A computer model of normal conduction in the human atria

Multiplatform modeling of atrial fibrillation identifies phospholamban as a central regulator of cardiac rhythm

Atrial fibrillation (AF) is a common and genetically inheritable form of cardiac arrhythmia; however, it is currently not known how these genetic predispositions contribute to the initiation and/or maintenance of AF-associated phenotypes. One major barrier to progress is the lack of experimental systems to investigate the effects of gene function on rhythm parameters in models with human atrial and whole-organ relevance. Here, we assembled a multi-model platform enabling high-throughput characterization of the effects of gene function on action potential duration and rhythm parameters using human induced pluripotent stem cell-derived atrial-like cardiomyocytes and a Drosophila heart model, and validation of the findings using computational models of human adult atrial myocytes and tissue. As proof of concept, we screened 20 AF-associated genes and identified phospholamban loss of function as a top conserved hit that shortens action potential duration and increases the incidence of arrhythmia phenotypes upon stress. Mechanistically, our study reveals that phospholamban regulates rhythm homeostasis by functionally interacting with L-type Ca2+ channels and NCX. In summary, our study illustrates how a multi-model system approach paves the way for the discovery and molecular delineation of gene regulatory networks controlling atrial rhythm with application to AF.

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

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

Conditional immortalization of human atrial myocytes for the generation of in vitro models of atrial fibrillation

The lack of a scalable and robust source of well-differentiated human atrial myocytes constrains the development of in vitro models of atrial fibrillation (AF). Here we show that fully functional atrial myocytes can be generated and expanded one-quadrillion-fold via a conditional cell-immortalization method relying on lentiviral vectors and the doxycycline-controlled expression of a recombinant viral oncogene in human foetal atrial myocytes, and that the immortalized cells can be used to generate in vitro models of AF. The method generated 15 monoclonal cell lines with molecular, cellular and electrophysiological properties resembling those of primary atrial myocytes. Multicellular in vitro models of AF generated using the immortalized atrial myocytes displayed fibrillatory activity (with activation frequencies of 6-8 Hz, consistent with the clinical manifestation of AF), which could be terminated by the administration of clinically approved antiarrhythmic drugs. The conditional cell-immortalization method could be used to generate functional cell lines from other human parenchymal cells, for the development of in vitro models of human disease.

Atrial Flutter Mechanism Detection Using Directed Network Mapping

Atrial flutter (AFL) is a common atrial arrhythmia typically characterized by electrical activity propagating around specific anatomical regions. It is usually treated with catheter ablation. However, the identification of rotational activities is not straightforward, and requires an intense effort during the first phase of the electrophysiological (EP) study, i.e., the mapping phase, in which an anatomical 3D model is built and electrograms (EGMs) are recorded. In this study, we modeled the electrical propagation pattern of AFL (measured during mapping) using network theory (NT), a well-known field of research from the computer science domain. The main advantage of NT is the large number of available algorithms that can efficiently analyze the network. Using directed network mapping, we employed a cycle-finding algorithm to detect all cycles in the network, resembling the main propagation pattern of AFL. The method was tested on two subjects in sinus rhythm, six in an experimental model of in-silico simulations, and 10 subjects diagnosed with AFL who underwent a catheter ablation. The algorithm correctly detected the electrical propagation of both sinus rhythm cases and in-silico simulations. Regarding the AFL cases, arrhythmia mechanisms were either totally or partially identified in most of the cases (8 out of 10), i.e., cycles around the mitral valve, tricuspid valve and figure-of-eight reentries. The other two cases presented a poor mapping quality or a major complexity related to previous ablations, large areas of fibrotic tissue, etc. Directed network mapping represents an innovative tool that showed promising results in identifying AFL mechanisms in an automatic fashion. Further investigations are needed to assess the reliability of the method in different clinical scenarios.

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling.

CVAR-Seg: An Automated Signal Segmentation Pipeline for Conduction Velocity and Amplitude Restitution

BACKGROUND

Rate-varying S1S2 stimulation protocols can be used for restitution studies to characterize atrial substrate, ionic remodeling, and atrial fibrillation risk. Clinical restitution studies with numerous patients create large amounts of these data. Thus, an automated pipeline to evaluate clinically acquired S1S2 stimulation protocol data necessitates consistent, robust, reproducible, and precise evaluation of local activation times, electrogram amplitude, and conduction velocity. Here, we present the CVAR-Seg pipeline, developed focusing on three challenges: (i) No previous knowledge of the stimulation parameters is available, thus, arbitrary protocols are supported. (ii) The pipeline remains robust under different noise conditions. (iii) The pipeline supports segmentation of atrial activities in close temporal proximity to the stimulation artifact, which is challenging due to larger amplitude and slope of the stimulus compared to the atrial activity.

METHODS AND RESULTS

The S1 basic cycle length was estimated by time interval detection. Stimulation time windows were segmented by detecting synchronous peaks in different channels surpassing an amplitude threshold and identifying time intervals between detected stimuli. Elimination of the stimulation artifact by a matched filter allowed detection of local activation times in temporal proximity. A non-linear signal energy operator was used to segment periods of atrial activity. Geodesic and Euclidean inter electrode distances allowed approximation of conduction velocity. The automatic segmentation performance of the CVAR-Seg pipeline was evaluated on 37 synthetic datasets with decreasing signal-to-noise ratios. Noise was modeled by reconstructing the frequency spectrum of clinical noise. The pipeline retained a median local activation time error below a single sample (1 ms) for signal-to-noise ratios as low as 0 dB representing a high clinical noise level. As a proof of concept, the pipeline was tested on a CARTO case of a paroxysmal atrial fibrillation patient and yielded plausible restitution curves for conduction speed and amplitude.

