Spiral Tip Research Articles

Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol

A thin layer of the Belousov–Zhabotinsky reaction with pyrogallol (PG) supports meandering spiral waves with outward-petal trajectories. Increasing [PG] or lowering [H2SO4] leads to an enlargement of the outer diameter of the tip trajectory, as well as an increment of the number of petals. Far from the spiral tip, the wavelength and the wave period also increase. However, the wave speed decreases, when [PG] is elevated or [H2SO4] is reduced. This reaction is suitable for further investigations of three-dimensional spiral dynamics with optical tomography because of slowly propagating waves, no bubbles, no induction time, and no inhibitory effects of oxygen.

EFFECT OF EXTERNAL PERIODIC PULSES ON SPIRAL DYNAMICS AND CONTROL OF SPIRAL WAVES

In this paper, we study the effect of external periodic pulses on spiral dynamics. Resonant entrainment bands were observed on the period T-axis, and T is close to rational multiples of the path curvature period of the spiral tip on the bands. It is also shown that spiral waves are drifted and eliminated by applying the driving method with suitable control parameters, and we reveal the mechanism which forces the spiral wave to periodically shift and rotate. In the domain near the spiral tip, the bidirectional wave excitations are periodically generated by external pulses, and each excitation induces a straight drift of the spiral wave tip. Numerical results show that the parameter range of the external pulse period T, used to successfully eliminate spiral waves, is broaden by appropriately increasing the values of the pulse width and the amplitude. The low-amplitude control scheme is operable in many real systems, and its study is beneficial to understand the forced spiral dynamics.

Spiral waves in systems with fractal heterogeneity

The influence of fractal heterogeneity on a spiral wave in an excitable system is numerically studied based on the Barkley model. The heterogeneity is implemented by letting the diffusive coefficient in the heterogeneous area be different from the other area. The results show that fruitful transitions of the spiral tip trajectories are induced by the fractal heterogeneity. In particular, when the heterogeneity increases to a sufficiently high level the spiral tip trajectory always changes to a stable rotating trajectory (closed-circle tip trajectory), whatever transitions have been induced by a lower level of heterogeneity. We qualitatively ascribe the transitions to the attraction on the spiral tip exerted by the heterogeneous area.

SPIRAL DYNAMICS IN EXCITABLE MEDIUM INDUCED BY EXTERNAL PERIODIC MODULATION

Spatiotemporal dynamics of spiral tip and the evolution of spiral wave induced by external periodic modulation has been investigated in a generic excitable model. Tip dynamics of spiral wave depending on the frequency and strength of the external modulation is revealed by the meandering size variable Rx of the tip trajectory. Different effects of frequency and strength on spiral dynamics are observed and the corresponding mechanisms are explained. Finally, we can eliminate spiral wave out of the boundary successfully by suitably choosing the frequency and the strength of the external periodic modulation.

Dynamics of spiral waves driven by a rotating electric field

We study the behavior of spiral wave under the driving of a rotating electric field. The rotating electric field can drive a spiral wave to be synchronous, depending on four factors: its frequency and amplitude, chirality, and polarized modes. Rotation-synchronization characterized by the rotating direction is focused on. We discuss the behavior of synchronization, such as the dependence of angle-differences between the spiral tip and the electric field on ratio of frequency, the influences of different polarized modes of the electric field, the radius of synchronous spiral wave, and so on. A circularly polarized electric fields (CPEF) can suppress meandering spiral to rigid one and prevent breakup of spiral in medium with low excitability. The phase diagram describing the controllable region in excitability-period plane is presented. The influences of polarized modes of electric field on minimum excitability of medium are also studied.

