Filament behavior in a computational model of ventricular fibrillation in the canine heart

AF driver detection in pulmonary vein area by electropcardiographic imaging: Relation with a favorable outcome of pulmonary vein isolation

Pulmonary vein isolation (PVI) is the most successful treatment for atrial fibrillation (AF) nowadays. However, not all AF patients benefit from PVI. In this study, we evaluate the use of ECGI to identify reentries and relate rotor density in the pulmonary vein (PV) area as an indicator of PVI outcome. Rotor maps were computed in a set of 29 AF patients using a new rotor detection algorithm. The relationship between the distribution of reentrant activity and the clinical outcome after PVI was studied. The number of rotors and proportion of PSs in different atrial regions were computed and compared retrospectively in two groups of patients: patients that remained in sinus rhythm 6 months after PVI and patients with arrhythmia recurrence. The total number of rotors obtained was higher in patients returning to arrhythmia after the ablation (4.31 ± 2.77 vs. 3.58 ± 2.67%, p = 0.018). However, a significantly higher concentration of PSs in the pulmonary veins was found in patients that remained in sinus rhythm (10.20 ± 12.40% vs. 5.19 ± 9.13%, p = 0.011) 6 months after PVI. The results obtained show a direct relationship between the expected AF mechanism and the electrophysiological parameters provided by ECGI, suggesting that this technology offers relevant information to predict the clinical outcome after PVI in AF patients.

On the Role of Ionic Modeling on the Signature of Cardiac Arrhythmias for Healthy and Diseased Hearts

Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies.

Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study

Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses.

Filament Dynamics during Simulated Ventricular Fibrillation in a High-Resolution Rabbit Heart

The mechanisms underlying ventricular fibrillation (VF) are not well understood. The electrical activity on the heart surface during VF has been recorded extensively in the experimental setting and in some cases clinically; however, corresponding transmural activation patterns are prohibitively difficult to measure. In this paper, we use a high-resolution biventricular heart model to study three-dimensional electrical activity during fibrillation, focusing on the driving sources of VF: “filaments,” the organising centres of unstable reentrant scroll waves. We show, for the first time, specific 3D filament dynamics during simulated VF in a whole heart geometry that includes fine-scale anatomical structures. Our results suggest that transmural activity is much more complex than what would be expected from surface observations alone. We present examples of complex intramural activity, including filament breakup and reattachment, anchoring to the thin right ventricular apex; rapid transitions among various filament shapes; and filament lengths much greater than wall thickness. We also present evidence for anatomy playing a major role in VF development and coronary vessels and trabeculae influencing filament dynamics. Overall, our results indicate that intramural activity during simulated VF is extraordinarily complex and suggest that further investigation of 3D filaments is necessary to fully comprehend recorded surface patterns.

Transmural dispersion of repolarization determines scroll wave behavior during ventricular tachyarrhythmias

BACKGROUND

Ventricular tachyarrhythmia is the leading cause of sudden cardiac death, and scroll wave re-entry is known to underlie this condition. Class III antiarrhythmic drugs are commonly used worldwide to treat ventricular tachyarrhythmias; however, these drugs have a proarrhythmic adverse effect and can cause Torsade de Pointes or ventricular fibrillation. Transmural dispersion of repolarization (TDR) has been suggested to be a strong indicator of ventricular tachyarrhythmia induction. However, the role of TDR during sustained scroll wave re-entry is poorly understood. The purpose of the present study was to investigate how TDR affects scroll wave behavior and to provide a novel analysis of the mechanisms that sustain tachyarrhythmias, using computer simulations.

METHODS AND RESULTS

Computer simulations were carried out to quantify the TDR and QT interval under a variety of I(Ks) and I(Kr) during transmural conduction. Simulated scroll wave re-entries were done under a variety of I(Ks) and I(Kr) in a ventricular wall slab model, and the scroll wave behavior and the filament dynamics (3-dimensional organizing center) were analyzed. A slight increase in TDR, but not in the QT interval, reflected antiarrhythmic properties resulting from the restraint of scroll wave breakup, whereas a marked increase in TDR was proarrhythmic, as a result of scroll wave breakup.

CONCLUSIONS

The TDR determines the sustainment of ventricular tachyarrhythmias, through control of the scroll wave filament dynamics.

Integrative computational models of cardiac arrhythmias -- simulating the structurally realistic heart

Simulation of cardiac electrical function, and specifically, simulation aimed at understanding the mechanisms of cardiac rhythm disorders, represents an example of a successful integrative multiscale modeling approach, uncovering emergent behavior at the successive scales in the hierarchy of structural complexity. The goal of this article is to present a review of the integrative multiscale models of realistic ventricular structure used in the quest to understand and treat ventricular arrhythmias. It concludes with the new advances in image-based modeling of the heart and the promise it holds for the development of individualized models of ventricular function in health and disease.

