Spiral Wave Breakup Research Articles

Bariatric surgery partially reverses subclinical proarrhythmic structural, electrophysiological, and autonomic changes in obesity

BackgroundObesity confers higher risks of cardiac arrhythmias. The extent to which weight loss reverses subclinical proarrhythmic adaptations in arrhythmia-free obese individuals is unknown. ObjectiveThe purpose of this study was to study structural, electrophysiological, and autonomic remodeling in arrhythmia-free obese patients and their reversibility with bariatric surgery using electrocardiographic imaging (ECGi). MethodsSixteen arrhythmia-free obese patients (mean age 43 ± 12 years; 13 (81%) female participants; BMI 46.7 ± 5.5 kg/m2) had ECGi pre–bariatric surgery, of whom 12 (75%) had ECGi postsurgery (BMI 36.8 ± 6.5 kg/m2). Sixteen age- and sex-matched lean healthy individuals (mean age 42 ± 11 years; BMI 22.8 ± 2.6 kg/m2) acted as controls and had ECGi only once. ResultsObesity was associated with structural (increased epicardial fat volumes and left ventricular mass), autonomic (blunted heart rate variability), and electrophysiological (slower atrial conduction and steeper ventricular repolarization time gradients) remodeling. After bariatric surgery, there was partial structural reverse remodeling, with a reduction in epicardial fat volumes (68.7 cm3 vs 64.5 cm3; P = .0010) and left ventricular mass (33 g/m2.7 vs 25 g/m2.7; P < .0005). There was also partial electrophysiological reverse remodeling with a reduction in mean spatial ventricular repolarization gradients (26 mm/ms vs 19 mm/ms; P = .0009), although atrial activation remained prolonged. Heart rate variability, quantified by standard deviation of successive differences in R-R intervals, was also partially improved after bariatric surgery (18.7 ms vs 25.9 ms; P = .017). Computational modeling showed that presurgical obese hearts had a larger window of vulnerability to unidirectional block and had an earlier spiral-wave breakup with more complex reentry patterns than did postsurgery counterparts. ConclusionObesity is associated with adverse electrophysiological, structural, and autonomic remodeling that is partially reversed after bariatric surgery. These data have important implications for bariatric surgery weight thresholds and weight loss strategies.

Prokaryotic voltage-gated sodium channels are more effective than endogenous Nav1.5 channels in rescuing cardiac action potential conduction: an in silico study.

Methods to augment Na+ current in cardiomyocytes hold potential for the treatment of various cardiac arrhythmias involving conduction slowing. Because the gene coding cardiac Na+ channel (Nav1.5) is too large to fit in a single adeno-associated virus (AAV) vector, new gene therapies are being developed to enhance endogenous Nav1.5 current (by overexpression of chaperon molecules or use of multiple AAV vectors) or to exogenously introduce prokaryotic voltage-gated Na+ channels (BacNav) whose gene size is significantly smaller than that of the Nav1.5. In this study, based on experimental measurements in heterologous expression systems, we developed an improved computational model of the BacNav channel, NavSheP D60A. We then compared in silico how NavSheP D60A expression vs. Nav1.5 augmentation affects the electrophysiology of cardiac tissue. We found that the incorporation of BacNav channels in both adult guinea pig and human cardiomyocyte models increased their excitability and reduced action potential duration. When compared with equivalent augmentation of Nav1.5 current in simulated settings of reduced tissue excitability, the addition of the BacNav current was superior in improving the safety of conduction under conditions of current source-load mismatch, reducing the vulnerability to unidirectional conduction block during premature pacing, preventing the instability and breakup of spiral waves, and normalizing the conduction and ECG in Brugada syndrome tissues with mutated Nav1.5. Overall, our studies show that compared with a potential enhancement of the endogenous Nav1.5 current, expression of the BacNav channels with their slower inactivation kinetics can provide greater anti-arrhythmic benefits in hearts with compromised action potential conduction.NEW & NOTEWORTHY Slow action potential conduction is a common cause of various cardiac arrhythmias; yet, current pharmacotherapies cannot augment cardiac conduction. This in silico study compared the efficacy of recently proposed antiarrhythmic gene therapy approaches that increase peak sodium current in cardiomyocytes. When compared with the augmentation of endogenous sodium current, expression of slower-inactivating bacterial sodium channels was superior in preventing conduction block and arrhythmia induction. These results further the promise of antiarrhythmic gene therapies targeting sodium channels.