Shannon Entropy Mapping of AF Rotors-Theoretical Extensions to a Novel Conceptual Paradigm

The pivot is critical to rotors maintaining AF. We have shown that high Shannon entropy (ShEn), a measure of information uncertainty, localises the pivot of rotors recorded with bipolar electrograms, and that targeted ablation of high ShEn EGMs is associated with termination in human AF This study evaluated ShEn colocalisation of rotors under conditions of: (i) rotor meander; (ii) electrogram filtering and (iii) effect of ShEn box size (iv) effect of myocyte model. Methods: Bipolar EGM recordings were studied in simulated (i) atrial (ii) ventricular and (iii) FitzHugh Nagumo rotors. Model meshes contained 100 × 100 elements with 0.5 mm spatial distance. Unipolar EGMs were calculated, which were used to construct bipolar EGMs. Spiral wave tip was localised with phase integration. ShEn was calculated as for each bipole. We simulated the effects of: (i) rotor meander, (ii) EGM filtering, with simulated high-pass Butterworth filters with cutoffs at 0.5, 10, and 30 Hz, (iii) ShEn box size in each model rotor system. Results: In each of the model systems, the highest region of ShEn colocalised with the pivoting region identified by the spiral wave tip. ShEn was inversely correlated with distance from the pivot (Pearson's r = −0.61, p < 0.001). The region of maximum Max ShEn colocalised with the pivot zone in ShEn box size from 0.01mV to 1 mV. Max ShEn remained colocalised with the pivot over a range of bipolar EGM cut-off frequencies, and with rotor meander, in each model system. Conclusion: These data confirm ShEn as a mechanistically based potential tool to map stable rotors.

Spiral-wave dynamics in an excitable medium with many excitability obstacles

Many real excitable systems can be descibed as inhomogeneous media, where the inhomogeneity is an important factor for the formation of spiral waves and the changing of their dynamics. In this paper, we investigate the effect of excitability obstacles on spiral-wave dynamics. For an excitability-reduced obstacle, the neighbor spiral tip is attracted into the obstacle. When more localized obstacles are placed, the attactive case depends on the distribution, size and excitability of the obstcales. On the basis of analyzing the small-value area of the inhibitor variable, we illustrate the mechanism of these behaviors occuring. For an excitability-enhanced obstacle, the nearby spiral tip is repelled. The tip motion after the repelsive effect depends on the type of the initial spiral wave, i.e. rigidily rotating spiral wave or meandering spiral wave. In the present of more localized obstacles, there exist different behaviors for different distributions, sizes and excitabilities of the obstcales, and different types of initial waves.

Laryngeal pacing in minipigs: in vivo test of a new minimal invasive transcricoidal electrode insertion method for functional electrical stimulation of the PCA

Functional electrical stimulation (FES) of the posterior cricoarytenoid muscle (PCA) to restore respiratory function of the larynx may become an option for the treatment of bilateral recurrent laryngeal nerve paralysis (RLNP) in the near future. The feasibility of this has been shown in several animal trials and in a human pilot study. The common open surgical inferolateral approach for electrode insertion into the PCA for FES has a risk of damaging the recurrent laryngeal nerve (RLN) and may result in postoperative swelling and scaring of the larynx. Therefore, a minimal invasive electrode insertion technique is needed. A new miniaturized bipolar spiral tip electrode and a new electrical stimulatable insertion needle were tested in a short-term trial for an endoscopically guided and functionally controlled transcricoidal electrode insertion in eight Göttingen minipigs with bilateral normal RLN function. The feasibility of this technique was evaluated and the achieved positions of the electrodes in the PCA were analyzed using intraoperative stimulation threshold data and 3D-CT reconstructions. In seven cases it was possible to place two well-performing electrodes into the PCA. They were positioned one on either side. In one animal no functioning electrode position could be achieved because the PCA was missed. Thresholds of the electrode tips varied between 0.2 and 2.5 mA (mean 0.71 mA). In any case maximal glottal opening could be reached before adductors were co-activated. The majority of electrodes were placed into the central lower part of the PCA with no apparent correlation between threshold and electrode position. Surgical trauma might be further reduced by using endoscopy via a laryngeal mask avoiding the temporary tracheostomy used in this trial. If the implanted electrodes remain stable in long-term tests, we suggest that this method could soon be transferred into human application.

