Dynamics of large-scale brain activity in normal arousal states and epileptic seizures

Abstract

Links between electroencephalograms (EEGs) and underlying aspects of neurophysiology and anatomy are poorly understood. Here a nonlinear continuum model of large-scale brain electrical activity is used to analyze arousal states and their stability and nonlinear dynamics for physiologically realistic parameters. A simple ordered arousal sequence in a reduced parameter space is inferred and found to be consistent with experimentally determined parameters of waking states. Instabilities arise at spectral peaks of the major clinically observed EEG rhythms-mainly slow wave, delta, theta, alpha, and sleep spindle-with each instability zone lying near its most common experimental precursor arousal states in the reduced space. Theta, alpha, and spindle instabilities evolve toward low-dimensional nonlinear limit cycles that correspond closely to EEGs of petit mal seizures for theta instability, and grand mal seizures for the other types. Nonlinear stimulus-induced entrainment and seizures are also seen, EEG spectra and potentials evoked by stimuli are reproduced, and numerous other points of experimental agreement are found. Inverse modeling enables physiological parameters underlying observed EEGs to be determined by a new, noninvasive route. This model thus provides a single, powerful framework for quantitative understanding of a wide variety of brain phenomena.

Onset of polyspike complexes in a mean-field model of human electroencephalography and its application to absence epilepsy

“…The specific relay nuclei also receive the sensory input f n , which is modelled as a constant field in our research. Incoming synaptic fields f a , received by each compartment, are assumed to be linearly summed in the dendritic tree (Robinson et al 2002), hence…”

“…First of all, the cortical inhibitory interneurons are relatively sparse compared with pyramidal cells (a ratio of 4 : 1 in favour of the pyramidal cells). The excitatory (e) neurons are believed to be the main source of the EEG, hence we approximate V i zV e and 2 i z2 e (Robinson et al 2002). Furthermore, a a represents a ratio between an axonal velocity, and a typical length scale for axonal propagations.…”

“…In Robinson et al (2002), it is shown that removing the time derivative in the right-hand side of (3.3) does not influence the numerical results; hence, it can be dropped for all the neural masses. If we combine this with g i,r,s /N, equation (3.3) reduces to f i,r,s Z2 i,r,s .…”

“…In §3, we pointed out that f e can be approximated to be linearly related to the EEG voltages. An often used convention is that the constant of proportionality is taken to be negative (Robinson et al 2002). Figure 6a shows the EEG traces from our seizure database, taken from three different patients with CAE.…”

Control of absence seizures induced by the pathways connected to SRN in corticothalamic system

“…In addition, the absence seizures can originate from the mutual roles between the cerebral cortex and the thalamus, which form the corticothalamic circuits. This can be witnessed by a number of clinical researches and computational modeling studies (Breakspear et al 2006;Coenen and van Luijtelaar 2003;Marten et al 2009;Robinson et al 2002;Timofeev and Steriade 2004). For example, Roberts and Robinson (2008) used a physiologically based continuum model (i.e., the mean-field model) of the corticothalamic system to explain the basic mechanisms of the seizure activity.…”