CONCLUSION

The proposed openly available CVAR-Seg pipeline promises fast, fully automated, robust, and accurate evaluations of atrial signals even with low signal-to-noise ratios. This is achieved by solving the proximity problem of stimulation and atrial activity to enable standardized evaluation without introducing human bias for large data sets.

Bioengineering Clinically Relevant Cardiomyocytes and Cardiac Tissues from Pluripotent Stem Cells

The regenerative capacity of cardiomyocytes is insufficient to functionally recover damaged tissue, and as such, ischaemic heart disease forms the largest proportion of cardiovascular associated deaths. Human-induced pluripotent stem cells (hiPSCs) have enormous potential for developing patient specific cardiomyocytes for modelling heart disease, patient-based cardiac toxicity testing and potentially replacement therapy. However, traditional protocols for hiPSC-derived cardiomyocytes yield mixed populations of atrial, ventricular and nodal-like cells with immature cardiac properties. New insights gleaned from embryonic heart development have progressed the precise production of subtype-specific hiPSC-derived cardiomyocytes; however, their physiological immaturity severely limits their utility as model systems and their use for drug screening and cell therapy. The long-entrenched challenges in this field are being addressed by innovative bioengingeering technologies that incorporate biophysical, biochemical and more recently biomimetic electrical cues, with the latter having the potential to be used to both direct hiPSC differentiation and augment maturation and the function of derived cardiomyocytes and cardiac tissues by mimicking endogenous electric fields.

Atrial fibrillation source area probability mapping using electrogram patterns of multipole catheters

BACKGROUND

Catheter ablation therapy involving isolation of pulmonary veins (PVs) from the left atrium is performed to terminate atrial fibrillation (AF). Unfortunately, standalone PV isolation procedure has shown to be a suboptimal success with AF continuation or recurrence. One reason, especially in patients with persistent or high-burden paroxysmal AF, is known to be due to the formation of repeating-pattern AF sources with a meandering core inside the atria. However, there is a need for accurate mapping and localization of these sources during catheter ablation.

METHODS

A novel AF source area probability (ASAP) mapping algorithm was developed and evaluated in 2D and 3D atrial simulated tissues with various arrhythmia scenarios and a retrospective study with three cases of clinical human AF. The ASAP mapping analyzes the electrograms collected from a multipole diagnostic catheter that is commonly used during catheter ablation procedure to intelligently sample the atria and delineate the trajectory path of a meandering repeating-pattern AF source. ASAP starts by placing the diagnostic catheter at an arbitrary location in the atria. It analyzes the recorded bipolar electrograms to build an ASAP map over the atrium anatomy and suggests an optimal location for the subsequent catheter location. ASAP then determines from the constructed ASAP map if an AF source has been delineated. If so, the catheter navigation is stopped and the algorithm provides the area of the AF source. Otherwise, the catheter is navigated to the suggested location, and the process is continued until an AF-source area is delineated.

RESULTS

ASAP delineated the AF source in over 95% of the simulated human AF cases within less than eight catheter placements regardless of the initial catheter placement. The success of ASAP in the clinical AF was confirmed by the ablation outcomes and the electrogram patterns at the delineated area.

CONCLUSION

Our analysis indicates the potential of the ASAP mapping to provide accurate information about the area of the meandering repeating-pattern AF sources as AF ablation targets for effective AF termination. Our algorithm could improve the success of AF catheter ablation therapy by locating and subsequently targeting patient-specific and repeating-pattern AF sources inside the atria.

Multicellular In vitro Models of Cardiac Arrhythmias: Focus on Atrial Fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia in clinical practice with a large socioeconomic impact due to its associated morbidity, mortality, reduction in quality of life and health care costs. Currently, antiarrhythmic drug therapy is the first line of treatment for most symptomatic AF patients, despite its limited efficacy, the risk of inducing potentially life-threating ventricular tachyarrhythmias as well as other side effects. Alternative, in-hospital treatment modalities consisting of electrical cardioversion and invasive catheter ablation improve patients' symptoms, but often have to be repeated and are still associated with serious complications and only suitable for specific subgroups of AF patients. The development and progression of AF generally results from the interplay of multiple disease pathways and is accompanied by structural and functional (e.g., electrical) tissue remodeling. Rational development of novel treatment modalities for AF, with its many different etiologies, requires a comprehensive insight into the complex pathophysiological mechanisms. Monolayers of atrial cells represent a simplified surrogate of atrial tissue well-suited to investigate atrial arrhythmia mechanisms, since they can easily be used in a standardized, systematic and controllable manner to study the role of specific pathways and processes in the genesis, perpetuation and termination of atrial arrhythmias. In this review, we provide an overview of the currently available two- and three-dimensional multicellular in vitro systems for investigating the initiation, maintenance and termination of atrial arrhythmias and AF. This encompasses cultures of primary (animal-derived) atrial cardiomyocytes (CMs), pluripotent stem cell-derived atrial-like CMs and (conditionally) immortalized atrial CMs. The strengths and weaknesses of each of these model systems for studying atrial arrhythmias will be discussed as well as their implications for future studies.

