Generation and escape of local waves from the boundary of uncoupled cardiac tissue

We aim to understand the formation of abnormal waves of activity from myocardial regions with diminished cell-to-cell coupling. En route to this goal, we studied the behavior of a heterogeneous myocyte network in which a sharp coupling gradient was placed under conditions of increasing network automaticity. Experiments were conducted in monolayers of neonatal rat cardiomyocytes using heptanol and isoproterenol as means of altering cell-to-cell coupling and automaticity, respectively. Experimental findings were explained and expanded using a modified Beeler-Reuter numerical model. The data suggest that the combination of a heterogeneous substrate, a gradient of coupling, and an increase in oscillatory activity of individual cells creates a rich set of behaviors associated with self-generated spiral waves and ectopic sources. Spiral waves feature a flattened shape and a pin-unpin drift type of tip motion. These intercellular waves are action-potential based and can be visualized with either voltage or calcium transient measurements. A source/load mismatch on the interface between the boundary and well-coupled layers can lock wavefronts emanating from both ectopic sources and rotating waves within the inner layers of the coupling gradient. A numerical approach allowed us to explore how 1), the spatial distribution of cells, 2), the amplitude and dispersion of cell automaticity, and 3), the speed at which the coupling gradient moves in space affect wave behavior, including its escape into well-coupled tissue.     

Interaction of spiral and flat periodic autowaves in an active medium

Interaction between the rotating wave and a periodic external source in the model of Fitz Hugh--Nagumo type was computed. When the periods of the external source are longer than the rotation period of the spiral wave (T greater than Ts) the external source does not affect the spiral wave. At T less than Ts autowave synchronization effects are observed. The oscillation period predetermined by the external source is set in all the points of the medium except the neighbourhood of the spiral wave. The dislocation (wavebreak) persists in the medium drifting slowly at the angle to the wave vector of the flat waves. After the external source is eliminated, the spiral wave with the original period restores from this dislocation. When the dislocation reaches the interface, it disappears. In this case after the switching off of the external source the resting state is established. A theory of the drift is proposed which connects the drift velocity with the nucleus size and the rotation period of spiral wave.     

Spiral waves in two-dimensional models of ventricular muscle: formation of a stationary core.

Previous experimental studies have clearly demonstrated the existence of drifting and stationary electrical spiral waves in cardiac muscle and their involvement in cardiac arrhythmias. Here we present results of a study of reentrant excitation in computer simulations based on a membrane model of the ventricular cell. We have explored in detail the parameter space of the model, using tools derived from previous numerical studies in excitation-dynamics models. We have found appropriate parametric conditions for sustained stable spiral wave dynamics (1 s of activity or approximately 10 rotations) in simulations of an anisotropic (ratio in velocity 4:1) cardiac sheet of 2 cm x 2 cm. Initially, we used a model that reproduced well the characteristics of planar electrical waves exhibited by thin sheets of sheep ventricular epicardial muscle during rapid pacing at a cycle length of 300 ms. Under these conditions, the refractory period was 147 ms; the action potential duration (APD) was 120 ms; the propagation velocity along fibers was 33 cm/s; and the wavelength along fibers was 4.85 cm. Using cross-field stimulation in this model, we obtained a stable self-sustaining spiral wave rotating around an unexcited core of 1.75 mm x 7 mm at a period of 115 ms, which reproduced well the experimental results. Thus the data demonstrate that stable spiral wave activity can occur in small cardiac sheets whose wavelength during planar wave excitation in the longitudinal direction is larger than the size of the sheet. Analysis of the mechanism of this observation demonstrates that, during rotating activity, the core exerts a strong electrotonic influence that effectively abbreviates APD (and thus wavelength) in its immediate surroundings and is responsible for the stabilization and perpetuation of the activity. We conclude that appropriate adjustments in the kinetics of the activation front (i.e., threshold for activation and upstroke velocity of the initiating beat) of currently available models of the cardiac cell allow accurate reproduction of experimentally observed self-sustaining spiral wave activity. As such, the results set the stage for an understanding of functional reentry in terms of ionic mechanisms.     

