Distribution of excitation frequencies on the epicardial and endocardial surfaces of fibrillating ventricular wall of the sheep heart.

Tissue heterogeneities may play an important role in the mechanism of ventricular tachycardia (VT) and fibrillation (VF) and can lead to a complex spatial distribution of excitation frequencies. Here we used optical mapping and Fourier analysis to determine the distribution of excitation frequencies in >20 000 sites of fibrillating ventricular tissue. Our objective was to use such a distribution as a tool to quantify the degree of organization during VF. Fourteen episodes of VT/VF were induced via rapid pacing in 9 isolated, coronary perfused, and superfused sheep ventricular slabs (3x3 cm(2)). A dual-camera video-imaging system was used for simultaneous optical recordings from the entire epi- and endocardial surfaces. The local frequencies of excitation were determined at each pixel and displayed as dominant frequency (DF) maps. A typical DF map consisted of several (8.2+/-3.6) discrete areas (domains) with a uniform DF within each domain. The DFs in adjacent domains were often in 1:2, 3:4, or 4:5 ratios, which was shown to be a result of an intermittent Wenckebach-like conduction block at the domain boundaries. The domain patterns were relatively stable and could persist from several seconds to several minutes. The complexity in the organization of the domains, the number of domains, and the dispersion of frequencies increased with the rate of the arrhythmia. Domain patterns on the epicardial and endocardial surfaces were not correlated. Sustained epicardial or endocardial reentry was observed in only 3 episodes. Observed frequency patterns during VT/VF suggest that the underlying mechanism may be a sustained intramural reentrant source interacting with tissue heterogeneities.

Rectification of the background potassium current: a determinant of rotor dynamics in ventricular fibrillation.

Ventricular fibrillation (VF) is the leading cause of sudden cardiac death. Yet, the mechanisms of VF remain elusive. Pixel-by-pixel spectral analysis of optical signals was carried out in video imaging experiments using a potentiometric dye in the Langendorff-perfused guinea pig heart. Dominant frequencies (peak with maximal power) were distributed throughout the ventricles in clearly demarcated domains. The fastest domain (25 to 32 Hz) was always on the anterior left ventricular (LV) wall and was shown to result from persistent rotor activity. Intermittent block and breakage of wavefronts at specific locations in the periphery of such rotors were responsible for the domain organization. Patch-clamping of ventricular myocytes from the LV and the right ventricle (RV) demonstrated an LV-to-RV drop in the amplitude of the outward component of the background rectifier current (I(B)). Computer simulations suggested that rotor stability in LV resulted from relatively small rectification of I(B) (presumably I(K1)), whereas instability, termination, and wavebreaks in RV were a consequence of strong rectification. This study provides new evidence in the isolated guinea pig heart that a persistent high-frequency rotor in the LV maintains VF, and that spatially distributed gradients in I(K1) density represent a robust ionic mechanism for rotor stabilization and wavefront fragmentation.

Simulation of voltage-sensitive optical signals in three-dimensional slabs of cardiac tissue: application to transillumination and coaxial imaging methods.

Voltage-sensitive dyes are an important tool in visualizing electrical activity in cardiac tissue. Until today, they have mainly been applied in cardiac electrophysiology to subsurface imaging. In the present study, we assess different imaging methods used in optical tomography with respect to their effectiveness in visualizing 3D cardiac activity. To achieve this goal, we simulate optical signals produced by excitation fronts initiated at different depths inside the myocardial wall and compare their properties for various imaging modes. Specifically, we consider scanning and broad-field illumination, including trans- and epi-illumination. We focus on the lateral optical resolution and signal intensity, as a function of the source depth. Optical diffusion theory is applied to derive a computationally efficient approximation of the point-spread function and to predict voltage-sensitive signals. Computations were performed both for fluorescent and absorptive voltage-sensitive dyes. Among all the above-mentioned methods, fluorescent coaxial scanning yields the best resolution (<2.5 mm) and gives the most information about the intramural cardiac activity.

Intramural wave propagation in cardiac tissue: asymptotic solutions and cusp waves.

