodeling. The aim of this review is to comprehensively examine the bench mechanisms of atrial fibrosis moving, then to describe the principal imaging techniques that characterize it, such as cardiac magnetic resonance (CMR) and multidetector cardiac computed tomography (MDCT), in order to tailor atrial fibrillation ablation to each individual.

Non-Invasive and Quantitative Estimation of Left Atrial Fibrosis Based on P Waves of the 12-Lead ECG-A Large-Scale Computational Study Covering Anatomical Variability

The arrhythmogenesis of atrial fibrillation is associated with the presence of fibrotic atrial tissue. Not only fibrosis but also physiological anatomical variability of the atria and the thorax reflect in altered morphology of the P wave in the 12-lead electrocardiogram (ECG). Distinguishing between the effects on the P wave induced by local atrial substrate changes and those caused by healthy anatomical variations is important to gauge the potential of the 12-lead ECG as a non-invasive and cost-effective tool for the early detection of fibrotic atrial cardiomyopathy to stratify atrial fibrillation propensity. In this work, we realized 54,000 combinations of different atria and thorax geometries from statistical shape models capturing anatomical variability in the general population. For each atrial model, 10 different volume fractions (0-45%) were defined as fibrotic. Electrophysiological simulations in sinus rhythm were conducted for each model combination and the respective 12-lead ECGs were computed. P wave features (duration, amplitude, dispersion, terminal force in V1) were extracted and compared between the healthy and the diseased model cohorts. All investigated feature values systematically in- or decreased with the left atrial volume fraction covered by fibrotic tissue, however value ranges overlapped between the healthy and the diseased cohort. Using all extracted P wave features as input values, the amount of the fibrotic left atrial volume fraction was estimated by a neural network with an absolute root mean square error of 8.78%. Our simulation results suggest that although all investigated P wave features highly vary for different anatomical properties, the combination of these features can contribute to non-invasively estimate the volume fraction of atrial fibrosis using ECG-based machine learning approaches.

Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation

Non-linear electrical waves propagate through the heart and control cardiac contraction. Abnormal wave propagation causes various forms of the heart disease and can be lethal. One of the main causes of abnormality is a condition of cardiac fibrosis, which, from mathematical point of view, is the presence of multiple non-conducting obstacles for wave propagation. The fibrosis can have different texture which varies from diffuse (e.g., small randomly distributed obstacles), patchy (e.g., elongated interstitional stria), and focal (e.g., post-infarct scars) forms. Recently, Nezlobinsky et al. (2020) used 2D biophysical models to quantify the effects of elongation of obstacles (fibrosis texture) and showed that longitudinal and transversal propagation differently depends on the obstacle length resulting in anisotropy for wave propagation. In this paper, we extend these studies to 3D tissue models. We show that 3D consideration brings essential new effects; for the same obstacle length in 3D systems, anisotropy is about two times smaller compared to 2D, however, wave propagation is more stable with percolation threshold of about 60% (compared to 35% in 2D). The percolation threshold increases with the obstacle length for the longitudinal propagation, while it decreases for the transversal propagation. Further, in 3D, the dependency of velocity on the obstacle length for the transversal propagation disappears.