Computational modeling of the human atrial anatomy and electrophysiology

A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method

Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca²⁺ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

Techniques for automated local activation time annotation and conduction velocity estimation in cardiac mapping

Measurements of cardiac conduction velocity provide valuable functional and structural insight into the initiation and perpetuation of cardiac arrhythmias, in both a clinical and laboratory context. The interpretation of activation wavefronts and their propagation can identify mechanistic properties of a broad range of electrophysiological pathologies. However, the sparsity, distribution and uncertainty of recorded data make accurate conduction velocity calculation difficult. A wide range of mathematical approaches have been proposed for addressing this challenge, often targeted towards specific data modalities, species or recording environments. Many of these algorithms require identification of activation times from electrogram recordings which themselves may have complex morphology or low signal-to-noise ratio. This paper surveys algorithms designed for identifying local activation times and computing conduction direction and speed. Their suitability for use in different recording contexts and applications is assessed.

Optimization of catheter ablation of atrial fibrillation: insights gained from clinically-derived computer models

Atrial fibrillation (AF) is the most common heart rhythm disturbance, and its treatment is an increasing economic burden on the health care system. Despite recent intense clinical, experimental and basic research activity, the treatment of AF with current antiarrhythmic drugs and catheter/surgical therapies remains limited. Radiofrequency catheter ablation (RFCA) is widely used to treat patients with AF. Current clinical ablation strategies are largely based on atrial anatomy and/or substrate detected using different approaches, and they vary from one clinical center to another. The nature of clinical ablation leads to ambiguity regarding the optimal patient personalization of the therapy partly due to the fact that each empirical configuration of ablation lines made in a patient is irreversible during one ablation procedure. To investigate optimized ablation lesion line sets, in silico experimentation is an ideal solution. 3D computer models give us a unique advantage to plan and assess the effectiveness of different ablation strategies before and during RFCA. Reliability of in silico assessment is ensured by inclusion of accurate 3D atrial geometry, realistic fiber orientation, accurate fibrosis distribution and cellular kinetics; however, most of this detailed information in the current computer models is extrapolated from animal models and not from the human heart. The predictive power of computer models will increase as they are validated with human experimental and clinical data. To make the most from a computer model, one needs to develop 3D computer models based on the same functionally and structurally mapped intact human atria with high spatial resolution. The purpose of this review paper is to summarize recent developments in clinically-derived computer models and the clinical insights they provide for catheter ablation.

Role of the P-wave high frequency energy and duration as noninvasive cardiovascular predictors of paroxysmal atrial fibrillation

A normal cardiac activation starts in the sinoatrial node and then spreads throughout the atrial myocardium, thus defining the P-wave of the electrocardiogram. However, when the onset of paroxysmal atrial fibrillation (PAF) approximates, a highly disturbed electrical activity occurs within the atria, thus provoking fragmented and eventually longer P-waves. Although this altered atrial conduction has been successfully quantified just before PAF onset from the signal-averaged P-wave spectral analysis, its evolution during the hours preceding the arrhythmia has not been assessed yet. This work focuses on quantifying the P-wave spectral content variability over the 2h preceding PAF onset with the aim of anticipating as much as possible the arrhythmic episode envision. For that purpose, the time course of several metrics estimating absolute energy and ratios of high- to low-frequency power in different bands between 20 and 200Hz has been computed from the P-wave autoregressive spectral estimation. All the analyzed metrics showed an increasing variability trend as PAF onset approximated, providing the P-wave high-frequency energy (between 80 and 150Hz) a diagnostic accuracy around 80% to discern between healthy subjects, patients far from PAF and patients less than 1h close to a PAF episode. This discriminant power was similar to that provided by the most classical time-domain approach, i.e., the P-wave duration. Furthermore, the linear combination of both metrics improved the diagnostic accuracy up to 88.07%, thus constituting a reliable noninvasive harbinger of PAF onset with a reasonable anticipation. The information provided by this methodology could be very useful in clinical practice either to optimize the antiarrhythmic treatment in patients at high-risk of PAF onset and to limit drug administration in low risk patients.

