Predicting the duration of chaotic transients in excitable media

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.

Download Full-text

Feedback control of wave propagation patterns in excitable media

10.33915/etd.1846 ◽

2003 ◽

Author(s):

Florin Chirila

Keyword(s):

Wave Propagation ◽

Feedback Control ◽

Excitable Media

Download Full-text

Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

Journal of The Royal Society Interface ◽

10.1098/rsif.2014.0352 ◽

2014 ◽

Vol 11 (97) ◽

pp. 20140352 ◽

Cited By ~ 99

Author(s):

Alfonso Bueno-Orovio ◽

David Kay ◽

Vicente Grau ◽

Blanca Rodriguez ◽

Kevin Burrage

Keyword(s):

Structural Heterogeneity ◽

Biological Tissues ◽

Tissue Level ◽

Fractional Diffusion ◽

Diffusion Models ◽

Excitable Media ◽

Research Fields ◽

Dispersion Of Repolarization ◽

Electrical Propagation

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Download Full-text