Spiral breakup due to mechanical deformation in excitable media

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Cardiac contraction induces discordant alternans and localized block

In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e., alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be proarrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e., from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity θ and the wavelength λ of a plane wave; we show that PD leads to a periodic, spatial modulation of θ and a temporally periodic modulation of λ; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNP04 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNP04 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Attractive and repulsive contributions of localized excitability inhomogeneities and elimination of spiral waves in excitable media

The attracting and repelling of spiral waves in a two-dimensional excitable medium in the presence of localized excitability inhomogeneities are studied. The choice of two effects depends on the comparison of excitabilities inside and outside the localized obstacle. We inspect the changes in attracting and repelling behaviors with respect to the size of the obstacle and the initial distance between the center of the spiral core and the obstacle. To understand the occurrence of these phenomena, we investigated the small v-value areas near the tip and the function of the wave velocity as the excitability parameter ε. Considering the attributes of the attractive obstacle, an eliminating scheme of spiral waves is proposed in which the attractive obstacle is rapidly moved at several fixed times. This method can avoid the high-amplitude and high-frequency stimulus in most conventional methods.

Spiral wave breakup in excitable media with an inhomogeneity of conduction anisotropy

Many conditions remodel the heart muscle such that it results in a perturbation of cells coupling. The effect of this perturbation on the stability of the spiral waves of electrochemical activity is not clear. We used the FitzHugh-Nagumo model of an excitable medium to model the conduction of the activation waves in a two-dimensional system with inhomogeneous anisotropy level. Inhomogeneity of the anisotropy level was modeled by adding Gaussian noise to diffusion coefficients corresponding with lateral coupling of the cells. Low noise levels resulted in a stable propagation of the spiral wave. For large noise level conduction was not possible due to insufficient coupling in direction perpendicular to fibers. For intermediate noise intensities, the initial wave broke up into several independent spiral waves or waves circulating around conduction obstacles. At an optimal noise intensity, the number of wavelets was maximized-a form of anti-coherent resonance was obtained. Our results suggest that the inhomogeneity of conduction anisotropy may promote wave breakup and hence play an important role in the initiation and perpetuation of the cardiac arrhythmias.

Global coupling in excitable media provides a simplified description of mechanoelectrical feedback in cardiac tissue

Cardiac mechanoelectric feedback can play an important role in different heart pathologies. In this paper, we show that mechanoelectric models which describe both the electric propagation and the mechanic contraction of cardiac tissue naturally lead to close systems of equations with global coupling among the variables. This point is exemplified using the Nash-Panfilov model, which reduces to a FitzHugh-Nagumo-type equation with global coupling in the linear elastic regime. We explain the appearance of self-oscillatory regimes in terms of the system nullclines and describe the different dynamical attractors. Finally, we study their basin of attraction in terms of the system size and the strength of the stretch-induced currents.

Influences of periodic mechanical deformation on spiral breakup in excitable media

Influences of periodic mechanical deformation (PMD) on spiral breakup that results from Doppler instability in excitable media are investigated. We present a new effect: a high degree of homogeneous PMD is favored to prevent the low-excitability-induced breakup of spiral waves. The frequency and amplitude of PMD are also significant for achieving this purpose. The underlying mechanism of successful control is also discussed, which is believed to be related to the increase of the minimum temporal period of the meandering spiral when the suitable PMD is applied.