The effect of mechanical deformation on spiral turbulence

Abstract

Abstract. -The behavior of spiral turbulence in mechanically deformed excitable media is investigated. Numerical simulations show that when the forcing frequency is chosen around the characteristic frequency of the system, complicated spiral turbulence may be quenched within a shorter evolution time, compared to the case free of mechanical deformation. It is shown that the observed phenomenon occurs due to enhancing the drift of spiral tips induced by mechanical deformation.A wide range of self-organized phenomena exists in spatially distributed systems. One of the most paradigmatic examples of spatiotemporal self-organized structures is a class of spiral waves, which have been observed in a variety of physical [1], chemical [2][3][4][5] and biological systems [6][7][8][9]. The attractiveness of investigating the dynamics of spiral waves is not only because they own a special structure, i.e., the core regarded as a phase-singular in mathematical language, but more important they contribute to the underlying class of cardiac disease also, such as tachycardia and fibrillation [6][7][8][9]. It is thus that, from a practical point of view, controlling the behaviors of spiral waves, particularly eliminating spiral waves and spiral turbulence, is extremely important and meaningful. Up to now, various methods to control two-, and even three-dimensional spiral waves and turbulence have been put forward [10][11][12][13][14][15][16][17][18][19].On the other hand, Munuzuri et al. [20] designed an appropriate elastic excitable medium by incorporating the BZ reaction into a polyacrylamide-silica gel and experimentally studied the influence of periodic mechanical contraction of excitable media on the behavior of rotating spiral waves. Recently, we derived, directly from origin reaction-diffusion equations, a formula of drifting velocity using weak-deformation approximation and explained the drift of spiral waves under resonant frequency [21]. Besides, spiral breakup due to mechanical deformation was studied in our recent work [22]. To our knowledge, however, the influences of mechanical

Cardiac contraction induces discordant alternans and localized block

“…This is often considered to be a passive consequence of electrical activity. However, simulations of simplified models of excitation-contraction coupling [14], as well as of reaction-diffusion equations in a medium with a varying (oscillatory) metric [15], suggest that mechanical deformation play an important role for, e.g., the stability of spiral waves. This is due to mechanoelectric feedback whereby mechanical deformations (e.g., stretch) can modulate electric activity [16].…”

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

“…We follow the method suggested in Zhang et al (2004, 2006) and Chen et al (2008) for the introduction of PD into a mathematical model for cardiac tissue. In particular, we note that any point x = ( x, y ) in the medium changes to x ′( t ) = ( x ′( t ), y ′( t )) with $\begin{array}{c}left{x}^{\prime }(t)=x\left[1+A_x(t)\right],\\ y^{\prime }(t)=y\left[1+A_y(t)\right],\end{array}$ if we impose a PD with A x ( t ) = A x cos (2π f x t ) and A y ( t ) = A y cos (2π f y t ).…”

“…Recently, some groups (Zhang et al, 2004, 2006; Panfilov et al, 2007; Chen et al, 2008; Weise et al, 2011) have begun to study the effects of the deformation of cardiac tissue on the RS-ST transition; such a transition arises either because of periodic deformation or the stretch-activated current associated with such deformation. These studies have used simple, two-variable mathematical models for electrical activation in such tissue.…”

“…Several studies have investigated the transition from RS to ST, both in experiments on cardiac tissue and in computational studies of mathematical models for cardiac tissue; they find that this transition can occur because of (a) a steep, increasing initial segment in the restitution curve, a plot of the action potential duration (APD) versus the diastolic interval (DI) (Koller et al, 1998 ; Garfinkel et al, 2000 ; Fenton et al, 2002 ), (b) a similar steep part in an analogous plot of the conduction velocity θ versus DI (Qu et al, 2000b ; Fenton et al, 2002 ), (c) alternans (Karma, 1994 ; Koller et al, 1998 ; Qu et al, 1999 ; Cherry and Fenton, 2008 ), and (d) heterogeneities, such as, conduction and ionic inhomogeneities (Xie et al, 1998 ; Shajahan et al, 2007 , 2009 ; Majumder et al, 2011a , b ). Recently, some groups (Zhang et al, 2004 , 2006 ; Panfilov et al, 2007 ; Chen et al, 2008 ; Weise et al, 2011 ) have begun to study the effects of the deformation of cardiac tissue on the RS-ST transition; such a transition arises either because of periodic deformation or the stretch-activated current associated with such deformation. These studies have used simple, two-variable mathematical models for electrical activation in such tissue.…”

“…These studies have used simple, two-variable mathematical models for electrical activation in such tissue. One of the goals of our study is to investigate spiral-wave dynamics in general, and RS-ST transitions in particular, in a simple mathematical model for periodic deformation (PD) of cardiac tissue (Zhang et al, 2004 , 2006 ; Chen et al, 2008 ) that we couple with ionically realistic human-ventricular-tissue mathematical models, namely, (a) the TP06 model, due to ten Tusscher and Panfilov (Ten Tusscher and Panfilov, 2006 ), or (b) the TNNP04 model, of ten Tusscher, Noble, Noble, and Panfilov (Ten Tusscher et al, 2004 ). A deformation of cardiac tissue leads to modifications of ion-channel parameters, because of stretch-activated currents, and also a modification of intracellular couplings.…”