Supernormal conduction in cardiac tissue promotes concordant alternans and action potential bunching

Abstract

Supernormal conduction (SNC) in excitable cardiac tissue refers to an increase of pulse (or action potential) velocity with decreasing distance to the preceding pulse. Here we employ a simple ionic model to study the effect of SNC on the propagation of action potentials (APs) and the phenomenology of alternans in excitable cardiac tissue. We use bifurcation analysis and simulations to study attraction between propagating APs caused by SNC that leads to AP pairs and bunching. It is shown that SNC stabilizes concordant alternans in arbitrarily long paced one-dimensional cables. As a consequence, spiral waves in two-dimensional tissue simulations exhibit straight nodal lines for SNC in contrast to spiraling ones in the case of normal conduction. Propagation of pulse trains in excitable media is usually characterized by a so-called dispersion curve that gives the velocity of a pulse in a periodic train as a function of its wavelength [1]. In cardiac tissue the dispersion properties are often summarized in the conduction velocity (CV) restitution curve that relates the velocity of an action potential (AP) to its diastolic interval (DI), that is, the time between two consecutive APs (see, e.g., Ref.[2]).Since a pulse typically is followed by a refractory zone of decreased excitability, the pulse velocity monotonically increases with increasing wavelength (=normal dispersion). In the context of excitable cardiac tissue, normal dispersion corresponds to normal conduction. In this paper we focus on the alternative situation where the velocity of a pulse is decreasing with increasing wavelength. In generic excitable media this case is known as anomalous dispersion. For excitable cardiac tissue it corresponds to supernormal conduction (SNC) [3]. Normal and supernormal conduction may appear for a different wavelength in the same systems, then the dispersion curve has to be nonmonotonic.The simplest case of a nonmonotonic dispersion relation is a curve with a single maximum separating anomalous dispersion at long wavelength from normal dispersion at short wavelength. Such behavior has been discovered in various experiments in chemical reaction-diffusion systems [4,5]. It has been found to coincide with attractive long-range interaction between pulses that may lead to stable bound states [6] merging or bunching of pulses [7]. While most excitable cardiac tissues and related models exhibit normal conduction, nevertheless examples of SNC are frequent (for a short review see, e.g., Ref.[8]). SNC is found, for example, in the Iyer-Mazhari-Winslow [9] or in the Drouhard-RobergeBeeler-Reuter (DRBR) model [10,11] employed in the study here, and it is often observed under conditions of low extracellular potassium concentration [12]. Recently, it has been shown to potentiate the onset of alternans in cultured cardiac cell strands [13] and also in generic models of spiral wave formation [14].Alternans is an oscillation in the duration of the AP that usually occurs at short stimulation periods [15]. In a paced cable or tissue alternans ...

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

“…The amplitude equation formalism can be applied to diverse situations, as gradients of electrophysiological properties [244], anomalous dispersion [252], control of alternans [253][254][255][256][257], or coupling with intracellular calcium [258,259]. It also provides us with some insight into another important problem, not jet completely understood: the influence of alternans on the stability of spiral waves.…”

Cardiac contraction induces discordant alternans and localized block

“…This phenomenological formulation has been extended to include such effects as memory [10], intracellular calcium dynamics [11], and nonmonotonic APD [12] or CV restitution curves [13]. In this paper, we consider an effect that is usually neglected when studying the stability of cardiac waves: the contraction of the tissue.…”

Induced spiral motion in cardiac tissue due to alternans

“…This behavior typically occurs when the time interval between subsequent APs is sufficiently short and it has been extensively studied in the context of paced cables and tissue (see Refs. [11][12][13] and references therein). While alternans is widely acknowledged as a precursor of the development of cardiac fibrillation, leading to sudden cardiac death [14][15][16], its occurrence in and interaction with spiral waves, corresponding to tachycardia, remains largely unexplored.…”

“…Motivated by the above-mentioned experimental observation of spirals exhibiting alternans behavior in rat heart tissue cultures [10], recent theoretical investigations have started to focus on period-two spirals and SDLs in models of excitable cardiac tissue [13,28,29]. While some questions related to the number of SDLs attached to a spiral [28] and the shape of SDLs [13] have already been addressed, this is not the case for the motion of period-two spirals in such systems.…”