Changes in Global and Regional Mechanics Due to Atrial Fibrillation: Insights from a Coupled Finite-Element and Circulation Model

Atrial fibrillation (AF) is a rhythm disorder with rapidly increasing prevalence due to the aging of the population. AF triggers structural remodeling and a gradual loss of function; however, the relative contributions of specific features of AF-induced remodeling to changes in atrial mechanical function are unclear. We constructed and validated a finite-element model (FEM) of the normal human left atrium using anatomic information from cardiac magnetic resonance imaging, material properties and fiber orientations from published studies, and an iterative algorithm to estimate unloaded geometry. We coupled the FEM to a circuit model to capture hemodynamic interactions between the atrium, pulmonary circulation, and left ventricle. The normal model reproduced measured volumes within 1 SD, as well as most metrics of regional mechanics. Using this validated human model as a starting point, we explored the impact of individual features of atrial remodeling on atrial mechanics and found that a combination of dilation, increased pressure, and fibrosis can explain most of the observed changes in mechanics in patients with paroxysmal AF. However, only impaired ventricular relaxation could reproduce the increased reliance on active emptying we observed in these patients. The resulting model provides new insight into the mechanics of AF and a platform for exploring future therapies.

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.

Human atrial cell models to analyse haemodialysis-related effects on cardiac electrophysiology: work in progress

During haemodialysis (HD) sessions, patients undergo alterations in the extracellular environment, mostly concerning plasma electrolyte concentrations, pH, and volume, together with a modification of sympathovagal balance. All these changes affect cardiac electrophysiology, possibly leading to an increased arrhythmic risk. Computational modeling may help to investigate the impact of HD-related changes on atrial electrophysiology. However, many different human atrial action potential (AP) models are currently available, all validated only with the standard electrolyte concentrations used in experiments. Therefore, they may respond in different ways to the same environmental changes. After an overview on how the computational approach has been used in the past to investigate the effect of HD therapy on cardiac electrophysiology, the aim of this work has been to assess the current state of the art in human atrial AP models, with respect to the HD context. All the published human atrial AP models have been considered and tested for electrolytes, volume changes, and different acetylcholine concentrations. Most of them proved to be reliable for single modifications, but all of them showed some drawbacks. Therefore, there is room for a new human atrial AP model, hopefully able to physiologically reproduce all the HD-related effects. At the moment, work is still in progress in this specific field.

Disrupted calcium release as a mechanism for atrial alternans associated with human atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (ki_Ca) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca²⁺-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca²⁺ release slope. Iterated map analysis revealed that because SR Ca²⁺ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in ki_Ca were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca²⁺ homeostasis which drives proarrhythmic APD alternans in patients with AF.

Atrial fibrillation is an irregular heart rhythm affecting millions of people worldwide. Effective treatment of this cardiac disorder relies upon our detailed knowledge and understanding of the mechanisms that lead to arrhythmia. Recent clinical observations have suggested that alternans, a phenomenon where the shape of the electrical signal in the heart alternates from beat to beat, may play an important role in this process, but the underlying mechanisms remain unknown. In this study, we use computational models to conduct a detailed examination of the causes and contributors to alternans associated with human atrial fibrillation. We find that in atria remodeled by atrial fibrillation, alternans appears near resting heart rates because several aspects of calcium cycling are disrupted in the atrial cells. In particular, the release and uptake of calcium from the cellular storage compartment, the sarcoplasmic reticulum, becomes imbalanced, leading to alternation in calcium signals from beat to beat. These findings provide important insights into the mechanisms of proarrhythmic alternans in human atrial fibrillation which may be used to develop novel therapeutic targets and treatment strategies in the future.

