A computational study of mother rotor VF in the human ventricles

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Computer based method for identification of fibrotic scars from electrograms and local activation times on the epi- and endocardial surfaces of the ventricles

Cardiac fibrosis stands as one of the most critical conditions leading to lethal cardiac arrhythmias. Identifying the precise location of cardiac fibrosis is crucial for planning clinical interventions in patients with various forms of ventricular and atrial arrhythmias. As fibrosis impedes and alters the path of electrical waves, detecting fibrosis in the heart can be achieved through analyzing electrical signals recorded from its surface. In current clinical practices, it has become feasible to record electrical activity from both the endocardial and epicardial surfaces of the heart. This paper presents a computational method for reconstructing 3D fibrosis using unipolar electrograms obtained from both surfaces of the ventricles. The proposed method calculates the percentage of fibrosis in various ventricular segments by analyzing the local activation times and peak-to-peak amplitudes of the electrograms. Initially, the method was tested using simulated data representing idealized fibrosis in a heart segment; subsequently, it was validated in the left ventricle with fibrosis obtained from a patient with nonischemic cardiomyopathy. The method successfully determined the location and extent of fibrosis in 204 segments of the left ventricle model with an average error of 0.0±4.3% (N = 204). Moreover, the method effectively detected fibrotic scars in the mid-myocardial region, a region known to present challenges in accurate detection using electrogram amplitude as the primary criterion.

Reordering and synchronization of electrical turbulence in cardiac tissue through global and partial optogenetical illumination

Electrical turbulence in the heart is considered the culprit of cardiac disease, including the fatal ventricular fibrillation. Optogenetics is an emerging technology that has the capability to produce action potentials of cardiomyocytes to affect the electric wave propagation in cardiac tissue, thereby possessing the potential to control the turbulence, by shining a rotating spiral pattern onto the tissue. In this paper, we present a method to reorder and synchronize electrical turbulence through optogenetics. A generic two-variable reaction-diffusion model and a simplified three-variable ionic cardiac model are used. We discuss cases involving either global or partial illumination.

Spiral wave drift under optical feedback in cardiac tissue

Spiral waves occur in various types of excitable media and their dynamics determine the spatial excitation patterns. An important type of spiral wave dynamics is drift, as it can control the position of a spiral wave or eliminate a spiral wave by forcing it to the boundary. In theoretical and experimental studies of the Belousov-Zhabotinsky reaction, it was shown that the most direct way to induce the controlled drift of spiral waves is by application of an external electric field. Mathematically such drift occurs due to the onset of additional gradient terms in the Laplacian operator describing excitable media. However, this approach does not work for cardiac excitable tissue, where an external electric field does not result in gradient terms. In this paper, we propose a method of how to induce a directed linear drift of spiral waves in cardiac tissue, which can be realized as an optical feedback control in tissue where photosensitive ion channels are expressed. We illustrate our method by using the FitzHugh-Nagumo model for cardiac tissue and the generic model of photosensitive ion channels. We show that our method works for continuous and discrete light sources and can effectively move spiral waves in cardiac tissue, or eliminate them by collisions with the boundary or with another spiral wave. We finally implement our method by using a biophysically motivated photosensitive ion channel model included to the Luo-Rudy model for cardiac cells and show that the proposed feedback control also induces directed linear drift of spiral waves in a wide range of light intensities.

Control of spiral waves in optogenetically modified cardiac tissue by periodic optical stimulation

Resonant drift of nonlinear spiral waves occurs in various types of excitable media under periodic stimulation. Recently a novel methodology of optogenetics has emerged, which allows to affect excitability of cardiac cells and tissues by optical stimuli. In this paper we study if resonant drift of spiral waves in the heart can be induced by a homogeneous weak periodic optical stimulation of cardiac tissue. We use a two-variable and a detailed model of cardiac tissue and add description of depolarizing and hyperpolarizing optogenetic ionic currents. We show that weak periodic optical stimulation at a frequency equal to the natural rotation frequency of the spiral wave induces resonant drift for both depolarizing and hyperpolarizing optogenetic currents. We quantify these effects and study how the speed of the drift and its direction depend on the initial conditions. We also derive analytical formulas based on the response function theory which correctly predict the drift velocity and its trajectory. We conclude that optogenetic methodology can be used for control of spiral waves in cardiac tissue and discuss its possible applications.