Inwardly rotating spirals in nonuniform excitable media

Inwardly rotating spirals (IRSs) have attracted great attention since their observation in an oscillatory reaction-diffusion system. However, IRSs have not yet been reported in planar excitable media. In the present work we investigate rotating waves in a nonuniform excitable medium, consisting of an inner disk part surrounded by an outer ring part with different excitabilities, by numerical simulations of a simple FitzHugh-Nagumo model. Depending on the excitability of the medium as well as the inhomogeneity, we find the occurrence of IRSs, of which the excitation propagates inwardly to the geometrical spiral tip.

Numerical simulation of 3D flow past a real-life marine hydrokinetic turbine

We simulate three-dimensional, turbulent flow past an axial-flow marine hydrokinetic (MHK) turbine mounted on the bed of a rectangular open channel by adapting a computational framework developed for carrying out high-resolution large-eddy simulation (LES) in arbitrarily complex domains involving moving or stationary boundaries. The complex turbine geometry, including the rotor and all stationary components, is handled by employing the curvilinear immersed boundary (CURVIB) method [1,2]. Velocity boundary conditions near all solid surfaces are reconstructed using a wall model based on solving the simplified boundary layer equations [2]. To demonstrate the capabilities of the model we apply it to simulate the flow past a Gen4 axial flow MHK turbine developed by Verdant Power for the Roosevelt Island Tidal Energy (RITE) project in the East River in New York City, USA. We carry out systematic grid refinement studies, using grids with up to 185 million nodes, for only the turbine rotor placed in an infinite free stream to show that the computed torque converges to a grid insensitive value, which is in good agreement with field measurements. We also carry out LES for the complete turbine configuration, including the pylon, nacelle and rotor, mounted on the bed of a straight rectangular open channel. The computed results illustrate the complexity of the flow and show that the power output of the complete turbine is primarily dependent on the rotor geometry and tip speed ratio, and is not affected by the stationary components of the turbine and the presence of the channel bed. The complete turbine simulation also reveals that the downstream wake of the turbine consists of three main regions: (1) the outer layer with the spiral blade tip vortices rotating in the same direction as the blades; (2) the counter-rotating inner layer surrounded by the spiral tip vortices; and (3) the core layer co-rotating with respect to the tip vortices. This study is the first to report the three-dimensional wake structure of MHK turbines.

Sparse and dense spiral waves in heterogeneous excitable media

Dynamic behaviors of sparse and dense spirals are investigated numerically based on a Barkley model in heterogeneous excitable media. It is found that the rotating frequency of sparse spiral wave decreases rapidly with b increasing and then tends to saturation, which is different from that of dense spiral wave. The period and wavelength of dense spiral wave increase with the increase of parameter or the size R of localized inhomogeneity, which depends more sensitively on the size R than those of sparse sprial wave. The change of the speed of dense spiral wave tip with R is opposite to that of the sparse spiral wave tip. In addition, inhomogeneous effect gives rise to a defect point in arm of each of the two spiral waves when or b increases above a critical value.

The influence of spatiotemporal modulation on spiral tip dynamics in excitable medium and its application for spiral control

In this paper, the influence of spatiotemporal modulation on tip dynamics of periodic spiral wave in excitable medium is studied first. By varying spatiotemporal modulation item, the dynamics of spiral wave changes dramatically and the system undergoes periodic spiral wave, epicycloid meandering spiral wave, traveling spiral wave and hypocycloid meandering spiral wave. An order parameter is introduced to detect the critical conditions of non-equilibrium transition between different patterns. And the variation of spiral tip radius induced by spatiotemporal modulation can also be reflected by this order parameter. When spatiotemporal modulation increases to a critical value, spiral waves break up. And spiral waves will damp to homogeneous rest state if spatiotemporal modulation increases further. The mechanisms of spiral breakup and damping are explained in the paper. Finally we apply the spatiotemporal modulation method to the meandering spiral waves and can successfully control meandering spiral waves into periodic spiral waves or homogeneous rest state.