Mathematical Modelling of Leptin-Induced Effects on Electrophysiological Properties of Rat Cardiomyocytes and Cardiac Arrhythmias

Elevated plasma leptin levels, or hyperleptinemia, have been demonstrated to correlate with metabolic syndrome markers, including obesity, and may be an independent risk factor for the development of cardiovascular disease. In this paper, we use cardiac models to study possible effects of hyperleptinemia on the electrophysiological properties of cardiomyocytes and cardiac arrhythmias. We modified the parameters of an improved Gattoni 2016 model of rat ventricular cardiomyocytes to simulate experimental data for the leptin effects on ionic currents. We used four model variants to investigate the effects of leptin-induced parameter modification at the cellular level and in 2D tissue. In all models, leptin was found to increase the duration of the action potential. In some cases, we observed a dramatic change in the shape of the action potential from triangular, characteristic of rat cardiomyocytes, to a spike-and-dome, indicating predisposition to arrhythmias. In all 2D tissue models, leptin increased the period of cardiac arrhythmia caused by a spiral wave and enhanced dynamic instability, manifesting as increased meandering, onset of hypermeandering, and even spiral wave breakup. The leptin-modified cellular models developed can be used in subsequent research in rat heart anatomy models.

Spiral wave breakup: Optical mapping in an explanted human heart shows the transition from ventricular tachycardia to ventricular fibrillation and self-termination.

Since the first demonstration of ventricular fibrillation induction by electrical stimulation in 1850 by Hoffa and Ludwig, 1 Hoffa M. Ludwig C. Einige neue Versuche uber Herzbewegung. Zeitschr Rat Med. 1850; 9: 107-144 Google Scholar many mechanisms 2 Jalife J. Ventricular fibrillation: mechanisms of initiation and maintenance. Annu Rev Physiol. 2000; 62: 25-50 Crossref PubMed Scopus (288) Google Scholar ,3 Fenton F.H. Cherry E.M. Hastings H.M. Evans S.J. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. Chaos. 2002; 12: 852-892 Crossref PubMed Scopus (504) Google Scholar have been identified that initiate the complex dynamics of fibrillation. We report a high-resolution visualization of a spiral wave transitioning into multiple waves in human ventricles by using optical mapping (voltage and calcium) from the posterior epicardial surface (∼7 × 7 cm2) of an explanted heart from a 38-year-old female transplant recipient.

Verification of the Efficacy of Mexiletine Treatment for the A1656D Mutation on Downgrading Reentrant Tachycardia Using a 3D Cardiac Electrophysiological Model.

The SCN5A mutations have been long associated with long QT variant 3 (LQT3). Recent experimental and computation studies have reported that mexiletine effectively treats LQT3 patients associated with the A1656D mutation. However, they have primarily focused on cellular level evaluations and have only looked at the effects of mexiletine on action potential duration (APD) or QT interval reduction. We further investigated mexiletine’s effects on cardiac cells through simulations of single-cell (behavior of alternant occurrence) and 3D (with and without mexiletine). We discovered that mexiletine could shorten the cell’s APD and change the alternant’s occurrence to a shorter basic cycle length (BCL) between 350 and 420 ms. The alternant also appeared at a normal heart rate under the A1656D mutation. Furthermore, the 3D ventricle simulations revealed that mexiletine could reduce the likelihood of a greater spiral wave breakup in the A1656D mutant condition by minimizing the appearance of rotors. In conclusion, we found that mexiletine could provide extra safety features during therapy for LQT3 patients because it can change the alternant occurrence from a normal to a faster heart rate, and it reduces the chance of a spiral wave breakup. Therefore, these findings emphasize the promising efficacy of mexiletine in treating LQT3 patients under the A1656D mutation.