Scroll wave with negative filament tension in a model of the left ventricle of the human heart and its overdrive pacing

Nonlinear waves of electrical excitation initiate cardiac contraction. Abnormal wave propagation in the heart, e.g., spiral waves, can lead to sudden cardiac arrest. This study analyzed the dynamics of spiral waves under the influence of an instability called negative filament tension, and examined how the spiral waves can be eliminated through high-frequency pacing. A generic anatomical model of the left ventricle of the human heart and the Aliev-Panfilov model for cardiac tissue were used. The study showed that the source of such arrhythmia is elongated filaments with lengths that can be 10-20 times greater than the characteristic thickness of the heart wall. In anisotropic tissue, the filament elongated before it was annihilated at the base of the heart. The spiral waves were eliminated through overdrive pacing with stimulation periods from 0.8 to 0.95 relative to the spiral wave period. The minimum time for the expulsion was about 10 s.

High-frequency pacing of scroll waves in a three-dimensional slab model of cardiac tissue

Vortices in excitable media underlie dangerous cardiac arrhythmias. One way to eliminate them is by stimulating the excitable medium with a period smaller than the period of the vortex. So far, this phenomenon has been studied mostly for two-dimensional vortices known as spiral waves. Here we present a first study of this phenomenon for three-dimensional vortices, or scroll waves, in a slab. We consider two main types of scroll waves dynamics: with positive filament tension and with negative filament tension and show that such elimination is possible for some values of the period in all cases. However, in the case of negative filament tension for relatively long stimulation periods, three-dimensional instabilities occur and make elimination impossible. We derive equations of motion for the drift of paced filaments and identify a bifurcation parameter that determines whether the filaments orient themselves perpendicular to the impeding wave train or not.

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

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

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

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

Cardiac fibrosis occurs in many forms of heart disease. It is well established that the spatial pattern of fibrosis, its texture, substantially affects the onset of arrhythmia. However, in most modelling studies fibrosis is represented by multiple randomly distributed short obstacles that mimic only one possible texture, diffuse fibrosis. An important characteristic feature of other fibrosis textures, such as interstitial and patchy textures, is that fibrotic inclusions have substantial length, which is suggested to have a pronounced effect on wave propagation. In this paper, we study the effect of the elongation of inexcitable inclusions (obstacles) on wave propagation in a 2D model of cardiac tissue described by the TP06 model for human ventricular cells. We study in detail how the elongation of obstacles affects various characteristics of the waves. We quantify the anisotropy induced by the textures, its dependency on the obstacle length and the effects of the texture on the shape of the propagating wave. Because such anisotropy is a result of zig-zag propagation we show, for the first time, quantification of the effects of geometry and source-sink relationship, on the zig-zag nature of the pathway of electrical conduction. We also study the effect of fibrosis in the case of pre-existing anisotropy and introduce a procedure for scaling of the fibrosis texture. We show that fibrosis can decrease or increase the preexisting anisotropy depending on its scaled texture.

Absence of Rapid Propagation through the Purkinje Network as a Potential Cause of Line Block in the Human Heart with Left Bundle Branch Block

Background: Cardiac resynchronization therapy is an effective device therapy for heart failure patients with conduction block. However, a problem with this invasive technique is the nearly 30% of non-responders. A number of studies have reported a functional line of block of cardiac excitation propagation in responders. However, this can only be detected using non-contact endocardial mapping. Further, although the line of block is considered a sign of responders to therapy, the mechanism remains unclear.

Methods: Herein, we created two patient-specific heart models with conduction block and simulated the propagation of excitation based on a cellmodel of electrophysiology. In one model with a relatively narrow QRS width (176 ms), we modeled the Purkinje network using a thin endocardial layer with rapid conduction. To reproduce a wider QRS complex (200 ms) in the second model, we eliminated the Purkinje network, and we simulated the endocardial mapping by solving the inverse problem according to the actual mapping system.

Results: We successfully observed the line of block using non-contact mapping in the model without the rapid propagation of excitation through the Purkinje network, although the excitation in the wall propagated smoothly. This model of slow conduction also reproduced the characteristic properties of the line of block, including dense isochronal lines and fractionated local electrocardiograms. Further, simulation of ventricular pacing from the lateral wall shifted the location of the line of block. By contrast, in the model with the Purkinje network, propagation of excitation in the endocardial map faithfully followed the actual propagation in the wall, without showing the line of block. Finally, switching the mode of propagation between the two models completely reversed these findings.

