On the formation of circulating patterns of excitation in anisotropic excitable media

We present a model of excitable media with the feature that it has a vulnerable phase during which a premature current stimulus will result in the formation of a reentrant selfsustained wave of excitation. The model exploits anisotropic coupling of identical cells, and is therefore useful as a model for the myocardium. We give rigorous verification that there is a vulnerable phase, and demonstrate numerically that permanently rotating waves are formed. Finally, it is shown that the direction of fastest propagation in myocardium is not necessarily the direction of highest safety factor, contrary to commonly accepted opinion.     

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.

     

A mathematical model for the vulnerable phase in myocardium

We present a model of excitable media with the feature that it has a vulnerable phase during which a premature current stimulus will result in the formation of a reentrant self-sustained wave of excitation. The model exploits anisotropic coupling of identical cells, and is therefore useful as a model for the myocardium. We discuss why there is a vulnerable phase and how to determine it quantitatively in models of excitable media, and we demonstrate numerically that permanently rotating waves are formed when a stimulus is applied during this vulnerable phase. Finally, it is shown that the direction of fastest propagation in myocardium is not necessarily the direction of highest safety factor, contrary to commonly accepted opinion. As a result, a reentrant wave is formed after a stimulus is blocked in the axial direction and successfully propagates away from the stimulus site in the lateral direction.     

Different sensitivities of two mechanisms of excitation waves in heart tissue to anti-arrhythmia agents--blockers of fast sodium currents

In experiments with rabbit ventricular tissue sensitivity of two kinds of spiral wave sources of excitation to fast sodium current inhibition was compared. These spiral wave sources were circulation in a ring around an obstacle and circulation in tissue without an obstacle (reverberator). It was observed that after application of antiarrhythmic drugs lidocaine or mexiletine there was a prominent growth of cycle length of reverberator during first few seconds of circulation and a little change of cycle length for the circus movement around obstacle. It is proposed that different sensitivity of both kinds of spiral wave sources to antiarrhythmic drugs can be used for their distinguishing in clinical practice.     

Unidirectional block of propagation of a single autowave in a narrow gap and emergence of a two-dimensional reentry depends on geometry of the obstacle and on excitability of the media

Using mathematical simulation we show that the occurrence of excitation wave circulation (reentry) around an unexcitable obstacle depends on both the geometry of the obstacle and the excitation threshold. The reentry formation is shown to take place in a wide range of model parameters.     

Problems related to infarct size measurements in the rat heart.

The feasibility of measuring the extent of hypoperfused myocardium and the infarct size was examined in rat hearts after occlusion of the left coronary artery. The extent of hypoperfused myocardium was examined by autoradiography and after perfusion with fluorescent microspheres. Both methods appeared unreliable in this model. Triphenyltetrazolium chloride (TTC) staining, however, provided a distinct demarcation line between viable myocardium, which was stained red, and the necrotic myocardium, consistent with the ultrastructural border between normal and severely damaged myocytes 5 h after coronary occlusion. TTC staining gives the best demarcation of ischemic tissues. In verapamil-treated rats, there was an apparent reduction in infarct size as compared with untreated rats; 20% reduction in infarct size 5 h after coronary occlusion and 12% reduction after 24 h. There was, however, a large postoperative mortality among the verapamil-treated rats. These problems, and the nonuniform infarct size in rats, may in part explain why infarct size limitation by verapamil has been reported from rat experiments, but not from clinical trials.     

Sequential pattern of the propagation of excitation in the heart of the sheep Ovis brachyurae

With the aid of intramural multipolar technique, the earliest focus of the depolarization is revealed in the myocard thickness of the cranioventral region of the right atrium of the sheep. From there the depolarization wave with a saw-edged front is spread along the thickness of the atria. The chronotopography of the intramural activation wave front shows a more complicated picture of the atrial excitation than a smiply radial one. Apparently it is connected with the presence of the atrial conduction system. The main mass of myocardium of free ventricle walls and the lower two thirds of the septum are activated by means of multifocal depolarization. The base third of the septum is the last to be activated. These features of excitation of the ovine ventricle myocardium can be explained by special character of distribution of the Purkinje fibers in myocardium ventricles.     

