Dynamical Mean Field approximation of a canonical cortical model for studying inter-population synchrony

The goal of this paper is twofold. We propose and explore a model to study the synchronization among populations in the canonical model of the neocortex proposed previously by (R.J. Douglas, K.A.C. Martin, A functional microcircuit for cat visual cortex. J.Physiol. 440(1991) 735–769). For this, a model describing N synapses of each m-population (m = 1, 2,3) is proposed. Each synapse is described by a system of 2 stochastic differential equations (SDEs). Then, by using the dynamical mean field approximation (DMA) (H. Hasegawa, Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises, Phys. Rev. E. (2003)1-19.) the system of several SDEs is reduced to 12 ordinary differential equations for the means and the second-order moments of global variables. The connectivity among populations is obtained by summarizing in the canonical model the detailed information from a quantitative description of the circuits formed in cat area 17 given in (T.Binzegger, R.J. Douglas, K.A. Martin, A Quantitative Map of the Circuit of Cat Primary Visual Cortex, J. Neurosci. 24 (2004) 8441- 8453). In the framework of the used DMA we propose a measure for inter-population synchronization. Simulations are carried out for exploring how inter-population synchrony is related to the variation of firing frequency of each population. Our results suggest that superficial pyramidal clusters appear to have a predominant influence on the synchronization process among pyramidal populations as well as put forward the active role of inhibition in the rest of the synchronizations between populations

Simulation α of EEG using brain network model

In this paper, we developed a large-scale brain network model comprising of four cerebral areas in the left hemisphere, and each area is modelled as an oscillator Jansen and Rit (JR) model. Our model is based on the structural connectivity of human connectome (SC) which was a hybrid from CoCoMac neuroinformatics database and diffusion spectrum imaging (DSI.) This brain network model was designed and implemented on the neuroinformatics platform using The Virtual Brain (TVB v1.5.3). The results demonstrated that incorporating the large-scale connectivity of brain regions and neural mass of JR model can generate signals similar to the α oscillation in frequency range of (7-12HZ) of EEG

Metabifurcation analysis of a mean field model of the cortex

Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space capturing neurobiological attributes relevant to brain dynamics. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two families. After investigating and characterizing these, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli, distribution of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They emerge when the parameter space is partitioned according to bifurcation responses. This partitioning cannot be achieved by the investigation of only a small number of parameter sets, but is the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Identification of the parameters of an electroencephalographic recording system

Elektroencefalografický záznamový systém slouží k vyšetření mozkové aktivity. Na základě tohoto vyšetření lze stanovit diagnózu některých nemocí, například epilepsie. Účelem této práce bylo zpracování signálu z toho systému a vytvoření modelového signálu, který bude s reálným signálem porovnán. Uměle vytvořený signál vychází z Jansenova matematického modelu, který byl dále implementován v prostředí MATLAB a rozšířen ze základního modelu na komplexnější zahrnující nelinearity a model rozhraní elektroda – elektrolyt. Dále bylo provedeno měření signálů na EEG fantomu a následná identifikace parametrů naměřených signálu. V první fázi byly testovány jednoduché signály. Identifikace parametrů těchto signálů sloužila k validaci daného EEG fantomu. V druhé fázi bylo přistoupeno k testování EEG signálů navržených podle matematického Jansenova modelu. Analýza veškerých signálů zahrnuje mimo jiné časově frekvenční analýzu či ověření platnosti principu superpozice.Electroencephalographic recording system is used to examine a brain activity. Based on this examination we can establish the diagnosis of certain diseases, such as epilepsy. The purpose of this study has been the signal processing and a signal generation which were compared with the real signal. Artificially generated signal is based on Jansen‘s mathematical model which has been also implemented in MATLAB and then that model has been extended to more complex model including nonlinearities and model electrode – electrolyte. Also a signal measurements on EEG phantom and identification of the parameters of these signals were performed. Firstly a simply signals were tested and the identification of their parameters has served to validate the EEG phantom. Secondly the created signal designed by Jansen model were tested also. Besides an analysis of all signals includes the time frequency analysis or a superposition principle testing.