COLLECTIVE BEHAVIORS OF SPIRAL WAVES IN THE NETWORKS OF HODGKIN-HUXLEY NEURONS IN PRESENCE OF CHANNEL NOISE

2010 ◽  
Vol 18 (01) ◽  
pp. 243-259 ◽  
Author(s):  
JUN MA ◽  
AI-HUA ZHANG ◽  
JUN TANG ◽  
WU-YIN JIN
Keyword(s):  
Internal Noise ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Channel Noise ◽  
Collective Behaviors ◽  
Numerical Studies ◽  
Factor Of Synchronization ◽  
Quantitative Factor ◽  
Fixed Membrane ◽  
Membrane Patch

Collective behaviors of spiral waves in the networks of Hodgkin-Huxley neuron are investigated. A stable rotating spiral wave can be developed to occupy the quiescent areas in networks of neurons by selecting appropriate initial values for the variables in the networks of neurons. In our numerical studies, most neurons are quiescent and finite (few) numbers of neurons are selected with different values to form a spiral seed. In this way, neurons communicating are carried by propagating spiral wave to break through the quiescent domains (areas) in networks of neurons. The effect of membrane temperature on the formation of spiral wave is investigated by selecting different fixed membrane temperatures in the networks, and it is found that a spiral wave cannot be developed if the membrane temperature is close to a certain threshold. A quantitative factor of synchronization is defined to measure the statistical properties and collective behaviors of the spiral wave. And a distinct phase transition, which indicates the critical condition for spiral survival, is observed in the sudden changing point of the factors of synchronization curve vs. certain bifurcation parameter. Internal noise is introduced into ion channels (channel noise) with the Langevin method. It is found that a stable rotating spiral wave is developed and the spiral wave is robust to weak channel noise (the membrane patch is not small). The spiral wave can not grow up and the stable rotating spiral wave encounters instability in presence of strong channel noise. Coherence resonance-like behavior is observed in calculating the factors of synchronization in presence of channel noise.

DYNAMICS OF SPIRAL WAVE IN THE COUPLED HODGKIN–HUXLEY NEURONS

2010 ◽  
Vol 24 (23) ◽  
pp. 4555-4562 ◽  
Author(s):  
GUANG YU ◽  
JUN MA ◽  
YA JIA ◽  
JUN TANG
Keyword(s):  
Spiral Wave ◽  
Channel Noise ◽  
Initial Values ◽  
Membrane Patch

In this paper, the dynamics of the coupled Hodgkin–Huxley neurons (HHn) is investigated. At first, appropriate initial values and reasonable parameters are used to induce spiral wave in the coupled HHn. The temperature and channel noise are also considered to induce the birth and transition of spiral wave, respectively. It is found that the spiral wave can be generated in the absence of channel noise, and the seed of spiral wave cannot grow up when the intensity of channel noise exceeds the threshold (the noise is distributed on all the channels and s describes the membrane patch, the threshold is suggested with s = 3.2). The spiral wave disappears and all the coupled HHn become homogeneous when the temperature exceeds the threshold about T = 22° C .

TRANSITION OF ORDERED WAVES IN NEURONAL NETWORK INDUCED BY DIFFUSIVE POISONING OF ION CHANNELS

2013 ◽  
Vol 21 (01) ◽  
pp. 1350002 ◽  
Author(s):  
LONG HUANG ◽  
JUN MA ◽  
JUN TANG ◽  
FAN LI
Keyword(s):  
Ion Channels ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Channel Noise ◽  
Channel Blocking ◽  
Adjacent Site ◽  
Line Defects ◽  
Ion Channel Blocking ◽  
Wave Induced ◽  
Target Wave

Normal physiological activities are often affected by some drugs, and some ion channels are blocked due to the katogene of drugs. This paper investigates the propagation of ordered waves in neuronal networks induced by diffusive poisoning, where the process is measured by increasing the number of neurons in the poisoned area of the networks. A coefficient of poisoning K is defined to measure the time units from one poisoned site to the adjacent site, a smaller K means that more neurons are poisoned in a certain period (a higher poisoning speed). A statistical factor of synchronization R in the two-dimensional array is defined to detect the transition of spiral waves induced by ion channel blocking. It is confirmed that the evolution of the spiral waves depends on the coefficient of poisoning K and number of poisoned neurons. Furthermore, breakup of the spirals is observed when weak channel noise is considered. Finally, the formation of the spiral wave induced by blocking the target wave with line defects is briefly discussed.

