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

Prevalence of endoepicardial asynchrony and breakthrough patterns in a bilayer computational model of heterogeneous endoepicardial dissociation in the left atrium

BACKGROUND

Transmural propagation and endoepicardial delays in activation observed in patients with atrial fibrillation are hypothesized to be associated with structural remodeling and endoepicardial dissociation. We aim to explore in a computational model how the distribution of delays and the rate of endo- and epicardial breakthrough activation patterns are affected by fibrosis and heterogeneous layer dissociation.

METHODS

A bilayer interconnected cable model of the left atrium was used to simulate a total of 4,800 episodes of atrial fibrillation on 960 different arrhythmogenic substrates with up to 30% epicardium-only diffuse fibrosis. Endoepicardial connections were heterogeneously distributed following random spatial patterns (characteristic length scale from 1.6 to 11.4 mm). Intermediate nodes were introduced in the transmural connections to enable the simulation of weaker coupling. This heterogeneous interlayer dissociation divided the atrial bilayer into connected and disconnected regions (from 27 to 48,000 connected regions). Activation time series were extracted in both layers to compute endoepicardial delays and detect breakthrough patterns.

RESULTS

Because of epicardial fibrosis, fibrillatory waves were driven by the endocardium, which generated endoepicardial delays. The delays in the connected regions (up to 10 ms, but generally < 5 ms) were prolonged by higher fibrosis density and weaker coupling. Disconnected regions allowed longer delays (> 15 ms) and promoted the occurrence of breakthroughs. These breakthroughs had short lifespan (< 10-20 ms) and were more prevalent with higher fibrosis density and heterogeneous dissociation (larger disconnected regions). Severe remodeling (< 500 connected regions) was needed to produce clinically reported rates (> 0.1 breakthrough/cycle/cm2).

CONCLUSION

Heterogeneous endoepicardial dissociation aggravates activation delays and increases the prevalence of epicardial breakthroughs.

Translation of pathophysiological mechanisms of atrial fibrosis into new diagnostic and therapeutic approaches

Atrial fibrosis is one of the main manifestations of atrial cardiomyopathy, an array of electrical, mechanical and structural alterations associated with atrial fibrillation (AF), stroke and heart failure. Atrial fibrosis can be both a cause and a consequence of AF and, once present, it accelerates the progression of AF. The pathophysiological mechanisms leading to atrial fibrosis are diverse and include stretch-induced activation of fibroblasts, systemic inflammatory processes, activation of coagulation factors and fibrofatty infiltrations. Importantly, atrial fibrosis can occur in different forms, such as reactive and replacement fibrosis. The diversity of atrial fibrosis mechanisms and patterns depends on sex, age and comorbidity profile, hampering the development of therapeutic strategies. In addition, the presence and severity of comorbidities often change over time, potentially causing temporal changes in the mechanisms underlying atrial fibrosis development. This Review summarizes the latest knowledge on the molecular and cellular mechanisms of atrial fibrosis, its association with comorbidities and the sex-related differences. We describe how the various patterns of atrial fibrosis translate into electrophysiological mechanisms that promote AF, and critically appraise the clinical applicability and limitations of diagnostic tools to quantify atrial fibrosis. Finally, we provide an overview of the newest therapeutic interventions under development and discuss relevant knowledge gaps related to the association between clinical manifestations and pathological mechanisms of atrial fibrosis and to the translation of this knowledge to a clinical setting.

Improved algorithm for generating evenly-spaced streamlines from an orientation field on a triangulated surface

BACKGROUND

Vector fields such as cardiac fiber orientation can be visualized on a surface using streamlines. The application of evenly-spaced streamline generation to the construction of interconnected cable structure for cardiac propagation models has more stringent requirements imperfectly fulfilled by current algorithms.

METHOD

We developed an open-source C++/python package for the placement of evenly-spaced streamlines on a triangulated surface. The new algorithm improves upon previous works by more accurately handling streamline extremities, U-turns and limit cycles, by providing stronger geometrical guarantees on inter-streamline minimal distance, particularly when a high density of streamlines (up to 10μm spacing) is desired, and by making a more efficient parallel implementation available. The approach requires finding intersections between geometrical capsules and triangles to update an occupancy mask defined on the triangles. This enables fast streamline integration from thousands of seed points to identify optimal streamline placement.

RESULTS

The algorithm was assessed qualitatively on different left atrial models of fiber orientation with varying mesh resolutions (up to 375k triangles) and quantitatively by measuring streamline lengths and distribution of inter-streamline minimal distance. The complexity and the computational performance of the algorithm were studied as a function of streamline spacing in relation to triangular mesh resolution.