The cardiac muscle is well known to conduct electric impulses anisotropically, showing a larger conduction velocity along than across fibers. Fiber orientation is not uniform within the cardiac wall, but rotates by as much as 180 degrees throughout the wall thickness. Numerical simulations and experiments have indicated that this rotational anisotropy considerably affects the spread of excitation in cardiac tissue: the wave front shows a complex intramural shape with trailing cusps. The cusps can travel across layers and reach the epicardial and endocardial surfaces where they cause apparent accelerations of propagation. In the present study we provide an analytical description of the asymptotic wave front, as well as of cusp waves. We investigate the motion of cusp waves, based on the assumption that they occur at the intersection of asymptotic solutions, and we show that our theoretical analysis is in close agreement with numerical simulations. The asymptotic solutions are found to be determined purely by the fiber organization within the cardiac wall, independent of the excitable properties of cardiac tissue.

Shaping of a scroll wave filament by cardiac fibers.

Scroll waves of electrical excitation in heart tissue are implicated in the development of lethal cardiac arrhythmias. Here we study the relation between the geometry of myocardial fibers and the equilibrium shape of a scroll wave filament. Our theory accommodates a wide class of myocardial models with spatially varying diffusivity tensor, adjusted to fit fiber geometry. We analytically predict the exact equilibrium shapes of the filaments. The major conclusion is that the filament shape is a compromise between a straight line and full alignment with the fibers. The degree of alignment increases with the anisotropy ratio. The results, being purely geometrical, are independent of details of ionic membrane mechanisms. Our theoretical predictions have been verified to excellent accuracy by numerically simulating the stable equilibration of a scroll filament in a model of the FitzHugh-Nagumo type.

[Initiation mechanism of the first extrasystole in short-term atrial arrhythmia]. / Mekhanizm vozniknoveniia pervoi ékstrasistoly pri korotkozhivushchei predserdnoi aritmii.

Excitation propagation during arrhythmias induced by electric stimulation into the vulnerable phase was studied on rabbit' left auricle bands by mapping (in 80-150 points). Arrhythmias were initiated under normal conditions and at acetylcholine background (0.2 mg/l). Recording of the electrical activity was realized by surface electrodes. The first extrasystole wave was shown to be conditioned as a result of the appearance of one or several point or ring-like excitation sources on the myocardium surface. There is no continuous circulation of the excitation wave on the surface of the cardiac tissue. Probable mechanisms of the appearance of such sources are discussed. Excitation circulation in the myocardium thickness (intramural re-entry) is considered as a more probable mechanism.

[Mechanism of spiral waves initiation in active media, connected with critical curvature phenomenon]. / Mekhanizm vozniknoveniia spiral'nykh voli v aktivnykh sredakh, sviazannyi s iavleniem kriticheskoi krivizny.

While studying on a digital computer a dimeric active medium described by Fitz-Hew, Nagumo equations a new mechanism of spiral waves initiation was observed. It has been shown that when the wave rounds the barrier where Neuman baundary conditions are set (dE/dn = 0) the wave separates from the border and the breakage of the front takes place; then it develops into a spiral. The effect is observed when the curvature of breakage is close to the critical one for the given medium. The results obtained may be of interest for explaining the mechanism of initiation of spiral waves in the damaged regions of the myocardium tissues.

[Experimental evaluation of the critical size of the myocardial reverberator]. / Eksperimental'naia otsenka kriticheskogo razmera reverberatora v miokarde.

Two independent experimental methods for estimating the minimal size of myocardium where a rotating wave could still arise (the crucial wave size) were proposed and realized. The first one was based on measuring the wavelength, the second--on the determination of the crucial size of an unexcited obstacle. The crucial rotating wave size in the myocardium without an obstacle was shown to increase under lidocaine effect.

[Fiber interaction during impulse propagation in smooth muscle and myocardial tissues. Electrotonic interaction]. / Vzaimodeistvie volokon pri rasprostranenii vozbuzhdeniia v gladkomyshechnoi i miokardial'noi tkaniakh. Elektrotonicheskoe vzaimodeistvie.

