Unified neurophysical model of EEG spectra and evoked potentials

Analysis of the electroencephalographic activity associated with thalamic tumors

A physiologically based model of corticothalamic dynamics is used to investigate the electroencephalographic (EEG) activity associated with tumors of the thalamus. Tumor activity is modeled by introducing localized two-dimensional spatial non-uniformities into the model parameters, and calculating the resulting activity via the coupling of spatial eigenmodes. The model is able to reproduce various qualitative features typical of waking eyes-closed EEGs in the presence of a thalamic tumor, such as the appearance of abnormal peaks at theta ( approximately 3Hz) and spindle ( approximately 12Hz) frequencies, the attenuation of normal eyes-closed background rhythms, and the onset of epileptic activity, as well as the relatively normal EEGs often observed. The results indicate that the abnormal activity at theta and spindle frequencies arises when a small portion of the brain is forced into an over-inhibited state due to the tumor, in which there is an increase in the firing of (inhibitory) thalamic reticular neurons. The effect is heightened when there is a concurrent decrease in the firing of (excitatory) thalamic relay neurons, which are in any case inhibited by the reticular ones. This is likely due to a decrease in the responsiveness of the peritumoral region to cholinergic inputs from the brainstem, and a corresponding depolarization of thalamic reticular neurons, and hyperpolarization of thalamic relay neurons, similar to the mechanism active during slow-wave sleep. The results indicate that disruption of normal thalamic activity is essential to generate these spectral peaks. Furthermore, the present work indicates that high-voltage and epileptiform EEGs are caused by a tumor-induced local over-excitation of the thalamus, which propagates to the cortex. Experimental findings relating to local over-inhibition and over-excitation are discussed. It is also confirmed that increasing the size of the tumor leads to greater abnormalities in the observable EEG. The usefulness of EEG for localizing the tumor is investigated.

Unifying and interpreting the spectral wavenumber content of EEGs, ECoGs, and ERPs

A biological model of corticothalamic dynamics is used to investigate the spatial power spectrum (wavenumber spectrum) of electrical activity in the brain. The model provides a single framework for unifying different aspects of activity. Comparisons of the predicted spectra with published electrocorticographic, electroencephalographic, and evoked response potential data enable physiology and anatomy to be inferred, producing results which are complementary to those obtained from comparisons in the frequency domain; the inferred quantities are consistent with, and complementary to, direct physiological and anatomical measurements. We also use the model to quantify the interdependence of the wavenumber and frequency domains, and deduce that further experiments that cover large wavenumber and frequency ranges simultaneously would greatly increase our knowledge of brain function. We conclude that both the frequency and wavenumber domains should be studied in order to build the fullest picture of brain dynamics: the two domains are both complementary and interdependent.

Estimation of neurophysiological parameters from the waking EEG using a biophysical model of brain dynamics

This paper presents the results from using electroencephalographic (EEG) data to estimate the values of key neurophysiological parameters using a detailed biophysical model of brain activity. The model incorporates spatial and temporal aspects of cortical function including axonal transmission delays, synapto-dendritic rates, range-dependent connectivities, excitatory and inhibitory neural populations, and intrathalamic, intracortical, corticocortical and corticothalamic pathways. Parameter estimates were obtained by fitting the model's theoretical spectrum to EEG spectra from each of 100 healthy human subjects. Statistical analysis was used to infer significant parameter variations occurring between eyes-closed and eyes-open states, and a correlation matrix was used to investigate links between the parameter variations and traditional measures of quantitative EEG (qEEG). Accurate fits to all experimental spectra were observed, and both inter-subject and between-state variability were accounted for by the variance in the fitted biophysical parameters, which were in turn consistent with known independent experimental and theoretical estimates. These values thus provide physiological information regarding the state. transitions (eyes-closed vs. eyes-open) and phenomena including cortical idling and alpha desynchronization. The parameters are also consistent with traditional qEEG, but are more informative, since they provide links to underlying physiological processes. To our knowledge, this is the first study where a detailed biophysical model of the brain is used to estimate neurophysiological parameters underlying the transitions in a broad range (0.25-50 Hz) of EEG spectra obtained from a large set of human data.

A hybrid neural network model for consciousness

A new framework for consciousness is introduced based upon traditional artificial neural network models. This framework reflects explicit connections between two parts of the brain: one global working memory and distributed modular cerebral networks relating to specific brain functions. Accordingly this framework is composed of three layers, physical mnemonic layer and abstract thinking layer, which cooperate together through a recognition layer to accomplish information storage and cognition using algorithms of how these interactions contribute to consciousness: (1) the reception process whereby cerebral subsystems group distributed signals into coherent object patterns; (2) the partial recognition process whereby patterns from particular subsystems are compared or stored as knowledge; and (3) the resonant learning process whereby global workspace stably adjusts its structure to adapt to patterns' changes. Using this framework, various sorts of human actions can be explained, leading to a general approach for analyzing brain functions.

