Termination of spiral waves during cardiac fibrillation via shock-induced phase resetting

Chaos control in cardiac dynamics: terminating chaotic states with local minima pacing

Current treatments of cardiac arrhythmias like ventricular fibrillation involve the application of a high-energy electric shock, that induces significant electrical currents in the myocardium and therefore involves severe side effects like possible tissue damage and post-traumatic stress. Using numerical simulations on four different models of 2D excitable media, this study demonstrates that low energy pulses applied shortly after local minima in the mean value of the transmembrane potential provide high success rates. We evaluate the performance of this approach for ten initial conditions of each model, ten spatially different stimuli, and different shock amplitudes. The investigated models of 2D excitable media cover a broad range of dominant frequencies and number of phase singularities, which demonstrates, that our findings are not limited to a specific kind of model or parameterization of it. Thus, we propose a method that incorporates the dynamics of the underlying system, even during pacing, and solely relies on a scalar observable, which is easily measurable in numerical simulations.

Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

Spatial phase discontinuity at the center of moving cardiac spiral waves

BACKGROUND

Precise analysis of cardiac spiral wave (SW) dynamics is essential for effective arrhythmia treatment. Although the phase singularity (PS) point in the spatial phase map has been used to determine the cardiac SW center for decades, quantitative detection algorithms that assume PS as a point fail to trace complex and rapid PS dynamics. Through a detailed analysis of numerical simulations, we examined our hypothesis that a boundary of spatial phase discontinuity induced by a focal conduction block exists around the moving SW center in the phase map.

METHOD

In a numerical simulation model of a 2D cardiac sheet, three different types of SWs (short wavelength; long wavelength; and low excitability) were induced by regulating ion channels. Discontinuities of all boundaries among adjacent cells at each instance were evaluated by calculating the phase bipolarity (PB). The total amount of phase transition (PTA) in each cell during the study period was evaluated.

RESULTS

Pivoting, drifting, and shifting SWs were observed in the short-wavelength, low-excitability, and long-wavelength models, respectively. For both the drifting and shifting cases, long high-PB edges were observed on the SW trajectories. In all cases, the conduction block (CB) was observed at the same boundaries. These were also identical to the boundaries in the PTA maps.

CONCLUSIONS

The analysis of the simulations revealed that the conduction block at the center of a moving SW induces discontinuous boundaries in spatial phase maps that represent a more appropriate model of the SW center than the PS point.

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.

Asymmetric couplings enhance the transition from chimera state to synchronization

Chimera state has been well studied recently, but little attention has been paid to its transition to synchronization. We study this topic here by considering two groups of adaptively coupled Kuramoto oscillators. By searching the final states of different initial conditions, we find that the system can easily show a chimera state with robustness to initial conditions, in contrast to the sensitive dependence of chimera state on initial conditions in previous studies. Further, we show that, in the case of symmetric couplings, the behaviors of the two groups are always complementary to each other, i.e., robustness of chimera state, except a small basin of synchronization. Interestingly, we reveal that the basin of synchronization will be significantly increased when either the coupling of inner groups or that of intergroups are asymmetric. This transition from the attractor of chimera state to the attractor of synchronization is closely related to both the phase delay and the asymmetric degree of coupling strengths, resulting in a diversity of attractor's patterns. A theory based on the Ott-Antonsen ansatz is given to explain the numerical simulations. This finding may be meaningful for the control of competition between two attractors in biological systems, such as the cardiac rhythm and ventricular fibrillation, etc.

Toward a More Efficient Implementation of Antifibrillation Pacing

We devise a methodology to determine an optimal pattern of inputs to synchronize firing patterns of cardiac cells which only requires the ability to measure action potential durations in individual cells. In numerical bidomain simulations, the resulting synchronizing inputs are shown to terminate spiral waves with a higher probability than comparable inputs that do not synchronize the cells as strongly. These results suggest that designing stimuli which promote synchronization in cardiac tissue could improve the success rate of defibrillation, and point towards novel strategies for optimizing antifibrillation pacing.

Capture of fixation by rotational flow; a deterministic hypothesis regarding scaling and stochasticity in fixational eye movements

Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modeled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of oculomotor postural control. We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity. Spiral waves play an organizational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales.

Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes

Optical mapping has become an increasingly important tool to study cardiac electrophysiology in the past 20 years. Multiple methods are used to process and analyze cardiac optical mapping data, and no consensus currently exists regarding the optimum methods. The specific methods chosen to process optical mapping data are important because inappropriate data processing can affect the content of the data and thus alter the conclusions of the studies. Details of the different steps in processing optical imaging data, including image segmentation, spatial filtering, temporal filtering, and baseline drift removal, are provided in this review. We also provide descriptions of the common analyses performed on data obtained from cardiac optical imaging, including activation mapping, action potential duration mapping, repolarization mapping, conduction velocity measurements, and optical action potential upstroke analysis. Optical mapping is often used to study complex arrhythmias, and we also discuss dominant frequency analysis and phase mapping techniques used for the analysis of cardiac fibrillation.

Reentrant spiral waves of spreading depression cause macular degeneration in hypoglycemic chicken retina

Spreading depression (SD), a slow diffusion-mediated self-sustained wave of depolarization that severely disrupts neuronal function, has been implicated as a cause of cellular injury in a number of central nervous system pathologies, including blind spots in the retina. Here we show that in the hypoglycemic chicken retina, spontaneous episodes of SD can occur, resulting in irreversible punctate lesions in the macula, the region of highest visual acuity in the central region of the retina. These lesions in turn can act as sites of origin for secondary self-sustained reentrant spiral waves of SD that progressively enlarge the lesions. Furthermore, we show that the degeneration of the macula under hypoglycemic conditions can be prevented by blocking reentrant spiral SDs or by blocking caspases. The observation that spontaneous formation of reentrant spiral SD waves leads to the development of progressive retinal lesions under conditions of hypoglycemia establishes a potential role of SD in initiation and progression of macular degeneration, one of the leading causes of visual disability worldwide.

PHASE RESETTING ANALYSIS OF HIGH POTASSIUM EPILEPTIFORM ACTIVITY IN CA3 REGION OF THE RAT HIPPOCAMPUS

The theory of phase resetting can reveal important information about the dynamic behavior of a periodic system when a single brief stimulus is applied to that system at the appropriate time. Phase resetting studies have revealed the existence in some biological systems of a vulnerable stimulus window generating desynchronization and suppression of the activity. The objective of this study was to test the hypothesis that a "singular" stimulus could annihilate this activity. Perfusion with the high-K solution produced synchronous, quasi-periodic population bursts with inter-burst interval of ~0.8–1.5 seconds. A single 0.1 ms duration anodic pulse of programmable delay and magnitude was applied to the somatic layer of the CA3 pyramidal cells. Three types of phase-resetting behavior were observed: (1) Weak resetting with little or no effect on the timing of the subsequent burst, (2) Strong resetting where the applied current pulse delayed the next event by one time period, (3) Singular behavior where the applied pulse partially or completely suppressed the subsequent bursting. The singular stimulus parameter window, however, was very narrow making it difficult to generate the singular behavior reliably. Nevertheless, the results indicate that singularities exist for high potassium neural activity and that a well timed pulse applied with the right amplitude can suppress this activity. This study suggests that phase resetting of a population of neurons is possible for quasi-periodic interictal activity and similar techniques could be applied to the control of epileptic seizures.

Regional cooling facilitates termination of spiral-wave reentry through unpinning of rotors in rabbit hearts

BACKGROUND

Moderate global cooling of myocardial tissue was shown to destabilize 2-dimensional (2-D) reentry and facilitate its termination.

OBJECTIVE

This study sought to test the hypothesis that regional cooling destabilizes rotors and facilitates termination of spontaneous and DC shock-induced subepicardial reentry in isolated, endocardially ablated rabbit hearts.

METHODS

Fluorescent action potential signals were recorded from 2-D subepicardial ventricular myocardium of Langendorff-perfused rabbit hearts. Regional cooling (by 5.9°C ± 1.3°C) was applied to the left ventricular anterior wall using a transparent cooling device (10 mm in diameter).

