Spiral Wave Breakup Research Articles

Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.

Mechanism for Amplitude Alternans in Electrocardiograms and the Initiation of Spatiotemporal Chaos.

It is widely believed that one major life-threatening transition to chaotic fibrillation occurs via spiral-wave breakup that is preceded by spatiotemporal dispersion of refractoriness due to alternations in the duration of the cardiac action potential (AP). However, recent clinical and experimental evidence suggests that other characteristics of the AP may contribute to, and perhaps drive, this dangerous dynamical instability. To identify the relative roles of AP characteristics, we performed experiments in rabbit hearts under conditions to minimize AP duration dynamics which unmasked pronounced AP amplitude alternans just before the onset of fibrillation. We used a simplified ionic cell model to derive a return map and a stability condition that elucidates a novel underlying mechanism for AP alternans and spiral breakup. We found that inactivation of the sodium current is key to developing amplitude alternans and is directly connected to conduction block and initiation of arrhythmias. Simulations in 2D where AP amplitude alternation led to turbulence confirm our hypothesis.

Afterdepolarlizations induced by wave pattern in human ventricular tissue

Recently, arrhythmogenic condition has attracted special attention of scientists in the field of different disciplines because sudden cardiac death is often caused by cardiac arrhythmia. Arrhythmias can have different underlying causes. But the underlying mechanism of arrhythmia is not fully understood due to cardiac complexity. As is well known, one particular group of arrhythmias is often associated with the afterdepolarizations. So far, afterdepolarizations have been studied mainly in isolated cardiac cells. The question how the afterdepolarization is produced at a tissue level has not been widely studied yet. In this paper, we use the model of human heart to study how spiral wave or other wave patterns induces the afterdepolarizations in two-dimensional myocardial tissue. We try to obtain the instantaneous spatial distribution of afterdepolarizations by changing the L-type calcium and fast potassium conductance. In order to avoid bringing in afterdepolarizations, the applied parameters avoid evoking the afterdepolarizations at a single-cell and one-dimensional tissues level. The numerical simulation results show that spiral wave and other wave patterns can cause the phase II and III early afterdepolarizations, the delayed afterdepolarization, the enhanced automaticity, the delayed excitation and the delayed enhanced automaticity to occur. Moreover, we observe the weak oscillation of the membrane potential during the phase I of action potential. The afterdepolarizations generally occur in the spiral-wave core. They are generated by the phase singularity of spiral wave. The afterpolarizations can also appear in other region of spiral wave pattern. The afterpolarization is characterized by scattered distribution. When parameters are appropriately chosen, we observe the outbreaks of different afterpolarizations under the state of spiral wave. The corresponding spatial and temporal distributions of the early afterdepolarizations, the delayed afterdepolarizations, and the enhanced automaticity become spiral line distributions, which exhibits memory effect. It is shown that the outbreaks of afterdepolarizations in the system do not necessarily lead to the breakup of spiral wave. By observing the changes of different ion currents we find that when sodium current exciting cell is very small, the weak excitation with small sodium current can cause the L-type calcium current and the sodium calcium exchange current to increase, and the slow potassium current and rapid potassium current to decrease, leading to the occurrences of various afterdepolarizations. Therefore, increasing sodium current can effectively suppress the occurrences of afterdepolarizations.

Suppression of Spiral Breakup in Excitable Media by Local Periodic Forcing

Lowered excitability leads to unstable meandering of spiral tip, which result in breakup of spiral waves into chaotic states induced by Doppler effects. This phenomenon is responsible for the transition from tachycardia to ventricular fibrillation in cardiac tissues. Numerical simulations show that low-energy local periodic forcing (LPF) applied around spiral tip can efficiently suppress the meandering behavior and consequently prevent spiral breakup. The controllable phase diagrams that describe the amplitude and period of LPF against excitability parameter are presented to illustrate the control region. The underlying mechanism of suppressing spiral meandering behavior is explored by greatly decreasing the radius of the meandering tip. The proposed scheme can potentially contribute to controlling cardiac arrhythmia.