Collision-Based Spiral Acceleration in Cardiac Media: Roles of Wavefront Curvature and Excitable Gap

We have previously shown in experimental cardiac cell monolayers that rapid point pacing can convert basic functional reentry (single spiral) into a stable multiwave spiral that activates the tissue at an accelerated rate. Here, our goal is to further elucidate the biophysical mechanisms of this rate acceleration without the potential confounding effects of microscopic tissue heterogeneities inherent to experimental preparations. We use computer simulations to show that, similar to experimental observations, single spirals can be converted by point stimuli into stable multiwave spirals. In multiwave spirals, individual waves collide, yielding regions with negative wavefront curvature. When a sufficient excitable gap is present and the negative-curvature regions are close to spiral tips, an electrotonic spread of excitatory currents from these regions propels each colliding spiral to rotate faster than the single spiral, causing an overall rate acceleration. As observed experimentally, the degree of rate acceleration increases with the number of colliding spiral waves. Conversely, if collision sites are far from spiral tips, excitatory currents have no effect on spiral rotation and multiple spirals rotate independently, without rate acceleration. Understanding the mechanisms of spiral rate acceleration may yield new strategies for preventing the transition from monomorphic tachycardia to polymorphic tachycardia and fibrillation.     

Electric field perturbations of spiral waves attached to millimeter-size obstacles

Reentrant spiral waves can become pinned to small anatomical obstacles in the heart and lead to monomorphic ventricular tachycardia that can degenerate into polymorphic tachycardia and ventricular fibrillation. Electric field-induced secondary source stimulation can excite directly at the obstacle, and may provide a means to terminate the pinned wave or inhibit the transition to more complex arrhythmia. We used confluent monolayers of neonatal rat ventricular myocytes to investigate the use of low intensity electric field stimulation to perturb the spiral wave. A hole 2-4 mm in diameter was created in the center to pin the spiral wave. Monolayers were stained with voltage-sensitive dye di-4-ANEPPS and mapped at 253 sites. Spiral waves were initiated that attached to the hole (n = 10 monolayers). Electric field pulses 1-s in duration were delivered with increasing strength (0.5-5 V/cm) until the wave terminated after detaching from the hole. At subdetachment intensities, cycle length increased with field strength, was sustained for the duration of the pulse, and returned to its original value after termination of the pulse. Mechanistically, conduction velocity near the wave tip decreased with field strength in the region of depolarization at the obstacle. In summary, electric fields cause strength-dependent slowing or detachment of pinned spiral waves. Our results suggest a means to decelerate tachycardia that may help to prevent wave degeneration.     

The Fundamental Structure and the Reproduction of Spiral Wave in a Two-Dimensional Excitable Lattice

In this paper we have systematically investigated the fundamental structure and the reproduction of spiral wave in a two-dimensional excitable lattice. A periodically rotating spiral wave is introduced as the model to reproduce spiral wave artificially. Interestingly, by using the dominant phase-advanced driving analysis method, the fundamental structure containing the loop structure and the wave propagation paths has been revealed, which can expose the periodically rotating orbit of spiral tip and the charity of spiral wave clearly. Furthermore, the fundamental structure is utilized as the core for artificial spiral wave. Additionally, the appropriate parameter region, in which the artificial spiral wave can be reproduced, is studied. Finally, we discuss the robustness of artificial spiral wave to defects.     