RESULTS

Regional cooling during constant stimulation (2.5 Hz) prolonged the action potential duration (by 36% ± 9%) and slightly reduced conduction velocity (by 4% ± 4%) in the cooled region. Ventricular tachycardias (VTs) induced during regional cooling terminated earlier than those without cooling (control): VTs lasting >30 seconds were reduced from 17 of 39 to 1 of 61. When regional cooling was applied during sustained VTs (>120 seconds), 16 of 33 (48%) sustained VTs self-terminated in 12.5 ± 5.1 seconds. VT termination was the result of rotor destabilization, which was characterized by unpinning, drift toward the periphery of the cooled region, and subsequent collision with boundaries. The DC shock intensity required for cardioversion of the sustained VTs decreased significantly by regional cooling (22.8 ± 4.1 V, n = 16, vs 40.5 ± 17.6 V, n = 21). The major mode of reentry termination by DC shocks was phase resetting in the absence of cooling, whereas it was unpinning in the presence of cooling.

CONCLUSION

Regional cooling facilitates termination of 2-D reentry through unpinning of rotors.

Low-energy control of electrical turbulence in the heart

Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves in a heterogeneous anatomical substrate. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation. Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ E(α). These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.

Phase-resolved analysis of the susceptibility of pinned spiral waves to far-field pacing in a two-dimensional model of excitable media

Life-threatening cardiac arrhythmias are associated with the existence of stable and unstable spiral waves. Termination of such complex spatio-temporal patterns by local control is substantially limited by anchoring of spiral waves at natural heterogeneities. Far-field pacing (FFP) is a new local control strategy that has been shown to be capable of unpinning waves from obstacles. In this article, we investigate in detail the FFP unpinning mechanism for a single rotating wave pinned to a heterogeneity. We identify qualitatively different phase regimes of the rotating wave showing that the concept of vulnerability is important but not sufficient to explain the failure of unpinning in all cases. Specifically, we find that a reduced excitation threshold can lead to the failure of unpinning, even inside the vulnerable window. The critical value of the excitation threshold (below which no unpinning is possible) decreases for higher electric field strengths and larger obstacles. In contrast, for a high excitation threshold, the success of unpinning is determined solely by vulnerability, allowing for a convenient estimation of the unpinning success rate. In some cases, we also observe phase resetting in discontinuous phase intervals of the spiral wave. This effect is important for the application of multiple stimuli in experiments.

Nonlinear dynamics of cardiovascular ageing

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

Origin choice and petal loss in the flower garden of spiral wave tip trajectories

Rotating spiral waves have been observed in numerous biological and physical systems. These spiral waves can be stationary, meander, or even degenerate into multiple unstable rotating waves. The spatiotemporal behavior of spiral waves has been extensively quantified by tracking spiral wave tip trajectories. However, the precise methodology of identifying the spiral wave tip and its influence on the specific patterns of behavior remains a largely unexplored topic of research. Here we use a two-state variable FitzHugh-Nagumo model to simulate stationary and meandering spiral waves and examine the spatiotemporal representation of the system's state variables in both the real (i.e., physical) and state spaces. We show that mapping between these two spaces provides a method to demarcate the spiral wave tip as the center of rotation of the solution to the underlying nonlinear partial differential equations. This approach leads to the simplest tip trajectories by eliminating portions resulting from the rotational component of the spiral wave.

Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase differences from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example.

Preshock phase singularity and the outcome of ventricular defibrillation

BACKGROUND

Phase singularity (PS) is a topological defect that serves as a source of ventricular fibrillation (VF). Whether or not the quantity of preshock PS determines defibrillation outcome is unclear.

OBJECTIVE

The purpose of this study was to test the hypothesis that the number of PSs at the time of shock is an important factor that determines the shock outcome.

METHODS

Isolated, perfused rabbit hearts (n = 7) were optically mapped with a potentiometric dye (di-4-ANNEPS). Shocks were delivered during short (10 seconds) and long (1 minute) VF, and the outcome was classified as successful type A (immediate termination), type B (postshock repetitive responses before termination), and unsuccessful.