Estimation of multiscale neurophysiologic parameters by electroencephalographic means

It is shown that new model-based electroencephalographic (EEG) methods can quantify neurophysiologic parameters that underlie EEG generation in ways that are complementary to and consistent with standard physiologic techniques. This is done by isolating parameter ranges that give good matches between model predictions and a variety of experimental EEG-related phenomena simultaneously. Resulting constraints range from the submicrometer synaptic level to length scales of tens of centimeters, and from timescales of around 1 ms to 1 s or more, and are found to be consistent with independent physiologic and anatomic measures. In the process, a new method of obtaining model parameters from the data is developed, including a Monte Carlo implementation for use when not all input data are available. Overall, the approaches used are complementary to other methods, constraining allowable parameter ranges in different ways and leading to much tighter constraints overall. EEG methods often provide the most restrictive individual constraints. This approach opens a new, noninvasive window on quantitative brain analysis, with the ability to monitor temporal changes, and the potential to map spatial variations. Unlike traditional phenomenologic quantitative EEG measures, the methods proposed here are based explicitly on physiology and anatomy.

Spatially uniform and nonuniform analyses of electroencephalographic dynamics,with application to the topography of the alpha rhythm

Corticothalamic dynamics are investigated using a model in which spatial nonuniformities are incorporated via the coupling of spatial eigenmodes. Comparison of spectra generated using the nonuniform analysis with those generated using a uniform one demonstrates that, for most frequencies, local activity is only weakly dependent on activity elsewhere in the cortex; however, dispersion of low-wave-number activity ensures that distant dynamics influence local dynamics at low frequencies (below approximately 2 Hz ), and at the alpha frequency (approximately 10 Hz ), where propagating signals are inherently weakly damped, and wavelengths are large. When certain model parameters have similar spatial profiles, as is expected from physiology, the low-frequency discrepancies tend to cancel, and the uniform analysis with local parameter values is an adequate approximation to the full nonuniform one across the whole spectrum, at least for large-scale nonuniformities. After comparing the uniform and nonuniform analyses, we consider one possible application of the nonuniform analysis: studying the phenomenon of occipital alpha dominance, whereby the alpha frequency and power are greater at the back of the head (occipitally) than at the front. In order to infer realistic nonuniformities in the model parameters, the uniform version of the model is first fitted to data recorded from 98 normal subjects in a waking, eyes-closed state. This yields a set of parameters at each of five electrode sites along the midline. The inferred parameter nonuniformities are consistent with anatomical and physiological constraints. Introducing these spatial profiles into the full nonuniform model then quantitatively reproduces observed site-dependent variations in the alpha power and frequency. The results confirm that the frequency shift is mainly due to a decrease in the corticothalamic propagation delay, but indicate that the delay nonuniformity cannot account for the observed occipital increase in alpha power; the occipital alpha dominance is due to decreased cortical gains and increased thalamic gains in occipital regions compared to frontal ones.

Nonuniform corticothalamic continuum model of electroencephalographic spectra with application to split-alpha peaks

Recent theoretical work has successfully predicted electroencephalographic spectra from physiology using a model corticothalamic system with spatially uniform parameters. The present work incorporates parameter nonuniformities into this model via the coupling they induce between spatial eigenmodes. Splitting of the spectral alpha peak, an effect seen in a small percentage of the normal population, is investigated as an illustrative special case. It is confirmed that weak splitting can arise from mode structure if the peak is sufficiently sharp, even for uniform parameters. However, it is further demonstrated that greater splitting can result from nonuniformities, and it is argued that this mechanism for split alpha is better able to account quantitatively for this effect than previously suggested alternatives of pacemakers or purely cortical resonances. On introducing nonuniformities in corticothalamic loop time delays, we find that the alpha frequency also varies as one moves from the front to the back of the head, in accord with observations, and that analogous (but less distinct) variations are seen in the beta peak. Analysis shows realistic variations of around +/-10 ms relative to the mean loop delay of approximately 80 ms can account for observed splittings of about 1 Hz. It is also suggested that subjects who display clear alpha splitting form the tail of a distribution of magnitude of cortical inhomogeneity, rather than a separate population.

Neurophysical modeling of brain dynamics

A recent neurophysical model of brain electrical activity is outlined and applied to EEG phenomena. It incorporates single-neuron physiology and the large-scale anatomy of corticocortical and corticothalamic pathways, including synaptic strengths, dendritic propagation, nonlinear firing responses, and axonal conduction. Small perturbations from steady states account for observed EEGs as functions of arousal. Evoked response potentials (ERPs), correlation, and coherence functions are also reproduced. Feedback via thalamic nuclei is critical in determining the forms of these quantities, the transition between sleep and waking, and stability against seizures. Many disorders correspond to significant changes in EEGs, which can potentially be quantified in terms of the underlying physiology using this theory. In the nonlinear regime, limit cycles are often seen, including a regime in which they have the characteristic petit mal 3 Hz spike-and-wave form.

