107 research outputs found
Analysis of Jansen's model of a single cortical column
In this report we present a mathematical analysis of a simple model of a cortical column. We first recall some known biological facts about cortical columns. We then present a mathematical model of such a column, developed by a number of people including Lopes Da Silva, Jansen, Rit. Finally we analyze some aspects of its behaviour in the framework of the theory of dynamical systems using bifurcation theory and the software package XPP-Aut developed by B. Ermentrout. This mathematical approach leads us to a compact representation of the model that allows to finally discuss its adequacy with biology
Visual masking: past accomplishments, present status, future developments
Visual masking, throughout its history, has been used as an investigative tool in
exploring the temporal dynamics of visual perception, beginning with retinal
processes and ending in cortical processes concerned with the conscious
registration of stimuli. However, visual masking also has been a phenomenon
deemed worthy of study in its own right. Most of the recent uses of visual
masking have focused on the study of central processes, particularly those
involved in feature, object and scene representations, in attentional control
mechanisms, and in phenomenal awareness. In recent years our understanding of
the phenomenon and cortical mechanisms of visual masking also has benefited from
several brain imaging techniques and from a number of sophisticated and
neurophysiologically plausible neural network models. Key issues and problems
are discussed with the aim of guiding future empirical and theoretical
research
Brain Model State Space Reconstruction Using an LSTM Neural Network
Objective
Kalman filtering has previously been applied to track neural model states and
parameters, particularly at the scale relevant to EEG. However, this approach
lacks a reliable method to determine the initial filter conditions and assumes
that the distribution of states remains Gaussian. This study presents an
alternative, data-driven method to track the states and parameters of neural
mass models (NMMs) from EEG recordings using deep learning techniques,
specifically an LSTM neural network.
Approach
An LSTM filter was trained on simulated EEG data generated by a neural mass
model using a wide range of parameters. With an appropriately customised loss
function, the LSTM filter can learn the behaviour of NMMs. As a result, it can
output the state vector and parameters of NMMs given observation data as the
input.
Main Results
Test results using simulated data yielded correlations with R squared of
around 0.99 and verified that the method is robust to noise and can be more
accurate than a nonlinear Kalman filter when the initial conditions of the
Kalman filter are not accurate. As an example of real-world application, the
LSTM filter was also applied to real EEG data that included epileptic seizures,
and revealed changes in connectivity strength parameters at the beginnings of
seizures.
Significance
Tracking the state vector and parameters of mathematical brain models is of
great importance in the area of brain modelling, monitoring, imaging and
control. This approach has no need to specify the initial state vector and
parameters, which is very difficult to do in practice because many of the
variables being estimated cannot be measured directly in physiological
experiments. This method may be applied using any neural mass model and,
therefore, provides a general, novel, efficient approach to estimate brain
model variables that are often difficult to measure
The complexity of dynamics in small neural circuits
Mean-field theory is a powerful tool for studying large neural networks.
However, when the system is composed of a few neurons, macroscopic differences
between the mean-field approximation and the real behavior of the network can
arise. Here we introduce a study of the dynamics of a small firing-rate network
with excitatory and inhibitory populations, in terms of local and global
bifurcations of the neural activity. Our approach is analytically tractable in
many respects, and sheds new light on the finite-size effects of the system. In
particular, we focus on the formation of multiple branching solutions of the
neural equations through spontaneous symmetry-breaking, since this phenomenon
increases considerably the complexity of the dynamical behavior of the network.
For these reasons, branching points may reveal important mechanisms through
which neurons interact and process information, which are not accounted for by
the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of
figures 8 and 9 fixed, results unchange
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
Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model
NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep
Realistic modeling of entorhinal cortex field potentials and interpretation of epileptic activity in the guinea pig isolated brain preparation.
Mechanisms underlying epileptic activities recorded from entorhinal cortex (EC) were studied through a computational model based on review of cytoarchitectonic and neurobiological data about this structure. The purpose of this study is to describe and use this model to interpret epileptiform discharge patterns recorded in an experimental model of ictogenesis (guinea-pig isolated brain perfused with bicuculline). A macroscopic modeling approach representing synaptic interactions between cells subpopulations in the EC was chosen for its adequacy to mimic field potentials reflecting overall dynamics rising from interconnected cells populations. Therefore, intrinsic properties of neurons were not included in the modeling design. Model parameters were adjusted from an identification procedure based on quantitative comparison between real and simulated signals. For both EC deep and superficial layers, results show that the model generates very realistic signals regarding temporal dynamics, spectral features and cross-correlation values. These simulations allowed us to infer information about the evolution of synaptic transmission between principal cell and interneuronal populations and about connectivity between deep and superficial layers during the transition from background to ictal activity. In the model, this transition was obtained for increased excitation in deep versus superficial layers. Transitions between epileptiform activities (interictal spikes, fast onset activity (25Hz), ictal bursting activity) were explained by changes of parameters mainly related to GABAergic interactions. Notably, the model predicted an important role of GABA(a,fast) and GABA(b) receptor-mediated inhibition in the generation of ictal fast onset and burst activities, respectively. These findings are discussed with respect to experimental data
A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation
Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12–15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols
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