Spatially discordant alternans in cardiomyocyte monolayers

Repolarization alternans is a harbinger of sudden cardiac death, particularly when it becomes spatially discordant. Alternans, a beat-to-beat alternation in the action potential duration (APD) and intracellular Ca (Cai), can arise from either tissue heterogeneities or dynamic factors. Distinguishing between these mechanisms in normal cardiac tissue is difficult because of inherent complex three-dimensional tissue heterogeneities. To evaluate repolarization alternans in a simpler two-dimensional cardiac substrate, we optically recorded voltage and/or Cai in monolayers of cultured neonatal rat ventricular myocytes during rapid pacing, before and after exposure to BAY K 8644 to enhance dynamic factors promoting alternans. Under control conditions (n = 37), rapid pacing caused detectable APD alternans in 81% of monolayers, and Cai transient alternans in all monolayers, becoming spatially discordant in 62%. After BAY K 8644 (n = 28), conduction velocity restitution became more prominent, and APD and Cai alternans developed and became spatially discordant in all monolayers, with an increased number of nodal lines separating out-of-phase alternating regions. Nodal lines moved closer to the pacing site with faster pacing rates and changed orientation when the pacing site was moved, as predicted for the dynamically generated, but not heterogeneity-based, alternans. Spatial APD gradients during spatially discordant alternans were sufficiently steep to induce conduction block and reentry. These findings indicate that spatially discordant alternans severe enough to initiate reentry can be readily induced by pacing in two-dimensional cardiac tissue and behaves according to predictions for a predominantly dynamically generated mechanism.     

Region [corrected] of slowed conduction acts as core for spiral wave reentry in cardiac cell monolayers

Pathophysiological heterogeneity in cardiac tissue is related to the occurrence of arrhythmias. Of importance are regions of slowed conduction, which have been implicated in the formation of conduction block and reentry. Experimentally, it has been a challenge to produce local heterogeneity in a manner that is both reversible and well controlled. Consequently, we developed a dual-zone superfusion chamber that can dynamically create a small (5 mm) central island of heterogeneity in cultured cardiac cell monolayers. Three different conditions were studied to explore the effect of regionally slowed conduction on wave propagation and reentry: depolarization by elevated extracellular potassium, sodium channel inhibition with lidocaine, and cell-cell decoupling with palmitoleic acid. Using optical mapping of transmembrane voltage, we found that the central region of slowed conduction always served as the core region around which a spiral wave formed and then revolved following a period of rapid pacing. Because of the localized slowing in the core region, we observed experimentally for the first time an S shape of the spiral wave front near its tip. These results indicate that a small region of slowed conduction can play a crucial role in the formation, anchoring, and modulation of reentrant spiral waves.     

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.     

Effect of the form and anisotropy of the left ventricle on the drift of spiral waves

Three-dimensional spiral waves of electrical excitation in the myocardium are sources of dangerous cardiac arrhythmias. In this work, the dynamics of spiral waves of electrical excitation were studied in a symmetric anatomical model of the human heart left ventricle and a realistic ionic cell model of the human ventricular myocardium. Three factors that affect the drift waves in the heart were compared for the first time: the geometry of the heart wall, myocardial anisotropy, and wave chirality. Cardiac anisotropy was identified as a main factor in determining the drift of spiral waves. In the isotropic case, the dynamics were determined by the wall thickness, but did not depend on the wave chirality. In the anisotropic case, chirality was found to play a crucial role.

     

Attraction and repulsion of spiral waves by inhomogeneity of conduction anisotropy—a model of spiral wave interaction with electrical remodeling of heart tissue

Various forms of heart disease are associated with remodeling of the heart muscle, which results in a perturbation of cell-to-cell electrical coupling. These perturbations may alter the trajectory of spiral wave drift in the heart muscle. We investigate the effect of spatially extended inhomogeneity of transverse cell coupling on the spiral wave trajectory using a simple active media model. The spiral wave was either attracted or repelled from the center of inhomogeneity as a function of cell excitability and gradient of the cell coupling. High levels of excitability resulted in an attraction of the wave to the center of inhomogeneity, whereas low levels resulted in an escape and termination of the spiral wave. The spiral wave drift velocity was related to the gradient of the coupling and the initial position of the wave. In a diseased heart, a region of altered transverse coupling corresponds with local gap junction remodeling that may be responsible for stabilization-destabilization of spiral waves and hence reflect potentially important targets in the treatment of heart arrhythmias.     

Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model

Heterogeneity of cardiac tissue is an important factor determining the initiation and dynamics of cardiac arrhythmias. In this paper, we studied the effects of gradients of electrophysiological heterogeneity on reentrant excitation patterns using computer simulations. We investigated the dynamics of spiral waves in a two-dimensional sheet of cardiac tissue described by the Luo-Rudy phase 1 (LR1) ventricular action potential model. A gradient of action potential duration (APD) was imposed by gradually varying the local current density of K(+) current or inward rectifying K(+) current along one axis of the tissue sheet. We show that a gradient of APD resulted in spiral wave drift. This drift consisted of two components. The longitudinal (along the gradient) component was always directed toward regions of longer spiral wave period. The transverse (perpendicular to the gradient) component had a direction dependent on the direction of rotation of the spiral wave. We estimated the velocity of the drift as a function of the magnitude of the gradient and discuss its implications.     

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.     

Selection of Multiarmed Spiral Waves in a Regular Network of Neurons

Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.     

Hormonal and testing conditions for the induction of conditioned place preference by paced mating

The ability to control or pace the sexual interaction has important physiological and behavioral consequences for the female rat. Paced mating favors reproduction and induces a positive affective state as revealed by conditioned place preference (CPP). In the present experiment we evaluated: 1) If paced mating induces CPP in naturally cycling females; 2) If females developed a positive affective state if they paced the sexual interaction through a 1- or a 3-hole pacing chamber; 3) If females that mate with the same male without pacing the sexual interaction develop CPP. In the first experiment intact females were divided in 4 different groups; 2 paced the sexual interaction until receiving 1 or 3 ejaculations; the other 2 groups mated, without pacing the sexual interaction, until receiving 1 or 3 ejaculations. Only the group that paced the sexual interaction until receiving 3 ejaculations developed a positive affective state. In experiments 2 and 3 hormonally treated ovariectomized females were used. In experiment 2 females were allowed to pace the sexual interaction through a 1- or a 3-hole pacing chamber: A clear positive affective state was induced in both testing conditions. Finally, in experiment 3 females did not develop CPP for non-paced sex despite the fact that they mated with the same male in the conditioning sessions. These results demonstrate that the pattern of vaginocervical stimulation that the females received by engaging in approach and avoidance behaviors to pace the sexual interaction can induce a positive affective state in naturally cycling females. They also confirm the existence of a threshold of vaginocervical stimulation for paced mating to induce CPP in female rats.     

Voltage-mediated mechanism for calcium wave synchronization and arrhythmogenesis in atrial tissue

A wide range of atrial arrythmias are caused by molecular defects in proteins that regulate calcium (Ca) cycling. In many cases, these defects promote the propagation of subcellular Ca waves in the cell, which can perturb the voltage time course and induce dangerous perturbations of the action potential (AP). However, subcellular Ca waves occur randomly in cells and, therefore, electrical coupling between cells substantially decreases their effect on the AP. In this study, we present evidence that Ca waves in atrial tissue can synchronize in-phase owing to an order-disorder phase transition. In particular, we show that, below a critical pacing rate, Ca waves are desynchronized and therefore do not induce substantial AP fluctuations in tissue. However, above this critical pacing rate, Ca waves gradually synchronize over millions of cells, which leads to a dramatic amplification of AP fluctuations. We exploit an underlying Ising symmetry of paced cardiac tissue to show that this transition exhibits universal properties common to a wide range of physical systems in nature. Finally, we show that in the heart, phase synchronization induces spatially out-of-phase AP duration alternans which drives wave break and reentry. These results suggest that cardiac tissue exhibits a phase transition that is required for subcellular Ca cycling defects to induce a life-threatening arrhythmia.     