Application of the RIMARC algorithm to a large data set of action potentials and clinical parameters for risk prediction of atrial fibrillation

Ex vivo recorded action potentials (APs) in human right atrial tissue from patients in sinus rhythm (SR) or atrial fibrillation (AF) display a characteristic spike-and-dome or triangular shape, respectively, but variability is huge within each rhythm group. The aim of our study was to apply the machine-learning algorithm ranking instances by maximizing the area under the ROC curve (RIMARC) to a large data set of 480 APs combined with retrospectively collected general clinical parameters and to test whether the rules learned by the RIMARC algorithm can be used for accurately classifying the preoperative rhythm status. APs were included from 221 SR and 158 AF patients. During a learning phase, the RIMARC algorithm established a ranking order of 62 features by predictive value for SR or AF. The model was then challenged with an additional test set of features from 28 patients in whom rhythm status was blinded. The accuracy of the risk prediction for AF by the model was very good (0.93) when all features were used. Without the seven AP features, accuracy still reached 0.71. In conclusion, we have shown that training the machine-learning algorithm RIMARC with an experimental and clinical data set allows predicting a classification in a test data set with high accuracy. In a clinical setting, this approach may prove useful for finding hypothesis-generating associations between different parameters.

Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach

Under diseased conditions, remodeling of the cardiac tissue properties (“passive properties”) takes place; these are aspects of electrophysiological behavior that are not associated with active ion transport across cell membranes. Remodeling of the passive electrophysiological properties most often results from structural remodeling, such as gap junction down-regulation and lateralization, fibrotic growth infiltrating the myocardium, or the development of an infarct scar. Such structural remodeling renders atrial or ventricular tissue as a major substrate for arrhythmias. The current review focuses on these aspects of cardiac arrhythmogenesis. Due to the inherent complexity of cardiac arrhythmias, computer simulations have provided means to elucidate interactions pertinent to this spatial scale. Here we review the current state-of-the-art in modeling atrial and ventricular arrhythmogenesis as arising from the disease-induced changes in the passive tissue properties, as well as the contributions these modeling studies have made to our understanding of the mechanisms of arrhythmias in the heart. Because of the rapid advance of structural imaging methodologies in cardiac electrophysiology, we chose to present studies that have used such imaging methodologies to construct geometrically realistic models of cardiac tissue, or the organ itself, where the regional remodeling properties of the myocardium can be represented in a realistic way. We emphasize how the acquired knowledge can be used to pave the way for clinical applications of cardiac organ modeling under the conditions of structural remodeling.

Inter-subject variability in human atrial action potential in sinus rhythm versus chronic atrial fibrillation

AIMS

Human atrial electrophysiology exhibits high inter-subject variability in both sinus rhythm (SR) and chronic atrial fibrillation (cAF) patients. Variability is however rarely investigated in experimental and theoretical electrophysiological studies, thus hampering the understanding of its underlying causes but also its implications in explaining differences in the response to disease and treatment. In our study, we aim at investigating the ability of populations of human atrial cell models to capture the inter-subject variability in action potential (AP) recorded in 363 patients both under SR and cAF conditions.

METHODS AND RESULTS

Human AP recordings in atrial trabeculae (n = 469) from SR and cAF patients were used to calibrate populations of computational SR and cAF atrial AP models. Three populations of over 2000 sampled models were generated, based on three different human atrial AP models. Experimental calibration selected populations of AP models yielding AP with morphology and duration in range with experimental recordings. Populations using the three original models can mimic variability in experimental AP in both SR and cAF, with median conductance values in SR for most ionic currents deviating less than 30% from their original peak values. All cAF populations show similar variations in G(K1), G(Kur) and G(to), consistent with AF-related remodeling as reported in experiments. In all SR and cAF model populations, inter-subject variability in I(K1) and I(NaK) underlies variability in APD90, variability in I(Kur), I(CaL) and I(NaK) modulates variability in APD50 and combined variability in Ito and I(Kur) determines variability in APD20. The large variability in human atrial AP triangulation is mostly determined by I(K1) and either I(NaK) or I(NaCa) depending on the model.

CONCLUSION

Experimentally-calibrated human atrial AP models populations mimic AP variability in SR and cAF patient recordings, and identify potential ionic determinants of inter-subject variability in human atrial AP duration and morphology in SR versus cAF.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This article aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention.

