Formation of multi-armed spiral waves in neuronal network induced by adjusting ion channel conductance

2015 ◽  
Vol 29 (07) ◽  
pp. 1550043 ◽  
Author(s):  
Chunni Wang ◽  
Jun Ma ◽  
Bolin Hu ◽  
Wuyin Jin

The Hodgkin–Huxley neuron model is used to describe the local dynamics of nodes in a two-dimensional regular network with nearest-neighbor connections. Multi-armed spiral waves emerge when a group of spiral waves rotate the same core synchronously. Here we have numerically investigated how multi-armed spiral waves are formed in such a system. Under the appropriate conditions, multi-armed spiral waves were able to develop as a result of adjusting the conductance of ion channels of particular neurons in the network. In a realistic neuron model, it can be practiced by blocking potassium of ion channels embedded in the membrane of neurons. For example, decreasing the potassium channel conductance in some neurons with a certain transient period can lead to the development of a group of double spirals in a localized area of the network. Furthermore, decreasing the excitability and the external forcing current to zero led to the growth of these double spirals and the formation of a stable multi-armed spiral wave that occupied the network under inhomogeneity.

1999 ◽  
Vol 09 (08) ◽  
pp. 1501-1516 ◽  
Author(s):  
E. V. NIKOLAEV ◽  
V. N. BIKTASHEV ◽  
A. V. HOLDEN

We describe the simplest bifurcations of spiral waves in reaction–diffusion systems in the plane and present the list of model systems. One-parameter bifurcations of one-armed spiral waves are fold and Hopf bifurcations. Multiarmed spiral waves may additionally undergo a period-doubling pitchfork bifurcation, when two congruent spiral wave solutions, having the "double" period, branch from the original spiral wave at the bifurcation point.


2013 ◽  
Vol 21 (01) ◽  
pp. 1350002 ◽  
Author(s):  
LONG HUANG ◽  
JUN MA ◽  
JUN TANG ◽  
FAN LI

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.


2012 ◽  
Vol 22 (06) ◽  
pp. 1250148
Author(s):  
GUOYONG YUAN ◽  
ZHICHENG FENG ◽  
AIGUO XU ◽  
GUANGRUI WANG ◽  
SHAOYING CHEN

The dynamics in excitable media driven by a specific spatiotemporal wave are studied by investigating wave states, the motion of tips and synchronized behaviors. We demonstrate that multiple-armed spiral waves can be generated in excitable media with rest initial conditions by directly injecting a rigidly rotating spiral wave, also that the meandering driver can induce the spiral wave, with the wider excited parts and the same frequency as the driving wave, in the driven system. It is more interesting to find that the higher similarity between the driving and driven waves occurs when the driving strength is smaller. We also study the dynamics of spiral waves in the driven system when the external driving wave is introduced by the form of difference, and find that the stronger synchronized behaviors appear when the driving strength is larger. The dynamical behaviors can be understood by considering various characteristics of the excitable system, for example the existence of "refractory period" and "vulnerable period" and so on.


2020 ◽  
Vol 34 (17) ◽  
pp. 2050157 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Sajad Jafari ◽  
Fatemeh Parastesh ◽  
Christos Volos ◽  
...  

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.


2021 ◽  
Vol 42 (Supplement_1) ◽  
Author(s):  
T De Coster ◽  
B Ordog ◽  
A A F De Vries ◽  
A V Panfilov ◽  
D A Pijnappels

Abstract Background Recently it was demonstrated how the heart itself could be enabled to quickly restore its rhythm by realizing a biologically-integrated cardiac defibrillator (BioICD) through modification and subsequent expression of ion channels in cardiomyocytes [1]. By incorporating these frequency-dependent depolarizing ion channels, abnormal cardiac rhythm could be rapidly detected and terminated to restore sinus rhythm in a fully biological and shock-free manner. However, from a translational point of view, it remains unclear how such rhythm restoration can be realized via ion channel gene therapy. Purpose To explore and understand the importance of the distribution and number of BioICD-expressing cardiomyocytes in realizing fully biological restoration of cardiac rhythm. Methods To this purpose, two different realistic gene therapy configurations, i.e. those corresponding to systemic and local transgene delivery, were tested in human ventricular virtual cardiac monolayers. For the systemic delivery group, BioICD-expressing cells were homogeneously distributed (10 random variations) over the tissue with fixed total expression percentage (14 percentages). For the local delivery group, circular areas (7 radii) were given BioICD-expressing cells randomly patterned (10 variations) in a Gaussian distribution with 3 fixed total expression percentages. For both groups, spiral waves were initiated (9 locations) and studied for the following 10 seconds for each test condition, thereby equaling 1260 and 1890 conditions, respectively. Results For systemic delivery, normal rhythm was restored in all cases for >50% BioICD expressing cells, with time till termination being inversely related to the percentage, resulting in only 4.3s and 2.5s for 50% and 100%, respectively. Regarding termination, it was observed that conduction blocks appeared throughout the tissue and subsequently connected to force arrhythmic waves to terminate, while this process remained incomplete in the <50% groups. Local delivery, on the other hand, resulted in islands of ionic heterogeneity, causing attraction and anchoring of the spiral waves in a size and distance-dependent manner. Hence, BioICD-based self-termination was not observed in any of the investigated conditions, leaving spiral waves to persist. Conclusion This study reveals that wide-spread distribution of BioICD-expressing cardiomyocytes is required for the realization of fully biological self-restoration of cardiac rhythm, of which the efficiency is dosage-dependent. Local expression, however, results in stabilization of spiral wave activity. Further exploration of this emerging concept of biological cardioversion may not only expand our understanding of cardiac arrhythmias, but also pave the way to breakthrough advances in arrhythmia management. FUNDunding Acknowledgement Type of funding sources: Public grant(s) – EU funding. Main funding source(s): European Research Council (Starting grant 716509) to D.A. Pijnappels.


2014 ◽  
Vol 57 (10) ◽  
pp. 1918-1926 ◽  
Author(s):  
HuiXin Qin ◽  
Jun Ma ◽  
ChunNi Wang ◽  
RunTong Chu

2006 ◽  
Vol 06 (04) ◽  
pp. L379-L386
Author(s):  
STEVEN WU

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.


Author(s):  
Shreyas Punacha ◽  
Sebastian Berg ◽  
Anupama Sebastian ◽  
Valentin I. Krinski ◽  
Stefan Luther ◽  
...  

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.


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