Extended paced mating tests induces conditioned place preference without affecting sexual arousal

One way to evaluate sexual arousal is by measuring approach behavior to sexual incentive stimuli. In our case we measure approach behavior to an originally non-preferred compartment which is associated with the physiological state induced by mating. This change of preference indicative of a positive affective (reward) state can be evaluated by conditioned place preference (CPP). We have shown that the CPP induced by paced mating is mediated by opioids. The administration of opioids also induces a reward state. The present study was designed to compare the rewarding properties of paced mating and a morphine injection. One group of females was allowed to pace the sexual interaction before being placed in the non-preferred compartment. In alternate sessions they received a morphine injection before being placed in the preferred compartment. In another group of females, the treatments were reversed. Only the females placed in the originally non-preferred compartment after paced mating changed their original preference, suggesting that paced mating induces a positive affective, reward, state of higher intensity than a morphine injection of 1 mg/kg. In a second experiment we determined if females allowed to pace the sexual interaction for 1 h would still developed CPP. No change in preference was observed in the females that mated for 1 h without pacing the sexual interaction. On the other hand, females that received between 10 and 15 paced intromissions as well as females that paced the sexual interaction for 1 h developed a clear CPP. The second experiment demonstrated that pacing is rewarding even in an extended mating session in which the females received around 25 intromissions and several ejaculations. These results further demonstrate the biological relevance associated with the ability of the female to space coital stimulation received during mating. This positive affective state will contribute to increase sexual arousal the next time a rat finds an appropriate mate.     

Left ventricular myocardal activation under ventricular paced beats in chickens Gallus gallus domesticus

The aim of the study was to advance our knowledge regarding the activation process of the ventricular myocardium in birds in which Purkinje fibres penetrate into the ventricular wall to reach the epicardium. A depolarization pattern of the left ventricular free wall was studied in chickens (Gallus gallus) during ventricular paced beats. Duration of the activation process of the left ventricular free wall is significantly increased during ventricular ectopic excitation as compared with sinus rhythm. Its lowest increase occurs during subendocardial pacing of the middle part of the left ventricle, but its greatest increase is observed during subepicardial pacing of the left ventricular base. Multifocality and mosaicity of depolarization of the left ventricular free wall myocardium in chicken are expressed in a considerably less degree during ventricular paced beats in comparison with sinus rhythm. During ventricular paced beats, excitation of the left ventricular free wall is mostly due to the successive spreading of the depolarization wave from pacing sites.     

The structure and stability of phospholipid bilayers by atomic force microscopy.

Atomic force microscopy (AFM) was used to investigate the structure, stability, and defects of the hydrophilic surfaces of Langmuir-Blodgett bilayer films of distearoylphosphatidylcholine (DSPC) and dipalmitoylphosphatidylethanolamine (DPPE) in the solid phase, and dilinoleoylphosphatidylethanolamine (DLPE) in the fluid phase. Their relative resilience to external mechanical stress by the scanning tip and by fluid exchange were also investigated. DPPE monolayers showed parallel ridges at the surface with a period of 0.49 nm, corresponding to the rows of aligned headgroups consistent with the known crystallographic structure. DSPC and DLPE monolayers did not show any periodic order. The solid DSPC and DPPE monolayers were stable to continued rastering by the AFM tip; however, the stability of DLPE monolayers depended on the pH of the aqueous environment. Structural defects in the form of monolayer gaps and holes were observed after fluid exchange, but the defects in DLPE monolayer at pH 11 were stable during consecutive scanning. At pH 9 and below, the defects induced by fluid exchange over DLPE monolayers were more extensive and were deformed easily by consecutive scanning of the AFM tip at a force of 10 nN. The pH dependence of resilience was explained by the increasing bending energy or frustration due to the high spontaneous curvature of DLPE monolayers at low pH. The tangential stress exerted by the AFM tip on the deformable monolayers eventually produced a ripple pattern, which could be described as a periodic buckling known as Shallamach waves.