Conclusions: Our simulation data suggest that the absence of rapid propagation of excitation through the Purkinje network is the major cause of the functional line of block recorded by non-contact endocardial mapping. The line of block can be used to identify responders as these patients loose rapid propagation through the Purkinje network.

Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles

Early Afterdepolarizations, EADs, are defined as the reversal of the action potential before completion of the repolarization phase, which can result in ectopic beats. However, the series of mechanisms of EADs leading to these ectopic beats and related cardiac arrhythmias are not well understood. Therefore, we aimed to investigate the influence of this single cell behavior on the whole heart level. For this study we used a modified version of the Ten Tusscher-Panfilov model of human ventricular cells (TP06) which we implemented in a 3D ventricle model including realistic fiber orientations. To increase the likelihood of EAD formation at the single cell level, we reduced the repolarization reserve (RR) by reducing the rapid delayed rectifier Potassium current and raising the L-type Calcium current. Varying these parameters defined a 2D parametric space where different excitation patterns could be classified. Depending on the initial conditions, by either exciting the ventricles with a spiral formation or burst pacing protocol, we found multiple different spatio-temporal excitation patterns. The spiral formation protocol resulted in the categorization of a stable spiral (S), a meandering spiral (MS), a spiral break-up regime (SB), spiral fibrillation type B (B), spiral fibrillation type A (A) and an oscillatory excitation type (O). The last three patterns are a 3D generalization of previously found patterns in 2D. First, the spiral fibrillation type B showed waves determined by a chaotic bi-excitable regime, i.e. mediated by both Sodium and Calcium waves at the same time and in same tissue settings. In the parameter region governed by the B pattern, single cells were able to repolarize completely and different (spiral) waves chaotically burst into each other without finishing a 360 degree rotation. Second, spiral fibrillation type A patterns consisted of multiple small rotating spirals. Single cells failed to repolarize to the resting membrane potential hence prohibiting the Sodium channel gates to recover. Accordingly, we found that Calcium waves mediated these patterns. Third, a further reduction of the RR resulted in a more exotic parameter regime whereby the individual cells behaved independently as oscillators. The patterns arose due to a phase-shift of different oscillators as disconnection of the cells resulted in continuation of the patterns. For all patterns, we computed realistic 9 lead ECGs by including a torso model. The B and A type pattern exposed the behavior of Ventricular Tachycardia (VT). We conclude that EADs at the single cell level can result in different types of cardiac fibrillation at the tissue and 3D ventricle level.

Spatial Patterns of Excitation at Tissue and Whole Organ Level Due to Early Afterdepolarizations

Early after depolarizations (EAD) occur in many pathological conditions, such as congenital or acquired channelopathies, drug induced arrhythmias, and several other situations that are associated with increased arrhythmogenicity. In this paper we present an overview of the relevant computational studies on spatial EAD dynamics in 1D, 2D, and in 3D anatomical models and discuss the relation of EADs to cardiac arrhythmias. We also discuss unsolved problems and highlight new lines of research in this area.

Murine Electrophysiological Models of Cardiac Arrhythmogenesis

Cardiac arrhythmias can follow disruption of the normal cellular electrophysiological processes underlying excitable activity and their tissue propagation as coherent wavefronts from the primary sinoatrial node pacemaker, through the atria, conducting structures and ventricular myocardium. These physiological events are driven by interacting, voltage-dependent, processes of activation, inactivation, and recovery in the ion channels present in cardiomyocyte membranes. Generation and conduction of these events are further modulated by intracellular Ca2+ homeostasis, and metabolic and structural change. This review describes experimental studies on murine models for known clinical arrhythmic conditions in which these mechanisms were modified by genetic, physiological, or pharmacological manipulation. These exemplars yielded molecular, physiological, and structural phenotypes often directly translatable to their corresponding clinical conditions, which could be investigated at the molecular, cellular, tissue, organ, and whole animal levels. Arrhythmogenesis could be explored during normal pacing activity, regular stimulation, following imposed extra-stimuli, or during progressively incremented steady pacing frequencies. Arrhythmic substrate was identified with temporal and spatial functional heterogeneities predisposing to reentrant excitation phenomena. These could arise from abnormalities in cardiac pacing function, tissue electrical connectivity, and cellular excitation and recovery. Triggering events during or following recovery from action potential excitation could thereby lead to sustained arrhythmia. These surface membrane processes were modified by alterations in cellular Ca2+ homeostasis and energetics, as well as cellular and tissue structural change. Study of murine systems thus offers major insights into both our understanding of normal cardiac activity and its propagation, and their relationship to mechanisms generating clinical arrhythmias.

