Spiral waves meandering in a model of an excitable medium Presenter: Mike Malatt Phil McNicholas Jianfeng Zhu

Introduction  Spiral waves are two-dimensional(2D) vortices that occurs in a variety of excitable media.  Scroll waves are three-dimensional (3D) vortices, which are extensions of spiral waves.  We will focus on the spiral wave, which is usually characterized by its core.

Excitable medium  Excitable medium is the system which has the ability to propagate signals without damping. e.g. forest is an excitable medium when the forest fire travels as a wave; also soccer fans in a stadium performing the “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  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  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 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.

Analysis

are the blue lines and are the red lines

Vector field

Numerical method  Explicit Euler finite difference method with on flux boundary condition.  for the value e at the grid point

Numerical results  spiral waves and its core ( the white lines) in a 2D excitable medium of elements. (hs=0.6 and ht=0.03)  The light gray area represents the excited state of the tissue (e>0.6). (Panfilov, et al., 2005)

References  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 ,1996.