Stochastic termination of spiral wave dynamics in cardiac tissue.

Rotating spiral waves are self-organized features in spatially extended excitable media and may play an important role in cardiac arrhythmias including atrial fibrillation (AF). In homogeneous media, spiral wave dynamics are perpetuated through spiral wave breakup, leading to the continuous birth and death of spiral waves, but have a finite probability of termination. In non-homogeneous media, however, heterogeneities can act as anchoring sources that result in sustained spiral wave activity. It is thus unclear how and if AF may terminate following the removal of putative spiral wave sources in patients. Here, we address this question using computer simulations in which a stable spiral wave is trapped by an heterogeneity and is surrounded by spiral wave breakup. We show that, following ablation of spatial heterogeneity to render that region of the medium unexcitable, termination of spiral wave dynamics is stochastic and Poisson-distributed. Furthermore, we show that the dynamics can be accurately described by a master equation using birth and death rates. To validate these predictions in vivo, we mapped spiral wave activity in patients with AF and targeted the locations of spiral wave sources using radiofrequency ablation. Targeted ablation was indeed able to terminate AF, but only after a variable delay of up to several minutes. Furthermore, and consistent with numerical simulations, termination was not accompanied by gradual temporal or spatial organization. Our results suggest that spiral wave sources and tissue heterogeneities play a critical role in the maintenance of AF and that the removal of sources results in spiral wave dynamics with a finite termination time, which could have important clinical implications.

Effects of dynamic change of action potential on evolution behavior of spiral wave

It is observed in cardiac patients that the steepnesses of action potential duration (APD) restitution curve of cardiomyocytes in different regions of the ventricle are significantly different from region to region. However, the steep APD restitution curve can either lead the spiral wave to break up and set up the ventricular fibrillation in certain conditions or result in no breakup of spiral wave in other conditions. The relationship between the dynamic behavior of spiral wave and steep APD restitution curve is still not completely clear. Therefore, further research is needed. In this paper, a two-dimensional excitable medium cellular automata model is used to study the influences of the APD restitution curves with different steepnesses on the dynamic behavior of spiral wave. Numerical simulation results show that the steep APD restitution curve can stabilize the meandering spiral wave, causing the stable spiral wave to roam or break, and even to disappear. When the total average slope of APD restitution curve is greater than 1, it is observed that spiral wave may be still stable or meandering. When the total average slope of APD restitution curve is much smaller than 1, the breakup of spiral waves may occur. Three types of spiral wave breakups are observed. They are the Doppler instability, Eckhaus instability, and APD alternation. The Doppler instability and Eckhaus instability are related to the total average slope of APD restitution curve greater than 1, and the spiral wave breakup caused by APD alternans may occur when the total average slope of APD restitution curve is much smaller than 1. When the total average slope of APD restitution curve is greater than 1, the phenomena that spiral waves disappear by meandering out of the system boundary and conduction barriers are observed. In addition, we also find that increasing cellular APD is beneficial to preventing spiral wave from breaking up. The physical mechanisms behind those phenomena are heuristically analyzed.

Why Is Only Type 1 Electrocardiogram Diagnostic of Brugada Syndrome? Mechanistic Insights From Computer Modeling.

Three types of characteristic ST-segment elevation are associated with Brugada syndrome but only type 1 is diagnostic. Why only type 1 ECG is diagnostic remains unanswered. Computer simulations were performed in single cells, 1-dimensional cables, and 2-dimensional tissues to investigate the effects of the peak and late components of the transient outward potassium current (Ito), sodium current, and L-type calcium current (ICa,L) as well as other potassium currents on the genesis of ECG morphologies and phase 2 reentry (P2R). Although a sufficiently large peak Ito was required to result in the type 1 ECG pattern and P2R, increasing the late component of Ito converted type 1 ECG to type 2 ECG and suppressed P2R. Increasing the peak Ito promoted spiral wave breakup, potentiating the transition from tachycardia to fibrillation, but increasing the late Ito prevented spiral wave breakup by flattening the action potential duration restitution and preventing P2R. A sufficiently large ICa,L conductance was needed for P2R to occur, but once above the critical conductance, blocking ICa,L promoted P2R. However, selectively blocking the window and late components of ICa,L suppressed P2R, countering the effect of the late Ito. Blocking either the peak or late components of sodium current promoted P2R, with the late sodium current blockade having the larger effect. As expected, increasing other potassium currents potentiated P2R, with ATP-sensitive potassium current exhibiting a larger effect than rapid and slow component of the delayed rectifier potassium current. The peak Ito promotes type 1 ECG and P2R, whereas the late Ito converts type 1 ECG to type 2 ECG and suppresses P2R. Blocking the peak ICa,L and either the peak or the late sodium current promotes P2R, whereas blocking the window and late ICa,L suppresses P2R. These results provide important insights into the mechanisms of arrhythmogenesis and potential therapeutic targets for treatment of Brugada syndrome. Graphic Abstract: A graphic abstract is available for this article.

