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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.

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.

We modified the FitzHugh-Nagumo model of an excitable medium so that it describes adequately the dymanics of pulse propagation in the canine myocardium. The modified model is simple enough to be used for intensive 3-dimensional (3D) computations of the whole heart. It simulates the pulse shape and the restitution property of the canine myocardium with good precision.

With the aid of detailed computer simulations, we have estimated distributions of membrane potential and ionic currents in the core region of a sinoatrial node reentry. We observe reduced amplitudes of the measured quantities in the core; the core sizes for potential and currents did not always coincide. Simulations revealed that acetylcholine, when applied in the vicinity of unstable reentry, attracted the reentry to become the core and to stabilize its rotation. Anatomically detailed simulations of sinoatrial node and surrounding atrial tissue revealed that reentry always rotated around small strips of connective tissue. Acetylcholine superfusion over superior part of the sinoatrial node resulted in a drift of reentry in the cranial direction. Under the latter conditions, reentry may coexist with the pacemaker in the caudal part of the sinoatrial node. Copyright © 2016 John Wiley & Sons, Ltd.

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.

The model of the ferroin-catalyzed Belousov-Zhabotinsky reaction is modified for the temperature range 10-30°C, which is more appropriate for experiments.

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.

The time delay for transmission of chemical waves via a geometrically asymmetric gap is studied based on the Rovinsky-Zhabotinsky model of the Belousov-Zhabotinsky reaction. It decreases with acidity and increases with the gap width. The time delay is assumed to be the sum of two components: the diffusion process within the gap and the reaction process at the receiving boundary. The latter accounts for the presence of the critical gap width above which no transmission occurs, and consequently, for switching of unidirectional transmission. An equation for the time delay is proposed as a function of the gap width.