Spontaneous spiral wave breakup caused by pinning to the tissue defect

The work presents a mechanism of spiral wave initiation due to the specific boundary conditions on a border of cardiac tissue defect. There are known scenarios when anatomical or functional defects in cardiac tissue may provoke the spiral wave origination, including unidirectional blockage while passing through the narrow gates, bent over critical curvature wave fronts, inhomogeneous recovery of the tissue, etc. We show a new scenario of spiral wave breakup on a small defect, which is unexcitable but permeable for ionic currents supporting the excitation wave. It was believed that such defects stabilize the rotating wave; however, as shown, instead of stabilizing it leads to the spiral breakup and subsequent multiplication of the rotating waves.

A Parsimonious Model of the Rabbit Action Potential Elucidates the Minimal Physiological Requirements for Alternans and Spiral Wave Breakup.

Elucidating the underlying mechanisms of fatal cardiac arrhythmias requires a tight integration of electrophysiological experiments, models, and theory. Existing models of transmembrane action potential (AP) are complex (resulting in over parameterization) and varied (leading to dissimilar predictions). Thus, simpler models are needed to elucidate the “minimal physiological requirements” to reproduce significant observable phenomena using as few parameters as possible. Moreover, models have been derived from experimental studies from a variety of species under a range of environmental conditions (for example, all existing rabbit AP models incorporate a formulation of the rapid sodium current, INa, based on 30 year old data from chick embryo cell aggregates). Here we develop a simple “parsimonious” rabbit AP model that is mathematically identifiable (i.e., not over parameterized) by combining a novel Hodgkin-Huxley formulation of INa with a phenomenological model of repolarization similar to the voltage dependent, time-independent rectifying outward potassium current (IK). The model was calibrated using the following experimental data sets measured from the same species (rabbit) under physiological conditions: dynamic current-voltage (I-V) relationships during the AP upstroke; rapid recovery of AP excitability during the relative refractory period; and steady-state INa inactivation via voltage clamp. Simulations reproduced several important “emergent” phenomena including cellular alternans at rates > 250 bpm as observed in rabbit myocytes, reentrant spiral waves as observed on the surface of the rabbit heart, and spiral wave breakup. Model variants were studied which elucidated the minimal requirements for alternans and spiral wave break up, namely the kinetics of INa inactivation and the non-linear rectification of IK.The simplicity of the model, and the fact that its parameters have physiological meaning, make it ideal for engendering generalizable mechanistic insight and should provide a solid “building-block” to generate more detailed ionic models to represent complex rabbit electrophysiology.

Digital image communication scheme based on the breakup of spiral waves

Abstract A digital image communication scheme based on the breakup of spiral waves is presented in this paper. This communication system does not require spatially homogeneous random initial conditions. Moreover, the secret image is not embedded into the initial conditions of the evolving self-organizing patterns. Such features increase the security of the communication, but still enable an effective transmission of the secret image. Computational experiments are used to demonstrate the properties and efficiency of the proposed scheme.

Partial IK1 blockade destabilizes spiral wave rotation center without inducing wave breakup and facilitates termination of reentrant arrhythmias in ventricles.

It has been reported that blockade of the inward rectifier K(+) current (IK1) facilitates termination of ventricular fibrillation. We hypothesized that partial IK1 blockade destabilizes spiral wave (SW) re-entry, leading to its termination. Optical action potential (AP) signals were recorded from left ventricles of Langendorff-perfused rabbit hearts with endocardial cryoablation. The dynamics of SW re-entry were analyzed during ventricular tachycardia (VT), induced by cross-field stimulation. Intercellular electrical coupling in the myocardial tissue was evaluated by the space constant. In separate experiments, AP recordings were made using the microelectrode technique from right ventricular papillary muscles of rabbit hearts. Ba(2+) (10-50 μM) caused a dose-dependent prolongation of VT cycle length and facilitated termination of VT in perfused hearts. Baseline VT was maintained by a stable rotor, where an SW rotated around an I-shaped functional block line (FBL). Ba(2+) at 10 μM prolonged I-shaped FBL and phase-singularity trajectory, whereas Ba(2+) at 50 μM transformed the SW rotation dynamics from a stable linear pattern to unstable circular/cycloidal meandering. The SW destabilization was not accompanied by SW breakup. Under constant pacing, Ba(2+) caused a dose-dependent prolongation of APs, and Ba(2+) at 50 μM decreased conduction velocity. In papillary muscles, Ba(2+) at 50 μM depolarized the resting membrane potential. The space constant was increased by 50 μM Ba(2+) Partial IK1 blockade destabilizes SW rotation dynamics through a combination of prolongation of the wave length, reduction of excitability, and enhancement of electrotonic interactions, which facilitates termination of ventricular tachyarrhythmias.