Heterogeneous and anisotropic integrative model of pulmonary veins: computational study of arrhythmogenic substrate for atrial fibrillation

Mechanisms underlying the genesis of re-entrant substrate for the most common cardiac arrhythmia, atrial fibrillation (AF), are not well understood. In this study, we develop a multi-scale three-dimensional computational model that integrates cellular electrophysiology of the left atrium (LA) and pulmonary veins (PVs) with the respective tissue geometry and fibre orientation. The latter is reconstructed in unique detail from high-resolution (approx. 70 μm) contrast micro-computed tomography data. The model is used to explore the mechanisms of re-entry initiation and sustenance in the PV region, regarded as the primary source of high-frequency electrical activity in AF. Simulations of the three-dimensional model demonstrate that an initial break-down of normal electrical excitation wave-fronts can be caused by the electrical heterogeneity between the PVs and LA. High tissue anisotropy is then responsible for the slow conduction and generation of a re-entrant circuit near the PVs. Evidence of such circuits has been seen clinically in AF patients. Our computational study suggests that primarily the combination of electrical heterogeneity and conduction anisotropy between the PVs and LA tissues leads to the generation of a high-frequency (approx. 10 Hz) re-entrant source near the PV sleeves, thus providing new insights into the arrhythmogenic mechanisms of excitation waves underlying AF.

Fibroblast-myocyte electrotonic coupling: does it occur in native cardiac tissue?

Heterocellular electrotonic coupling between cardiac myocytes and non-excitable connective tissue cells has been a long-established and well-researched fact in vitro. Whether or not such coupling exists in vivo has been a matter of considerable debate. This paper reviews the development of experimental insight and conceptual views on this topic, describes evidence in favour of and against the presence of such coupling in native myocardium, and identifies directions for further study needed to resolve the riddle, perhaps less so in terms of principal presence which has been demonstrated, but undoubtedly in terms of extent, regulation, patho-physiological context, and actual relevance of cardiac myocyte–non-myocyte coupling in vivo. This article is part of a Special Issue entitled "Myocyte-Fibroblast Signalling in Myocardium."

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Electrical coupling of cardiomyocytes and fibroblasts is well-established in vitro

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Whether such hetero-cellular coupling exists in vivo has been a matter of debate

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We review the development of experimental and conceptual insight into the topic

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Conclusion 1: hetero-cellular coupling in heart tissue has been shown in principle

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Conclusion 2: extent, regulation, context, and relevance remain to be established

Patient-specific modeling of atrial fibrosis increases the accuracy of sinus rhythm simulations and may explain maintenance of atrial fibrillation

Left atrial fibrosis is thought to contribute to the manifestation of atrial fibrillation (AF). Late Gadolinium enhancement (LGE) MRI has the potential to image regions of low perfusion, which can be related to fibrosis. We show that a simulation with a patient-specific model including left atrial regional fibrosis derived from LGE-MRI reproduces local activation in the left atrium more precisely than the regular simulation without fibrosis. AF simulations showed a spontaneous termination of the arrhythmia in the absence of fibrosis and a stable rotor center in the presence of fibrosis. The methodology may provide a tool for a deeper understanding of the mechanisms maintaining AF and eventually also for the planning of substrate-guided ablation procedures in the future.

A simple model of the right atrium of the human heart with the sinoatrial and atrioventricular nodes included

