Download Scroll waves meandering in a model of an excitable medium

Scroll waves
meandering in a
model of an excitable
medium
Presenter: Jianfeng Zhu
Advisor: Mark Alber
Introduction
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Scroll waves are three-dimensional(3D)
vortices which are extensions of spiral
waves (2D) that occurs in a variety of
excitable media.
A scroll wave is usually characterized by its
filament, which is an extension into three
dimensions of the notion of the core of the
spiral wave.
Excitable medium
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Excitable medium is the systems which
have the ability to propagate signals without
damping.
e.g. forest is an excitable medium when the
forest fire travels as a wave.
Passive medium : the wave propagation is
characterized by a gradual damping of signal
amplitude due to friction.
e.g. sound waves passing through the air.
Heart as an excitable medium
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Heartbeat is a wave that passes across the heart
muscle. A small triggering impulse can lead to a
large response (an electrical discharge across the
cell membranes, together with a contraction of the
heart muscle).
A piece of heart tissue can be triggered by the
excitation of a neighboring piece of tissue, which is
the basis for the wave action
Heart undergoes scroll waves when the heart is
malfunctioning, such as cardiac arrhythmia and
fibrillation in the ventricles of the heart.
Aliev-Panfilov Model

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 e
2


e  ke(e  a)(e  1)  er ,

 t
 r
1r

 [ 
][ r  ke(e  b  1)].

2  e
 t
e: membrane potential
r: conductance of the slow inward current
The parameters are related to the key characteristics of the
cardiac tissue, such as the shape of the action potential,
refractoriness and the restitution of action potential duration.
we choose 2  1.3, k  8,   0.01, b  0.1, 1  0.2
and a is varied between 0.12 and 0.18
Action potential

The cardiac action
potential is the
electrical activity of the
individual cells of the
electrical conduction
system of the heart.
The cardiac action potential has five
phases.
Numerical computation
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spiral waves and its core ( the white lines) in a 2D excitable
medium of 128128 elements. (hs=0.6 and ht=0.03)
(Panfilov, et al., 2005)
The light gray area represents the excited state of the tissue
(e>0.6).
Extend the computations to
3D(128*128*128) domain

Copy the 2D spiral wave pattern to all layers
of our numerical grid in z-direction.
Shift the whole 2D spiral wave for each (z)
slice of the system in the x-direction as

xnew  xold  0.5  sin ( / L0 ) z 
L0 -- thickness of the medium (12.7mm)
Filament under different time
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Filament dynamics at
a=0.18 at t =0s (a),
t =1s (b) and t = 3s (c)
(aperiodic meandering)
(Panfilov, et al. 2005)
The length of the filament
(Panfilov, et al. 2005)
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a=0.18 with (black solid line)
a=0.18 with periodic boundary conditions (upper
gray solid line)
a=0.15(lower gray solid line)
a=0.12(long dashed line) (quasi-2D meandering)
3D meandering pattern depends
on medium thickness
(Panfilov, et al. 2005)
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(a) Relative filament length vs time for a=0.18 and the
medium thickness of 12.7 mm (solid line), 3.1 mm ( gray line)
and 2.5 mm ( dashed line).
(b) Filament meandering for the medium of 3.1 mm thick
(periodic meandering).
Discussion
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We find three types of meandering of a scroll
wave filament:quasi-2D, periodic and
aperiodic meandering in a model of cardiac
tissue.
Different meanderings depend on parameter
settings and thickness of the medium.
References
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A.V.Panfilov, Scroll waves meandering in a
model of an excitable medium, Physical
Review E 72,022902(2005)
A.V.Panfilov, A simple Two-variable Model of
Cardiac Excitation, Chaos, Solitons and
Fractals Vol.7,No,3,pp.293-301,1996.
L.Glass, Scroll waves in spherical shell
geometries, Chaos, December 2001.