A neurophysiologically-based mathematical model of flash visual evoked potentials

Jansen, Ben H.; Zouridakis, George; Brandt, Michael E.

doi:10.1007/bf00224863

Cited by 236 publications

(261 citation statements)

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“…For example, Schuster et al [5] proposed a columnar model to simulate the synchronized oscillation discovered in visual cortex. Jansen [6,7] presented a mathematical model of coupled cortical columns which produced EEG-like waveform and evoked potentials. Fukai [8] designed a network model in columnar structure to simulate visual pattern retrieval.…”

Section: Doi: 101360/03yc0240mentioning

confidence: 99%

Synchronized oscillation in a modular neural network composed of columns

Qi²,

et al. 2005

Sci China Ser C

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The columnar organization is a ubiquitous feature in the cerebral cortex. In this study, a neural network model simulating the cortical columns has been constructed. When fed with random pulse input with constant rate, a column generates synchronized oscillations, with a frequency varying from 3 to 43 Hz depending on parameter values. The behavior of the model under periodic stimulation was studied and the input-output relationship was non-linear. When identical columns were sparsely interconnected, the column oscillator could be locked in synchrony. In a network composed of heterogeneous columns, the columns were organized by intrinsic properties and formed partially synchronized assemblies.Keywords: cortical column, synchronized oscillation, Rose-Hindmarsh model. DOI: 10.1360/03yc0240Since it was first reported in 1957 [1] , the columnar organization has been found in somatic sensory cortex, visual cortex, auditory cortex, motor cortex and association cortex of various different species including mice, rat, cats, rabbits, monkeys and humans [2] . These experimental findings strongly supported that the cortical columns are basic anatomical and physiological units of the cortex and suggested that columns might be of fundamental importance for the function of the brain [2,3] .Mathematical models were constructed and simulated to investigate the biological function of the column in the information processing in the brain. Wilson-Cowan model [4] is most frequently used to simulate the electrophysiological activities of the cortical columns in the previous studies. For example, Schuster et al. [5] proposed a columnar model to simulate the synchronized oscillation discovered in visual cortex. Jansen [6,7] presented a mathematical model of coupled cortical columns which produced EEG-like waveform and evoked potentials. Fukai [8] designed a network model in columnar structure to simulate visual pattern retrieval. Some of the column models are phase models which assume a column as an oscillator and simulate mere the phase of oscillating activities [9,10] .There has been few modeling of columns based on spiking single neurons. By replacing the single cell as the functional unit by multiple cells in cortical columns, an attractor network model was constructed and simulated to perform associative memory [11] . Hansel and Sompolinsky [12] constructed a hypercolumn model according to the physiological organization in the orientation columns in visual cortex. The synchronous and chaotic activities in the hypercolumn were studied and the model was used to explore the cortical mechanisms for orientation selectivity.

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Section: Doi: 101360/03yc0240mentioning

confidence: 99%

Synchronized oscillation in a modular neural network composed of columns

Qi²,

et al. 2005

Sci China Ser C

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“…The noise used in the models of Jansen et al (1993), Jansen and Rit (1995), and Wendling et al (2000) is not fully characterized in those papers. But we can infer likely parameters and compare reproducing the results using both ODE and SDE integration algorithms.…”

Section: Estimation Of Noise Intensity For Jansen-rit Modelmentioning

confidence: 99%

“…Building on the earlier work of Lopes da Silva et al (1974) and Wilson and Cowan (1972), Jansen and Rit developed a simple computational model of a small cortical region (Jansen et al, 1993;Jansen and Rit, 1995). The model produces an output signal similar to spontaneous EEG alpha oscillations, and also shows responses similar to evoked potentials following pulsatile input.…”

Section: Jansen-rit Neural Mass Modelmentioning

confidence: 99%

“…In the original model (Jansen et al, 1993), both pyramidal and excitatory interneuron populations were the targets of extrinsic inputs, with the two inputs being always proportional (fully correlated). In the model of Jansen and Rit (1995), all extrinsic input was delivered to the pyramidal neurons only, with external stimulation of the other population dropped.…”

Section: Bifurcation Parametersmentioning

confidence: 99%

“…As a neural mass model of a single cortical region capable of oscillation the Jansen-Rit model (Jansen et al, 1993;Jansen and Rit, 1995) was introduced in Section 2.2.1. When treated as a deterministic system of first order ordinary differential equations in the variables…”

