Scaling regime of spiral wave propagation in single-diffusive media

1992 ◽  
Vol 68 (3) ◽  
pp. 397-400 ◽  
Author(s):  
Alain Karma
Keyword(s):  
Wave Propagation ◽  
Spiral Wave

scholarly journals Spiral Wave Propagation in Communities with Spatially Correlated Heterogeneity

2020 ◽  
Vol 118 (7) ◽  
pp. 1721-1732 ◽  
Author(s):  
Xiaoling Zhai ◽  
Joseph W. Larkin ◽  
Gürol M. Süel ◽  
Andrew Mugler
Keyword(s):  
Wave Propagation ◽  
Spiral Wave ◽  
Spatially Correlated

Wave propagation and spiral wave formation in a Hindmarsh–Rose neuron model with fractional-order threshold memristor synaps

2020 ◽  
Vol 34 (17) ◽  
pp. 2050157 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Sajad Jafari ◽  
Fatemeh Parastesh ◽  
Christos Volos ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Fractional Order ◽  
Electromagnetic Induction ◽  
Neuron Model ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Bifurcation Diagrams ◽  
External Current ◽  
Proposed Model ◽  
External Stimuli

In this paper, a modified Hindmarsh–Rose neuron model is presented, which has a fractional-order threshold magnetic flux. The dynamics of the model is investigated by bifurcation diagrams and Lyapunov exponents in two cases of presence and absence of the external electromagnetic induction. Then the emergence of the spiral waves in the network of the proposed model is studied. To find the effects of different factors on the formation and destruction of spiral waves, the external current, the coupling strength and the external stimuli amplitude are varied. It is observed that all of these parameters have significant impacts on the spiral waves. Furthermore, the external electromagnetic induction influences the existence of spiral waves in specific external current values.

Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue

2014 ◽  
Vol 307 (7) ◽  
pp. H1024-H1035 ◽  
Author(s):  
Rupamanjari Majumder ◽  
Rahul Pandit ◽  
A. V. Panfilov
Keyword(s):  
Wave Propagation ◽  
Cardiac Tissue ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Delayed Rectifier ◽  
High Frequency Stimulation ◽  
Secondary Importance ◽  
Ionic Model ◽  
Delayed Rectifier Current ◽  
Human Cardiac Tissue

Wave propagation around various geometric expansions, structures, and obstacles in cardiac tissue may result in the formation of unidirectional block of wave propagation and the onset of reentrant arrhythmias in the heart. Therefore, we investigated the conditions under which reentrant spiral waves can be generated by high-frequency stimulation at sharp-edged obstacles in the ten Tusscher-Noble-Noble-Panfilov (TNNP) ionic model for human cardiac tissue. We show that, in a large range of parameters that account for the conductance of major inward and outward ionic currents of the model [fast inward Na+ current ( INa), L—type slow inward Ca2+ current ( ICaL), slow delayed-rectifier current ( IKs), rapid delayed-rectifier current ( IKr), inward rectifier K+ current ( IK1)], the critical period necessary for spiral formation is close to the period of a spiral wave rotating in the same tissue. We also show that there is a minimal size of the obstacle for which formation of spirals is possible; this size is ∼2.5 cm and decreases with a decrease in the excitability of cardiac tissue. We show that other factors, such as the obstacle thickness and direction of wave propagation in relation to the obstacle, are of secondary importance and affect the conditions for spiral wave initiation only slightly. We also perform studies for obstacle shapes derived from experimental measurements of infarction scars and show that the formation of spiral waves there is facilitated by tissue remodeling around it. Overall, we demonstrate that the formation of reentrant sources around inexcitable obstacles is a potential mechanism for the onset of cardiac arrhythmias in the presence of a fast heart rate.

SPATIOTEMPORAL STRUCTURES IN DISCRETELY-COUPLED ARRAYS OF NONLINEAR CIRCUITS: A REVIEW

1995 ◽  
Vol 05 (01) ◽  
pp. 17-50 ◽  
Author(s):  
A.P. MUÑUZURI ◽  
V. PÉREZ-MUÑUZURI ◽  
M. GÓMEZ-GESTEIRA ◽  
L.O. CHUA ◽  
V. PÉREZ-VILLAR
Keyword(s):  
Wave Propagation ◽  
Pattern Formation ◽  
Spatial Organization ◽  
Nonlinear Dynamical Systems ◽  
Spiral Wave ◽  
Continuous Media ◽  
Transport Processes ◽  
Coupled Systems ◽  
Spatiotemporal Pattern ◽  
Characteristic Time Scale

Spatiotemporal pattern formation occurring in discretely-coupled nonlinear dynamical systems has been studied numerically. Reaction-diffusion systems can be viewed as an assembly of a large number of identical local subsystems which are coupled to each other by diffusion. Here, the local subsystems are defined by a system of nonlinear ordinary differential equations. While for continuous systems, the characteristic time scale corresponding to the diffusion is slower than that corresponding to the local subsystems, in discretely-coupled systems, both time scales can be of the same order of magnitude. Discrete systems can exhibit behaviors different from those exhibited by their equivalent continuous model: the wave propagation failure phenomenon occurring in nerve-pulse propagation due to transmission blockage is a case in point. In this case, it is found that the wave fails to propagate at or below some critical value of the coupling coefficient. Systems of coupled cells can be found to occur in the transformation and transport processes in living cells, tissues, neuron networks, physiological systems and ecosystems, as well as in all forms of chemical, biochemical reactors and combustion systems. In this paper, we review the possibilities of using arrays of discretely-coupled nonlinear electronic circuits to study these systems. The possibility of building large arrays of these circuits via VLSI technology makes this approach a unique tool for real time applications. Classical examples occurring in other continuous media, such as spiral wave initiation and propagation, and Turing pattern formation, are depicted here. Because of the discrete nature of our system, the influence of inhomogeneities arising from damaged cells, or from an anisotropic media, is analyzed for spiral wave propagation. Spiral wave initiation and vulnerability effects are considered and compared with their corresponding effects in continuous media. More complex spatiotemporal structures are also studied via three-dimensional arrays of discretely-coupled circuits. Straight and twisted scroll waves, as well as scroll ring waves, are shown to exist in these arrays, where their properties can be easily measured. Sidewall forcing of Turing patterns is shown to be capable of driving the system into a perfect spatial organization, namely, a rhombic pattern, where no defects occur. The dynamics of the two layers supporting Turing and Hopf modes, respectively, is analyzed as a function of the coupling strength between them. The competition between these two modes is shown to increase with the diffusion between layers.

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