On the genesis of spike-wave activity in a mean-field model of human brain activity

In this letter, the genesis of spike-wave activity - a hallmark of many generalized epileptic seizures - is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modeling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the external signal, interplay to generate the spike-wave oscillation. We demonstarte that this is a nonlinear phenomena and that linear stability analysis is not appropriate to explain such solutions

audiology 2012

<p>All other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000092#pcbi-1000092-g010" target="_blank">Figure 10</a>. (A) Individual mean synaptic currents of all nonsensory nodes. (B) Total synaptic currents averaged across the nonsensory sheet. The injection of the externally evoked sensory currents into the prior activity actually has a slightly desynchronizing effect.</p

A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis

The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain’s mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific predictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions and reveals processes unique to the global bifurcation set. Specifically, we argue that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted by the global bifurcation diagram of the model’s dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain

Gabor filtering by excitatory and inhibitory receptor densities.

<p>(<b>A</b>) Density profiles for excitatory (blue) and inhibitory (red) receptor populations which combine to form a Gabor filter (black). In this case, the excitatory density was nominated as Gaussian. (<b>B</b>) Spatial frequency response of the Gabor filter. Peaks correspond to waves of length 300 µm. (<b>C</b>) Excitatory (blue) and inhibitory (red) receptor samples taken from the density distributions in panel A. The combined receptor field (blue+red) represents the dendritic field of the neuron. (<b>D</b>) Spatial frequency response of the combined receptor field. Peaks correspond to vertically oriented waves of length 300 µm. (<b>E</b>) The combined receptor field superimposed on its preferred wave pattern. The wave pattern propagates from left to right at 6 mm/sec to simulate 20 Hz oscillations in the cortical field. (<b>F</b>) Time course of the net excitatory (blue shading) and inhibitory (red shading) conductances in response the preferred wave pattern. Faint lines show individual post-synaptic conductances for n = 40 randomly selected receptors (not to scale). Each receptor fires 20 spikes/sec on average. Heavy black line shows the dendritic current induced by the net changes in conductance. The amplitude of the dendritic current is modulated as the wave propagates across the receptor field. (<b>G</b>) The combined receptor field superimposed on the orthogonal wave pattern which propagates from top to bottom at 6 mm/sec. (<b>H</b>) Time course of the dendritic response to the orthogonal wave pattern. In this case the wave pattern does not modulate the dendritic current even though the individual receptors still fire at 20 spikes/sec on average.</p

Tuning curves of the PTNs.

<p>(<b>A</b>) Tuning curve of the PTN dendritic compartment. The amplitude of the dendritic response current (vertical axis) is modulated by the orientation of the cortical wave pattern (horizontal axis). Heavy black line indicates the mean amplitude of the dendritic response for any given wave orientation. Shaded region indicates the 90% confidence interval. The large variation is due to local defects in the wave pattern. (<b>B</b>) The likelihood of the soma responding at each of the dominant firing rates. (<b>C</b>) Net firing rates of a population of neurons in response to wave orientation.</p

Modeling the descending motor system.

<p>(<b>A</b>) Major fiber tracts of the descending motor system, redrawn from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003260#pcbi.1003260-Gray1" target="_blank">[105]</a>. Axons of the pyramidal tract neurons (red) descend from the motor cortex to monosynaptically innervate motor neurons in the spinal cord. (<b>B</b>) Schematic representation of the dendritic arbors of a typical pyramidal tract neuron (PTN). The apical dendrites project widely throughout the superficial layers of cortex and thus are ideally placed to detect surface wave patterns in the neural activity (top). (<b>C</b>) Simulated cortical wave pattern. (<b>D</b>) The descending motor model. Cortical wave patterns are generated by a sheet of spatially-coupled phase oscillators (circles, 1–8). These wave patterns are spatially filtered by the dendritic trees of the pyramidal tract neurons to produce an amplitude-modulated oscillatory current at the soma. Spikes initiated by the PTN are transmitted to a randomly selected pool of motor neurons (MN) in the spine. Each MN integrates the incoming spikes to produce a muscle drive spike train. Net muscle drive is quantified by simulated Electromyogram (EMG). The cortical wave model is adapted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003260#pcbi.1003260-Heitmann1" target="_blank">[17]</a>. The MN and EMG models are adapted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003260#pcbi.1003260-Boonstra1" target="_blank">[41]</a>.</p

The effect of wave orientation on the output of the descending motor system.

<p>Each column presents the responses of the descending motor system for pyramidal neurons with a given dendritic orientation ( and ) relative to the cortical pattern. (<b>A</b>) Orientation of the dendritic kernels. The cortical pattern is the same in all cases. (<b>B</b>) Firing rate distribution of the pyramidal tract neurons. (<b>C</b>) Firing rate distribution of the motor neurons. (<b>D</b>) Time course of the simulated EMG. (<b>E</b>) Magnitude squared coherence between LFP and EMG. Light gray lines represent individual trials (n = 100). Black line shows the trial average. In red, average MEG-EMG coherence in 16 subjects while they perform a precision grip task at different force levels (2.0 N, 1.65 N, 0.95 N, 0.0 N). Dashed horizontal line indicates the 95% confidence level for the coherence distribution in each frequency bin. Peaks above that line are statistically significant at <i>p = 0.05</i>.</p

The PTN model.

<p>(<b>A</b>) Spatial profiles of the dendritic filter. (<b>B</b>) Spatial contours of the dendritic filter. (<b>C</b>) Preferred cortical oscillation pattern for this dendritic filter. (<b>D</b>) Orthogonal oscillation pattern. (<b>E</b>) Time course of the neural response to the preferred cortical pattern. Bottom trace (red) is the dendritic current. Top trace (black) is the somatic membrane potential. Light gray traces show the responses of four other PTNs located at random positions on the same cortical pattern. (<b>F</b>) Time course of neural response to the orthogonal pattern. Panels <i>E</i> and <i>F</i> have the same scales.</p

Parameters of the dendritic conductance model.

<p>Parameters of the dendritic conductance model.</p

Asymmetric dendritic kernels induce phase shifts in the PTN spike trains.

<p>Profiles of the dendritic kernels are shown on the left. Spike trains produced by the PTN model are shown on the right. The thick gray line is the simulated LFP of the cortical pattern which is the same in all cases. (<b>A</b>) Case of a Gabor filter with zero phase shift. (<b>B</b>) Case of +90 degree phase shift. (<b>C</b>) Case of +180 degree phase shift. (<b>D</b>) Case of −90 degree phase shift. Light gray spike traces in B–D reproduce the case of zero phase shift for ease of comparison.</p