Section: Application To Neural Mass Model and Synchronizationmentioning

confidence: 99%

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Critical fluctuations and coupling of stochastic neural mass models

Aburn¹

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Neuroimaging and implanted medical devices give a view onto large scale oscillations in the brain that rapidly change in both power and synchrony at different frequencies. These measured time series reveal a projection to just one dimension for each location, a moving shadow of the complex underlying activity. For this reason mathematical models of the activity are essential to make full use of the time series. The flexible onset and cessation of oscillations may have an important role in allowing the brain rapidly to rearrange its effective network structure. The onset of pathological oscillations is also central to neurological disorders such as epilepsy and Parkinson's disease. It is in the regime close to linear instability that transitions to and from oscillation can readily occur, by mechanisms of bifurcation and multistability. Empirical evidence of critical fluctuations and critical slowing down in neural dynamics also suggest proximity to linear instability. This thesis develops novel methods to analyze stochastic dynamical models near the point of transitionwhere oscillations start and stop, allowing to relate transitions in the models to changes in time series statistics that are accessible in clinical and experimental recordings.Taking as an example a widely used biophysical model of collective neural dynamics (the Jansen-Rit model) we show that near the point of oscillation onset at a supercritical Hopf bifurcation there can be a dramatic increase in autocorrelation length as well as power law scaling over four orders of magnitude in fluctuation size and duration, but that these time series indicators will depend sensitively on the direction in state space of input fluctuations and hence on which neuronal subpopulation is stochastically perturbed.In general near a supercritical Hopf bifurcation non-circular oscillations emerge on an arbitrarily curved two-dimensional surface embedded within the N -dimensional state space. This makes it difficult to determine exactly how noise will affect oscillation phase and amplitude. By applying Poincaré normal form transformations to find a parameter-dependent coordinate system in which the unperturbed oscillations are simple circles in a flat plane, then using Stratonovich stochastic calculus to transform noise perturbations to the same coordinate system, this makes explicit the effect of noise on phase and amplitude. We give a criterion for this reduced model to be a good approximation, balancing noise intensity and center manifold stability. Abstract iiOptionally averaging the diffusion process in Fokker-Planck form gives a still simpler weak approximation of the oscillations in a symmetrical standard form that retains the leading order stochastic effects on phase and amplitude dynamics. We demonstrate by large scale numerical simulation of the stochastic differential equations that the oscillation time series statistics of interest are preserved by transformation to this symmetrical weak approximation.Close to instability, dynamic synchrony of networ...

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Addressing Global Environmental Challenges to Mental Health Using Population Neuroscience

Schumann,

Andreassen,

Banaschewski

et al. 2023

JAMA Psychiatry

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ImportanceClimate change, pollution, urbanization, socioeconomic inequality, and psychosocial effects of the COVID-19 pandemic have caused massive changes in environmental conditions that affect brain health during the life span, both on a population level as well as on the level of the individual. How these environmental factors influence the brain, behavior, and mental illness is not well known.ObservationsA research strategy enabling population neuroscience to contribute to identify brain mechanisms underlying environment-related mental illness by leveraging innovative enrichment tools for data federation, geospatial observation, climate and pollution measures, digital health, and novel data integration techniques is described. This strategy can inform innovative treatments that target causal cognitive and molecular mechanisms of mental illness related to the environment. An example is presented of the environMENTAL Project that is leveraging federated cohort data of over 1.5 million European citizens and patients enriched with deep phenotyping data from large-scale behavioral neuroimaging cohorts to identify brain mechanisms related to environmental adversity underlying symptoms of depression, anxiety, stress, and substance misuse.Conclusions and RelevanceThis research will lead to the development of objective biomarkers and evidence-based interventions that will significantly improve outcomes of environment-related mental illness.

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A neurophysiologically-based mathematical model of flash visual evoked potentials

Cited by 236 publications

References 29 publications

Synchronized oscillation in a modular neural network composed of columns

Synchronized oscillation in a modular neural network composed of columns

Critical fluctuations and coupling of stochastic neural mass models

Addressing Global Environmental Challenges to Mental Health Using Population Neuroscience

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