Electrotonic potential appearing in a single muscle fibre during excitation spread was calculated in the mathematical model of closely packed parallel fibres. Electrotonic depolarization values for heart and smooth muscle were shown to be 10--20 mV, that is comparable to the excitation threshold value. Tissue parameter values were estimated where the coupling coefficient was maximal. The parameter values proved to be similar to those measured in heart and smooth muscles. The data obtained indicate that the electrotonic interaction of muscle fibres should play a significant role in excitation conduction.

[Effect of specialized contacts on fiber interaction during the spread of excitation in smooth muscle and myocardial tissues]. / Vliianie spetsializirovannykh kontaktov na vzaimodeistvie volokon pri rasprostranenii vozbuzhdeniia i gladkomyshechnoi i miokardial'nykh tkanei.

A mathematical model of closely packed parallel muscle fibres with side by side junctions was studied. High coupling coefficient for both heart and smooth muscle fibres was shown to be available at rather low junction permeability. The coupling coefficient for heart fibers is equal to 0.5 at specific junction membrane resistance as high as 100 omega cm2. For the same coupling ratio in smooth muscle the specific junction membrane resistance should be even greater (1000 omega cm2). The role of nexuses and tight junctions in conduction of excitation is discussed.

[Electric coupling in cells without highly permeable cell contacts]. / Elektricheskaia sviaz' kletok bez vysokopronitsaemykh kletochnykh kontaktov

A mathematical model of two contacting cells is studied. Simple analytical formula are obtained which connect the transmission coefficient k with the parameters of contact zone (dimension of the contact region, resistence of the contact membrane, specific resistence of the interslit medium, width of intercellular slit) and with geometry of contacting cells. It is shown that in the absence of conductivity increase in the contact zone the values of transmission coefficient. k = 0.2 divided by 0.3. are available. k is evaluated for early embryonic cells. The mechanisms of electric coupling in early embryonic cells and in heart tissue are discussed.

[Drift of vortex in the myocardium]. / Dreif vikhria v miokarde.

The behavior of a vortex in rabbit myocardium with artificial inhomogeneity was studied using mapping technique. The inhomogeneity was created by perfusion of a part of the preparation with quinidine solution. Quinidine increased the refractory period of the myocardium and diminished the conduction velocity. It has been found that the vortex drifts along the border of the inhomogeneity because of the difference of refractory periods. The drift velocity was about 4 cm/s, which was five times less than the wave velocity. The direction of the drift was determined by the vector (----omega X----delta R), where ----omega is the angular velocity of vortex rotation, and ----delta R is a gradient of the refractory period.

[Analysis of the electrophysiologic characteristics of the trabecular membrane in the atria of frogs by recording ionic currents during potential fixation. II. Accomodation. Repeated responses. Anode-breaking excitation]. / Analiz élektrofiziologicheskikh kharakteristik membrany trabekuly predserdiia liagushki po zapisiam ionnykh tokov pri fiksatsii potentsiala. II. Akkomodatsiia. Povtornye otvety. Andonorazmykatel'noe vozbuzhdenie

Measurements were carried out by the method of double succrose gap. Accommodation was practically absent in all the preparations studied: the minimal gradient was not observed, the mean value of accommodation was 0.02 rheobasa/s, saturation current/H practically coincided with the current of rheobase IO(IH/IO = 1.0 +/- 0.1). Repeated responses were initiated in 1/3 of samples. The current of initiating the repeated responses IRR was insignificantly higher than the rheobase one (IRR/IO = 1.2 +/- 0.1). In the samples where the replated responses were absent the effect of uneven depolarization was observed. At depolarization current which was insignificantly higher than the threshold one (IO), the potential did not return to the resting potential and was settled at the level of -20 mV. Anode disconnecting excitation was absent in all the samples. The hyperpolarization level varied from -90 to -160 mV. The data obtained well agree with the results of the analysis of the mathematical model of frog auricle trabecula membrane constructed on the basis of the data on the potential fixation.

