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It was found via the mathematical simulation of the effect of fibroblasts on the electrical activity of the sinoatrial node cells that the interaction with fibroblasts through gap junctions increases the oscillation frequency of pacemakers. Under the effect of fibroblasts, the oscillation amplitude of a true pacemaker decreases until the end of the spontaneous activity. The oscillation amplitude of a latent pacemaker decreases considerably less.

We study spectral energy transformations in the electroencephalogram associated with visual evoked potentials initiated by red, green and yellow light flashes. With the aid of a complex continuous wavelet transform we show spectral energy changes to occur non-monotonically in delta, theta, alpha and beta bands. Each band has inherent energy flow patterns for 1s after stimulation. Energy flows in alpha and beta bands are alike and differ from those in theta and delta bands. Beta band power and energy flows are small.

We have studied the dynamics of reentry inside the sinoatrial node (SAN). We have found that reentry is unstable at high intercellular conductance. Rotating reentry induces a slow migrating crescent-shaped functional block near the SAN boundary. Abnormal conduction from atrial tissue into the SAN occurs after decay of the reentry. Acetylcholine increases the lifespan of reentry in the SAN.

The initiation and propagation of electrical pulses in the sinoatrial node under normal conditions and after application of acetylcholine have been simulated. It has been found that normally a single or a few leading centers are formed in the tissue. When acetylcholine is applied, a temporary functional block of conduction may appear; the leading center migrates under these conditions.

The duration of the preautomatic pause as a function of sinoatrial node, the type of pacemaker cells, acetylcholine concentration, the duration of high-frequency stimulation, and the conductivity of gap junctions has been studied. It was found that the preautomatic pause in peripheral pacemakers occurs at a higher concentration of acetylcholine as compared with central pacemakers. The dependence of the duration of the preautomatic pause on the gap junction conductivity is a nonlinear one.

We simulated the electric current distribution in the brain during transcranial direct current stimulation (tDCS) using an anatomically accurate human head model. We estimated an effect of common electrode montages on spatial distribution of the electric field during tDCS procedure and analyzed a sensitivity of the technique to variations of electrode size and orientation. We concluded that the used electrode montages are stable with respect to minor changes in electrode size and position, while an assumption of homogeneity and isotropy of the head model results in crucial changes of the electric field distribution. We determined the electrode montages suited to deliver strong effect on hippocampus and cerebellum.

Mathematical modeling of the electric activity of pairs of true (central) and latent (peripheral) sinoatrial pacemaker cells coupled through gap junctions revealed that attenuation of coupling conductance increases the beat phase shift; below a critical conductance there is no synchronization. The phase difference also depends on the type of interacting cells, being maximal for a “central”-“peripheral” cell pair.

We studied the dynamics of a chemical vortex whose core was disturbed by visible light. The observed sharp change of the shape of the vortex and the unfolding increase in the vortex wavelength proved to be tightly related to a transformation of trigger waves to phase waves. Analytical estimations and direct measurements show that the shape of the vortex is well-fitted by a logarithmic spiral. The results of experiments and of computer simulations are in a good agreement.

The dynamics of phase disturbances in the 1D uniform medium described by FitzHugh-Nagumo equations was studied. It was found that the system synchronizes its oscillations if the initial disturbances are small. Large disturbances resulted in the appearance of phase breaks. Dependent on the system parameters, phase breaks were found to be either stable or unstable; stable breaks led to target pattern-like sources, unstable to extended chaos.

A set of dimensionless parameters describing pulse propagation in the heart, BZ reaction and FHN model is estimated for comparison of the systems. The ranges of the parameters measured allow the BZ reaction to be considered as a rough experimental model of excitable heart tissue. Vulnerability in the BZ reaction is used as an analogue for vulnerability in cardiac tissue.