The transient outward potassium current plays a key role in spiral wave breakup in ventricular tissue.

Spiral wave reentry as a mechanism of lethal ventricular arrhythmias has been widely demonstrated in animal experiments and recordings from human hearts. It has been shown that in structurally normal hearts spiral waves are unstable, breaking up into multiple wavelets via dynamical instabilities. However, many of the second-generation action potential models give rise only to stable spiral waves, raising issues regarding the underlying mechanisms of spiral wave breakup. In this study, we carried out computer simulations of two-dimensional homogeneous tissues using five ventricular action potential models. We show that the transient outward potassium current (Ito), although it is not required, plays a key role in promoting spiral wave breakup in all five models. As the maximum conductance of Ito increases, it first promotes spiral wave breakup and then stabilizes the spiral waves. In the absence of Ito, speeding up the L-type calcium kinetics can prevent spiral wave breakup, however, with the same speedup kinetics, spiral wave breakup can be promoted by increasing Ito. Increasing Ito promotes single-cell dynamical instabilities, including action potential duration alternans and chaos, and increasing Ito further suppresses these action potential dynamics. These cellular properties agree with the observation that increasing Ito first promotes spiral wave breakup and then stabilizes spiral waves in tissue. Implications of our observations to spiral wave dynamics in the real hearts and action potential model improvements are discussed.NEW & NOTEWORTHY Spiral wave breakup manifesting as multiple wavelets is a mechanism of ventricular fibrillation. It has been known that spiral wave breakup in cardiac tissue can be caused by a steeply sloped action potential duration restitution curve, a property mainly determined by the recovery of L-type calcium current. Here, we show that the transient outward potassium current (Ito) is another current that plays a key role in spiral wave breakup, that is, spiral waves can be stable for low and high maximum Ito conductance but breakup occurs for intermediate maximum Ito conductance. Since Ito is present in normal hearts of many species and required for Brugada syndrome, it may play an important role in the spiral wave stability and arrhythmogenesis under both normal condition and Brugada syndrome.

Circadian Rhythms of Early Afterdepolarizations and Ventricular Arrhythmias in a Cardiomyocyte Model

Sudden cardiac arrest is a malfunction of the heart’s electrical system, typically caused by ventricular arrhythmias, that can lead to sudden cardiac death (SCD) within minutes. Epidemiological studies have shown that SCD and ventricular arrhythmias are more likely to occur in the morning than in the evening, and laboratory studies indicate that these daily rhythms in adverse cardiovascular events are at least partially under the control of the endogenous circadian timekeeping system. However, the biophysical mechanisms linking molecular circadian clocks to cardiac arrhythmogenesis are not fully understood. Recent experiments have shown that L-type calcium channels exhibit circadian rhythms in both expression and function in guinea pig ventricular cardiomyocytes. We developed an electrophysiological model of these cells to simulate the effect of circadian variation in L-type calcium conductance. In our simulations, we found that there is a circadian pattern in the occurrence of early afterdepolarizations (EADs), which are abnormal depolarizations during the repolarization phase of a cardiac action potential that can trigger fatal ventricular arrhythmias. Specifically, the model produces EADs in the morning, but not at other times of day. We show that the model exhibits a codimension-2 Takens-Bogdanov bifurcation that serves as an organizing center for different types of EAD dynamics. We also simulated a two-dimensional spatial version of this model across a circadian cycle. We found that there is a circadian pattern in the breakup of spiral waves, which represents ventricular fibrillation in cardiac tissue. Specifically, the model produces spiral wave breakup in the morning, but not in the evening. Our computational study is the first, to our knowledge, to propose a link between circadian rhythms and EAD formation and suggests that the efficacy of drugs targeting EAD-mediated arrhythmias may depend on the time of day that they are administered.