Hepatic arterial infusion chemotherapy with a coaxial reservoir system using a non-braided spiral tip microcatheter

To evaluate the efficacy and safety of a coaxial reservoir system with a non-braided spiral tip microcatheter and exclusive port for hepatic arterial infusion chemotherapy. In vitro evaluation included evaluation of pressure tolerance/flow rate of the coaxial reservoir system, and the strength of connection between the 2.7-F catheter and port. Due to the difficulty of implanting conventional reservoirs, coaxial reservoirs were implanted via the femoral artery of 80 patients. We implanted a non-braided 2.7-F microcatheter with a spiral shaped tip, 5-F catheter, and a port. Clinical assessment included evaluation of technical success and complications. In vitro evaluation of the coaxial reservoir at its maximum pressure load showed that flow rates for 300 mg I/mL iopamidol contrast medium were 0.25 ± 0.04 mL/s (undiluted), 1.03 ± 0.01 mL/s (50% dilution), and 2.91 ± 0.01 mL/s (30% dilution). Connection strength between the 2.7-F catheter and port was 13.4 ± 0.57 N. Percutaneous port catheter placement was successful in all patients (100%, n = 80). Complications included hepatic arterial occlusion (10%, n = 8), catheter tip dislocation (1.3%, n = 1), and catheter occlusion (1.3%, n = 1). A coaxial reservoir system with a non-braided microcatheter and exclusive port is safe and effective for difficulty of implanting conventional reservoir.

Lasers in Endodontics

Er: YAG laser irradiation utilizing the newly developed RCLase side-firing spiral tip was used for the cleansing of root canals following their bio-mechanical preparation with ProTaper Ni-Ti files. The distal and palatal roots of 20 freshly extracted molar teeth were instrumented to size F3 with ProTaper files. In the experimental group (10 teeth) the pulp chamber and the root canals were filled with EDTA 17% and the root canals were lased for 30 s using the Er: YAG laser irradiation at 600 mJ per pulse and a frequency of 12 Hz. In the control group (10 teeth) the root canals were not lased. Scanning electron microscope analysis showed clean wall surfaces of the lased root canals with open dentinal tubules, free of smear layer and debris. In the scanning electron microscope photographs of the walls of the non-lased root canals a considerable amount of debris could be detected. It appears that an efficient cleansing of the root canal system can be achieved by using the Er: YAG laser irradiation with the RCLase Side-firing Spiral Tip following bio-mechanical preparation of the root canal with Ni-Ti Taper files.

CONTROL OF SPIRAL WAVE BREAKUP BY SPATIOTEMPORAL MODULATION

The control of spiral wave breakup due to Doppler instability has been investigated. It is found that by applying the spatiotemporal modulation method with suitable control parameters, spiral wave breakup can be prevented. Further numerical simulations show that preventing spiral wave breakup is a result of the decrease of meandering motion of the spiral tip.

Chemical wave studies in the bromate-pyrocatechol beads system

We studied the chemical wave activity of the pyrocatechol-acidic bromate system in the presence of ferroin-loaded beads. The wave activity lasted for more than 24 h while meandering spirals continued for up to 10 h. Rigid and meandering spiral waves were investigated. We have analyzed the wave propagation speed and spiral tip trajectory versus the initial concentrations of all reagents as well as the age of the solution. Wave velocity depends on [H+] and [BrO] concentrations by the relationship v=k[H+]1/2[BrO]1/2, which is in agreement with other studies. This system is ideal to study wave activity and spiral waves as it does not produce precipitates under the studied conditions. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 198–203, 2011

Kinematics of spiral waves under feedback-related spatial gradients

The kinematics of spiral waves with artificially constructed spatial excitability is numerically investigated in the Oregonator model. On an assumption that the rotation center of spiral's tip drifts at angle δ to the direction of a local gradient, a kinematic formula of motion of spiral's tip is derived. To test the formula, we have presented two forms of feedback-related spatial fields with radial gradients (RGs) and concentric circular gradients (CGs) both centering on a reference point. It is found that both rigidly rotating and meandering spiral waves are attracted to the reference point of an inward RG and a clockwise CG perturbation but moved away from it under an outward RG and a counterclockwise CG. Simulations of the drift-velocity formulas provide a quantitative testing of the numerical results.