Pattern selection in neuronal network driven by electric autapses with diversity in time delays

2014 ◽  
Vol 29 (01) ◽  
pp. 1450239 ◽  
Author(s):  
Jun Ma ◽  
Huxin Qin ◽  
Xinlin Song ◽  
Runtong Chu
Keyword(s):  
Time Delay ◽  
Traveling Wave ◽  
Time Delays ◽  
Electric Activity ◽  
Local Area ◽  
Spiral Waves ◽  
Collective Behaviors ◽  
Numerical Studies ◽  
Local Areas ◽  
Delay Diversity

The electric activity of neuron and collective behaviors of neurons can be modulated by autapse, which can be described by self-feedback current in close loop with time delay being considered. Distribution of electric autapses in a local area can introduce heterogeneity in the network and thus traveling wave emits from this area. In this paper, diversity in time delay of electric autapse is considered and collision between emitting waves from different local areas driven by electric autapses under different time delays is observed. In the numerical studies, neurons in the square area with 15×15 (and/or 20×20) nodes are connected electric autapses with different time delays and target-like waves are induced and converted into, spiral waves after continuous collision between wave fronts. It is found that a group of spiral waves can emerge in the network, or coexist with target waves under appropriate coupling intensity due to time delay diversity in autapse and these waves can regulate the collective behaviors of neurons as continuous pacemakers.

DEFECT-LINE DYNAMICS IN OSCILLATORY SPIRAL WAVES

2006 ◽  
Vol 06 (04) ◽  
pp. L379-L386
Author(s):  
STEVEN WU
Keyword(s):  
Critical Point ◽  
Period Doubling ◽  
Spiral Wave ◽  
Chaotic Regime ◽  
Spiral Waves ◽  
Bifurcation Parameter ◽  
Local Dynamics ◽  
Total Length ◽  
Defect Line ◽  
Large Fluctuations

We study defect-line dynamics in a 2-D spiral-wave pair in the Rössler model for its underlying local dynamics in period-N and chaotic regimes with a single bifurcation parameter κ. We find that a spiral wave pair is always stable across the period-doubling cascade and in the chaotic regime. When N ≥ 2 defect lines appear spontaneously and a loop exchange occurs across the defect line. There exists a "critical point" κ c below and above which the time-averaged total length of defect lines L converges to almost constant but different values L1 and L2. When κ > κ c defect lines show large fluctuations due to creation and annihilation processes.

scholarly journals Spiral wave unpinning facilitated by wave emitting sites in cardiac monolayers

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190420
Author(s):  
Shreyas Punacha ◽  
Sebastian Berg ◽  
Anupama Sebastian ◽  
Valentin I. Krinski ◽  
Stefan Luther ◽  
...  
Keyword(s):  
Electric Field ◽  
Electrical Activity ◽  
Spiral Wave ◽  
Electrical Stimulus ◽  
Spiral Waves ◽  
Time Interval ◽  
Field Pulse ◽  
The Core ◽  
Rotating Wave ◽  
Multiple Obstacles

Rotating spiral waves of electrical activity in the heart can anchor to unexcitable tissue (an obstacle) and become stable pinned waves. A pinned rotating wave can be unpinned either by a local electrical stimulus applied close to the spiral core, or by an electric field pulse that excites the core of a pinned wave independently of its localization. The wave will be unpinned only when the pulse is delivered inside a narrow time interval called the unpinning window (UW) of the spiral. In experiments with cardiac monolayers, we found that other obstacles situated near the pinning centre of the spiral can facilitate unpinning. In numerical simulations, we found increasing or decreasing of the UW depending on the location, orientation and distance between the pinning centre and an obstacle. Our study indicates that multiple obstacles could contribute to unpinning in experiments with intact hearts.

scholarly journals Cardiac Spiral Wave Drifting Due to Spatial Temperature Gradients – a Numerical Study