Simulated electrocortical activity at microscopic, mesoscopic, and global scales

Simulation of electrocortical activity requires (a) determination of the most crucial features to be modelled, (b) specification of state equations with parameters that can be determined against independent measurements, and (c) explanation of electrical events in the brain at several scales. We report our attempts to address these problems, and show that mutually consistent explanations, and simulation of experimental data can be achieved for cortical gamma activity, synchronous oscillation, and the main features of the EEG power spectrum including the cerebral rhythms and evoked potentials. These simulations include consideration of dendritic and synaptic dynamics, AMPA, NMDA, and GABA receptors, and intracortical and cortical/subcortical interactions. We speculate on the way in which Hebbian learning and intrinsic reinforcement processes might complement the brain dynamics thus explained, to produce elementary cognitive operations.

Neurophysical theory of coherence and correlations of electroencephalographic and electrocorticographic signals

Correlation and coherence functions of electroencephalographic signals are calculated using a recent continuum theory that has previously yielded excellent agreement with observations of electroencephalographic spectra. The predicted properties of these functions are found to be in semiquantitative agreement with observations for parameters consistent with those used in previous studies of spectra. The corresponding results for electrocorticographic signals point to an additional contribution at characteristic scales of around 6mm, as has been previously inferred, and are consistent with a crossover to the long-range behavior seen in scalp data. Analysis within the framework of the model enables constraints on the relative strengths of the two contributions to be inferred, and makes it plausible that the short-range component reflects the point-spread function of external stimuli and corticothalamic feedback reaching the cortex.

Wave-number spectrum of electrocorticographic signals

A physiologically based continuum model of corticothalamic electrodynamics is generalized and used to derive the theoretical form of the electrocorticographic (ECoG) wave-number spectrum. A one-dimensional projection of the spectrum is derived, as is the azimuthally averaged two-dimensional spectrum for isotropic and anisotropic cortices. The predicted spectra are found to consist of a low-k plateau followed by three regions of power-law decrease, which result from filtering of the electrical activity through physical structures at different scales in the cortex. The magnitude of the maximum theoretical power-law exponent is larger for the two-dimensional (2D) spectrum than for its 1D counterpart. The predicted spectra agree well with experimental data obtained from 1D and 2D recording arrays on the cortical surface, enabling the structures in the brain that are important in determining spatial cortical dynamics to be identified. The cortical dispersion relation predicted by our model is also investigated, providing insight into the relationships between temporal and spatial brain dynamics.

Interpretation of scaling properties of electroencephalographic fluctuations via spectral analysis and underlying physiology

Detrended fluctuation analysis has recently demonstrated the existence of two approximate temporal scaling regimes in locally detrended human electroencephalographic (EEG) fluctuations, and has suggested a connection between the location of the breakpoint between regimes and the alpha resonance near 10 Hz. It is shown here that these scalings can be explained in terms of the filtering of the underlying power spectrum implied by the detrending process. Using a recent physiologically based model of EEG generation, the main features of the scalings, and deviations from them, are related to the underlying physiology of dendritic propagation and muscle electrical activity, and it is concluded that the effects of such physiological features are usually clearer in spectra.

Wave-number spectrum of electroencephalographic signals

A recently developed, physiologically based continuum model of corticothalamic electrodynamics is used to derive the theoretical form of the electroencephalographic wave-number spectrum and its projection onto a one-dimensional recording array. The projected spectrum is found to consist of a plateau followed by regions of power-law decrease with various exponents, which are dependent on both model parameters and temporal frequency. The theoretical spectrum is compared with experimental results obtained in other studies, showing good agreement. The model provides a framework for understanding the nature of the spatial power spectrum by linking the underlying physiology with the large-scale dynamics of the brain.

Toward an integrated continuum model of cerebral dynamics: the cerebral rhythms, synchronous oscillation and cortical stability

Continuum models of cerebral cortex with parameters derived from physiological data, provide explanations of the cerebral rhythms, synchronous oscillation, and autonomous cortical activity in the gamma frequency range, and suggest possible mechanisms for dynamic self-organization in the brain. Dispersion relations and derivations of power spectral response for the models, show that a low frequency resonant mode and associated travelling wave solutions of the models' equations of state can account for the predominant 1/f spectral content of the electroencephalogram (EEG). Large scale activity in the alpha, beta, and gamma bands, is accounted for by thalamocortical interaction, under regulation by diffuse cortical excitation. System impulse responses can be used to model Event-Related Potentials. Further classes of local resonance may be generated by rapid negative feedbacks at active synapses. Activity in the gamma band around 40 Hz, associated with large amplitude oscillations of pulse density, appears at higher levels of cortical activation, and is unstable unless compensated by synaptic feedbacks. Control of cortical stability by synaptic feedbacks offers a partial account of the regulation of autonomous activity within the cortex. Synchronous oscillation occurs between concurrently excited cortical sites, and can be explained by analysis of wave motion radiating from each of the co-active sites. These models are suitable for the introduction of learning rules-most notably the coherent infomax rule.