Origin choice and petal loss in the flower garden of spiral wave tip trajectories

Rotating spiral waves have been observed in numerous biological and physical systems. These spiral waves can be stationary, meander, or even degenerate into multiple unstable rotating waves. The spatiotemporal behavior of spiral waves has been extensively quantified by tracking spiral wave tip trajectories. However, the precise methodology of identifying the spiral wave tip and its influence on the specific patterns of behavior remains a largely unexplored topic of research. Here we use a two-state variable FitzHugh-Nagumo model to simulate stationary and meandering spiral waves and examine the spatiotemporal representation of the system's state variables in both the real (i.e., physical) and state spaces. We show that mapping between these two spaces provides a method to demarcate the spiral wave tip as the center of rotation of the solution to the underlying nonlinear partial differential equations. This approach leads to the simplest tip trajectories by eliminating portions resulting from the rotational component of the spiral wave.

Vortex filament dynamics in computational models of ventricular fibrillation in the heart

In three-dimensional cardiac tissue, the re-entrant waves that sustain ventricular fibrillation rotate around a line of phase singularity or vortex filament. The aim of this study was to investigate how the behavior of these vortex filaments is influenced by membrane kinetics, initial conditions, and tissue geometry in computational models of excitable tissue. A monodomain model of cardiac tissue was used, with kinetics described by a three-variable simplified ionic model (3V-SIM). Two versions of 3V-SIM were used, one with steep action potential duration restitution, and one with reduced excitability. Re-entrant fibrillation was then simulated in three tissue geometries: a cube, a slab, and an anatomically detailed model of rabbit ventricles. Filaments were identified using a phase-based method, and the number, size, origin, and orientation of filaments was tracked throughout each simulation. The main finding of this study is that kinetics, initial conditions, geometry, and anisotropy all affected the number, proliferation, and orientation of vortex filaments in re-entrant fibrillation. An important finding of this study was that the behavior of vortex filaments in simplified slab geometry representing part of the ventricular wall did not necessarily predict behavior in an anatomically detailed model of the rabbit ventricles.

Filament-induced surface spiral turbulence in three-dimensional excitable media

Filament-induced surface defect-mediated turbulence in bounded three-dimensional (3D) excitable media is investigated in the regime of negative line tension. In this regime turbulence arises due to unstable filaments associated with scroll waves and is purely a 3D phenomenon. It is shown that the statistical properties of the turbulent defect dynamics can be used to distinguish surface defect-mediated turbulence from its 2D analog. Mechanisms for the creation and annihilation of surface defects are discussed and Markov rate equations are employed to model the results.

Twisted vortex filaments in the three-dimensional complex Ginzburg-Landau equation

The structure and dynamics of vortex filaments that form the cores of scroll waves in three-dimensional oscillatory media described by the complex Ginzburg-Landau equation are investigated. The study focuses on the role that twist plays in determining the bifurcation structure in various regions of the (alpha,beta) parameter space of this equation. As the degree of twist increases, initially straight filaments first undergo a Hopf bifurcation to helical filaments; further increase in the twist leads to a secondary Hopf bifurcation that results in supercoiled helices. In addition, localized states composed of superhelical segments interspersed with helical segments are found. If the twist is zero, zigzag filaments are found in certain regions of the parameter space. In very large systems disordered states comprising zigzag and helical segments with positive and negative senses exist. The behavior of vortex filaments in different regions of the parameter space is explored in some detail. In particular, an instability for nonzero twist near the alpha=beta line suggests the existence of a nonsaturating state that reduces the stability domain of straight filaments. The results are obtained through extensive simulations of the complex Ginzburg-Landau equation on large domains for long times, in conjunction with simulations on equivalent two-dimensional reductions of this equation and analytical considerations based on topological concepts.

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.

The canine virtual ventricular wall: A platform for dissecting pharmacological effects on propagation and arrhythmogenesis

We have constructed computational models of canine ventricular cells and tissues, ultimately combining detailed tissue architecture and heterogeneous transmural electrophysiology. The heterogeneity is introduced by modifying the Hund-Rudy canine cell model in order to reproduce experimentally reported electrophysiological properties of endocardial, midmyocardial (M) and epicardial cells. These models are validated against experimental data for individual ionic current and action potential characteristics, and their rate dependencies. 1D and 3D heterogeneous virtual tissues are constructed, with detailed tissue architecture (anisotropy and orthotropy, due to fibre orientation and sheet structure) of the left ventricular wall wedge extracted from a diffusion tensor imaging data set. The models are used to study the effects of tissue heterogeneity and class III drugs on transmural propagation and tissue vulnerability to re-entry. We have determined relationships between the transmural dispersion of action potential duration (APD) and the vulnerable window in the 1D virtual ventricular wall, and demonstrated how changes in the transmural heterogeneity, and hence tissue vulnerability, can lead to generation of re-entry in the 3D ventricular wedge. Two class III drugs with opposite qualitative effects on transmural APD heterogeneity are considered: d-sotalol that increases transmural APD dispersion, and amiodarone that decreases it. Simulations with the 1D virtual ventricular wall show that under d-sotalol conditions the vulnerable window is substantially wider compared to amiodarone conditions, primarily in the epicardial region where unidirectional conduction block persists until the adjacent M cells are fully repolarised. Further simulations with the 3D ventricular wedge have shown that ectopic stimulation of the epicardial region results in generation of sustained re-entry under d-sotalol conditions, but not under amiodarone conditions or in control. Again, APD increase in M cells was identified as the major contributor to tissue vulnerability--re-entry was initiated primarily due to ectopic excitation propagating around the unidirectional conduction block in the M cell region. This suggests an electrophysiological mechanism for the anti- and proarrhythmic effects of the class III drugs: the relative safety of amiodarone in comparison to d-sotalol can be explained by relatively low transmural APD dispersion, and hence, a narrow vulnerable window and low probability of re-entry in the tissue.