Dynamics of Scroll Wave in a Three-Dimensional System with Changing Gradient.

The dynamics of a scroll wave in an excitable medium with gradient excitability is studied in detail. Three parameter regimes can be distinguished by the degree of gradient. For a small gradient, the system reaches a simple rotating synchronization. In this regime, the rigid rotating velocity of spiral waves is maximal in the layers with the highest filament twist. As the excitability gradient increases, the scroll wave evolutes into a meandering synchronous state. This transition is accompanied by a variation in twisting rate. Filament twisting may prevent the breakup of spiral waves in the bottom layers with a low excitability with which a spiral breaks in a 2D medium. When the gradient is large enough, the twisted filament breaks up, which results in a semi-turbulent state where the lower part is turbulent while the upper part contains a scroll wave with a low twisting filament.

Computational simulations of the effects of the G229D KCNQ1 mutation on human atrial fibrillation.

Atrial fibrillation (AF) is related to mutations at the genetic level. This includes mutations in genes that encode KCNQ1, a subunit of the I Ks channel. Here, we investigate the mechanism of gain-of-function in I Ks towards the occurrence of AF. We used the Courtemanche-Ramirez-Nattel (CRN) human atrial cell model (Am J Physiol Heart Circ Physiol 275:H301-H321, 1998) and applied the modification proposed by Hasegawa et al. (Heart Rhythm 11:67-75, 2014) to fit the behavior of I Ks due to the G229D mutation in KCNQ1 under a heterozygous mutant form. This was incorporated into two-(2D) and three-dimensional (3D) tissue models, where the mutation sustained a reentrant wave. However, under the wild-type condition, the reentrant wave terminated before the end of our simulations (in 2D, the spiral wave terminated before 10s, while in 3D, the spiral wave terminated before 13s). Sustained reentry under the mutation conditions also resulted in a spiral wave breakup in the 3D model, which was sustained until the end of the simulation (20s), indicating AF.

Prediction for breakup of spiral wave in a regular neuronal network

Target wave and spiral wave can regulate the collective behaviors of electrical activities in neuronal systems as a powerful ‘pacemaker’. Disordered states occur when normal signal propagation among neurons is disturbed and neuronal disease could be induced. In this paper, a stable rotating spiral wave is developed as initial state that the two-dimensional neuronal network of Hindmarsh–Rose neuron shows distinct periodicity and regularity in space, and then, some parameters are changed sharply to model the destruction effect induced by external large forcing or internal collapse, and the destructed areas will be expanded to occupy a larger area by expanding the damaged boundary in random way. The collapse and instability of spiral wave, ordered states could be predicated by monitoring and analyzing the time series of some nodes. It could be useful to detect the emergence of disaster in some biological or ecological systems.

Spiral wave classification using normalized compression distance: Towards atrial tissue spatiotemporal electrophysiological behavior characterization.