[Sharp increase in refractory period induced by oxidation suppression in Fitz Hugh-Nagumo model. New mechanism of antiarrhythmic drug action]. / Rezkii rost refrakternosti pri podavlenii vozbudimosti v modeli Fitz Hugh-Nagumo. Novyi mekhanizm deistviia antiaritmikov.

A change in fast inward and slow outward currents and their time constants was simulated in Fitz Hugh-Nagumo model. A decrease in fast inward current was shown to increase the refractory period. The same result was observed when the slow current was increased or its time constant was decreased. These results were used to explain the antiarrhythmic drug action. The antiarrhythmic effect of drugs blocking fast inward current should be stronger in the depressed myocardial tissue than in the normal one.

[Increase of heterogeneities at the interface of decrement conduction in Hodgkin-Huxley model]. / Rost neodnorodnostei na granitse oblasti dekrementnogo provedeniia v modeli Hodgkin-Huxley.

Spatial heterogeneity was simulated by a 2-fold increase in either of gNa, gK, g1 in the central part of the fibre. The interval-dependent conduction block was not observed in the cable with normal gNa, while the uniform decrease in gNa along the fibre resulted were the block appearance. Difference in the refractory period of these parts of the fibre were the higher, the lower was gNa. The mechanism of this phenomenon was investigated. The results obtained can be used for understanding the mechanism of post infarction arrhythmias.

[Instabilities of autowaves in excitable media associated with critical curvature phenomena]. / Neustoichivosti avtovoln v vozbudimykh sredakh, sviazannye s iavleniem kriticheskoi krivizny.

While studying a two-dimensional excitable medium described by the Fitz--Hugh equation on a digital computer a new type of instabilities was discovered which had no analogy in one-dimensional systems. It has been shown that when the wave encounters upon an obstacle the front breaks, diverge, thus destroying the excitation waves. Initiation of such instabilities is associated with critical curvative phenomenon. The instabilities appear when the front curvature in the region of wave break is greater than the critical one for the given medium. The instabilities found are observed when medium excitability is suppressed. This phenomenon may be related to the processes which occur in the damage regions of the myocardium tissue.

[Myocardial parameters controlling vulnerability. Analysis of mathematical models]. / Parametry miokarda, kontroliruiushchie uiazvimost'. Analiz matematicheskikh modelei.

Vulnerability induced by application of a properly timed premature stimulus was studied on mathematical models. Two mechanisms of vulnerability 1) reentry, 2) focal reexcitation were analysed. Tissue with a region of increased refractory period Rmax was simulated on Wiener's type model. The influence of high refractoriness region dimensions and tissue parameters on the duration of vulnarable period was studied. Reentry was shown to appear on the border of high refractoriness region, which minimal length lmin being the shorter, the greater was tau (maximal latency of response) and epsilon (epsilon = deltaR/R--degree of heterogeneity). The dependence of vulnerable period duration on current strength was computed for Nobel's model. The dip-phenomenon was found in this model, the vulnerable zone was located above the minimal value of threshold.

[Interaction of spiral and flat periodic autowaves in an active medium]. / Vzaimodeistvie spiral'nykh i ploskikh periodicheskikh avtovoln v aktivnoi srede.

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.

[Analysis of electrophysiologic characteristics of the frog atrial trabecular membrane by ionic currents at a fixed potential]. / Analiz élektrofiziologicheskikh kharakteristik membrany trabekuly predserdiia liagushki po ionnym tokam fiksatsii potentsiala

The membrane of frog auricle trabecula was studied by the method of potential fixation. On the basis of the records of ionic currents zyro-isoclines of approximative differential equations of the 2nd order, describing the membrane studied, were plotted. The mathematical model of this membrane was analysed with the help of qualitative methods of the oscillation theory. The analysis has shown that the following phenomena which have not been observed experimentally should take place in the membrane of frog auricle trabecula: 1. absence of the minimum gradient and accomodation growth of thresholds; 2. absence of anode-disconnecting excitation; 3. coincidence of the current of repeated responses with that of the rheobase; 4. uneven depolarization.