Controlling Spatiotemporal Chaos and Spiral Turbulence in Excitable Media

Abstract

Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating spiral waves. Instabilities in these structures may lead to spatiotemporal chaos through spiral turbulence, which has been linked to clinically diagnosed conditions such as cardiac fibrillation. Usual methods for controlling such phenomena involve very large amplitude perturbations and have several drawbacks. There have been several recent attempts to develop low-amplitude control procedures for spatiotemporal chaos in excitable media which are reviewed in this paper. The control schemes have been broadly classified by us into three types: (i) global, (ii) non-global spatially-extended and (iii) local, depending on the way the control signal is applied, and we discuss the merits and drawbacks for each.

Response to sub-threshold stimulus is enhanced by spatially heterogeneous activity

“…For example, rotating vortices in cardiac tissue that can lead to spiral chaos underlie many arrhythmias, i.e., life-threatening disturbances in the natural rhythm of the heart [14,15]. Thus, controlling irregular activity in excitable media is not only a problem of fundamental interest in the physics of nonlinear dynamical systems but also has potential clinical significance [16][17][18][19]. Existing methods of spatiotemporal chaos control in excitable systems are almost exclusively dependent on using suprathreshold signals, either through a local high-frequency source [20,21] or using a spatially extended array [22][23][24].…”

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

“…So far, various low-amplitude suppression algorithms have been developed to eliminate spiral waves in monodomain mathematical models of cardiac tissue; in these algorithms the control pulses are applied in several ways. These include the following: (a) periodic stimulation at a point (Zhang et al, 2003 ; Yuan et al, 2005 ); (b) a line stimulus that must be applied to one of the boundaries (Tang et al, 2008 ; Miguel et al, 2009 ); (c) an array of low-voltage control pulses, which must be swept over the simulation domain (Sinha and Sridhar, 2007 ; Sridhar and Sinha, 2008 ); or (d) the mesh-based, low-amplitude suppression scheme we describe (Sinha et al, 2001 ; Pandit et al, 2002 ). We have provided an overview of such low-amplitude suppression schemes, in the absence of PD, in earlier studies (Shajahan et al, 2009 ; Nayak, 2013 ); the most successful of these is based on a mesh-based suppression algorithm; this suppression scheme (Shajahan et al, 2009 ; Majumder et al, 2011a ; Nayak et al, 2013 ) can suppress spiral waves of electrical activation even in the presence of conduction, ionic, and fibroblast heterogeneities (Shajahan et al, 2009 ; Majumder et al, 2011a ; Nayak et al, 2013 ).…”

Nonlinear Dynamics in Cardiology

“…The idea being that if ventricular fibrillation is deterministic chaos, then it should be terminable using stimuli smaller, less painful and/or damaging, than large defibrillation shocks. Unfortunately, while chaos-control efficacy has been demonstrated in experimental work and computer simulations (141, 142), it has not been successful in terminating fibrillation in the clinic. New strategies for unpinning and suppressing spiral and scroll waves based on theoretical and simulation work are under development (e.g., (143, 144), and some show promise in experiments (145, 146).…”