[Spontaneous synchronous discharges in hippocampal slices. Simulation and experiment]. / Spontannye sinkhronnye razriady v srezakh gippokampa. Modelirovanie i éksperiment.

Chaotic oscillations of extracellular potential of field-type nerve tissues are simulated by a 2D coupled map lattice. These tissues, say, the fields of the hippocampus, are represented by neural mass sheets consisting of current sources. The relationship between the source-sink ensembles and the extracellular field potential at each discrete instant of time t = 1, 2, ... is described by a single-site map creating chaos. The 2D coupled map lattice is viewed as a network of diffusively coupled the maps creating spatiotemporal chaos. The conversion of chaotic oscillations into synchronous ones, which are typical for epileptiform discharges, is studied. The results obtained are in good agreement with those derived from hippocampal slices treated with picrotoxin.

Coupled map lattice simulation of epileptogenesis in hippocampal slices.

Bioelectric activity of a nervous tissue and its synchronization with formatting epileptiform bursts are simulated by a coupled map lattice. The functional units of the map located in the lattice sites represent neural masses which consist of current sources and sinks. The sources lead to depolarization of neurons, and sinks provide hyperpolarization. The map describes a single variable--the bioelectric potential. This potential is created by the interplay of all current sources and sinks in the neural masses. The neural masses are diffusively coupled with each other both by electronic influence and synaptic coupling. Both mechanisms mentioned are suggested to be essential for the formation of synchronous bursts. The transition from chaotic activity to bursts was studied.

[A model of stochastic variations of postsynaptic activity]. / Model'nye predstavleniia stokhasticheskikh kolebanii postsinapticheskoi aktivnosti.

Stochastic oscillations imitating postsynaptic activity in the excitatory neurons are produced by a nonlinear difference equation which does not contain any sources of noise. The given back inhibition via inhibitory interneurons presents a negative feedback loop due to which oscillations in the model system are realized. By means of variation of parameters of the system the patterns of stochastic oscillations can be changed in wide range of physiologically meaningful patterns of the neuronal activity.

[Stochastic oscillations in a dynamic system modeling macroscopic activity of neuronal tissue]. / Stokhasticheskie kolebaniia v dinamicheskoi sisteme, modeliruiushchie makroskopicheskuiu aktivnost' nervnykh tkanei.

A stochastic behaviour can be exhibited by dynamic systems with a simple organisation and in which the sources of uncontrolled noises are absent. This is the case of the system Zk+1 = (1 + exp (V-HZk))-1(mod I) which differs from Amari system suggested for description of macroscopic activity of neuron nets by addition of the term mod I with I less than 1. We have found that the sequence Z1, Z2, ..., Zk, ... corresponds to the oscillations of the postsynaptic potential of excitatory neurones and operation mod I is due to regulation functions of the inhibitory ones.

[Spike transmission in statistical neuronal ensembles. Induced epileptic focus in a model of hippocampal field CA3]. / Perenos spaikov v statisticheskikh neironnykh ansambliakh. Vyzvannyi épilepticheskii ochag v modeli polia CA3 gippokampa.

In a spatially heterogeneous model the transition to supercritical phase was investigated as to the parameter characterizing the activation level of the pyramidal cells related to one another assuming the nonuniformity radius to be R0 = const. This is a transition from spontaneous activity to epileptoid bursts. Before the onset of epileptoid bursts the region of stochastic nonequilibrium of solutions is developed likely to produce pathologic dynamic patterns. With further increase of the activation parameter the system comes to epileptoid state. This synchronized firing of pyramidal cells is accompanied with phases of inhibition. A decrease in the nonuniformity radius leads to the formation of an epileptic focus. It is a dissipative structure. The evolution of it is not further followed, since the transport equations do not include its dynamics.

[Spike transmission in statistical neuronal ensembles. IVa. Stating the problem in a diffusion approximation]. / Perenos spaikov v statisticheskikh neironnykh ansambliakh. IVa. Postanovka zadachi v diffuzionnom priblizhenii.

An area of tissue in the field CA3 of the Hippocampus has been selected controled by a basket cell. The functioning of the basket cell has been described by a point approximation method forthe transport equation, and that of the ensemble of pyramidal cells by a diffusion approximation one. Furthermore, the area of tissue is broken up into N2 of "cells" wherein a transition is effected from the diffusion equation of the N2 of the point equations involved. If the sizes of "cells" are commeasurable to the diffusional length of the pyramidal cell collaterals each "cells" being relatively independent generator of activity. In the latter case the fundamental interaction type is the mutual negative influence of the "cells" through the basket cell. Should the area be broken up into further, the mutual influence of the "cells" becomes noticeable and cannot be neglected. The behaviour of spatially homogenous diffusion approximation model is equivalent of the point approximation model.

[Spike transmission in statistical neuron ensembles. III. Phase transition in a model of hippocampal field CA3]. / Perenos spaikov v statisticheskikh neironnykh ansambliakh. III. Fazovyi perekhod v modeli polia CA3 gippokampa.

The model consists of two types of neurons i. e. excitatory pyramidal cells and inhibitory basket ones. (the problem was formulated by Drs. O. S. Vinogradova and A. G. Bragin). The analysis of neuron activity has been carried out on the basis of "point approximation" of spikes transport equations. The graphs were obtained by computer. These graphs of the postsynaptic potentials averaged over ensemble are in good agreement with experimental data. The model observed demonstrates the phase transition over parameter characterizing the conduction of excitation between pyramidal cells. For weak pyramidal cells link there takes place the spontaneous activity regime. For strong link there were observed the epileptoid firing of neurons at 3 divided by 5 hertz and 140 divided by 240 msec phases of inhibition between bursts.

[Spike tranfer in statistical neuron assemblies. II. Neuron--nonlinear spike source]. / Perenos spaikov v statistichesklikh neironnykh ansambliakh. II. Neiron--nelineinyi istochnik spaikov

The mathematical model of the neuron function is known to rely on space summing of excitement. The spikes contribute to the inner state of the neuron the farther from cell soma the synapses are located. The difference between excitatory and inhibitory effect results in spike firing if only neural firing threshold is achieved. The values of spike flux have been estimated on the basis of the model of CA3 sector of the Hippocampus and were found to be 15 divided by 35 imp/s.

[Propagation of spikes in statistical neuron ensembles. I. Concept of phase transitions]. / Perenos spaikov v statisticheskikh neironnykh ansambliakh. I. Kontseptsiia fazovykh perekhodov

A system of two coupled integro-differential equations for the propagation of sipkes is presented. A qualitative consideration of the system shows possibility of concentrational phase transition in the neuron ensemble from the state of spontaneous firing to the strong periodic oscilltation activity. Naer the point of the phase transition the neuron ensemble becomes labile, which maintains appropriate conditons for the existence of mosaic structures in the neuron network.