Analysis of a coupled fluid-structure interaction model of the left atrium and mitral valve

We present a coupled left atrium-mitral valve model based on computed tomography scans with fibre-reinforced hyperelastic materials. Fluid-structure interaction is realised by using an immersed boundary-finite element framework. Effects of pathological conditions, eg, mitral valve regurgitation and atrial fibrillation, and geometric and structural variations, namely, uniform vs non-uniform atrial wall thickness and rule-based vs atlas-based fibre architectures, on the system are investigated. We show that in the case of atrial fibrillation, pulmonary venous flow reversal at late diastole disappears, and the filling waves at the left atrial appendage orifice during systole have reduced magnitude. In the case of mitral regurgitation, a higher atrial pressure and disturbed flows are seen, especially during systole, when a large regurgitant jet can be found with the suppressed pulmonary venous flow. We also show that both the rule-based and atlas-based fibre defining methods lead to similar flow fields and atrial wall deformations. However, the changes in wall thickness from non-uniform to uniform tend to underestimate the atrial deformation. Using a uniform but thickened wall also lowers the overall strain level. The flow velocity within the left atrial appendage, which is important in terms of appendage thrombosis, increases with the thickness of the left atrial wall. Energy analysis shows that the kinetic and dissipation energies of the flow within the left atrium are altered differently by atrial fibrillation and mitral valve regurgitation, providing a useful indication of the atrial performance in pathological situations.

A robust computational framework for estimating 3D Bi-Atrial chamber wall thickness

Atrial fibrillation (AF) is the most prevalent form of cardiac arrhythmia. The atrial wall thickness (AWT) can potentially improve our understanding of the mechanism underlying atrial structure that drives AF and provides important clinical information. However, most existing studies for estimating AWT rely on ruler-based measurements performed on only a few selected locations in 2D or 3D using digital calipers. Only a few studies have developed automatic approaches to estimate the AWT in the left atrium, and there are currently no methods to robustly estimate the AWT of both atrial chambers. Therefore, we have developed a computational pipeline to automatically calculate the 3D AWT across bi-atrial chambers and extensively validated our pipeline on both ex vivo and in vivo human atria data. The atrial geometry was first obtained by segmenting the atrial wall from the MRIs using a novel machine learning approach. The epicardial and endocardial surfaces were then separated using a multi-planar convex hull approach to define boundary conditions, from which, a Laplace equation was solved numerically to automatically separate bi-atrial chambers. To robustly estimate the AWT in each atrial chamber, coupled partial differential equations by coupling the Laplace solution with two surface trajectory functions were formulated and solved. Our pipeline enabled the reconstruction and visualization of the 3D AWT for bi-atrial chambers with a relative error of 8% and outperformed existing algorithms by >7%. Our approach can potentially lead to improved clinical diagnosis, patient stratification, and clinical guidance during ablation treatment for patients with AF.

Directed Networks as a Novel Way to Describe and Analyze Cardiac Excitation: Directed Graph Mapping

Networks provide a powerful methodology with applications in a variety of biological, technological and social systems such as analysis of brain data, social networks, internet search engine algorithms, etc. To date, directed networks have not yet been applied to characterize the excitation of the human heart. In clinical practice, cardiac excitation is recorded by multiple discrete electrodes. During (normal) sinus rhythm or during cardiac arrhythmias, successive excitation connects neighboring electrodes, resulting in their own unique directed network. This in theory makes it a perfect fit for directed network analysis. In this study, we applied directed networks to the heart in order to describe and characterize cardiac arrhythmias. Proof-of-principle was established using in-silico and clinical data. We demonstrated that tools used in network theory analysis allow determination of the mechanism and location of certain cardiac arrhythmias. We show that the robustness of this approach can potentially exceed the existing state-of-the art methodology used in clinics. Furthermore, implementation of these techniques in daily practice can improve the accuracy and speed of cardiac arrhythmia analysis. It may also provide novel insights in arrhythmias that are still incompletely understood.

Heterogeneous Effects of Fibroblast-Myocyte Coupling in Different Regions of the Human Atria Under Conditions of Atrial Fibrillation

Background: Atrial fibrillation (AF), the most common cardiac arrhythmia, is characterized by alteration of the action potential (AP) propagation. Under persistent AF, myocytes undergo electrophysiological and structural remodeling, which involves fibroblast proliferation and differentiation, modifying the substrate for AP propagation. The aim of this study was to analyze the effects on the AP of fibroblast-myocyte coupling during AF and its propagation in different regions of the atria.

Methods: Isolated myocytes were coupled to different numbers of fibroblasts using the established AP models and tissue simulations were performed by randomly distributing fibroblasts. Fibroblast formulations were updated to match recent experimental data. Major ion current conductances of the myocyte model were modified to simulate AP heterogeneity in four different atrial regions (right atrium posterior wall, crista terminalis, left atrium posterior wall, and pulmonary vein) according to experimental and computational studies.

Results: The results of the coupled myocyte-fibroblast simulations suggest that a more depolarized membrane potential and higher fibroblast membrane capacitance have a greater impact on AP duration and myocyte maximum depolarization velocity. The number of coupled fibroblasts and the stimulation frequency are determining factors in altering myocyte AP. Strand simulations show that conduction velocity tends to homogenize in all regions, while the left atrium is more likely to be affected by fibroblast and AP propagation block is more likely to occur. The pulmonary vein is the most affected region, even at low fibroblast densities. In 2D sheets with randomly placed fibroblasts, wavebreaks are observed in the low density (10%) central fibrotic zone and when fibroblast density increases (40%) propagation in the fibrotic region is practically blocked. At densities of 10 and 20% the width of the vulnerable window increases with respect to control but is decreased at 40%.

