Flavio H. Fenton

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to reentrant waves, i.e., electrical wave(s) that recirculate repeatedly throughout the tissue at a higher frequency than the waves produced by the hearts natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, have made it extremely difficult to pinpoint the detailed dynamics of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols. (c) 2002 American Institute of Physics.

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.

Effects of Pacing Site and Stimulation History on Alternans Dynamics and the Development of Complex Spatiotemporal Patterns in Cardiac Tissue

Alternans of action potential duration has been associated with T wave alternans and the development of arrhythmias because it produces large gradients of repolarization. However, little is known about alternans dynamics in large mammalian hearts. Using optical mapping to record electrical activations simultaneously from the epicardium and endocardium of 9 canine right ventricles, we demonstrate novel arrhythmogenic complex spatiotemporal dynamics. (i) Alternans predominantly develops first on the endocardium. (ii) The postulated simple progression from normal rhythm to concordant to discordant alternans is not always observed; concordant alternans can develop from discordant alternans as the pacing period is decreased. (iii) In contrast to smaller tissue preparations, multiple stationary nodal lines may exist and need not be perpendicular to the pacing site or to each other. (iv) Alternans has fully three-dimensional dynamics and the epicardium and endocardium can show significantly different dynamics: multiple nodal surfaces can be transmural or intramural and can form concave/convex surfaces resulting in islands of discordant alternans. (v) The complex spatiotemporal patterns observed during alternans are very sensitive to both the site of stimulation and the stimulation history. Alternans in canine ventricles not only exhibit larger amplitudes and persist for longer cycle length regimes compared to those found in smaller mammalian hearts, but also show novel dynamics not previously described that enhance dispersion and show high sensitivity to initial conditions. This indicates some underlying predisposition to chaos and can help to guide the design of new drugs and devices controlling and preventing arrhythmic events.

Minimal model for human ventricular action potentials in tissue

Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular (MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher-Noble-Noble-Panfilov (TNNP), and the Iyer-Mazhari-Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.

Low-energy control of electrical turbulence in the heart

Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves in a heterogeneous anatomical substrate. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation. Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ Eα. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.

Visualization of spiral and scroll waves in simulated and experimental cardiac tissue

The heart is a nonlinear biological system that can exhibit complex electrical dynamics, complete with period-doubling bifurcations and spiral and scroll waves that can lead to fibrillatory states that compromise the hearts ability to contract and pump blood efficiently. Despite the importance of understanding the range of cardiac dynamics, studying how spiral and scroll waves can initiate, evolve, and be terminated is challenging because of the complicated electrophysiology and anatomy of the heart. Nevertheless, over the last two decades advances in experimental techniques have improved access to experimental data and have made it possible to visualize the electrical state of the heart in more detail than ever before. During the same time, progress in mathematical modeling and computational techniques has facilitated using simulations as a tool for investigating cardiac dynamics. In this paper, we present data from experimental and simulated cardiac tissue and discuss visualization techniques that facilitate understanding of the behavior of electrical spiral and scroll waves in the context of the heart. The paper contains many interactive media, including movies and interactive two- and three-dimensional Java applets.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Cardiac cell modelling: observations from the heart of the cardiac physiome project.

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Termination of Atrial Fibrillation Using Pulsed Low-Energy Far-Field Stimulation

Background— Electrically based therapies for terminating atrial fibrillation (AF) currently fall into 2 categories: antitachycardia pacing and cardioversion. Antitachycardia pacing uses low-intensity pacing stimuli delivered via a single electrode and is effective for terminating slower tachycardias but is less effective for treating AF. In contrast, cardioversion uses a single high-voltage shock to terminate AF reliably, but the voltages required produce undesirable side effects, including tissue damage and pain. We propose a new method to terminate AF called far-field antifibrillation pacing, which delivers a short train of low-intensity electric pulses at the frequency of antitachycardia pacing but from field electrodes. Prior theoretical work has suggested that this approach can create a large number of activation sites (“virtual” electrodes) that emit propagating waves within the tissue without implanting physical electrodes and thereby may be more effective than point-source stimulation. Methods and Results— Using optical mapping in isolated perfused canine atrial preparations, we show that a series of pulses at low field strength (0.9 to 1.4 V/cm) is sufficient to entrain and subsequently extinguish AF with a success rate of 93% (69 of 74 trials in 8 preparations). We further demonstrate that the mechanism behind far-field antifibrillation pacing success is the generation of wave emission sites within the tissue by the applied electric field, which entrains the tissue as the field is pulsed. Conclusions— AF in our model can be terminated by far-field antifibrillation pacing with only 13% of the energy required for cardioversion. Further studies are needed to determine whether this marked reduction in energy can increase the effectiveness and safety of terminating atrial tachyarrhythmias clinically.

Modeling wave propagation in realistic heart geometries using the phase-field method

We present a novel algorithm for modeling electrical wave propagation in anatomical models of the heart. The algorithm uses a phase-field approach that represents the boundaries between the heart muscle and the surrounding medium as a spatially diffuse interface of finite thickness. The chief advantage of this method is to automatically handle the boundary conditions of the voltage in complex geometries without the need to track the location of these boundaries explicitly. The algorithm is shown to converge accurately in nontrivial test geometries with no-flux (zero normal current) boundary conditions as the width of the diffuse interface becomes small compared to the width of the cardiac action potential wavefront. Moreover, the method is illustrated for anatomically realistic models of isolated rabbit and canine ventricles as well as human atria.