Pro-arrhythmogenic effects of CACNA1C G1911R mutation in human ventricular tachycardia: insights from cardiac multi-scale models

Mutations in the CACNA1C gene are associated with ventricular tachycardia (VT). Although the CACNA1C mutations were well identified in patients with cardiac arrhythmias, mechanisms by which cardiac arrhythmias are generated in such genetic mutation conditions remain unclear. In this study, we identified a novel mechanism of VT resulted from enhanced repolarization dispersion which is a key factor for arrhythmias in the CACNA1C G1911R mutation using multi-scale computational models of the human ventricle. The increased calcium influx in the mutation prolonged action potential duration (APD), produced steepened action potential duration restitution (APDR) curves as well as augmented membrane potential differences among different cell types during repolarization, increasing transmural dispersion of repolarization (DOR) and the spatial and temporal heterogeneity of cardiac electrical activities. Consequentially, the vulnerability to unidirectional conduction block in response to a premature stimulus increased at tissue level in the G1911R mutation. The increased functional repolarization dispersion anchored reentrant excitation waves in tissue and organ models, facilitating the initiation and maintenance of VT due to less meandering rotor tip. Thus, the increased repolarization dispersion caused by the G1911R mutation is a primary factor that may primarily contribute to the genesis of cardiac arrhythmias in Timothy Syndrome.

Integrated whole-heart computational workflow for inverse potential mapping and personalized simulations

Background

Integration of whole-heart activation simulations and inverse potential mapping (IPM) could benefit the guidance and planning of electrophysiological procedures. Routine clinical application requires a fast and adaptable workflow. These requirements limit clinical translation of existing simulation models. This study proposes a comprehensive finite element model (FEM) based whole-heart computational workflow suitable for IPM and simulations.

Methods

Three volunteers and eight patients with premature ventricular contractions underwent body surface potential (BSP) acquisition followed by a cardiac MRI (CMR) scan. The cardiac volumes were segmented from the CMR images using custom written software. The feasibility to integrate tissue-characteristics was assessed by generating meshes with virtual edema and scar. Isochronal activation maps were constructed by identifying the fastest route through the cardiac volume using the Möller–Trumbore and Floyd–Warshall algorithms. IPM’s were reconstructed from the BSP’s.

Results

Whole-heart computational meshes were generated within seconds. The first point of atrial activation on IPM was located near the crista terminalis of the superior vena cave into the right atrium. The IPM demonstrated the ventricular epicardial breakthrough at the attachment of the moderator band with the right ventricular free wall. Simulations of sinus rhythm were successfully performed. The conduction through the virtual edema and scar meshes demonstrated delayed activation or a complete conductional block respectively.

Conclusion

The proposed FEM based whole-heart computational workflow offers an integrated platform for cardiac electrical assessment using simulations and IPM. This workflow can incorporate patient-specific electrical parameters, perform whole-heart cardiac activation simulations and accurately reconstruct cardiac activation sequences from BSP’s.

Electronic supplementary material

The online version of this article (doi:10.1186/s12967-016-0902-0) contains supplementary material, which is available to authorized users.

The Contribution of Ionic Currents to Rate-Dependent Action Potential Duration and Pattern of Reentry in a Mathematical Model of Human Atrial Fibrillation