Analysis of electrical activation patterns such as re-entries during atrial fibrillation (Afib) is crucial in understanding arrhythmic mechanisms and assessment of diagnostic measures. Spiral waves are a phenomena that provide intuitive basis for re-entries occurring in cardiac tissue. Distinct spiral wave behaviors such as stable spiral waves, meandering spiral waves, and spiral wave break-up may have distinct electrogram manifestations on a mapping catheter. Hence, it is desirable to have an automated classification of spiral wave behavior based on catheter recordings for a qualitative characterization of spatiotemporal electrophysiological activity on atrial tissue. In this study, we propose a method for classification of spatiotemporal characteristics of simulated atrial activation patterns in terms of distinct spiral wave behaviors during Afib using two different techniques: normalized compressed distance (NCD) and normalized FFT (NFFTD). We use a phenomenological model for cardiac electrical propagation to produce various simulated spiral wave behaviors on a 2D grid and labeled them as stable, meandering, or breakup. By mimicking commonly used catheter types, a star shaped and a circular shaped both of which do the local readings from atrial wall, monopolar and bipolar intracardiac electrograms are simulated. Virtual catheters are positioned at different locations on the grid. The classification performance for different catheter locations, types and for monopolar or bipolar readings were also compared. We observed that the performance for each case differed slightly. However, we found that NCD performance is superior to NFFTD. Through the simulation study, we showed the theoretical validation of the proposed method. Our findings suggest that a qualitative wavefront activation pattern can be assessed during Afib without the need for highly invasive mapping techniques such as multisite simultaneous electrogram recordings.

Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study.

The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.

空间异质性对于可激发介质螺旋波的影响

本文以二维耦合Fitzhugh-Nagumo (FHN)神经元细胞体系为研究对象，考察了老龄化因素对神经元细胞耦合网络中螺旋波稳定性的影响。研究结果表明，随着细胞死亡比例的增加，一定数量的死亡细胞像杂质一样随机分布于机体组织中，导致神经元网络中的螺旋波容易出现破裂甚至死亡现象。其次，在一定程度的细胞老龄化条件下，若引入外界一定频率的电信号刺激，则可以在一定程度上减轻或抑制螺旋波的破裂。最后，通过计算细胞膜电压的同步因子，进一步分析了体系的耦合强度、外界刺激信号强度均可以减轻老龄化的负面效应，发现这些因素对维持螺旋波的稳定性有一定调控作用。In this paper, by using the 2D coupled Fitzhugh-Nagumo (FHN) neurons system as the research object, we have studied the effect of aging on the stability and breakup of spiral wave in the network of neuron cell system. It shows that, with the increment of cell death ratio to a certain level, a certain number of death cells randomly distribute as impurities in the tissue of the body, thus, the spiral wave may easily show the phenomenon of breakup or even death. Secondly, under the con-dition of certain ratio, if the stimulation of signal with proper frequency is introduced, the breakup of spiral wave could be reduced or inhibited. Finally, it is found that, by calculating the syn-chronizing factor of the cell membrane voltage, the negative effect of aging could be reduced by adjusting the coupling strength and the stimulus intensity of external signal. Especially, our results show that there is a certain regulation effect of these factors on maintaining the stability of spiral wave.

Spatiotemporal Transitions in Cardiac Neuronal Co-Cultures

A variety of arrhythmias have been attributed to formation of large scale patterns of excitation such as formation and break-up of spiral waves. We investigate the relationship between neuronal activity and evolution of macroscopic spatiotemporal dynamics. We also aim to understand the role of target-derived trophic nerve growth factors (NGF) on the formation and function of synapses between sympathetic neurons and heart tissue.Hearts were isolated from neonatal rat pups, ventricular myocytes were isolated, cultured and after 24h, stellate ganglia were isolated from litter mates enzymatically digested, and neurons were plated on top on myocyte dishes. We used dye-free imaging techniques using to record wave pattern and beat-rate (in the presence/absence of NGF).For the first time, we report wave speeds in cardiac neuron co-cultures. Our results show that (i) basal speed of co-cultures is significantly faster than myocyte only cultures (p<0.001); (ii) nicotine causes an altered behaviour in wave patterns; (iii) application of nicotine to co-culture causes a transient increase in contraction rate; (iv) the spatial organization of cells in myocyte monocultures is significantly altered by the addition of NGF.Our observations may be relevant to understanding how neuronal activity modulates macroscopic cardiac function. The finding that NGF modulates the development and patterning of myocytes raises the question of how NGF and their receptors interact to lead to long term changes in cardiac and synaptic function.

