Spiral turbulence and spatiotemporal chaos: characterization and control in two excitable media

Pandit, Rahul; Pande, Ashwin; Sinha, Sitabhra; Sen, Aparajita

doi:10.1016/s0378-4371(02)00499-5

Cited by 20 publications

(26 citation statements)

References 15 publications

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“…The last subsection 3 examines the efficacy of the low-amplitude, mesh-based control scheme of Refs. [16], [18], [19] in the elimination of spiral waves in the homogeneous MF bilayer and the sheet of myocytes with an MF-bilayer inhomogeneity.…”

Section: Resultsmentioning

confidence: 99%

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

et al. 2013

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Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

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Section: Resultsmentioning

confidence: 99%

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

et al. 2013

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“…We then study the effects of PD on the suppression scheme of Pandit et al (2002) and Shajahan et al (2009). …”

Section: Resultsmentioning

confidence: 99%

“…We also investigate, in 2D simulations with PD, the efficacies of square-, rectangular-, and line-mesh-based, low-amplitude suppression techniques to eliminate spiral-wave turbulence in these models for cardiac tissue (Sinha et al, 2001; Pandit et al, 2002; Shajahan et al, 2009; Majumder et al, 2011a). …”

Section: Discussionmentioning

confidence: 99%

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

Nayak

Pandit

2014

Front. Physiol.

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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.

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“…In the physical system the deviation can often be measured at one (or both) of the boundaries, say z = 0 and z = l z (e.g., oxygen concentration on the surface of platinum catalyst in CO oxidation [63]), in a plane z = z 0 between the boundaries (e.g., velocity for a turbulent shear flow [51] or temperature for RBC [77]), or an integrated deviation for 0 < z < l z can be used (e.g.,…”

Section: Model-based Controlmentioning

confidence: 99%

Localized Control of Spatiotemporal Chaos

Grigoriev

Handel²

2007

Handbook of Chaos Control

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Spiral turbulence and spatiotemporal chaos: characterization and control in two excitable media

Cited by 20 publications

References 15 publications

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

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

Localized Control of Spatiotemporal Chaos

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