Existing atrial models with detailed anatomical structure and multi-variable cardiac transmembrane current models are too complex to allow to combine an investigation of long time dycal properties of the heart rhythm with the ability to effectively simulate cardiac electrical activity during arrhythmia. Other ways of modeling need to be investigated. Moreover, many state-of-the-art models of the right atrium do not include an atrioventricular node (AVN) and only rarely--the sinoatrial node (SAN). A model of the heart tissue within the right atrium including the SAN and AVN nodes was developed. Looking for a minimal model, currently we are testing our approach on chosen well-known arrhythmias, which were until now obtained only using much more complicated models, or were only observed in a clinical setting. Ultimately, the goal is to obtain a model able to generate sequences of RR intervals specific for the arrhythmias involving the AV junction as well as for other phenomena occurring within the atrium. The model should be fast enough to allow the study of heart rate variability and arrhythmias at a time scale of thousands of heart beats in real-time. In the model of the right atrium proposed here, different kinds of cardiac tissues are described by sets of different equations, with most of them belonging to the class of Liénard nonlinear dynamical systems. We have developed a series of models of the right atrium with differing anatomical simplifications, in the form of a 2D mapping of the atrium or of an idealized cylindrical geometry, including only those anatomical details required to reproduce a given physiological phenomenon. The simulations allowed to reconstruct the phase relations between the sinus rhythm and the location and properties of a parasystolic source together with the effect of this source on the resultant heart rhythm. We model the action potential conduction time alternans through the atrioventricular AVN junction observed in cardiac tissue in electrophysiological studies during the ventricular-triggered atrial tachycardia. A simulation of the atrio-ventricular nodal reentry tachycardia was performed together with an entrainment procedure in which the arrhythmia circuit was located by measuring the post-pacing interval (PPI) at simulated mapping catheters. The generation and interpretation of RR times series is the ultimate goal of our research. However, to reach that goal we need first to (1) somehow verify the validity of the model of the atrium with the nodes included and (2) include in the model the effect of the sympathetic and vagal ANS. The current paper serves as a partial solution of the 1). In particular we show, that measuring the PPI-TCL entrainment response in proximal (possibly-the slow-conducting pathway), the distal and at a mid-distance from CS could help in rapid distinction of AVNRT from other atrial tachycardias. Our simulations support the hypothesis that the alternans of the conduction time between the atria and the ventricles in the AV orthodromic reciprocating tachycardia can occur within a single pathway. In the atrial parasystole simulation, we found a mathematical condition which allows for a rough estimation of the location of the parasystolic source within the atrium, both for simplified (planar) and the cylindrical geometry of the atrium. The planar and the cylindrical geometry yielded practically the same results of simulations.

In-silico modeling of atrial repolarization in normal and atrial fibrillation remodeled state

Atrial fibrillation (AF) is the most common cardiac arrhythmia, and the total number of AF patients is constantly increasing. The mechanisms leading to and sustaining AF are not completely understood yet. Heterogeneities in atrial electrophysiology seem to play an important role in this context. Although some heterogeneities have been used in in-silico human atrial modeling studies, they have not been thoroughly investigated. In this study, the original electrophysiological (EP) models of Courtemanche et al., Nygren et al. and Maleckar et al. were adjusted to reproduce action potentials in 13 atrial regions. The parameter sets were validated against experimental action potential duration data and ECG data from patients with AV block. The use of the heterogeneous EP model led to a more synchronized repolarization sequence in a variety of 3D atrial anatomical models. Combination of the heterogeneous EP model with a model of persistent AF-remodeled electrophysiology led to a drastic change in cell electrophysiology. Simulated Ta-waves were significantly shorter under the remodeling. The heterogeneities in cell electrophysiology explain the previously observed Ta-wave effects. The results mark an important step toward the reliable simulation of the atrial repolarization sequence, give a deeper understanding of the mechanism of atrial repolarization and enable further clinical investigations.

Pro-arrhythmogenic effects of atrial fibrillation-induced electrical remodelling: insights from the three-dimensional virtual human atria