Conclusion: Myocyte-fibroblast coupling characteristics heterogeneously affect AP propagation and features in the different atrial zones, and myocytes from the left atria are more sensitive to fibroblast coupling.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Novel Insights in the Activation Patterns at the Pulmonary Vein Area

BACKGROUND

Extensiveness of conduction delay and block at the pulmonary vein area (PVA) was quantified in a previous study. We hypothesized that the combination of lines of conduction block with multiple concomitantly entering sinus rhythm wavefronts at the PVA may result in increased arrhythmogenicity and susceptibility to atrial fibrillation (AF).

METHODS

Intraoperative high-density epicardial mapping of PVA (N≈450 sites, interelectrode distances: 2 mm) was performed during sinus rhythm in 327 patients (241 male [74%], 67±10 [21-84] years) with and without preoperative AF. For each patient, activation patterns at the PVA were quantified, including the location of entry sites of wavefronts, direction of propagation, and their relative activation times. The association between activation patterns and the presence of AF was examined.

RESULTS

Excitation of the PVA occurred via multiple consecutive wavefronts in the vast majority of patient (N=216, 81%). In total, 561 wavefronts were observed, which mostly propagated through the septal or paraseptal regions towards the PVA (N=461, 82%). A substantial dissociation of consecutive wavefronts was observed with Δactivation times of 10.6±8.8 (0-46) ms. No difference was observed in Δactivation times of consecutive wavefronts during sinus rhythm between patients without and with AF. An excitation-based risk factor model, including conduction delay ≥6 mm, conduction block ≥6 mm, and conduction delay and block ≥16 mm, wavefronts via the posteroinferior to posterosuperior regions and multiple opposing wavefronts, demonstrated a 5-fold risk of AF when multiple risk factors were present.

CONCLUSIONS

In contrast to previous findings, quantification of activation patterns at the PVA on high-resolution scale demonstrated complex patterns with often multiple entry sites and high interindividual variability. Altered patterns of activation, consisting of multiple opposing wavefronts combined with long lines of conduction slowing, were associated with the presence of AF.

Muscle Thickness and Curvature Influence Atrial Conduction Velocities

Electroanatomical mapping is currently used to provide clinicians with information about the electrophysiological state of the heart and to guide interventions like ablation. These maps can be used to identify ectopic triggers of an arrhythmia such as atrial fibrillation (AF) or changes in the conduction velocity (CV) that have been associated with poor cell to cell coupling or fibrosis. Unfortunately, many factors are known to affect CV, including membrane excitability, pacing rate, wavefront curvature, and bath loading, making interpretation challenging. In this work, we show how endocardial conduction velocities are also affected by the geometrical factors of muscle thickness and wall curvature. Using an idealized three-dimensional strand, we show that transverse conductivities and boundary conditions can slow down or speed up signal propagation, depending on the curvature of the muscle tissue. In fact, a planar wavefront that is parallel to a straight line normal to the mid-surface does not remain normal to the mid-surface in a curved domain. We further demonstrate that the conclusions drawn from the idealized test case can be used to explain spatial changes in conduction velocities in a patient-specific reconstruction of the left atrial posterior wall. The simulations suggest that the widespread assumption of treating atrial muscle as a two-dimensional manifold for electrophysiological simulations will not accurately represent the endocardial conduction velocities in regions of the heart thicker than 0.5 mm with significant wall curvature.

Nonlinear electrocardiographic imaging using polynomial approximation networks

Electrocardiography is a valuable tool to aid in medical understanding and treatment of heart-related ailments, specifically atrial fibrillation (AF) and other irregular cardiac behavior. Although signs of AF will manifest in conventional electrocardiogram (ECG) recordings, interpretation and localization of AF sources require significant clinical expertise. In this vein, electrocardiographic imaging has emerged as an important medical imaging modality that provides reconstructions of the heart's electrical activity from non-invasive multi-lead body-surface ECG and anatomical x-ray computed tomography images. In this paper, we present a nonlinear inversion model for computing this mapping to improve upon the reconstruction performance of current methods. While contemporary techniques typically determine an inverse solution by discretizing and inverting an underdetermined linear system of partial differential equations governing the relationship between voltage potentials of the heart and torso, the presented technique re-casts this problem as a task in function approximation and provides a direct parameterization of the inverse operator using a polynomial neural network. That is, the outlined nonlinear inversion technique is a generalization of contemporary reconstruction techniques which allows geometrical and material parameterizations of the forward-model to be optimized using real experimental data collected from patients suffering from AF, as to better represent the inverse operator with respect to reconstruction metrics applicable to electrophysiology. The accuracy of our model is evaluated against a dataset of real-patient recordings to demonstrate its validity, and mathematical analysis is provided to support the polynomial expansion used in our inversion model.