Effects of randomization of characteristic times on spiral wave generation in a simple cellular automaton model of excitable media

Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions such as epilepsy and atrial fibrillation. We used a simple cellular automaton model to study propagation in excitable media, with a particular focus on understanding spiral wave behavior. The main ingredients of this cellular automaton model are an excitation condition and characteristic excitation and refractory periods. The literature shows that fixed excitation and refractory periods together with specific initial conditions generate stationary and stable spiral waves. In the present work, we allowed the activation and refractory periods to fluctuate uniformly over a range of values. Under these conditions, this very simplistic model can recreate the meandering and breakup of spiral waves that were observed in more elaborate models in the literature.

Delay differential equation-based models of cardiac tissue: Efficient implementation and effects on spiral-wave dynamics.

Delay differential equations (DDEs) recently have been used in models of cardiac electrophysiology, particularly in studies focusing on electrical alternans, instabilities, and chaos. A number of processes within cardiac cells involve delays, and DDEs can potentially represent mechanisms that result in complex dynamics both at the cellular level and at the tissue level, including cardiac arrhythmias. However, DDE-based formulations introduce new computational challenges due to the need for storing and retrieving past values of variables at each spatial location. Cardiac tissue simulations that use DDEs may require over 28 GB of memory if the history of variables is not managed carefully. This paper addresses both computational and dynamical issues. First, we present new methods for the numerical solution of DDEs in tissue to mitigate the memory requirements associated with the history of variables. The new methods exploit the different time scales of an action potential to dynamically optimize history size. We find that the proposed methods decrease memory usage by up to 95% in cardiac tissue simulations compared to straightforward history-management algorithms. Second, we use the optimized methods to analyze for the first time the dynamics of wave propagation in two-dimensional cardiac tissue for models that include DDEs. In particular, we study the effects of DDEs on spiral-wave dynamics, including wave breakup and chaos, using a canine myocyte model. We find that by introducing delays to the gating variables governing the calcium current, DDEs can induce spiral-wave breakup in 2D cardiac tissue domains.

Chaotic tip trajectories of a single spiral wave in the presence of heterogeneities.

Spiral waves have been observed in a variety of physical, chemical, and biological systems. They play a major role in cardiac arrhythmias, including fibrillation, where the observed irregular activation patterns are generally thought to arise from the continuous breakup of multiple unstable spiral waves. Using spatially extended simulations of different electrophysiological models of cardiac tissue, we show that a single spiral wave in the presence of heterogeneities can display chaotic tip trajectories, consistent with fibrillation. We also show that the simulated spiral tip dynamics, including chaotic trajectories, can be captured by a simple particle model which only describes the dynamics of the spiral tip. This shows that spiral wave breakup, or interactions with other waves, are not necessary to initiate chaos in spiral waves.

Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study.

Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses.

Dynamics of Spiral Waves Induced by Periodic Mechanical Deformation with Phase Difference**Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos. LQ14A050003 and LR17A050001; and the National Natural Science Foundation of China under Grant Nos. 11674080 and 11674379

The dynamics of spiral waves under the influences of periodic mechanical deformation are studied. Here, the mechanical deformation propagating along the medium with phase differences are considered. It is found that weak mechanical deformation may lead to resonant drift of spiral waves. The drift direction and velocity can be changed by the wave length of the deformation. Strong mechanical deformation may result in breakup of spiral waves. The characteristics of breakup are discussed. The critical amplitudes are determined by two factors, i.e. the wave length and frequency of the periodic mechanical deformation. When the wave length of mechanical deformation is comparable to the spiral wave, simulation shows that the critical amplitude is substantially increased. As the frequency of the mechanical deformation is around 1.5 times of the spiral wave, the critical amplitudes are minimal.