Chronic atrial fibrillation (AF) is associated with structural and electrical remodelling in the atria, which are associated with a high recurrence of AF. Through biophysically detailed computer modelling, this study investigated mechanisms by which AF-induced electrical remodelling promotes and perpetuates AF. A family of Courtemanche–Ramirez–Nattel variant models of human atrial cell action potentials (APs), taking into account of intrinsic atrial electrophysiological properties, was modified to incorporate various experimental data sets on AF-induced changes of major ionic channel currents (I_CaL, I_Kur, I_to, I_K1, I_Ks, I_NaCa) and on intracellular Ca²⁺ handling. The single cell models for control and AF-remodelled conditions were incorporated into multicellular three-dimensional (3D) atrial tissue models. Effects of the AF-induced electrical remodelling were quantified as the changes of AP profile, AP duration (APD) and its dispersion across the atria, and the vulnerability of atrial tissue to the initiation of re-entry. The dynamic behaviour of re-entrant excitation waves in the 3D models was characterised. In our simulations, AF-induced electrical remodelling abbreviated atrial APD non-uniformly across the atria; this resulted in relatively short APDs co-existing with marked regional differences in the APD at junctions of the crista terminalis/pectinate muscle, pulmonary veins/left atrium. As a result, the measured tissue vulnerability to re-entry initiation at these tissue junctions was increased. The AF-induced electrical remodelling also stabilized and accelerated re-entrant excitation waves, leading to rapid and sustained re-entry. Under the AF-remodelled condition, re-entrant scroll waves in the 3D model degenerated into persistent and erratic wavelets, leading to fibrillation. In conclusion, realistic 3D atrial tissue models indicate that AF-induced electrical remodelling produces regionally heterogeneous and shortened APD; these respectively facilitate initiation and maintenance of re-entrant excitation waves.

A three-dimensional finite element model of human atrial anatomy: new methods for cubic Hermite meshes with extraordinary vertices

High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology.

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

The most common sustained cardiac arrhythmias in humans are atrial tachyarrhythmias, mainly atrial fibrillation. Areas of complex fractionated atrial electrograms and high dominant frequency have been proposed as critical regions for maintaining atrial fibrillation; however, there is a paucity of data on the relationship between the characteristics of electrograms and the propagation pattern underlying them. In this study, a realistic 3D computer model of the human atria has been developed to investigate this relationship. The model includes a realistic geometry with fiber orientation, anisotropic conductivity and electrophysiological heterogeneity. We simulated different tachyarrhythmic episodes applying both transient and continuous ectopic activity. Electrograms and their dominant frequency and organization index values were calculated over the entire atrial surface. Our simulations show electrograms with simple potentials, with little or no cycle length variations, narrow frequency peaks and high organization index values during stable and regular activity as the observed in atrial flutter, atrial tachycardia (except in areas of conduction block) and in areas closer to ectopic activity during focal atrial fibrillation. By contrast, cycle length variations and polymorphic electrograms with single, double and fragmented potentials were observed in areas of irregular and unstable activity during atrial fibrillation episodes. Our results also show: (1) electrograms with potentials without negative deflection related to spiral or curved wavefronts that pass over the recording point and move away, (2) potentials with a much greater proportion of positive deflection than negative in areas of wave collisions, (3) double potentials related with wave fragmentations or blocking lines and (4) fragmented electrograms associated with pivot points. Our model is the first human atrial model with realistic fiber orientation used to investigate the relationship between different atrial arrhythmic propagation patterns and the electrograms observed at more than 43000 points on the atrial surface.

Generating anatomical models of the heart and the aorta from medical images for personalized physiological simulations

The anatomy and motion of the heart and the aorta are essential for patient-specific simulations of cardiac electrophysiology, wall mechanics and hemodynamics. Within the European integrated project euHeart, algorithms have been developed that allow to efficiently generate patient-specific anatomical models from medical images from multiple imaging modalities. These models, for instance, account for myocardial deformation, cardiac wall motion, and patient-specific tissue information like myocardial scar location. Furthermore, integration of algorithms for anatomy extraction and physiological simulations has been brought forward. Physiological simulations are linked closer to anatomical models by encoding tissue properties, like the muscle fibers, into segmentation meshes. Biophysical constraints are also utilized in combination with image analysis to assess tissue properties. Both examples show directions of how physiological simulations could provide new challenges and stimuli for image analysis research in the future.

