Waves In Cardiac Tissue Research Articles

A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue

Atrial fibrillation (AF) is the most common cardiac arrhythmia whose mechanisms are thought to be mainly due to the self perpetuation of spiral waves (SW). To date, available treatment strategies (antiarrhythmic drugs, radiofrequency ablation of the substrate, electrical cardioversion) to restore and to maintain a normal sinus rhythm have limitations and are associated with AF recurrences. The aim of this study was to assess a way of suppressing SW by applying multifocal electrical stimulations in a simulated cardiac tissue using a 2D FitzHugh–Nagumo model specially convenient for AF investigations. We identified stimulation parameters for successful termination of SW. However, SW reinduction, following the electrical stimuli, leads us to develop a hybrid strategy based on sodium channel modification for the simulated tissue.

Atrial and ventricular fibrillation: computational simulation of spiral waves in cardiac tissue

This manuscript proposes a novel, efficient finite element solution technique for the computational simulation of cardiac electrophysiology. We apply a two-parameter model that is characterized through a fast action potential and a slow recovery variable. The former is introduced globally as a nodal degree of freedom, whereas the latter is treated locally as internal variable on the integration point level. This particular discretization is extremely efficient and highly modular since different cardiac cell models can be incorporated straightforwardly through only minor local modifications on the integration point level. In this manuscript, we illustrate the algorithm in terms of the Aliev–Panfilov model for cardiomyocytes. To ensure unconditional stability, a backward Euler scheme is applied to discretize the evolution equation for both the action potential and the recovery variable in time. To increase robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton–Raphson scheme and illustrate the consistent linearization of the weak form of the excitation problem. The proposed algorithm is illustrated by means of two- and three-dimensional examples of re-entrant spiral and scroll waves characteristic of cardiac arrhythmias in atrial and ventricular fibrillation.

Line-defect patterns of unstable spiral waves in cardiac tissue

Spiral wave propagation in period-2 excitable media is accompanied by line defects, the locus of points with period-1 oscillations. Here we investigate spiral line defects in cardiac tissue where period-2 behavior has a known arrhythmogenic role. We find that the number of line defects, which is constrained to be an odd integer, is 3 for a freely rotating spiral, with and without meander, but 1 for a spiral anchored around a fixed heterogeneity. We interpret this finding analytically using a simple theory where spiral wave unstable modes with different numbers of line defects correspond to quantized solutions of a Helmholtz equation. Furthermore, the slow inward rotation of spiral line defects is described in different regimes.

Spiral-wave turbulence and its control in the presence of inhomogeneities in four mathematical models of cardiac tissue.

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Convergence of a finite volume scheme for the bidomain model of cardiac tissue

We analyze a finite volume scheme for the bidomain model, which is a degenerate reaction–diffusion system modeling electrophysiological waves in cardiac tissue. We establish existence and uniqueness of solutions to the finite volume scheme, and show that it converges to a weak solution of the bidomain model. The convergence proof is based on deriving series of a priori estimates and using a general L p compactness criterion.

The instability of the spiral wave induced by the deformation of elastic excitable media

There are some similarities between the spiral wave in excitable media and in cardiac tissue. Much evidence shows that the appearance and instability of the spiral wave in cardiac tissue can be linked to one kind of heart disease. There are many models that can be used to investigate the formation and instability of the spiral wave. Cardiac tissue is excitable and elastic, and it is interesting to simulate the transition and instability of the spiral wave induced by media deformation. For simplicity, a class of the modified Fitzhugh–Nagumo (MFHN) model, which can generate a stable rotating spiral wave, meandering spiral wave and turbulence within appropriate parameter regions, will be used to simulate the instability of the spiral wave induced by the periodical deformation of media. In the two-dimensional case, the total acreage of elastic media is supposed to be invariable in the presence of deformation, and the problem is described with Lx × Ly = N × ΔxN × Δy = L′xL′y = N × Δx′N × Δy′. In our studies, elastic media are decentralized into N × N sites and the space of the adjacent sites is changed to simulate the deformation of elastic media. Based on the nonlinear dynamics theory, the deformation effect on media is simplified and simulated by perturbing the diffusion coefficients Dx and Dy with different periodical signals, but the perturbed diffusion coefficients are compensatory. The snapshots of our numerical results find that the spiral wave can coexist with the spiral turbulence, instability of the spiral wave and weak deformation of the spiral wave in different conditions. The ratio parameter ε and the frequency of deformation forcing play a deterministic role in inducing instability of the spiral wave. Extensive studies confirm that the instability of the spiral wave can be induced and developed only if an appropriate frequency for deformation is used. We analyze the power spectrum for the time series of the mean activator of four sampled sites which are selected symmetrically in different cases, such as the condition that the spiral wave coexists with the spiral turbulence, spiral wave without evident deformation, complete instability of the spiral wave (turbulence) and weak deformation of the spiral wave. It is found that more new peaks appear in the power spectrum and the distribution of frequency becomes sparser when the spiral wave encounters instability.