Computational Modeling of Electrophysiology and Pharmacotherapy of Atrial Fibrillation: Recent Advances and Future Challenges

The pathophysiology of atrial fibrillation (AF) is broad, with components related to the unique and diverse cellular electrophysiology of atrial myocytes, structural complexity, and heterogeneity of atrial tissue, and pronounced disease-associated remodeling of both cells and tissue. A major challenge for rational design of AF therapy, particularly pharmacotherapy, is integrating these multiscale characteristics to identify approaches that are both efficacious and independent of ventricular contraindications. Computational modeling has long been touted as a basis for achieving such integration in a rapid, economical, and scalable manner. However, computational pipelines for AF-specific drug screening are in their infancy, and while the field is progressing quite rapidly, major challenges remain before computational approaches can fill the role of workhorse in rational design of AF pharmacotherapies. In this review, we briefly detail the unique aspects of AF pathophysiology that determine requirements for compounds targeting AF rhythm control, with emphasis on delimiting mechanisms that promote AF triggers from those providing substrate or supporting reentry. We then describe modeling approaches that have been used to assess the outcomes of drugs acting on established AF targets, as well as on novel promising targets including the ultra-rapidly activating delayed rectifier potassium current, the acetylcholine-activated potassium current and the small conductance calcium-activated potassium channel. Finally, we describe how heterogeneity and variability are being incorporated into AF-specific models, and how these approaches are yielding novel insights into the basic physiology of disease, as well as aiding identification of the important molecular players in the complex AF etiology.

Personalized computational modeling of left atrial geometry and transmural myofiber architecture

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

Incorporating inductances in tissue-scale models of cardiac electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and we examine the effect of intracellular and extracellular inductances on the virtual electrode phenomenon.

Towards personalized computational modelling of the fibrotic substrate for atrial arrhythmia

: Atrial arrhythmias involving a fibrotic substrate are an important cause of morbidity and mortality. In many cases, effective treatment of such rhythm disorders is severely hindered by a lack of mechanistic understanding relating features of fibrotic remodelling to dynamics of re-entrant arrhythmia. With the advent of clinical imaging modalities capable of resolving the unique fibrosis spatial pattern present in the atria of each individual patient, a promising new research trajectory has emerged in which personalized computational models are used to analyse mechanistic underpinnings of arrhythmia dynamics based on the distribution of fibrotic tissue. In this review, we first present findings that have yielded a robust and detailed biophysical representation of fibrotic substrate electrophysiological properties. Then, we summarize the results of several recent investigations seeking to use organ-scale models of the fibrotic human atria to derive new insights on mechanisms of arrhythmia perpetuation and to develop novel strategies for model-assisted individualized planning of catheter ablation procedures for atrial arrhythmias.

Modeling Atrial Fibrillation using Human Embryonic Stem Cell-Derived Atrial Tissue

Since current experimental models of Atrial Fibrillation (AF) have significant limitations, we used human embryonic stem cells (hESCs) to generate an atrial-specific tissue model of AF for pharmacologic testing. We generated atrial-like cardiomyocytes (CMs) from hESCs which preferentially expressed atrial-specific genes, and had shorter action potential (AP) durations compared to ventricular-like CMs. We then generated confluent atrial-like CM sheets and interrogated them using optical mapping techniques. Atrial-like CM sheets (~1 cm in diameter) showed uniform AP propagation, and rapid re-entrant rotor patterns, as seen in AF could be induced. Anti-arrhythmic drugs were tested on single atrial-like CMs and cell sheets. Flecainide profoundly slowed upstroke velocity without affecting AP duration, leading to reduced conduction velocities (CVs), curvatures and cycle lengths of rotors, consistent with increased rotor organization and expansion. By contrast, consistent with block of rapid delayed rectifier K+ currents (Ikr) and AP prolongation in isolated atrial-like CMs, dofetilide prolonged APs and reduced cycle lengths of rotors in cell sheets without affecting CV. In conclusion, using our hESC-derived atrial CM preparations, we demonstrate that flecainide and dofetilide modulate reentrant arrhythmogenic rotor activation patterns in a manner that helps explain their efficacy in treating and preventing AF.

Bayes Syndrome and Imaging Techniques

BACKGROUND

Interatrial block (IAB) is due to disruption in the Bachmann region (BR). According to whether interatrial electrical conduction is delayed or completely blocked through the BR, it can be classified as IAB of first, second or third degree. On the surface electrocardiogram, a P wave ≥ 120 ms (partial IAB) is observed or associated to the prolongation of the P wave with a biphasic (positive / negative) morphology in the inferior leads (advanced IAB). Bayes syndrome is defined as an advanced IAB associated with atrial arrhythmia, more specifically atrial fibrillation. Objective and Conclusion: The purpose of this review is to describe the latest evidence about an entity considered an anatomical and electrical substrate with its own name, which may be a predictor of supraventricular arrhythmia and cardioembolic cerebrovascular accidents, as well as the role of new imaging techniques, such as echocardiographic strain and cardiac magnetic resonance imaging, in characterizing atrial alterations associated with this syndrome and generally in the study of anatomy and atrial function.

3D Finite Element Electrical Model of Larval Zebrafish ECG Signals

Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace's equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions.

Anti-arrhythmic strategies for atrial fibrillation: The role of computational modeling in discovery, development, and optimization

Atrial fibrillation (AF), the most common cardiac arrhythmia, is associated with increased risk of cerebrovascular stroke, and with several other pathologies, including heart failure. Current therapies for AF are targeted at reducing risk of stroke (anticoagulation) and tachycardia-induced cardiomyopathy (rate or rhythm control). Rate control, typically achieved by atrioventricular nodal blocking drugs, is often insufficient to alleviate symptoms. Rhythm control approaches include antiarrhythmic drugs, electrical cardioversion, and ablation strategies. Here, we offer several examples of how computational modeling can provide a quantitative framework for integrating multiscale data to: (a) gain insight into multiscale mechanisms of AF; (b) identify and test pharmacological and electrical therapy and interventions; and (c) support clinical decisions. We review how modeling approaches have evolved and contributed to the research pipeline and preclinical development and discuss future directions and challenges in the field.