Benchmarking electrophysiological models of human atrial myocytes

Mathematical modeling of cardiac electrophysiology is an insightful method to investigate the underlying mechanisms responsible for arrhythmias such as atrial fibrillation (AF). In past years, five models of human atrial electrophysiology with different formulations of ionic currents, and consequently diverging properties, have been published. The aim of this work is to give an overview of strengths and weaknesses of these models depending on the purpose and the general requirements of simulations. Therefore, these models were systematically benchmarked with respect to general mathematical properties and their ability to reproduce certain electrophysiological phenomena, such as action potential (AP) alternans. To assess the models' ability to replicate modified properties of human myocytes and tissue in cardiac disease, electrical remodeling in chronic atrial fibrillation (cAF) was chosen as test case. The healthy and remodeled model variants were compared with experimental results in single-cell, 1D and 2D tissue simulations to investigate AP and restitution properties, as well as the initiation of reentrant circuits.

Comparison of simulated and clinical intracardiac electrograms

Intracardiac electrograms are the key in understanding, interpretation and treatment of cardiac arrhythmias. However, electrogram morphologies are strongly variable due to catheter position, orientation and contact. Simulations of intracardiac electrograms can improve comprehension and quantification of influencing parameters and therefore reduce misinterpretations. In this study simulated intracardiac electrograms are analyzed regarding tilt angles of the catheter relative to the propagation direction, electrode tissue distances as well as clinical filter settings. Catheter signals are computed on a realistic 3D catheter geometry using bidomain simulations of cardiac electrophysiology. Thereby high conductivities of the catheter electrodes are taken into account. For validation, simulated electrograms are compared with in vivo electrograms recorded during an EP-study with direct annotation of catheter orientation and tissue contact. Good agreement was reached regarding timing and signal width of simulated and measured electrograms. Correlation was 0.92±0.07 for bipolar, 0.92±0.05 for unipolar distal and 0.80 ± 0.12 for unipolar proximal electrograms for different catheter orientations and locations.

Towards personalized clinical in-silico modeling of atrial anatomy and electrophysiology

Computational atrial models aid the understanding of pathological mechanisms and therapeutic measures in basic research. The use of biophysical models in a clinical environment requires methods to personalize the anatomy and electrophysiology (EP). Strategies for the automation of model generation and for evaluation are needed. In this manuscript, the current efforts of clinical atrial modeling in the euHeart project are summarized within the context of recent publications in this field. Model-based segmentation methods allow for the automatic generation of ready-to-simulate patient-specific anatomical models. EP models can be adapted to patient groups based on a-priori knowledge and to the individual without significant further data acquisition. ECG and intracardiac data build the basis for excitation personalization. Information from late enhancement (LE) MRI can be used to evaluate the success of radio-frequency ablation (RFA) procedures and interactive virtual atria pave the way for RFA planning. Atrial modeling is currently in a transition from the sole use in basic research to future clinical applications. The proposed methods build the framework for model-based diagnosis and therapy evaluation and planning. Complex models allow to understand biophysical mechanisms and enable the development of simplified models for clinical applications.

Cross talk between cardiac myocytes and fibroblasts: from multiscale investigative approaches to mechanisms and functional consequences

The heart is comprised of a syncytium of cardiac myocytes (CM) and surrounding nonmyocytes, the majority of which are cardiac fibroblasts (CF). CM and CF are highly interspersed in the myocardium with one CM being surrounded by one or more CF. Bidirectional cross talk between CM and CF plays important roles in determining cardiac mechanical and electrical function in both normal and diseased hearts. Genetically engineered animal models and in vitro studies have provided evidence that CM and CF can regulate each other's function. Their cross talk contributes to structural and electrical remodeling in both atria and ventricles and appears to be involved in the pathogenesis of various heart diseases that lead to heart failure and arrhythmia disorders. Mechanisms of CM-CF cross talk, which are not yet fully understood, include release of paracrine factors, direct cell-cell interactions via gap junctions and potentially adherens junctions and nanotubes, and cell interactions with the extracellular matrix. In this article, we provide an overview of the existing multiscale experimental and computational approaches for the investigation of cross talk between CM and CF and review recent progress in our understanding of the functional consequences and underlying mechanisms. Targeting cross talk between CM and CF could potentially be used therapeutically for the modulation of the cardiac remodeling response in the diseased heart and may lead to new strategies for the treatment of heart failure or rhythm disturbances.