RESULTS

When shock strengths of 50% probability of successful defibrillation (DFT50) +/- 50 V were given in short VF, the types A and B and unsuccessful shocks were associated with a preshock PS number of 0.3 +/- 0.4, 1.4 +/- 0.3, and 1.5 +/- 0.4 (P <.01 by analysis of variance) and shock strengths of 205 +/- 77, 207 +/- 65, and 173 +/- 74 V (P <.01), respectively. When the same shocks were applied during long VF, the PS numbers were 1.7 +/- 0.5, 3.0 +/- 0.5, and 3.5 +/- 0.6, respectively (P <.01), and the shock strengths were 282 +/- 100, 283 +/- 135, and 256 +/- 126 V, respectively (P <.01). If we only analyze shocks with strength at DFT(50), the preshock PS number was still significantly different for short VF (0.6 +/- 0.5, 1.6 +/- 0.9, and 1.5 +/- 0.8; P <.05) and for long VF (1.4 +/- 0.5, 2.7 +/- 0.6, and 2.7+/-1.3; P <.05), respectively. All preshock PSs were eliminated by shocks. However, rapid repetitive activity was then reinitiated in unsuccessful and type B successful shocks but not in type A successful shocks.

CONCLUSIONS

A low number or an absence of preshock PS was associated with type A successful defibrillation. There was no difference in preshock PS numbers between unsuccessful and type B successful defibrillation.

Spiral-wave dynamics depend sensitively on inhomogeneities in mathematical models of ventricular tissue

Every sixth death in industrialized countries occurs because of cardiac arrhythmias such as ventricular tachycardia (VT) and ventricular fibrillation (VF). There is growing consensus that VT is associated with an unbroken spiral wave of electrical activation on cardiac tissue but VF with broken waves, spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus spiral-wave activity in cardiac tissue has been studied extensively. Nevertheless, many aspects of such spiral dynamics remain elusive because of the intrinsically high-dimensional nature of the cardiac-dynamical system. In particular, the role of tissue heterogeneities in the stability of cardiac spiral waves is still being investigated. Experiments with conduction inhomogeneities in cardiac tissue yield a variety of results: some suggest that conduction inhomogeneities can eliminate VF partially or completely, leading to VT or quiescence, but others show that VF is unaffected by obstacles. We propose theoretically that this variety of results is a natural manifestation of a complex, fractal-like boundary that must separate the basins of the attractors associated, respectively, with spiral breakup and single spiral wave. We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy I models, where we show that the suppression of spiral breakup depends sensitively on the position, size, and nature of the inhomogeneity.

Panoramic optical mapping reveals continuous epicardial reentry during ventricular fibrillation in the isolated swine heart

During ventricular fibrillation (VF), activation waves are fragmented and the heart cannot contract synchronously. It has been proposed that VF waves emanate from stable sources ("mother rotors"). Previously, we used new optical mapping technology to image VF wavefronts from nearly the entire epicardial surface of six isolated swine hearts. We found that VF was not driven by epicardial rotors, but could not exclude the presence of stable rotors hidden within the ventricular walls. Here, we use graph theoretic analysis to show that, in all 17 VF episodes we analyzed, it was always possible to trace sequences of wavefronts through series of fragmentation and collision events from the beginning to the end of the episode. The set of wavefronts that were so related (the dominant component) consisted of 92%+/-1% of epicardial wavefronts. Because each such wavefront sequence constitutes a continuous activation front, this finding shows that complete reentrant pathways were always present on the epicardial surface and therefore, that wavefront infusion from nonepicardial sources was not strictly necessary for VF maintenance. These data suggest that VF in this model is not driven by localized sources; thus, new anti-VF treatments designed to target such sources may be less effective than global interventions.

Spiral wave dynamics in excitable media with spherical geometries

We describe the spatial and temporal organization of spiral and scroll waves in spherical shells of different sizes and solid spheres. We present simulation results for the evolution of the dynamics and clustering of spiral waves as a function of the excitability of the medium. The excitability, topology, and size of the domain places restrictions on how single and multiarmed spiral waves are organized in space. The results in spherical geometries are compared with those in planar two-dimensional media. These studies are relevant to the dynamics of spiral waves in a variety of media including the heart, and chemical reactions on spherical surfaces.