Sharp Interface and Voltage Conservation in the Phase Field Method: Application to Cardiac Electrophysiology

We present a finite difference method for modeling the propagation of electrical waves in cardiac tissue using the cable equation with homogeneous Neumann boundary conditions. This method is novel in that it is derived by first discretizing the phase field method as described by Fenton et al. [Chaos, 15 (2005), p. 013502.] then taking a limit to recover a sharp interface. Our method provides for exact voltage conservation (up to floating point precision in application), can be used on arbitrary geometries, and can be implemented using only nearest neighbor coupling between grid points.

Abstract 1349: Overexpression And Dominant-negative Suppression Of Inwardly Rectifying Potassium Channel Protein (Kir2.1) Alters Electrophysiology And Spiral Wave Dynamics Of An In Vitro Model Of Cardiac Myocytes

Introduction : An important role for the inwardly rectifying potassium current (I K1 ) has been postulated in controlling the stability and frequency of rotors responsible for ventricular tachycardia and fibrillation. We investigated the effects of Kir2.1 overexpression and Kir2.1AAA dominant-negative mutant suppression on the electrophysiology and inducibility, stability and frequency of spiral waves in an in vitro cardiac tissue model. Methods/Results : Neonatal rat ventricular myocytes (NRVMs) were transduced by lentiviral vectors encoding Kir2.1 or Kir2.1AAA. Immunostaining revealed Kir2.1 or mutant Kir2.1 protein overexpression and whole cell-clamp confirmed the predicted effects on I K1 , resting potential, and action potential duration (APD 80 ). Optical mapping was performed on confluent NRVM monolayers containing a 5 mm diameter central island of gene-modified NRVMs created by a stenciling technique. APs propagated with increased CV (25.1±2.7 cm/sec, n=7) and shortened APD 80 (73±11 msec, n=7) in islands of Kir2.1 overexpression, or decreased CV (13.1±1.1 cm/sec, n=7) and prolonged APD 80 (263±14 msec, n=7) in islands of Kir2.1AAA suppression, compared with normal CV and APD 80 of 19.2±0.4 cm/sec and 169±14 msec (n=7) in non-transduced islands. Reentry was initiated by rapid pacing. With Kir2.1 overexpression, reentrant waves anchored to the island and remained stable (89±15 minutes, n=3) with a frequency of 8±2 Hz. Superfusion with 0.5 mM BaCl 2 to block I K1 slowed reentry to 1 Hz and terminated it shortly after initiation. NRVM monolayers with islands of Kir2.1AAA suppression (n=3) displayed rapid spontaneous activity. Rapid pacing of these monolayers initiated an unstable figure-of-eight reentry (n=3) that degraded into single and multi-armed spiral waves, anchored to varying parts of the island with a maximum frequency of 2±1 Hz. Importantly, no reentry could be initiated in monolayers with non-transduced islands (n=3). Conclusion : Functional reentrant waves induced by rapid pacing are anchored to islands of localized Kir2.1 overexpression whereas they drop in frequency and meander in islands of dominant-negative suppression of Kir2.1, confirming the importance of I K1 for the stability of these waves in cardiac tissue.

Interaction between spiral and paced waves in cardiac tissue

For prevention of lethal arrhythmias, patients at risk receive implantable cardioverter-defibrillators, which use high-frequency antitachycardia pacing (ATP) to convert tachycardias to a normal rhythm. One of the suggested ATP mechanisms involves paced-induced drift of rotating waves followed by their collision with the boundary of excitable tissue. This study provides direct experimental evidence of this mechanism. In monolayers of neonatal rat cardiomyocytes in which rotating waves of activity were initiated by premature stimuli, we used the Ca(2+)-sensitive indicator fluo 4 to observe propagating wave patterns. The interaction of the spiral tip with a paced wave was then monitored at a high spatial resolution. In the course of the experiments, we observed spiral wave pinning to local heterogeneities within the myocyte layer. High-frequency pacing led, in a majority of cases, to successful termination of spiral activity. Our data show that 1) stable spiral waves in cardiac monolayers tend to be pinned to local heterogeneities or areas of altered conduction, 2) overdrive pacing can shift a rotating wave from its original site, and 3) the wave break, formed as a result of interaction between the spiral tip and a paced wave front, moves by a paced-induced drift mechanism to an area where it may become unstable or collide with a boundary. The data were complemented by numerical simulations, which was used to further analyze experimentally observed behavior.

Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue

We prove well-posedness (existence and uniqueness) results for aclass of degenerate reaction-diffusion systems. A prototype system belongingto this class is provided by the bidomain model, which is frequently used tostudy and simulate electrophysiological waves in cardiac tissue. The existenceresult, which constitutes the main thrust of this paper, is proved by means ofa nondegenerate approximation system, the Faedo-Galerkin method, and thecompactness method.

Elimination of Spiral Waves and Competition between TravellingWave Impulses and Spiral Waves

The interaction between travelling wave impulses and spiral wavesis studied and the results of their competition are related to theexciting period. From the results, it is known that the formation anddevelopment of spiral waves in cardiac tissue depend on the period bywhich the travelling wave impulses are excited. A method is proposed toeliminate spiral waves, which is easily operated.

COMPLICATED ELECTRICAL ACTIVITIES IN CARDIAC TISSUE

It has become widely accepted that ventricular fibrillation, the most dangerous cardiac arrhythmias, is a major cause of death in the industrialized world. Alternans and conduction block have recently been related to the progression from ventricular tachycardia to ventricular fibrillation. From the point of view in cellular electrophysiology, ventricular tachycardia is the formation of reentrant wave in cardiac tissue. And ventricular fibrillation arises from subsequent breakdown of reentrant wave into multiple drifting and meandering spiral waves. In this paper, we numerically study pulse and vortex dynamics in cardiac tissue. Our numerical results include 1:1 normal sinus rhythm, 2:1 conduction block, complete conduction block, spiral wave, and spiral breakup. All of our numerical findings can be corresponding to clinical measurements in electrocardiogram. Various electrical activities in cardiac tissue will be discussed in detail in the present manuscript.

Exact Analytic Solution of the Simplified Telegraph Model of Propagation and Dissipation of Excitation Fronts

The telegraph equation is more suitable than ordinary diffusion equation in modeling reaction diffusion in several branches of sciences (E. Ahmed, H. A. Abdusalam, and E. S. Fahmy, 2001, Int. J. Mod. Phys. C 12(5), 717; E. Ahmed and H. A. Abdusalam, 2004, Chaos, Solitons and Fractals 22, 583; H. A. Abdusalam and E. S. Fahmy, 2003, Chaos, Solitons and Fractals 18, 259; Abdusalam, 2004 Appl. Math. Comp. 157, 515). An excitation wave in cardiac tissue fails to propagate if the transmembrane voltage at its front rises too slow and does not excite the tissue ahead of it. Then the sharp voltage profile of the front will dissipate, and subsequent spread of voltage will be purely diffusive. This mechanism is impossible in FitzHugh–Nagumo type system (V. N. Biktashev, 2003, Int. J. Bifarcation and Chaos 13(12), 3605). Biktashev suggested a simplified mathematical model for this mechanism and in the present work we generalize this model to telegraph system. Our generalized telegraph model has exact traveling front solutions and we show the effect of the time delay on the velocity and we show that, the post-front voltage depends on two parameters in which one of them is the time delay.

Dissipation of the excitation wave fronts.

An excitation wave in cardiac tissue will fail to propagate if the transmembrane voltage at its front rises too slowly and does not excite the tissue ahead of it. Then the sharp voltage profile of the front will dissipate, and the subsequent spread of voltage will be purely diffusive. This mechanism is impossible in FitzHugh-Nagumo type systems. Here a simplified mathematical model for this mechanism is suggested. The model has exact traveling front solutions, and gives conditions for the front dissipation. In particular, a front will dissipate if it is not allowed to propagate faster than a certain nonzero speed. This critical speed depends only on the properties of the fast sodium current.

Elimination of spiral waves in cardiac tissue by multiple electrical shocks.

We study numerically the elimination of a spiral wave in cardiac tissue by application of multiple shocks of external current. To account for the effect of shocks we apply a recently developed theory for the interaction of the external current with cardiac tissue. We compare two possible feedback algorithms for timing of the shocks: a "local" feedback algorithm 11 (using an external electrode placed directly on the tissue) and a "global" feedback algorithm 22 (using the electrocardiogram). Our main results are: application of the external current causes a parametric resonant drift similar to that reported in previous model computations; the ratio of the threshold of elimination of the spiral wave by multiple shocks to the threshold of conventional single shock defibrillation in our model for cardiac tissue is about 0.5, while earlier, less realistic models predicted the value about 0.2; we show that an important factor for successful defibrillation is the location of the feedback electrode and the best results are achieved if the feedback electrode or the ECG lead is located at the boundary (or edge) of the cardiac tissue; the "local" and the "global" feedback algorithms show similar efficiency.

Frequency locking of meandering spiral waves in cardiac tissue

Frequency locking of meandering spiral waves in cardiac tissue