Extracellular Matrix-Mediated Maturation of Human Pluripotent Stem Cell-Derived Cardiac Monolayer Structure and Electrophysiological Function

BACKGROUND

Human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) monolayers generated to date display an immature embryonic-like functional and structural phenotype that limits their utility for research and cardiac regeneration. In particular, the electrophysiological function of hPSC-CM monolayers and bioengineered constructs used to date are characterized by slow electric impulse propagation velocity and immature action potential profiles.

METHODS AND RESULTS

Here, we have identified an optimal extracellular matrix for significant electrophysiological and structural maturation of hPSC-CM monolayers. hPSC-CM plated in the optimal extracellular matrix combination have impulse propagation velocities ≈2× faster than previously reported (43.6±7.0 cm/s; n=9) and have mature cardiomyocyte action potential profiles, including hyperpolarized diastolic potential and rapid action potential upstroke velocity (146.5±17.7 V/s; n=5 monolayers). In addition, the optimal extracellular matrix promoted hypertrophic growth of cardiomyocytes and the expression of key mature sarcolemmal (SCN5A, Kir2.1, and connexin43) and myofilament markers (cardiac troponin I). The maturation process reported here relies on activation of integrin signaling pathways: neutralization of β1 integrin receptors via blocking antibodies and pharmacological blockade of focal adhesion kinase activation prevented structural maturation.

CONCLUSIONS

Maturation of human stem cell-derived cardiomyocyte monolayers is achieved in a 1-week period by plating cardiomyocytes on PDMS (polydimethylsiloxane) coverslips rather than on conventional 2-dimensional cell culture formats, such as glass coverslips or plastic dishes. Activation of integrin signaling and focal adhesion kinase is essential for significant maturation of human cardiac monolayers.

Catheter simulator software tool to generate electrograms of any multi-polar diagnostic catheter from 3D atrial tissue

Simulations are excellent tools for assessing new therapeutic strategies and are often conducted before implementing new therapy options in a clinical practice. For patients suffering from a heart arrhythmia, the main source of information comes from an intracardiac catheter. One of the common catheters is a Lasso multi-pole diagnostic catheter, which is a catheter that has 20 electrodes in a circular pattern. In this paper, we developed algorithm and simulation software that allows the users to place a multi-pole catheter on the atrial endocardial surface and record electrograms. In 3D atrial tissue, the plane of principal curvature is determined using eigenvectors of catheter vertices, from where the normals are projected and registered to the surface using 3D geodesic distance. This tool provides a platform for performing customized virtual cardiac experiments.

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria and the 'minimal model for human ventricular action potentials' by Bueno-Orovio, Cherry, and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistor-capacitor transmission condition. Various electrocardiograms (ECGs) are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, and Wolff-Parkinson-White syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article. Copyright © 2015 John Wiley & Sons, Ltd.

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.

Comprehensive Functional Assessment of Right-Sided Heart Using Speckle Tracking Strain for Patients with Pulmonary Hypertension

BACKGROUND

Right ventricular (RV) systolic function is one of the most important determinants of outcome for pulmonary hypertension (PH) patients, but the factors influencing prognosis vary widely. Elevated right atrial (RA) pressure is reported to be one of these prognostic factors, but its functional importance has scarcely been assessed.

METHODS

Eighty-two PH patients, all of whom underwent echocardiography and right heart catheterization, were recruited. RV function was assessed by two-dimensional speckle tracking longitudinal strain from RV-focused apical four-chamber view and calculated by averaging the three regional peak strains from the RV free wall (RV-free). RA function was determined as the sum of three peak strain values comprising reservoir, conduit, and contractile function (sum of RA strain).

RESULTS

Sum of RA strain correlated significantly with hemodynamic parameters such as mean right atrial pressure (r = -0.35, P = 0.002) and end-diastolic RV pressure (r = -0.29, P = 0.008). Patients with sum of RA strain ≥30.2% experienced more favorable outcomes than those with sum of RA strain <30.2% (log-rank P = 0.001). Furthermore, patients with impaired RV systolic function (RV-free <20%) and RA function (sum of RA strain <30.2%) showed the worst outcome (P = 0.001). A sequential Cox model based on clinical variables (χ(2) = 5.8) was improved by addition of RV-free (χ(2) = 8.7; P < 0.05) and further improved by addition of sum of RA strain (χ(2) = 12.0; P < 0.01).

CONCLUSION

Right atrial strain appears to be a valuable additive factor for predicting outcomes for PH patients, and comprehensive functional assessment of right-sided heart using speckle tracking strain may have potential clinical implications for better management of PH patients.

Noninvasive Estimation of Epicardial Dominant High-Frequency Regions During Atrial Fibrillation

INTRODUCTION

Ablation of high dominant frequency (DF) sources in patients with atrial fibrillation (AF) is an effective treatment option for paroxysmal AF. The aim of this study was to evaluate the accuracy of noninvasive estimation of DF and electrical patterns determination by solving the inverse problem of the electrocardiography.

METHODS

Four representative AF patients with left-to-right and right-to-left atrial DF patterns were included in the study. For each patient, intracardiac electrograms from both atria were recorded simultaneously together with 67-lead body surface recordings. In addition to clinical recordings, realistic mathematical models of atria and torso anatomy with different DF patterns of AF were used. For both mathematical models and clinical recordings, inverse-computed electrograms were compared to intracardiac electrograms in terms of voltage, phase, and frequency spectrum relative errors.