Persistent atrial fibrillation (PeAF) in humans is characterized by shortening of action potential duration (APD) and attenuation of APD rate-adaptation. However, the quantitative influences of particular ionic current alterations on rate-dependent APD changes, and effects on patterns of reentry in atrial tissue, have not been systematically investigated. Using mathematical models of human atrial cells and tissue and performing parameter sensitivity analysis, we evaluated the quantitative contributions to action potential (AP) shortening and APD rate-adaptation of ionic current remodeling seen with PeAF. Ionic remodeling in PeAF was simulated by reducing L-type Ca²⁺ channel current (I_CaL), increasing inward rectifier K⁺ current (I_K1) and modulating five other ionic currents. Parameter sensitivity analysis, which quantified how each ionic current influenced APD in control and PeAF conditions, identified interesting results, including a negative effect of Na⁺/Ca²⁺ exchange on APD only in the PeAF condition. At high pacing rate (2 Hz), electrical remodeling in I_K1 alone accounts for the APD reduction of PeAF, but at slow pacing rate (0.5 Hz) both electrical remodeling in I_CaL alone (-70%) and I_K1 alone (+100%) contribute equally to the APD reduction. Furthermore, AP rate-adaptation was affected by I_Kur in control and by I_NaCa in the PeAF condition. In a 2D tissue model, a large reduction (-70%) of I_CaL becomes a dominant factor leading to a stable spiral wave in PeAF. Our study provides a quantitative and unifying understanding of the roles of ionic current remodeling in determining rate-dependent APD changes at the cellular level and spatial reentry patterns in tissue.

Transmural, interventricular, apicobasal and anteroposterior action potential duration gradients are all essential to the genesis of the concordant and realistic T wave: A whole-heart model study

BACKGROUND

It has been reported that ventricular repolarization dispersion resulting from transmural, apicobasal and interventricular action potential duration (APD) gradients makes the T wave concordant with the QRS complex.

METHOD AND RESULTS

A whole-heart model integrating transmural, apicobasal, interventricular and anteroposterior APD gradients was used, and the corresponding electrocardiograms were simulated to study the influence of these APD gradients on the T-wave amplitudes. The simulation results showed that changing a single APD gradient (e.g., interventricular APD gradient alone) only made substantial changes to the T-wave amplitudes in a limited number of leads and was not able to generate T waves with amplitudes comparable with clinical findings in all leads. A combination of transmural, apicobasal and interventricular APD gradients could simulate T waves with amplitudes similar to clinical values in the limb leads only. Adding the anteroposterior APD gradient into the model greatly improved the consistency between the simulated T-wave amplitudes and the clinical values.

CONCLUSION

The simulation results support that the transmural, apicobasal, interventricular and the anteroposterior APD gradient are all essential to the genesis of the clinical T wave.

Electrophysiological Rotor Ablation in In-Silico Modeling of Atrial Fibrillation: Comparisons with Dominant Frequency, Shannon Entropy, and Phase Singularity

BACKGROUND

Although rotors have been considered among the drivers of atrial fibrillation (AF), the rotor definition is inconsistent. We evaluated the nature of rotors in 2D and 3D in- silico models of persistent AF (PeAF) by analyzing phase singularity (PS), dominant frequency (DF), Shannon entropy (ShEn), and complex fractionated atrial electrogram cycle length (CFAE-CL) and their ablation.

METHODS

Mother rotor was spatiotemporally defined as stationary reentries with a meandering tip remaining within half the wavelength and lasting longer than 5 s. We generated 2D- and 3D-maps of the PS, DF, ShEn, and CFAE-CL during AF. The spatial correlations and ablation outcomes targeting each parameter were analyzed.

RESULTS

1. In the 2D PeAF model, we observed a mother rotor that matched relatively well with DF (>9 Hz, 71.0%, p<0.001), ShEn (upper 2.5%, 33.2%, p<0.001), and CFAE-CL (lower 2.5%, 23.7%, p<0.001). 2. The 3D-PeAF model also showed mother rotors that had spatial correlations with DF (>5.5 Hz, 39.7%, p<0.001), ShEn (upper 8.5%, 15.1%, p <0.001), and CFAE (lower 8.5%, 8.0%, p = 0.002). 3. In both the 2D and 3D models, virtual ablation targeting the upper 5% of the DF terminated AF within 20 s, but not the ablations based on long-lasting PS, high ShEn area, or lower CFAE-CL area.

CONCLUSION

Mother rotors were observed in both 2D and 3D human AF models. Rotor locations were well represented by DF, and their virtual ablation altered wave dynamics and terminated AF.

Ventricular Tachycardia and Early Fibrillation in Patients With Brugada Syndrome and Ischemic Cardiomyopathy Show Predictable Frequency-Phase Properties on the Precordial ECG Consistent With the Respective Arrhythmogenic Substrate

Supplemental Digital Content is available in the text.