We have simulated 3D propagation of the action potential in the sinoatrial node to study the dynamics of the heart rhythm initiation. We have found that the leading center inside the sinoatrial node is formed by a group of cells, appears spontaneously under normal conditions, and migrates as acetylcholine is applied. The leading center drifts toward the center of the sinoatrial node, if we consider the effect of the surrounding atrial tissue. Abnormal electrical activity, rotating waves of action potential are observed in the sinoatrial node.

The control of spiral wave parameters by electric current was investigated in the Belousov-Zhabotinsky (BZ) reaction. It was found that the wavelength and the period of spiral waves increase by a factor of up to 3 with electric current (both dc and ac). Using this procedure spiral waves with a period higher than the period of medium bulk oscillations were observed. It was also found that hysteresis phenomena occur in the system considered.

We have created a new non-linear computer model to simulate electrical activity of the intestine. Unlike the widely used model by Sarna et al., who used a modified set of Van der Pol oscillators to simulate activity the of gastrointestinal (GI) tract, our model assumes a more realistic approach which involves (i) a description of electrical coupling between cells, and (ii) a description of the two interacting layers of longitudinal muscle (LM) and interstitial cells of Cajal (ICC). The dynamics in each layer are described by a pair of differential equations with variables representing the transmembrane potential and slow currents; the two equations describe the dynamics of the nonlinear membrane in the same spirit as the FitzHugh-Nagumo equations.

We use a 2-D FitzHugh-Nagumo (FHN) bidomain model to simulate activation patterns in cardiac tissue. We analyze the dynamics using vector calculus quantities such as curl and divergence of spatial gradients of the local phase /spl phi/.

Compared to steadily propagating waves (SPW), damped waves (DW), another solution to the nonlinear wave equation, are seldom studied. In cardiac tissue after electrical stimulation in an SPW wake, we observe DW with diminished amplitude and velocity that either gradually decrease as the DW dies, or exhibit a sharp amplitude increase after a delay to become an SPW. The cardiac DW-SPW transition is a key link in understanding defibrillation and stimulation close to the refractory period, and is ideal for a general study of DW dynamics.

We have simulated electrical activity of the intestine in a computer model that describes the coupled layers of longitudinal muscle (LM) and interstitial cells of Cajal (ICC). The model suggests that pacemaker activity is due to the ICC layer, while the pulse propagation involves the LM layer that is in the excitatory state. The model describes well the experimentally observed phenomena: frequency change along the intestine, synchronization along short distances and desynchronization for long distances, and the decrease of propagation distance and propagation time along the intestine. We have observed the occurrence of phase interruptions or breaks, which are responsible for the limited values of propagation distance and time.

We simulate wave propagation in the whole heart containing a local inhomogeneity whose properties mimic some properties of cardiac tissue during acute phase of infarction. The dynamics of cardiac tissue is described by a FitzHugh-Nagumo (FHN) model. We show that two or several short-period stimulations of the heart lead to the development of a three-dimensional vortex ring, which is a temporal source of high frequency waves. The vortex ring is located near the boundary of the infarction and induces wave patterns which appear as several focal wave sources on the epicard and endocard. We have traced the filament of the vortex and show its dynamics. Continuous stimulation of the heart at high frequency resulted in the Wenckebach effect.

We study vulnerability in the Belousov-Zhabotinsky reaction-using experimental and numerical methods. We show that the width of the vulnerable window (VW) decreases with increasing velocity of wave,propagation. A detailed study of the structure of the VW: revealed a new effect: the development of multiple responses to a single premature stimulus; a single premature stimulation in a homogeneous one-dimensional medium generates two or three propagating waves. We locate this effect in the parametric space and discuss its mechanism.

Experiments were carried out to study the effect of local disturbances on the vortex dynamics in the light-sensitive Belousov-Zhabotinsky (BZ) reaction. It was found that irradiation with visible light of the core region of a rotating spiral wave (vortex) in an oscillatory medium results in a bifurcation which dramatically changes the shape of the vortex. The bifurcation is seen as an unfolding increase in the vortex wavelength although only a negligible change in the vortex core size is observed. Similar dynamics is expected to occur in oscillatory media of different nature.