RESULTS

Comparison between intracardiac and inverse computed electrograms for AF patients showed 8.8 ± 4.4% errors for DF, 32 ± 4% for voltage, and 65 ± 4% for phase determination. These results were corroborated by mathematical simulations showing that the inverse problem solution was able to reconstruct the frequency spectrum and the DF maps with relative errors of 5.5 ± 4.1%, whereas the reconstruction of the electrograms or the instantaneous phase presented larger relative errors (i.e., 38 ± 15% and 48 ± 14 % respectively, P < 0.01).

CONCLUSIONS

Noninvasive reconstruction of atrial frequency maps can be achieved by solving the inverse problem of electrocardiography with a higher accuracy than temporal distribution patterns.

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

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

Atrial sources identification by causality analysis during atrial fibrillation

Ablation of electrical drivers during atrial fibrillation (AF) has been proved as an effective therapy to prevent recurrence of fibrillatory episodes. This study presents a new methodology based on causality analysis that is able to identify the hierarchical dominance of atrial areas driving AF. Realistic mathematical models of the atrial electrical activity during AF were used to assess the validity of our method. Identification of the dominant atrial propagation patterns was achieved by computing causal relations between multiple electrogram signals. The causal relationships between atrial areas during the fibrillatory processes were summarized into a recurrence map, highlighting the hierarchy and dominant areas. Recurrence maps computed from causality analysis allowed the identification of sites responsible for maintenance of the arrhythmia. These maps were able to locate the position of the atrial driver in fibrillatory processes with a single rotor, with 2 rotors or with several drivers. Additionally, the correspondence between the nodal values of the recurrence map and the distance to the rotor core has been established. Causal analysis consistently estimated propagation patterns and location of atrial drivers during AF. This methodology could guide ablation procedures in AF patients.

Effects of Persistent Atrial Fibrillation-Induced Electrical Remodeling on Atrial Electro-Mechanics - Insights from a 3D Model of the Human Atria

Aims

Atrial stunning, a loss of atrial mechanical contraction, can occur following a successful cardioversion. It is hypothesized that persistent atrial fibrillation-induced electrical remodeling (AFER) on atrial electrophysiology may be responsible for such impaired atrial mechanics. This simulation study aimed to investigate the effects of AFER on atrial electro-mechanics.

Methods and Results

A 3D electromechanical model of the human atria was developed to investigate the effects of AFER on atrial electro-mechanics. Simulations were carried out in 3 conditions for 4 states: (i) the control condition, representing the normal tissue (state 1) and the tissue 2–3 months after cardioversion (state 2) when the atrial tissue recovers its electrophysiological properties after completion of reverse electrophysiological remodelling; (ii) AFER-SR condition for AF-remodeled tissue with normal sinus rhythm (SR) (state 3); and (iii) AFER-AF condition for AF-remodeled tissue with re-entrant excitation waves (state 4). Our results indicate that at the cellular level, AFER (states 3 & 4) abbreviated action potentials and reduced the Ca²⁺ content in the sarcoplasmic reticulum, resulting in a reduced amplitude of the intracellular Ca²⁺ transient leading to decreased cell active force and cell shortening as compared to the control condition (states 1 & 2). Consequently at the whole organ level, atrial contraction in AFER-SR condition (state 3) was dramatically reduced. In the AFER-AF condition (state 4) atrial contraction was almost abolished.

Conclusions

This study provides novel insights into understanding atrial electro-mechanics illustrating that AFER impairs atrial contraction due to reduced intracellular Ca²⁺ transients.

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.

Modeling left and right atrial contributions to the ECG: A dipole-current source approach

This paper presents the mathematical formulation, the numerical validation and several illustrations of a forward-modeling approach based on dipole-current sources to compute the contribution of a part of the heart to the electrocardiogram (ECG). Clinically relevant applications include identifying in the ECG the contributions from the right and the left atrium. In a Courtemanche-based monodomain computer model of the atria and torso, 1000 dipoles distributed throughout the atrial mid-myocardium are found to be sufficient to reproduce body surface potential maps with a relative error <1% during both sinus rhythm and atrial fibrillation. When the boundary element method is applied to solve the forward problem, this approach enables fast offline computation of the ECG contribution of any anatomical part of the atria by applying the principle of superposition to the dipole sources. In the presence of a right-left activation delay (sinus rhythm), pulmonary vein isolation (sinus rhythm) or left-right differences in refractory period (atrial fibrillation), the decomposition of the ECG is shown to help interpret ECG morphology in relation to the atrial substrate. These tools provide a theoretical basis for a deeper understanding of the genesis of the P wave or fibrillatory waves in normal and pathological cases.

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.

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

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

A brief history of tissue models for cardiac electrophysiology

The last four decades have produced a number of significant advances in the developments of computer models to simulate and investigate the electrical activity of cardiac tissue. The tissue descriptions that underlie these simulations have been built from a combination of clever insight and careful comparison with measured data at multiple scales. Tissue models have not only led to greater insights into the mechanisms of life-threatening arrhythmias but have been used to engineer new therapies to treat the consequences of cardiac disease. This paper is a look back at the early years in the cardiac modeling and the challenges facing the field as models move toward the clinic.

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.

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.