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.     

Formation of myocardium after the initial development of the linear heart tube.

Well after formation of the primary linear heart tube, the mesenchymal cardiac septa become largely myocardial, and myocardial sleeves are formed along the caval and pulmonary veins. This second wave of myocardium formation can be envisioned to be the result of recruitment of cardiomyocytes by differentiation from flanking mesenchyme and/or by migration from existing myocardium (myocardialization). As a first step to elucidate the underlying mechanism, we studied in chicken heart development the formation of myocardial cells within intra- and extracardiac mesenchymal structures. We show that the second wave of myocardium formation proceeds in a caudal-to-cranial gradient in vivo. At the venous pole, loosely arranged networks of cardiomyocytes are observed in the dorsal mesocardium from H/H19 onward, in the atrioventricular cushion region from H/H26 onward, and in the proximal outflow tract (conus) from H/H29 onward. The process is completed at H/H stage 43. Subsequently, we determined the potential of the different cardiac compartments to form myocardial networks in a 3D in vitro culture assay. This analysis showed that the competency to form myocardial networks in vitro is a characteristic of the myocardium that is flanked by intra- or extracardiac mesenchyme, i.e., the inflow tract, atrioventricular canal, and outflow tract. These cardiac compartments can be induced to form myocardial networks by a temporally released or secreted signal that is similar throughout the entire heart. Atrial and ventricular compartments are not competent and do not produce the inducer. Moreover, cardiac cushion mesenchyme was found to be able to (trans-)differentiate into cardiomyocytes in the in vitro culture assay. The combined observations suggest that a common mechanism and molecular regulatory pathway underlies the recruitment of mesodermal cells into the cardiogenic lineage during this second wave of myocardium formation through the entire heart.     

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.     

Relaxation of the myocardium of the perfused and ischaemic rabbit heart

The decrease in the rate of relaxation of the myocardium during ischaemic impairment of metabolic processes is accompanied by a decrease in the size of contraction. If we stimulate the ischaemic heart with irregularly distributed pulses we can achieve, by an extrasystolic potentiation mechanism, isolated contractions. If we stimulate the ischaemic heart with irregularly distributed pulses we can achieve, by an extrasystolic potentiation mechanism, isolated contractions of the same size as average contractions in normal perfusion. When comparing the relaxation of such contractions in 15 perfused rabbit hearts, we found a linear correlation between the relaxation rate and the size of the contractions. If we relate to relaxation rate to contraction size, the relaxation rate in early ischaemia (1 min after stopping perfusion) is thus in most cases normal, despite the marked decrease in the size of the contractions. The size of the contractions of the ischaemic mammalian myocardium thus seems to diminish before relaxation (which is likewise energy-dependent) is affected.     

The emergence of synchronization behavior in Physarum polycephalum and its particle approximation

The regeneration process of contractile oscillation in the plasmodium of Physarum polycephalum is investigated experimentally and modelled computationally. When placed in a well, the Physarum cell restructures the body (fusion of small granule-like cells) and shows various complex oscillation patterns. After it completed the restructuring and regained synchronized oscillation within the body, the cell shows bilateral oscillation or rotating wave pattern. This regeneration process did not depend on the well size and all the cases tested here showed similar time course. Phase synchronization analysis based on Hilbert Transform also suggested that the cell can develop a fully synchronized oscillation within a fixed time no matter what the cell size is. A particle-based computational model was developed in order to model the emergence of oscillation patterns. Particles employing very simple and identical sensory and motor behaviors interacted with each other via the sensing and deposition of chemoattractants in a diffusive environment. From a random and almost homogeneous distribution, emergent domains of oscillatory activity emerged. By increasing the sensory radius the model simulated the regeneration process of the real plasmodium. In addition, the model replicated the rotating wave and bilateral oscillation pattern when the sensory radius was increased. The results suggest that complex emergent oscillatory behaviors (and thus the high-level systems which may utilize them, such as pumping and transport mechanisms) may be developed from simple materials inspired by Physarum slime mold.     