SELF-AVOIDING CHIRAL WALKS

We describe a simple, discrete model of deterministic chiral motion on a square lattice. The model is based on rotating walkers with trailing tails spanning L lattice bonds. These tail segments cannot overlap and their leading A segments cannot be crossed. As prescribed by their chirality, walkers must turn if possible, or go straight, or else correct earlier steps recursively. The resulting motion traces unbound trajectories and complex periodic orbits with various symmetries. Periods tend to decrease with increasing L and vary between L and L2. Interacting walkers can form intricate pair states. Some orbits match pinned spiral tip trajectories observed experimentally in excitable systems.

Theory of the propagation dynamics of spiral edges of diffusion flames in von Kármán swirling flows

This analysis addresses the propagation of spiral edge flames found in von Kármán swirling flows induced in rotating porous-disk burners. In this configuration, a porous disk is spun at a constant angular velocity in an otherwise quiescent oxidizing atmosphere. Gaseous methane is injected through the disk pores and burns in a flat diffusion flame adjacent to the disk. Among other flame patterns experimentally found, a stable, rotating spiral flame is observed for sufficiently large rotation velocities and small fuel flow rates as a result of partial extinction of the underlying diffusion flame. The tip of the spiral can undergo a steady rotation for sufficiently large rotational velocities or small fuel flow rates, whereas a meandering tip in an epicycloidal trajectory is observed for smaller rotational velocities and larger fuel flow rates. A formulation of this problem is presented in the equidiffusional and thermodiffusive limits within the framework of one-step chemistry with large activation energies. Edge-flame propagation regimes are obtained by scaling analyses of the conservation equations and exemplified by numerical simulations of straight two-dimensional edge flames near a cold porous wall, for which lateral heat losses to the disk and large strains induce extinction of the trailing diffusion flame but are relatively unimportant in the front region, consistent with the existence of the cooling tail found in the experiments. The propagation dynamics of a steadily rotating spiral edge is studied in the large-core limit, for which the characteristic Markstein length is much smaller than the distance from the center at which the spiral tip is anchored. An asymptotic description of the edge tangential structure is obtained, spiral edge shapes are calculated, and an expression is found that relates the spiral rotational velocity to the rest of the parameters. A quasiestatic stability analysis of the edge shows that the edge curvature at extinction in the tip region is responsible for the stable tip anchoring at the core radius. Finally, experimental results are analyzed, and theoretical predictions are tested.

Two‐dimensional changes and surface characteristics from an erbium laser used for root canal preparation

Erbium lasers have been advocated for use in root canal because of their ability to ablate dentin and remove biologic debris in the root canal space. This study evaluated the ability of an Er:YAG laser to remove dentin predictably in the root canal system and its cleaning ability. Twenty-eight single-rooted extracted teeth were assigned into two groups. The first group was cleaned and shaped using crown-down technique with GT rotary files (control). The second group used an Er:YAG laser with ceramic tip, above the dentin ablation threshold for root canal shaping. A separate group of three teeth was evaluated for cleanliness using an Er:YAG laser with spiral tips. Amount of dentin removed in the buccal-lingual and mesial-distal directions was measured, the data analyzed by ANOVA. Surface characteristics were qualitatively examined. The control group produced cleaner, better shaped root canals, faster than the Er:YAG group. The Er:YAG group removed more dentin in the coronal portion but less in the middle and apical thirds. The Er:YAG with spiral tip group left a dense smear layer in the middle and apical thirds. The Er:YAG group was subject to procedural errors more often than the control group. The Erbium laser studied was equivalent to rotary files in the coronal and middle thirds but not in the apical thirds of the root canal system.