Ventricular fibrillation (VF) has been proposed to be maintained by localized high-frequency sources. We tested whether spectral-phase analysis of the precordial ECG enabled identification of periodic activation patterns generated by such sources.

Effect of global cardiac ischemia on human ventricular fibrillation: insights from a multi-scale mechanistic model of the human heart

Acute regional ischemia in the heart can lead to cardiac arrhythmias such as ventricular fibrillation (VF), which in turn compromise cardiac output and result in secondary global cardiac ischemia. The secondary ischemia may influence the underlying arrhythmia mechanism. A recent clinical study documents the effect of global cardiac ischaemia on the mechanisms of VF. During 150 seconds of global ischemia the dominant frequency of activation decreased, while after reperfusion it increased rapidly. At the same time the complexity of epicardial excitation, measured as the number of epicardical phase singularity points, remained approximately constant during ischemia. Here we perform numerical studies based on these clinical data and propose explanations for the observed dynamics of the period and complexity of activation patterns. In particular, we study the effects on ischemia in pseudo-1D and 2D cardiac tissue models as well as in an anatomically accurate model of human heart ventricles. We demonstrate that the fall of dominant frequency in VF during secondary ischemia can be explained by an increase in extracellular potassium, while the increase during reperfusion is consistent with washout of potassium and continued activation of the ATP-dependent potassium channels. We also suggest that memory effects are responsible for the observed complexity dynamics. In addition, we present unpublished clinical results of individual patient recordings and propose a way of estimating extracellular potassium and activation of ATP-dependent potassium channels from these measurements.

Developing a novel comprehensive framework for the investigation of cellular and whole heart electrophysiology in the in situ human heart: historical perspectives, current progress and future prospects

Understanding the mechanisms of fatal ventricular arrhythmias is of great importance. In view of the many electrophysiological differences that exist between animal species and humans, the acquisition of basic electrophysiological data in the intact human heart is essential to drive and complement experimental work in animal and in-silico models. Over the years techniques have been developed to obtain basic electrophysiological signals directly from the patients by incorporating these measurements into routine clinical procedures which access the heart such as cardiac catheterisation and cardiac surgery. Early recordings with monophasic action potentials provided valuable information including normal values for the in vivo human heart, cycle length dependent properties, the effect of ischaemia, autonomic nervous system activity, and mechano-electric interaction. Transmural recordings addressed the controversial issue of the mid myocardial "M" cell. More recently, the technique of multielectrode mapping (256 electrodes) developed in animal models has been extended to humans, enabling mapping of activation and repolarisation on the entire left and right ventricular epicardium in patients during cardiac surgery. Studies have examined the issue of whether ventricular fibrillation was driven by a "mother" rotor with inhomogeneous and fragmented conduction as in some animal models, or by multiple wavelets as in other animal studies; results showed that both mechanisms are operative in humans. The simpler spatial organisation of human VF has important implications for treatment and prevention. To link in-vivo human electrophysiological mapping with cellular biophysics, multielectrode mapping is now being combined with myocardial biopsies. This technique enables region-specific electrophysiology changes to be related to underlying cellular biology, for example: APD alternans, which is a precursor of VF and sudden death. The mechanism is incompletely understood but related to calcium cycling and APD restitution. Multielectrode sock mapping during incremental pacing enables epicardial sites to be identified which exhibit marked APD alternans and sites where APD alternans is absent. Whole heart electrophysiology is assessed by activation repolarisation mapping and analysis is performed immediately on-site in order to guide biopsies to specific myocardial sites. Samples are analysed for ion channel expression, Ca(2+)-handling proteins, gap junctions and extracellular matrix. This new comprehensive approach to bridge cellular and whole heart electrophysiology allowed to identify 20 significant changes in mRNA for ion channels Ca(2+)-handling proteins, a gap junction channel, a Na(+)-K(+) pump subunit and receptors (particularly Kir 2.1) between the positive and negative alternans sites.