Spiral wave breakup manner in the excitable system with early afterdepolarizations

Early afterdepolarization (EAD) is an important cause of lethal ventricular arrhythmias in heart failure because afterdepolarizations can promote the transition from ventricular tachycardia to fibrillation, which is related to the transition from spiral wave to spatiotemporal chaos. However, it remains unclear about how the EAD results in the breakup of spiral wave. In this paper, we explore the manner of spiral wave breakup induced by EADs under evenly distributed cells. The two-dimensional tissue is simulated with the Greenberg-Hasting cellular automaton model. The normal cells and aging cells are introduced into the model, in which the EAD only occurs in aging cells and can excite the resting cells. The numerical results show that the EAD can produce backward waves as well as forward waves. The EAD has no influence on the behavior of spiral wave in a few cases. The ratio of the number of unaffected spiral waves to the number of all tests is about 26.4%. The EAD can have various effects on spiral wave in other cases. The small influences on spiral wave are that the EAD leads to the meander, drift, and the deformation of spiral wave. The serious influences on spiral wave are that the EAD results in the disappearance and breakup of spiral wave. We find that spiral wave can disappear through the conduction block and transition from spiral wave to target wave. We observe the eight kinds of spiral wave breakups in connection with the excitation of EADs, such as symmetry breaking-induced breakup, nonsymmetry breaking-induced breakup, asymmetric excitation-induced breakup, conduction block-induced breakup, double wave-induced breakup, etc. Spiral wave generally breaks up into multiple spiral waves and spatiotemporal chaos. The ratio of the number of spiral wave breakup to the number of all tests is about 13.8%. However, the ratio of spiral wave breakup can reach about 32.4% under appropriately chosen parameters. The results are basically consistent with the survey results of arrhythmia-induced death rate. Furthermore, we also find that the excitation of EAD can prevent the spiral wave from disappearing and promote the breakup of spiral wave. The physical mechanisms underlying those phenomena are also briefly analyzed.

Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons

Spatially uniform cross-correlated sine-Wiener (CCSW) noises are imposed on each Hodgkin-Huxley (HH) neuron in a two-dimensional (2D) regular network. Noise-induced spiral wave destruction and order-disorder spatial pattern transition can be observed by adjusting cross-correlation time or cross-correlation intensity of CCSW noises. The sudden change of the curve of synchronization factor R and the time series of average membrane voltage F can be used to semiquantitatively assess this spatial pattern transition and spiral wave destruction induced by CCSW noises, respectively. In addition, moderate cross-correlation time and strong cross-correlation intensity of CCSW noises are both detrimental to survival of spiral wave. Comparing with non-cross-correlated sine-Wiener noises, CCSW noises can destroy organized spiral wave with lesser noise amplitude.

Image hiding in dynamic unstable self-organizing patterns

A digital image hiding scheme based on the breakup of spiral waves is presented in this paper. This scheme does not require initial conditions perturbation and embedding of the secret image is done during the evolution of a self-organizing pattern. Such features increase the security, but still enable an effective decoding of the secret image. The concept of the order of a 2D linear recurrent sequences are used to estimate the complexity of the pattern and select the optimal timing required for the pattern to complete. Computational experiments are used to demonstrate the properties and efficiency of the proposed scheme.

Mechanism for Mechanical Wave Break in the Heart Muscle.

Using a reaction-diffusion-mechanics model we identify a mechanism for mechanical wave break in the heart muscle. For a wide range of strengths and durations an external mechanical load causes wave front dissipation leading to formation and breakup of spiral waves. We explain the mechanism, and discuss under which conditions it can cause or abolish cardiac arrhythmias.

Dynamical mechanism of atrial fibrillation: A topological approach.

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets' hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead, this complexity is maintained as a dynamical balance between wave coalescence-a unique, previously unidentified, topological process that increases the number of wavelets-and wave collapse-a different topological process that decreases their number.