2018 ◽  
Author(s):  
Guy Malki ◽  
Sharon Zlochiver
Keyword(s):  
Numerical Simulations ◽  
Single Cell ◽  
Numerical Study ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Temperature Gradients ◽  
Effect Of Temperature ◽  
Local Perturbation ◽  
Marginal Effect ◽  
Spatial Temperature

ABSTRACTCardiac rotors are believed to be a major driver source of persistent atrial fibrillation (AF), and their spatiotemporal characterization is essential for successful ablation procedures. However, electrograms guided ablation have not been proven to have benefit over empirical ablation thus far, and there is a strong need of improving the localization of cardiac arrhythmogenic targets for ablation. A new approach for characterize rotors is proposed that is based on induced spatial temperature gradients (STGs), and investigated by theoretical study using numerical simulations. We hypothesize that such gradients will cause rotor drifting due to induced spatial heterogeneity in excitability, so that rotors could be driven towards the ablating probe. Numerical simulations were conducted in single cell and 2D atrial models using AF remodeled kinetics. STGs were applied either linearly on the entire tissue or as a small local perturbation, and the major ion channel rate constants were adjusted following Arrhenius equation. In the AF-remodeled single cell, recovery time increased exponentially with decreasing temperatures, despite the marginal effect of temperature on the action potential duration. In 2D models, spiral waves drifted with drifting velocity components affected by both temperature gradient direction and the spiral wave rotation direction. Overall, spiral waves drifted towards the colder tissue region associated with global minimum of excitability. A local perturbation with a temperature of T=28°C was found optimal for spiral wave attraction for the studied conditions. This work provides a preliminary proof-of-concept for a potential prospective technique for rotor attraction. We envision that the insights from this study will be utilize in the future in the design of a new methodology for AF characterization and termination during ablation procedures.

"SPIRAL WAVE–TRAVELING CLUSTERING" INTERMITTENCY AND 1/f-NOISE IN A 2D COUPLED MAP LATTICE

1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Exponential Decay ◽  
Power Law ◽  
Strange Attractor ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
The Self ◽  
Saddle Node Bifurcation ◽  
Self Organized

Intermittency of checkerboard spiral waves and traveling clusterings originating from sudden shrinking of the strange attractor of the 2D CML in the neighborhood of the saddle-node bifurcation boundary is found. A power-law probability density for lifetimes in the spiral wave (laminar) phase is observed, while in the checkerboard clusterings (bursting) phase the above quantity exhibits an exponential decay. This difference can be interpreted through the self-organized behavior of the spiral waves, and the passive relaxation of the disordered checkerboard clusterings.

scholarly journals Predictability of spatio-temporal patterns in a lattice of coupled FitzHugh–Nagumo oscillators

2013 ◽  
Vol 10 (81) ◽  
pp. 20121016 ◽  
Author(s):  
Miriam Grace ◽  
Marc-Thorsten Hütt
Keyword(s):  
Dynamical System ◽  
Spiral Wave ◽  
Temporal Patterns ◽  
Spiral Waves ◽  
Generic Model ◽  
Homogeneous State ◽  
Drift Speed ◽  
Statistical Fluctuations ◽  
Self Organized ◽  
Spatio Temporal

In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a ‘developmental path’), together with differences in cell properties (‘desynchronization’ of cells on the developmental path) can establish self-organized spatio-temporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHugh–Nagumo oscillators, into a developmental-path framework. In this minimal model of spiral wave generation, we can now study the predictability of spatio-temporal patterns from cell properties as a function of desynchronization (or ‘spread’) of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatio-temporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.

scholarly journals LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH–NAGUMO SYSTEM

2006 ◽  
Vol 16 (05) ◽  
pp. 1547-1555 ◽  
Author(s):  
I. V. BIKTASHEVA ◽  
A. V. HOLDEN ◽  
V. N. BIKTASHEV
Keyword(s):  
External Force ◽  
Wave Solution ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Response Functions ◽  
Space And Time ◽  
Wave Drift ◽  
Linearized Problem ◽  
Small Periodic

Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh–Nagumo model, and show that they are effectively localized in the vicinity of the spiral core.

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