Data analysis in cardiac arrhythmias

Cardiac arrhythmias are an increasingly present in developed countries and represent a major health and economic burden. The occurrence of cardiac arrhythmias is closely linked to the electrical function of the heart. Consequently, the analysis of the electrical signal generated by the heart tissue, either recorded invasively or noninvasively, provides valuable information for the study of cardiac arrhythmias. In this chapter, novel cardiac signal analysis techniques that allow the study and diagnosis of cardiac arrhythmias are described, with emphasis on cardiac mapping which allows for spatiotemporal analysis of cardiac signals.Cardiac mapping can serve as a diagnostic tool by recording cardiac signals either in close contact to the heart tissue or noninvasively from the body surface, and allows the identification of cardiac sites responsible of the development or maintenance of arrhythmias. Cardiac mapping can also be used for research in cardiac arrhythmias in order to understand their mechanisms. For this purpose, both synthetic signals generated by computer simulations and animal experimental models allow for more controlled physiological conditions and complete access to the organ.

Three-dimensional computer model of the right atrium including the sinoatrial and atrioventricular nodes predicts classical nodal behaviours

The aim of the study was to develop a three-dimensional (3D) anatomically-detailed model of the rabbit right atrium containing the sinoatrial and atrioventricular nodes to study the electrophysiology of the nodes. A model was generated based on 3D images of a rabbit heart (atria and part of ventricles), obtained using high-resolution magnetic resonance imaging. Segmentation was carried out semi-manually. A 3D right atrium array model (∼3.16 million elements), including eighteen objects, was constructed. For description of cellular electrophysiology, the Rogers-modified FitzHugh-Nagumo model was further modified to allow control of the major characteristics of the action potential with relatively low computational resource requirements. Model parameters were chosen to simulate the action potentials in the sinoatrial node, atrial muscle, inferior nodal extension and penetrating bundle. The block zone was simulated as passive tissue. The sinoatrial node, crista terminalis, main branch and roof bundle were considered as anisotropic. We have simulated normal and abnormal electrophysiology of the two nodes. In accordance with experimental findings: (i) during sinus rhythm, conduction occurs down the interatrial septum and into the atrioventricular node via the fast pathway (conduction down the crista terminalis and into the atrioventricular node via the slow pathway is slower); (ii) during atrial fibrillation, the sinoatrial node is protected from overdrive by its long refractory period; and (iii) during atrial fibrillation, the atrioventricular node reduces the frequency of action potentials reaching the ventricles. The model is able to simulate ventricular echo beats. In summary, a 3D anatomical model of the right atrium containing the cardiac conduction system is able to simulate a wide range of classical nodal behaviours.

Interatrial block in the modern era

Interatrial block (IAB; P-wave duration ≥ 110 ms), which represents a delay in the conduction between the atria, is a pandemic conduction abnormality that is frequently underappreciated in clinical practice. Despite its comprehensive documentation in the medical literature, it has still not received adequate attention and also not adequately described and discussed in most cardiology textbooks. IAB can be of varying degrees and classified based on the degree of P-duration and its morphology. It can transform into a higher degree block and can also manifest transiently. IAB may be a preceding or causative risk factor for various atrial arrhythmias (esp. atrial fibrillation) and also be associated with various other clinical abnormalities ranging from left atrial dilation and thromboembolism including embolic stroke and mesenteric ischemia. IAB certainly deserves more attention and prospective studies are needed to formulate a standard consensus regarding appropriate management strategies.

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.

Fitting C² continuous parametric surfaces to frontiers delimiting physiologic structures

We present a technique to fit C(2) continuous parametric surfaces to scattered geometric data points forming frontiers delimiting physiologic structures in segmented images. Such mathematical representation is interesting because it facilitates a large number of operations in modeling. While the fitting of C(2) continuous parametric curves to scattered geometric data points is quite trivial, the fitting of C(2) continuous parametric surfaces is not. The difficulty comes from the fact that each scattered data point should be assigned a unique parametric coordinate, and the fit is quite sensitive to their distribution on the parametric plane. We present a new approach where a polygonal (quadrilateral or triangular) surface is extracted from the segmented image. This surface is subsequently projected onto a parametric plane in a manner to ensure a one-to-one mapping. The resulting polygonal mesh is then regularized for area and edge length. Finally, from this point, surface fitting is relatively trivial. The novelty of our approach lies in the regularization of the polygonal mesh. Process performance is assessed with the reconstruction of a geometric model of mouse heart ventricles from a computerized tomography scan. Our results show an excellent reproduction of the geometric data with surfaces that are C(2) continuous.

Optimisation of ionic models to fit tissue action potentials: application to 3D atrial modelling

A 3D model of atrial electrical activity has been developed with spatially heterogeneous electrophysiological properties. The atrial geometry, reconstructed from the male Visible Human dataset, included gross anatomical features such as the central and peripheral sinoatrial node (SAN), intra-atrial connections, pulmonary veins, inferior and superior vena cava, and the coronary sinus. Membrane potentials of myocytes from spontaneously active or electrically paced in vitro rabbit cardiac tissue preparations were recorded using intracellular glass microelectrodes. Action potentials of central and peripheral SAN, right and left atrial, and pulmonary vein myocytes were each fitted using a generic ionic model having three phenomenological ionic current components: one time-dependent inward, one time-dependent outward, and one leakage current. To bridge the gap between the single-cell ionic models and the gross electrical behaviour of the 3D whole-atrial model, a simplified 2D tissue disc with heterogeneous regions was optimised to arrive at parameters for each cell type under electrotonic load. Parameters were then incorporated into the 3D atrial model, which as a result exhibited a spontaneously active SAN able to rhythmically excite the atria. The tissue-based optimisation of ionic models and the modelling process outlined are generic and applicable to image-based computer reconstruction and simulation of excitable tissue.