Computational model of erratic arrhythmias in a cardiac cell network: the role of gap junctions

Cardiac morbidity and mortality increases with the population age. To investigate the underlying pathological mechanisms, and suggest new ways to reduce clinical risks, computational approaches complementing experimental and clinical investigations are becoming more and more important. Here we explore the possible processes leading to the occasional onset and termination of the (usually) non-fatal arrhythmias widely observed in the heart. Using a computational model of a two-dimensional network of cardiac cells, we tested the hypothesis that an ischemia alters the properties of the gap junctions inside the ischemic area. In particular, in agreement with experimental findings, we assumed that an ischemic episode can alter the gap junctions of the affected cells by reducing their average conductance. We extended these changes to include random fluctuations with time, and modifications in the gap junction rectifying conductive properties of cells along the edges of the ischemic area. The results demonstrate how these alterations can qualitatively give an account of all the main types of non-fatal arrhythmia observed experimentally, and suggest how premature beats can be eliminated in three different ways: a) with a relatively small surgical procedure, b) with a pharmacological reduction of the rectifying conductive properties of the gap-junctions, and c) by pharmacologically decreasing the gap junction conductance. In conclusion, our model strongly supports the hypothesis that non-fatal arrhythmias can develop from post-ischemic alteration of the electrical connectivity in a relatively small area of the cardiac cell network, and suggests experimentally testable predictions on their possible treatments.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Initiation and dynamics of a spiral wave around an ionic heterogeneity in a model for human cardiac tissue

In relation to cardiac arrhythmias, heterogeneity of cardiac tissue is one of the most important factors underlying the onset of spiral waves and determining their type. In this paper, we numerically model heterogeneity of realistic size and value and study formation and dynamics of spiral waves around such heterogeneity. We find that the only sustained pattern obtained is a single spiral wave anchored around the heterogeneity. Dynamics of an anchored spiral wave depend on the extent of heterogeneity, and for certain heterogeneity size, we find abrupt regional increase in the period of excitation occurring as a bifurcation. We study factors determining spatial distribution of excitation periods of anchored spiral waves and discuss consequences of such dynamics for cardiac arrhythmias and possibilities for experimental testings of our predictions.

Computational cardiology: the heart of the matter

This paper reviews the newest developments in computational cardiology. It focuses on the contribution of cardiac modeling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modeling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Modeling cardiac electromechanics and mechanoelectrical coupling in dyssynchronous and failing hearts: insight from adaptive computer models

Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are created that describe heart function at different length and time scales. In this review, we describe basic modules that can be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling, excitation-contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation, ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K⁺ current, (ii) elevated extracellular K⁺ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca²⁺ current I(Ca,L). Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.

Orthogonal recursive bisection as data decomposition strategy for massively parallel cardiac simulations

We present the orthogonal recursive bisection algorithm that hierarchically segments the anatomical model structure into subvolumes that are distributed to cores. The anatomy is derived from the Visible Human Project, with electrophysiology based on the FitzHugh-Nagumo (FHN) and ten Tusscher (TT04) models with monodomain diffusion. Benchmark simulations with up to 16,384 and 32,768 cores on IBM Blue Gene/P and L supercomputers for both FHN and TT04 results show good load balancing with almost perfect speedup factors that are close to linear with the number of cores. Hence, strong scaling is demonstrated. With 32,768 cores, a 1000 ms simulation of full heart beat requires about 6.5 min of wall clock time for a simulation of the FHN model. For the largest machine partitions, the simulations execute at a rate of 0.548 s (BG/P) and 0.394 s (BG/L) of wall clock time per 1 ms of simulation time. To our knowledge, these simulations show strong scaling to substantially higher numbers of cores than reported previously for organ-level simulation of the heart, thus significantly reducing run times. The ability to reduce runtimes could play a critical role in enabling wider use of cardiac models in research and clinical applications.

Empirical study of an adaptive multiscale model for simulating cardiac conduction

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.

Transmural and apicobasal gradients in repolarization contribute to T-wave genesis in human surface ECG

The cellular basis of the T-wave morphology of surface ECG remains controversial in clinical cardiology. We examined the effect of action potential duration (APD) distribution on T-wave morphology using a realistic model of the human ventricle and torso. We developed a finite-element model of the ventricle consisting of ∼26 million elements, including the conduction system, each implemented with the ion current model of cardiomyocytes. This model was embedded in a torso model with distinct organ structures to obtain the standard ECG leads. The APD distribution was changed in the transmural direction by locating the M cells in either the endocardial or epicardial region. We also introduced apicobasal gradients by modifying the ion channel parameters. Both the transmural gradient (with M cells on the endocardial side) and the apicobasal gradient produced positive T waves, although a very large gradient was required for the apicobasal gradient. By contrast, T waves obtained with the transmural gradient were highly symmetric and, therefore, did not represent the true physiological state. Only combination of the transmural and the moderate apicobasal gradients produced physiological T waves in surface ECG. Positive T waves in surface ECG mainly originated from the transmural distribution of APD with M cells on the endocardial side, although the apicobasal gradient was also required to attain the physiological waveform.