Interaction between spiral and paced waves in cardiac tissue

For prevention of lethal arrhythmias, patients at risk receive implantable cardioverter-defibrillators, which use high-frequency antitachycardia pacing (ATP) to convert tachycardias to a normal rhythm. One of the suggested ATP mechanisms involves paced-induced drift of rotating waves followed by their collision with the boundary of excitable tissue. This study provides direct experimental evidence of this mechanism. In monolayers of neonatal rat cardiomyocytes in which rotating waves of activity were initiated by premature stimuli, we used the Ca(2+)-sensitive indicator fluo 4 to observe propagating wave patterns. The interaction of the spiral tip with a paced wave was then monitored at a high spatial resolution. In the course of the experiments, we observed spiral wave pinning to local heterogeneities within the myocyte layer. High-frequency pacing led, in a majority of cases, to successful termination of spiral activity. Our data show that 1) stable spiral waves in cardiac monolayers tend to be pinned to local heterogeneities or areas of altered conduction, 2) overdrive pacing can shift a rotating wave from its original site, and 3) the wave break, formed as a result of interaction between the spiral tip and a paced wave front, moves by a paced-induced drift mechanism to an area where it may become unstable or collide with a boundary. The data were complemented by numerical simulations, which was used to further analyze experimentally observed behavior.     

The resolution capacity and the accuracy of acoustic measurement of sound frequency

It was shown that processes occurring in the internal air cochlea, which represents a wave guide with a travelling wave and resonance in the critical layer, are crucial for the resolution capacity and the accuracy of measurement of sound frequency by an acoustic analyzer.     

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.     

Myosin heavy chain isoforms in the myocardium of the atrioventricular junction of Scyliorhinus canicula (Chondrichthyes,Carcharhiniformes)

The atrioventricular junction of the fish heart, namely the segment interposed between the single atrium and the single ventricle, has been studied anatomically and histologically in several chondrichthyan and teleost species. Nonetheless, knowledge about myosin heavy chain (MyHC) in the atrioventricular myocardium remains scarce. The present report is the first one to provide data on the MyHC isoform distribution in the myocardium of the atrioventricular junction in chondrichthyans, specifically in the lesser spotted dogfish, Scyliorhinus canicula, a shark species whose heart reflects the primitive cardiac anatomical design in gnathostomes. Hearts from five dogfish were examined using histochemical and immunohistochemical techniques. The anti-MyHC A4.1025 antibody was used to detect differences in the occurrence of MyHC isoforms in the dogfish, as the fast-twitch isoforms MYH2 and MYH6 have a higher affinity for this antibody than the slow-twitch isoforms MYH7 and MYH7B. The histochemical findings show that myocardium of the atrioventricular junction connects the trabeculated myocardium of the atrium with the trabeculated layer of the ventricular myocardium. The immunohistochemical results indicate that the distribution of MyHC isoforms in the atrioventricular junction is not homogeneous. The atrial portion of the atrioventricular myocardium shows a positive reactivity against the A4.1025 antibody similar to that of the atrial myocardium. In contrast, the ventricular portion of the atrioventricular junction is not labelled, as is the case with the ventricular myocardium. This dual condition suggests that the myocardium of the atrioventricular junction has two contraction patterns: the myocardium of the atrial portion contracts in line with the atrial myocardium, whereas that of the ventricular portion follows the contraction pattern of the ventricular myocardium. Thus, the transition of the contraction wave from the atrium to the ventricle may be established in the atrioventricular segment because of its heterogeneous MyHC isoform distribution. The findings support the hypothesis that a distinct MyHC isoform distribution in the atrioventricular myocardium enables a synchronous contraction of inflow and outflow cardiac segments in vertebrates lacking a specialized cardiac conduction system.     

