Dynamics of scroll waves in inhomogeneous excitable media

1994 ◽  
Vol 347 (1685) ◽  
pp. 687-701 ◽  
Keyword(s):  
Nonlinear Waves ◽  
Cardiac Arrhythmias ◽  
Three Dimensions ◽  
Excitable Media ◽  
Linear Parameter ◽  
Wave Dynamics ◽  
Localized Defects ◽  
Scroll Wave ◽  
Scroll Waves

Nonlinear waves in excitable media often organize themselves into vortex-like patterns of activity, called ‘scroll waves’ in three dimensions. In this paper we review recent results concerning the effects of inhomogeneities on scroll wave dynamics. We concentrate on the dynamics of scroll waves with initially rectilinear filaments evolving in the presence of linear parameter gradients with different orientations relative to the filament. We describe how this evolution is affected by the presence of localized defects. The effects described here are important in the study of cardiac arrhythmias, and may lead to an understanding of the mechanism of termination and stabilization of these arrhythmias.

Twisted scroll wave dynamics: partially pinned waves in excitable chemical media

2019 ◽  
Vol 21 (5) ◽  
pp. 2419-2425 ◽  
Author(s):  
Porramain Porjai ◽  
Malee Sutthiopad ◽  
Kritsana Khaothong ◽  
Metinee Phantu ◽  
Nakorn Kumchaiseemak ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Excitable Media ◽  
Wave Dynamics ◽  
Scroll Wave ◽  
Scroll Waves

We present an investigation of the dynamics of scroll waves that are partially pinned to inert cylindrical obstacles of varying lengths and diameters in three-dimensional Belousov–Zhabotinsky excitable media.

TWISTED SCROLL WAVES IN HETEROGENEOUS EXCITABLE MEDIA

1993 ◽  
Vol 03 (02) ◽  
pp. 445-450 ◽  
Author(s):  
ALEXANDER V. PANFILOV ◽  
JAMES P. KEENER
Keyword(s):  
Stationary Process ◽  
Three Dimensional ◽  
Excitable Medium ◽  
Excitable Media ◽  
Type Model ◽  
Refractory Periods ◽  
Scroll Wave ◽  
Scroll Waves

We study numerically the behavior of a scroll wave in a three-dimensional excitable medium with stepwise heterogeneity, using a FitzHugh Nagumo type model. We find that if the refractory periods in the two homogeneous subregions are sufficiently different, the scroll breaks into two scrolls rotating independently in each part of the medium. Eventually, the faster scroll eliminates the slower one leading to a stationary process, in which the scroll wave surviving in the region of faster recovery acts as a source for planar waves in the region of slower recovery.

scholarly journals Drift of Scroll Wave Filaments in an Anisotropic Model of the Left Ventricle of the Human Heart

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Sergei Pravdin ◽  
Hans Dierckx ◽  
Vladimir S. Markhasin ◽  
Alexander V. Panfilov
Keyword(s):  
Left Ventricle ◽  
Cardiac Arrhythmias ◽  
Human Heart ◽  
Cardiac Tissue ◽  
Three Dimensional ◽  
Excitable Media ◽  
Filament Dynamics ◽  
Myocardial Wall ◽  
Scroll Wave ◽  
Generic Description

Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias.

EQUILIBRATION OF SCROLL WAVE FILAMENTS IN THE VENTRICULAR WALL AND THE MINIMAL PRINCIPLE

2003 ◽  
Vol 13 (12) ◽  
pp. 3723-3731 ◽  
Author(s):  
OMER BERENFELD ◽  
MARCEL WELLNER ◽  
ARKADY M. PERTSOV
Keyword(s):  
Cardiac Arrhythmias ◽  
Equilibrium Shape ◽  
Ventricular Wall ◽  
Electrical Excitation ◽  
Cardiac Wall ◽  
Self Organized ◽  
Lack Of Information ◽  
Scroll Wave ◽  
Minimal Resistance ◽  
Scroll Waves

Scroll waves of electrical excitation are self-organized reentrant waveforms circling a filament and are a suspected cause of lethal cardiac arrhythmias. The lack of information about the filaments inside the cardiac wall raises the question of what is the dynamics of scroll waves and what equilibrium shape, if any, can we expect for their filaments. Here, we analyze the filament configuration and describe their equilibration in a curved slab of twisted fibers, a reasonably close model of the ventricular wall. We then generalize our findings by the use of the recently developed minimal principle to show that the filaments are predictable; namely, they are aligned with minimal resistance paths (geodesics) determined by the fiber configuration.

Entrainment and Annihilation of Reentrant Excitation in a Periodically Stimulated Ring of Excitable Media

1997 ◽  
Vol 36 (04/05) ◽  
pp. 290-293
Author(s):  
L. Glass ◽  
T. Nomura
Keyword(s):  
Cardiac Arrhythmias ◽  
Initial Phase ◽  
Human Heart ◽  
Periodic Wave ◽  
Excitable Media ◽  
One Dimensional ◽  
Clinical Observations ◽  
Periodic Stimulation ◽  
Reentrant Excitation ◽  
Stimulation Of

Abstract:Excitable media, such as nerve, heart and the Belousov-Zhabo- tinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. As in the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimuli of the periodically circulating wave can be described by a one-dimensional Poincaré map. Depending on the period and intensity of the stimulus as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart.

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