Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model

An audit of uncertainty in multi-scale cardiac electrophysiology models

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Analysis of cardiac fibrillation using phase mapping

The sequence of myocardial electrical activation during fibrillation is complex and changes with each cycle. Phase analysis represents the electrical activation-recovery process as an angle. Lines of equal phase converge at a phase singularity at the center of rotation of a reentrant wave, and the identification of reentry and tracking of reentrant wavefronts can be automated. We examine the basic ideas behind phase analysis. With the exciting prospect of using phase analysis of atrial electrograms to guide ablation in the human heart, we highlight several recent developments in preprocessing electrograms so that phase can be estimated reliably.

Effective dynamics of twisted and curved scroll waves using virtual filaments

Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.

Cardiac bidomain bath-loading effects during arrhythmias: interaction with anatomical heterogeneity

Cardiac tissue is always surrounded by conducting fluid, both in vivo (blood) and in experimental preparations (Tyrode's solution), which acts to increase conduction velocity (CV) close to the tissue-fluid interface, inducing transmural wavefront curvature. Despite its potential importance, computer modeling studies focused on arrhythmia mechanisms have previously not accounted for these bath-loading effects. Here, we investigate the increase in CV and concomitant change in transmural wavefront profiles upon both propagation and arrhythmia dynamics within models of differing anatomical complexity. In simplified slab models, in absence of transmural fiber rotation, bath-loading induced transmural wavefront curvature dominates, significantly increasing arrhythmia complexity compared to no bath. In the presence of fiber rotation, bath-loading effects are less striking and depend upon propagation direction: the bath accentuates natural concave curvature caused by transmurally rotating fibers, but attenuates convex curvature, which negates overall impact upon arrhythmia complexity. Finally, we demonstrate that the high degree of anatomical complexity within whole ventricular models modulates bath-loading induced transmural wavefront curvature. However, key is the increased surface CV that dramatically reduces both arrhythmia inducibility and resulting complexity by increasing wavelength and reducing the available excitable gap. Our findings highlight the importance of including bath-loading effects during arrhythmia mechanism investigations, which could have implications for interpreting and comparing simulation results with experimental data where such effects are inherently present.

Models of cardiac tissue electrophysiology: progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

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.

Computational modeling for bedside application

Advances in computer power, novel diagnostic and therapeutic medical technologies, and an increasing knowledge of pathophysiology from gene to organ systems make it increasingly feasible to apply multiscale patient-specific modeling based on proven disease mechanisms. Such models may guide and predict the response to therapy in many areas of medicine. This is an exciting and relatively new approach, for which efficient methods and computational tools are of the utmost importance. Investigators have designed patient-specific models in almost all areas of human physiology. Not only will these models be useful in clinical settings to predict and optimize the outcome from surgery and non-interventional therapy, but they will also provide pathophysiologic insights from the cellular level to the organ system level. Models, therefore, will provide insight as to why specific interventions succeed or fail.

The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

In normal heart, ventricular fibrillation can be induced by a single properly timed strong electrical or mechanical stimulus. A mechanism first proposed by Winfree and coined the “pinwheel experiment” emphasizes the timing and strength of the stimulus in inducing figure-of-eight reentry. However, the effects of cellular electrophysiological properties on vulnerability to reentry in the pinwheel scenario have not been investigated. In this study, we extend Winfree's pinwheel experiment to show how the vulnerability to reentry is affected by the graded action potential responses induced by a strong premature stimulus, action potential duration (APD), and APD restitution in simulated monodomain homogeneous two-dimensional tissue. We find that a larger graded response, longer APD, or steeper APD restitution slope reduces the vulnerable window of reentry. Strong graded responses and long APD promote tip-tip interactions at long coupling intervals, causing the two initiated spiral wave tips to annihilate. Steep APD restitution promotes wave front-wave back interaction, causing conduction block in the central common pathway of figure-of-eight reentry. We derive an analytical treatment that shows good agreement with numerical simulation results.

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.

Forward Euler Stability of the Bidomain Model of Cardiac Tissue

The bidomain model describes the anisotropic electrical properties of cardiac tissue. One common numerical technique for solving the bidomain equations is the explicit forward Euler method. In this communication we derive a relationship between the time and space steps that ensures the stability of this numerical method.

Detection of intramyocardial scroll waves using absorptive transillumination imaging

Optical imaging using voltage-sensitive dyes has become an important tool for studying vortex-like electrical waves in the heart. Such waves, known as spiral or scroll waves, can spontaneously form in pathological ventricular myocardium, causing ventricular fibrillation and sudden death. Until recently, observations of scroll waves were limited to their surface manifestations, thus providing little information about the shape and location of their organizing center, the filament. We use computer modeling to assess the feasibility of visualizing filaments using dynamic transillumination imaging in conjunction with near-IR voltage-sensitive absorptive dyes (absorptive transillumination). We simulate transillumination signals produced by the intramural scroll waves in a realistic slab of ventricular tissue with trabeculated endocardial surface. The computations use a detailed ionic model of electrical excitation (LRd) coupled to a photon transport model for cardiac tissue. Our simulations show that dynamic absorptive transillumination data, with subsequent processing involving either amplitude maps, time-space plots, or power-of-the-dominant-frequency maps, can be used to reliably detect intramural scroll waves through the whole thickness (approximately 10 mm) of the ventricular wall. Neither variations in the thickness of the myocardial wall nor noise impeded the detection of intramural filaments.

Interactions between paced wavefronts and monomorphic ventricular tachycardia: implications for antitachycardia pacing

OBJECTIVES

Interactions between paced wavefronts and monomorphic ventricular tachycardia (VT) dictate antitachycardia pacing outcomes. We used optical mapping to assess those interactions during single and dual site pacing of rabbit ventricular epicardium.

METHODS AND RESULTS

Monomorphic VTs were initiated in six isolated rabbit hearts that were endocardially cryoablated to limit viable tissue to visible epicardium and establish apical tissue as the anatomic anchor. Preparations were optically mapped during single (n = 39) and dual (n = 43) site pacing at 50%-90% of VT cycle length (CL) with eight pulses per trial. Overall, we found six pulses that abruptly terminated VT. This occurred because the VT wavefront collided with the antidromic portion of the paced wavefront and the orthodromic portion of paced wavefront blocked in the VT's refractory region. When effective, dual site pacing that captured tissue at both leads simultaneously terminated the VT immediately, while single site pacing or dual site pacing that captured tissue at only one lead terminated the VT after resetting advanced the orthodromic wavefront. We found 12 pulses that induced polymorphic VT, with 11 of those pulses occurring during capture at only one lead. Expansion of the combined antidromic-VT wavefront around one or both ends of the arc of conduction block formed by the interaction of the orthodromic wavefront with the VT's refractory region initiated functional reentry. Six of these polymorphic VTs were nonsustained because the underlying wavefronts self-terminated. The wavefronts did persist for 4.2 +/- 3.5 cycles before self-terminating in these trials, and the post-pacing cycles presented a 146% increase in CL variability, compared with the variability prior to pacing. These temporal characteristics are similar to those of delayed termination in patients with ICDs.

CONCLUSIONS

The main difference between pulses that terminated abruptly and pulses that induced polymorphic VT was the effective separation of the antidromic and orthodromic portions of the paced wavefront from one another.