A guide to modelling cardiac electrical activity in anatomically detailed ventricles

One of the most recent trends in cardiac electrophysiology is the development of integrative anatomically accurate models of the heart, which include description of cardiac activity from sub-cellular and cellular level to the level of the whole organ. In order to construct this type of model, a researcher needs to collect a wide range of information from books and journal articles on various aspects of biology, physiology, electrophysiology, numerical mathematics and computer programming. The aim of this methodological article is to survey recent developments in integrative modelling of electrical activity in the ventricles of the heart, and to provide a practical guide to the resources and tools that are available for work in this exciting and challenging area.

Organization of ventricular fibrillation in the human heart

Sudden cardiac death is a major cause of death in the industrialized world, claiming approximately 300,000 victims annually in the United States alone. In most cases, sudden cardiac death is caused by ventricular fibrillation (VF). Experimental studies in large animal hearts have shown that the uncoordinated contractions during VF are caused by large numbers of chaotically wandering reentrant waves of electrical activity. However, recent clinical data on VF in the human heart seem to suggest that human VF may have a markedly different organization. Here, we use a detailed model of the human ventricles, including a detailed description of cell electrophysiology, ventricular anatomy, and fiber direction anisotropy, to study the organization of human VF. We show that characteristics of our simulated VF are qualitatively similar to the clinical data. Furthermore, we find that human VF is driven by only approximately 10 reentrant sources and thus is much more organized than VF in animal hearts of comparable size, where VF is driven by approximately 50 sources. We investigate the influence of anisotropy ratio, tissue excitability, and restitution properties on the number of reentrant sources driving VF. We find that the number of rotors depends strongest on minimum action potential duration, a property that differs significantly between human and large animal hearts. Based on these findings, we suggest that the simpler spatial organization of human VF relative to VF in large animal hearts may be caused by differences in minimum action potential duration. Both the simpler spatial organization of human VF and its suggested cause may have important implications for treating and preventing this dangerous arrhythmia in humans.

The virtual ventricular wall: a tool for exploring cardiac propagation and arrhythmogenesis

Methods for the experimental and clinical investigation of cardiac arrhythmias are limited to inferring propagation within the myocardium, from surface measurements, or from electrodes at a few sites within the cardiac wall. Biophysically and anatomically detailed computational models of cardiac tissues offer a powerful way for studying the electrical propagation processes and arrhythmias within the virtual heart. We use virtual tissues to study and visualise the effects of patho- and physiological conditions, and pharmacological interventions on transmural propagation in the virtual ventricular walls. Class III drug actions are quantitatively explained by changes induced in the transmural dispersion of action potential duration. We illustrate the automated construction of a virtual anisotropic ventricle from Diffusion Tensor MRI for individual hearts, and use it to explore mechanisms leading to ventricular fibrillation. The virtual ventricular wall provides an effective tool for exploring, evaluating and visualising processes during the initiation and maintenance of ventricular arrhythmias.

Dynamical and cellular electrophysiological mechanisms of ECG changes during ischaemia

The interpretation of normal and pathological electrocardiographic (ECG) patterns in terms of the underlying cellular and tissue electrophysiology is rudimentary, as the existing theories rely on geometrical aspects. We relate effects of sub-endocardial ischaemia on the ST-segment depression in ECG to patterns of transmural action potential propagation in a one-dimensional virtual ventricular wall. Our computational study exposes two electrophysiological mechanisms of ST depression: dynamic-predominantly positive spatial gradients in the membrane potential during abnormal repolarization of the wall, produced by action potential duration changes in the ischaemic region; and static-a negative spatial gradient of the resting membrane potential between the normal and ischaemic regions. Hyperkalaemia is the major contributor to both these mechanisms at the cellular level. These results complement simulations of the effects of cardiac geometry on the ECG, and dissect spatio-temporal and cellular electrophysiological mechanisms of ST depression seen in sub-endocardial ischaemia.

Quantifying ventricular fibrillation: in silico research and clinical implications

Cardiovascular disease remains the leading cause of death in otherwise healthy humans. In particular, most cases of sudden cardiac death occur as a result of failure of the mechanical function of the heart which is triggered by a turbulent pattern of electrical excitation of the heart e.g., ventricular fibrillation (VF). Although the exact mechanisms of VF remain unknown, increasing evidence indicates that it is organized by multiple reentrant sources (wavelets).