dc.contributor.author |
Sridhar, S. |
|
dc.date.accessioned |
2011-10-14T11:28:18Z |
|
dc.date.available |
2011-10-14T11:28:18Z |
|
dc.date.issued |
2011-10-14T11:28:18Z |
|
dc.date.submitted |
2010 |
|
dc.identifier.uri |
https://dspace.imsc.res.in/xmlui/handle/123456789/263 |
|
dc.description.abstract |
Excitable media is a generic term for a wide range of physical, chemical
and biological systems that exhibit spontaneous formation of spatial patterns.
Examples of such patterns include spiral waves in a two-dimensional medium
and their generalization in a three-dimensional system, scroll waves. Under
certain conditions, these waves may become unstable and break up, giving
rise to spatiotemporal chaos. Controlling these patterns using low-amplitude
external perturbations is of fundamental importance as these patterns are
known to have critical functional consequences for vital biological systems,
such as the heart. Specifically, spatial patterns of electrical excitation have
been implicated in many life-threatening disturbances to the natural rhythm
of the heart. Hence understanding the dynamics of these patterns is critical
for developing safe and efficient clinical treatment for these disturbances. In
this thesis we explore different aspects of the dynamics of spiral and scroll
waves using both simple and realistic models of excitable media. Specifically,
we study the dynamical evolution of these patterns upon their interaction
with different kinds of heterogeneities in the medium. We also propose several
low-amplitude control schemes to eliminate such patterns from an excitable
medium. This thesis begins with a brief overview of various features of excitable
systems in Chapter 1. In the first few sections, important concepts, terms
and models that are used throughout the thesis are defined. This is followed
by a brief discussion of the role of heterogeneities on spiral and scroll wave
dynamics. Following this is a section with a detailed review of various lowamplitude
chaos control schemes for spatially extended chaos in excitable media. In Chapter 2, we study the drift dynamics of spiral waves in the
presence of different gradients using simple models of excitable media. The
model parameters for which the spiral drifts to regions of lower and higher
excitability are determined. Drift of a spiral wave to a region where it rotates
faster is of special relevance as it suggests a possible mechanism for the onset
of “mother-rotor” fibrillation. We discuss the possible mechanism underlying
such anomalous drift. In Chapter 3, we discuss the conditions under
which a pinned spiral can be unpinned using a high frequency wave-train
in a simple model of excitable media. We then derive a relation between
pacing period and the size of the obstacle. We also show that unpinning
the spiral from an inexcitable obstacle becomes easier with the decrease of
medium excitability. In Chapter 4 we study the breakup of an otherwise
stable scroll wave in the presence of an inexcitable obstacle which does not
extend throughout the medium. The scroll wave breaks up at the edge of the
obstacle, where a transition from a quasi-two-dimensional propagation front
to a fully three-dimensional spherical wave front occurs. In Chapter 5 we
propose a non-global spatially extended low-amplitude chaos control scheme,
using an array of control points. A travelling wave of control is simulated as
the spatially separated array points are excited in a sequence. We find that,
depending on wave velocity and spacing of the control points, the chaotic
activity can be eliminated completely. Moreover our scheme is robust in the
presence of heterogeneities. In Chapter 6 we apply sub-threshold stimuli,
whose effect on a solitary wave propagating in an extended medium is negligible,
on a system with spatiotemporally heterogeneous activity. Surprisingly,
the signal which is not sufficient to excite a resting medium, fundamentally alters the recovery dynamics and terminates all activity in the medium. We
determine model-independent generic conditions under which this effect can
be observed. Finally we conclude in Chapter 7 with a summary of our
results on the role of heterogeneities in the dynamics of excitable media, and
how control of spatiotemporal patterns in these systems need to take into
account the presence of such features. |
en_US |
dc.relation.isbasedon |
List of Publications: S. Sinha and S. Sridhar, Controlling spatiotemporal chaos and
spiral turbulence in excitable media in Handbook of Chaos Control (Eds. E. Sch¨oll and H-G. Schuster) Weinheim: Wiley-VCH Verlag, pp 703-718 (2007) [also at arxiv:0710.2265].
• S. Sridhar and S. Sinha, Controlling spatiotemporal chaos in excitable media using an array of control points, Europhysics Letters 81, 50002 (2008) [also at arxiv:0711.1489].
• S. Sinha and S. Sridhar, Controlling spiral turbulence in simulated cardiac tissue by low-amplitude traveling wave stimulation in Complex Dynamics in Physiological Systems: From Heart to Brain (Eds. S. K. Dana, P. K. Roy and J. Kurths) Springer, pp 69-87 (2009).
• A. Pumir, S. Sinha, S. Sridhar, M. Argentina, M. Horning, S. Filippi,
C. Cherubini, S. Luther and V. Krinsky,Wave-train-induced termination of weakly anchored vortices in excitable media, Physical Review E 81, 010901(R) (2010) [also at arXiv:0902.3891].
• S. Sridhar, S. Sinha and A. V. Panfilov, Anomalous drift of spiral waves in heterogeneous excitable media, Physical Review E 82, 051908 (2010) [also at arxiv:0909.4398].
• S. Sridhar and S. Sinha, Response to sub-threshold stimulus is enhanced
by spatially heterogeneous activity, communicated [also at arxiv:1005.5032]. |
en_US |
dc.subject |
UNM Th 87 |
en_US |
dc.subject |
Excitable Media |
en_US |
dc.title |
Nonlinear Dynamics of wave propagation in Heterogeneous Excitable Media[UNM Th 88] |
en_US |
dc.type.degree |
Ph.D |
en_US |
dc.type.institution |
University of Madras |
en_US |
dc.description.advisor |
Sitabhra Sinha |
|
dc.type.mainsub |
Physics |
en_US |