CONCLUSION

More accurate geometrical computations, attention to details and fine-tuning led to an algorithm more amenable to applications that require precise positioning of streamlines.

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.

Individualization of Atrial Tachycardia Models for Clinical Applications: Performance of Fiber-Independent Model

One of the challenges in the development of patient-specific models of cardiac arrhythmias for clinical applications has been accounting for myocardial fiber organization. The fiber varies significantly from heart to heart, but cannot be directly measured in live tissue. The goal of this paper is to evaluate in-silico the accuracy of left atrium activation maps produced by a fiber-independent (isotropic) model with tuned diffusion coefficients, compares to a model incorporating myocardial fibers with the same geometry. For this study we utilize publicly available DT-MRI data from 7 ex-vivo hearts. The comparison is carried out in 51 cases of focal and rotor arrhythmias located in different regions of the atria. On average, the local activation time accuracy is 96% for focal and 93% for rotor arrhythmias. Given its reasonably good performance and the availability of readily accessible data for model tuning in cardiac ablation procedures, the fiber-independent model could be a promising tool for clinical applications.

25 years of basic and translational science in EP Europace: novel insights into arrhythmia mechanisms and therapeutic strategies

In the last 25 years, EP Europace has published more than 300 basic and translational science articles covering different arrhythmia types (ranging from atrial fibrillation to ventricular tachyarrhythmias), different diseases predisposing to arrhythmia formation (such as genetic arrhythmia disorders and heart failure), and different interventional and pharmacological anti-arrhythmic treatment strategies (ranging from pacing and defibrillation to different ablation approaches and novel drug-therapies). These studies have been conducted in cellular models, small and large animal models, and in the last couple of years increasingly in silico using computational approaches. In sum, these articles have contributed substantially to our pathophysiological understanding of arrhythmia mechanisms and treatment options; many of which have made their way into clinical applications. This review discusses a representative selection of EP Europace manuscripts covering the topics of pacing and ablation, atrial fibrillation, heart failure and pro-arrhythmic ventricular remodelling, ion channel (dys)function and pharmacology, inherited arrhythmia syndromes, and arrhythmogenic cardiomyopathies, highlighting some of the advances of the past 25 years. Given the increasingly recognized complexity and multidisciplinary nature of arrhythmogenesis and continued technological developments, basic and translational electrophysiological research is key advancing the field. EP Europace aims to further increase its contribution to the discovery of arrhythmia mechanisms and the implementation of mechanism-based precision therapy approaches in arrhythmia management.

Fiber Organization Has Little Effect on Electrical Activation Patterns During Focal Arrhythmias in the Left Atrium

Over the past two decades there has been a steady trend towards the development of realistic models of cardiac conduction with increasing levels of detail. However, making models more realistic complicates their personalization and use in clinical practice due to limited availability of tissue and cellular scale data. One such limitation is obtaining information about myocardial fiber organization in the clinical setting. In this study, we investigated a chimeric model of the left atrium utilizing clinically derived patient-specific atrial geometry and a realistic, yet foreign for a given patient fiber organization. We discovered that even significant variability of fiber organization had a relatively small effect on the spatio-temporal activation pattern during regular pacing. For a given pacing site, the activation maps were very similar across all fiber organizations tested.

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

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

Electrophysiological Consequences of Cardiac Fibrosis

For both the atria and ventricles, fibrosis is generally recognized as one of the key determinants of conduction disturbances. By definition, fibrosis refers to an increased amount of fibrous tissue. However, fibrosis is not a singular entity. Various forms can be distinguished, that differ in distribution: replacement fibrosis, endomysial and perimysial fibrosis, and perivascular, endocardial, and epicardial fibrosis. These different forms typically result from diverging pathophysiological mechanisms and can have different consequences for conduction. The impact of fibrosis on propagation depends on exactly how the patterns of electrical connections between myocytes are altered. We will therefore first consider the normal patterns of electrical connections and their regional diversity as determinants of propagation. Subsequently, we will summarize current knowledge on how different forms of fibrosis lead to a loss of electrical connectivity in order to explain their effects on propagation and mechanisms of arrhythmogenesis, including ectopy, reentry, and alternans. Finally, we will discuss a histological quantification of fibrosis. Because of the different forms of fibrosis and their diverging effects on electrical propagation, the total amount of fibrosis is a poor indicator for the effect on conduction. Ideally, an assessment of cardiac fibrosis should exclude fibrous tissue that does not affect conduction and differentiate between the various types that do; in this article, we highlight practical solutions for histological analysis that meet these requirements.

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.