Whole-heart modeling: applications to cardiac electrophysiology and electromechanics

Recent developments in cardiac simulation have rendered the heart the most highly integrated example of a virtual organ. We are on the brink of a revolution in cardiac research, one in which computational modeling of proteins, cells, tissues, and the organ permit linking genomic and proteomic information to the integrated organ behavior, in the quest for a quantitative understanding of the functioning of the heart in health and disease. The goal of this review is to assess the existing state-of-the-art in whole-heart modeling and the plethora of its applications in cardiac research. General whole-heart modeling approaches are presented, and the applications of whole-heart models in cardiac electrophysiology and electromechanics research are reviewed. The article showcases the contributions that whole-heart modeling and simulation have made to our understanding of the functioning of the heart. A summary of the future developments envisioned for the field of cardiac simulation and modeling is also presented. Biophysically based computational modeling of the heart, applied to human heart physiology and the diagnosis and treatment of cardiac disease, has the potential to dramatically change 21st century cardiac research and the field of cardiology.

Influences of sites and protocols on inducing ventricular fibrillation: A computer simulation study

In cardiac electrophysiological study, several electrical stimulation protocols have been employed to induce ventricular fibrillations (VF). In addition, sites of inducing may have different impacts on inducing results as well as different inducing protocols. To study whether VF inducing method is determinant of induced outcome, we simulated VFs induced with different protocols at different sites based on the Wei-Harumi whole heart model. Simulations showed that only certain combinations of pacing protocols and sites could induce sustainable VFs, which had similar frequency distributions. This result suggested that the interactions between protocols and sites determine the odds of successful inducing but once the VF was induced, the pattern was solely determined by inner cardiac properties.

Déjà vu in the theories of atrial fibrillation dynamics

This brief review looks back to the major theoretical, experimental, and clinical work on the dynamics and mechanisms of atrial fibrillation (AF). Its goal is to highlight the most important issues, controversies, and advances that have driven the field of investigation into AF mechanisms at any given time during the last ∼100 years. It emphasizes that while the history of AF research has been full of controversies from the start, such controversies have led to new information, and individual scientists have learned from those that have preceded them. However, in the face of the most common sustained cardiac arrhythmia seen in clinical practice, we are yet to fully understand its fundamental mechanisms and learn how to treat it effectively. Future research into AF dynamics and mechanisms should focus on the development and validation of new numerical and animal models. Such models should be relevant to and accurately reproduce the important substrates associated with ageing and with diseases such as hypertension, heart failure, and ischaemic heart disease which cause AF in the vast majority of patients. Knowledge derived from such models may help to greatly advance the field and hopefully lead to more effective prevention and therapy.

Anomalous drift of spiral waves in heterogeneous excitable media

We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in the distribution of ion-channel expression or cellular coupling. We report the anomalous drift of spiral waves toward regions having shorter period or stronger coupling, in reaction-diffusion models of excitable media. Such anomalous drift can promote the onset of complex spatiotemporal patterns, e.g., those responsible for life-threatening arrhythmias in the heart.

Electromechanical wavebreak in a model of the human left ventricle

In the present report, we introduce an integrative three-dimensional electromechanical model of the left ventricle of the human heart. Electrical activity is represented by the ionic TP06 model for human cardiac cells, and mechanical activity is represented by the Niederer-Hunter-Smith active contractile tension model and the exponential Guccione passive elasticity model. These models were embedded into an anatomic model of the left ventricle that contains a detailed description of cardiac geometry and the fiber orientation field. We demonstrated that fiber shortening and wall thickening during normal excitation were qualitatively similar to experimental recordings. We used this model to study the effect of mechanoelectrical feedback via stretch-activated channels on the stability of reentrant wave excitation. We found that mechanoelectrical feedback can induce the deterioration of an otherwise stable spiral wave into turbulent wave patterns similar to that of ventricular fibrillation. We identified the mechanisms of this transition and studied the three-dimensional organization of this mechanically induced ventricular fibrillation.