Success and failure of biphasic shocks: results of bidomain simulations.

The mechanisms behind the superiority of optimal biphasic defibrillation shocks over monophasic are not fully understood. This simulation study examines how the shock polarity and second-phase magnitude of biphasic shocks influence the virtual electrode polarization (VEP) pattern, and thus the outcome of the shock in a bidomain model representation of ventricular myocardium. A single spiral wave is initiated in a two-dimensional sheet of myocardium that measures 2 x 2 cm(2). The model incorporates non-uniform fiber curvature, membrane kinetics suitable for high strength shocks, and electroporation. Line electrodes deliver a spatially uniform extracellular field. The shocks are biphasic, each phase lasting 10 ms. Two different polarities of biphasic shocks are examined as the first-phase configuration is held constant and the second-phase magnitude is varied between 1 and 10 V/cm. The results show that for each polarity, varying the second-phase magnitude reverses the VEP induced by the first phase in an asymmetric fashion. Further, the size of the post-shock excitable gap is dependent upon the second-phase magnitude and is a factor in determining the success or failure of the shock. The maximum size of a post-shock excitable gap that results in defibrillation success depends on the polarity of the shock, indicating that the refractoriness of the tissue surrounding the gap also contributes to the outcome of the shock.     

Overcoming obstacles: the effect of obstacles on locomotor performance and behaviour

Sprinting and jumping ability are key performance measures that have been widely studied in vertebrates. The vast majority of these studies, however, use methodologies that lack an ecological context by failing to consider the complex habitats in which many animals live. Because successfully navigating obstacles within complex habitats is critical for predator escape, running, climbing, and/or jumping performance are each likely to be exposed to selection. In the present study, we quantify how behavioural strategies and locomotor performance change with increasing obstacle height. Obstacle size had a significant influence on behaviour (e.g. obstacle crossing strategy, intermittent locomotion) and performance (e.g. sprint speed, jump distance). Jump frequency and distance increased with obstacle size, suggesting that it likely evolved because it is more efficient (i.e. it reduces the time and distance required to reach a target position). Jump angle, jump velocity, and approach velocity accounted for 58% of the variation in jump distance on the large obstacle, and 33% on the small obstacle. Although these variables have been shown to significantly influence jump distance in static jumps, they do not appear to be influential in running (dynamic) jumps onto a small obstacle. Because selection operates in simple and complex habitats, future studies should consider quantifying additional measures such as jumping or climbing with respect to the evolution of locomotion performance. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.     

Pim-1 regulates cardiomyocyte survival downstream of Akt

The serine-threonine kinases Pim-1 and Akt regulate cellular proliferation and survival. Although Akt is known to be a crucial signaling protein in the myocardium, the role of Pim-1 has been overlooked. Pim-1 expression in the myocardium of mice decreased during postnatal development, re-emerged after acute pathological injury in mice and was increased in failing hearts of both mice and humans. Cardioprotective stimuli associated with Akt activation induced Pim-1 expression, but compensatory increases in Akt abundance and phosphorylation after pathological injury by infarction or pressure overload did not protect the myocardium in Pim-1-deficient mice. Transgenic expression of Pim-1 in the myocardium protected mice from infarction injury, and Pim-1 expression inhibited cardiomyocyte apoptosis with concomitant increases in Bcl-2 and Bcl-X(L) protein levels, as well as in Bad phosphorylation levels. Relative to nontransgenic controls, calcium dynamics were significantly enhanced in Pim-1-overexpressing transgenic hearts, associated with increased expression of SERCA2a, and were depressed in Pim-1-deficient hearts. Collectively, these data suggest that Pim-1 is a crucial facet of cardioprotection downstream of Akt.