SELECTION OF SPIRAL WAVE IN THE COUPLED NETWORK UNDER GAUSSIAN COLORED NOISE

The selection and breakup of spiral wave in a coupled network is investigated by imposing Gaussian colored noise on the network, respectively. The dynamics of each node of the network is described by a simplified Chua circuit, and nodes are uniformly placed in a two-dimensional array with nearest-neighbor connection type. The transition of spiral wave is detected by changing the coupling intensity, intensity and correlation time τ in the noise. A statistical variable is used to discern the parameter region for breakup of spiral wave and robustness to external noise. Spiral waves emerge in the network when the network with structure of complex-periodic and chaotic properties. It is found that asymmetric coupling can induce deformation of spiral wave, stronger intensity or smaller correlation time in noise does cause breakup of the spiral wave.

Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potassium, Sodium) is investigated, the dynamics of the node is described by Hodgkin—Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio xNa (and xK), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio xNa (and xK) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.

Effects of the aging and systole of heart on the dynamics of spiral wave

In this paper, the effects of the aging and systole of heart on the dynamics of spiral wave are studied by using the Greenberg-Hasting cellular automaton model. In this model the neighbor radius and the excitation threshold are increased in order to simulate the aging of heart, and the neighbor radius is changed alternately to simulate heart systole and diastole. The results show that the aging of heart can induce some influences on spiral wave, such as make spiral wave meandering, and even cause spiral wave to disappear; in addition, it can shorten the wavelength and keep period fixed, and also elongate the wavelength and increase the period of spiral wave. If the aging and the regular systole of heart take place at the same time, we observe some phenomena, such as different spiral wave patterns, the spiral wave breakup and disappearance. We also obtain the probabilities of heart failure, ventricular fibrillation and death. These results are essentially consistent with the results of relevant epidemiological survey.

Effect of ion channel random blocking on the spatiotemporal dynamics of neuronal network

Ion channels in the membrane of neuron can be blocked by some toxic chemicals. Blocking ion channels will reduce the conductivity and the number of activated channels, and affect the electrical activity of neurons. And then the spatiotemporal patterns of neuronal network would be changed. In this paper, the nearest-neighbor coupled Hodgkin-Huxley neuronal network with periodic boundary is adapted to the investigation of the evolution of spatiotemporal patterns of neuronal network when the sodium and potassium ion channels are blocked randomly, by using numerical method. The results indicate that sodium ion and potassium ion channel random blockage could lead to the breakup of spiral wave. Furthermore, we analyze the firing probability of neuronal network and find that sodium ion channel random blockage reduces the excitability of neuronal network, which is sensitive to noise; but potassium ion channel random blockage enhances the excitability of neuronal network. Compared with uniform blockage of ion channels, the random blockage of ion channels makes neuronal network have rich dynamics phenomena. Finally, the no-flux boundary condition is applied and the results are similar to the above ones.

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

The breakup of a spiral wave by blockade of sodium and potassium channels in a small-world network of Hodgkin-Huxley neurons is investigated in detail. The influence of ion channel block in poisoned excitable membrane patches of a certain size is measured, by varying channel noise and channel densities resulting from the change in conductance. For example, tetraethylammonium is known to cause a block (poisoning) of potassium channels, while tetrodotoxin blocks sodium channels. We observed the occurrence of spiral waves, which are ordered waves believed to play an important role in facilitating the propagation of electric signals across quiescent regions of the brain. In this paper, the effect of channel block was measured by the factors x K and x Na, which represent the ratios of unblocked, or active, ion channels, to the overall number of potassium or sodium ion channels, respectively. To quantify these observations, we use a simple but robust synchronization measure, which succinctly captures the transition from spiral waves to other collective states, such as broken segments resulting from the breakup of the spiral wave. The critical thresholds of channel block can be inferred from the abrupt changes occurring in plots of the synchronization measure against different values of x K and x Na. Notably, small synchronization factors can be tightly associated with states where the formation of spiral waves is robust to mild channel block.