Peter J. Cadusch

A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging

Two different methods to improve the spatial resolution of EEG are discussed: the surface Laplacian (e.g., current source density) and cortical imaging (e.g., spatial deconvolution). The former methods tend to be independent of head volume conductor model, whereas the latter methods are more model-dependent. Computer simulation of scalp potentials due to either a few isolated sources or 4200 distributed cortical sources and studies of actual EEG data both indicate that the two methods provide similar estimates of cortical potential distribution. Typical correlation coefficients between either spline-Laplacian or cortical image and simulated (calculated) cortical potential are in the 0.8-0.95 range, depending partly on CSF thickness. By contrast, correlation coefficients between simulated scalp and cortical potential are in the 0.4-0.5 range, suggesting that high resolution methods provide much better estimates of cortical potential than is obtained with conventional EEG. The two methods are also applied to steady-state visually evoked potentials and spontaneous EEG. Correlation coefficients obtained from real EEG data are in the same general ranges as correlations obtained from simulations. The new high resolution methods can provide a dramatic increase in the information content of EEG and appear to have widespread application in both clinical and cognitive studies.

EEG coherency II: experimental comparisons of multiple measures.

OBJECTIVE A concentric spheres model was used in an earlier paper to estimate the effects of volume conduction, reference electrode and spatial filtering on different EEG coherence measures. EEG data are used here to verify theoretical predictions. METHODS Three EEG data sets were: (1) 64 channel, recorded during 7 alternating periods of resting and mental calculation. (2) 128 channel, for comparison of eyes open versus eyes closed coherence. (3) 128 channel, recorded during deep sleep (stages 3 and 4) and REM. RESULTS The directions of large scale (lobeal) coherency changes between brain states are relatively independent of coherence measure. However, coherence between specific electrode pairs is sensitive to method and frequency. Average reference and digitally linked mastoids provide reasonable semi-quantitative estimates of large-scale neocortical source coherence. Close bipolar, Laplacian, and dura image methods remove most reference electrode and volume conduction distortion, but may underestimate coherence by spatial filtering. CONCLUSION Each EEG coherence method has its own potential sources of error and provides coherence estimates for different neural population sizes located in different locations. Thus, studies of coherence and brain state should include several different kinds of estimates to take full advantage of information in recorded signals.

Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials

SummaryThe electroencephalogram (EEG) is recorded by sensors physically separated from the cortex by resistive skull tissue that smooths the potential field recorded at the scalp. This smoothing acts as a low-pass spatial filter that determines the spatial bandwidth, and thus the required spatial sampling density, of the scalp EEG. Although it is better appreciated in the time domain, the Nyquist frequency for adequate discrete sampling is evident in the spatial domain as well. A mathematical model of the low-pass spatial filtering of scalp potentials is developed, using a four concentric spheres (brain, CSF, skull, and scalp) model of the head and plausible estimates of the conductivity of each tissue layer. The surface Laplacian estimate of radial skull current density or cortical surface potential counteracts the low-pass filtering of scalp potentials by shifting the spatial spectrum of the EEG, producing a band-passed spatial signal that emphasizes local current sources. Simulations with the four spheres model and dense sensor arrays demonstrate that progressively more detail about cortical potential distribution is obtained as sampling is increased beyond 128 channels.

A spatially continuous mean field theory of electrocortical activity

A set of nonlinear continuum field equations is presented which describes the dynamics of neural activity in cortex. These take into account the most pertinent anatomical and physiological features found in cortex with all parameter values obtainable from independent experiment. Derivation of a white noise fluctuation spectrum from a linearized set of equations shows the presence of strong resonances that correspond to electroencephalographically observed 0.3-4 Hz (mammalian delta), 4-8 Hz (mammalian theta), 8-13 Hz (mammalian alpha) and >13 Hz (mammalian beta) activity. Numerical solutions of a full set of one-dimensional nonlinear equations include properties analogous to cortical evoked potentials, travelling waves at experimentally observed velocities, threshold type spike activity and limit cycle, chaotic and noise driven oscillations at the frequency of the mammalian alpha rhythm. All these types of behaviour are generated with parameters that are within ranges reported experimentally. The strong dependence of the phenomena observed on inhibitory-inhibitory interactions is demonstrated. These results suggest that the classically described alpha may be instantiated in a number of qualitatively distinct dynamical regimes, all of which depend on the integrity of inhibitory-inhibitory population interactions.

Steady-state visual evoked potentials and travelling waves

OBJECTIVE The amplitude and phase of the steady-state visual evoked potential (SSVEP) is sensitive to cognition and attention but the underlying mechanism is not well understood. This study examines stimulus evoked changes in the SSVEP phase topography and the putative role of travelling waves. METHODS Eighteen subjects viewed a central-field checkerboard and full-field flicker stimulus temporally modulated at the peak alpha rhythm frequency. EEG was recorded from 10 midline scalp sites and the bipolar SSVEP obtained from differences between adjacent electrodes. RESULTS The SSVEP phase comprised either progressive variations consistent with travelling waves or a phase reversal consistent with standing waves. The checkerboard pattern elicited travelling wave patterns in 14 subjects with estimated phase velocities ranging from 7 to 11 m/s after correcting for folded cortex. The flicker stimulus elicited phase reversals in 9 subjects, suggesting standing waves. Six subjects demonstrated a phase topography specific to the stimulus with travelling wave patterns associated with the checkerboard and standing wave patterns associated with the flicker. CONCLUSIONS These differences suggest the emergence of travelling and standing waves under different spatial configurations of visual input to the cortex and that wave phenomena contribute to the spatiotemporal dynamics of the SSVEP.

A Continuum Theory of Electro-Cortical Activity

Abstract A set of non-linear continuum field equations are presented which describe the macroscopic dynamics of neural activity in cortex. Numerical solutions of the coupled non-linear system of partial differential equations show properties analogous to cortical evoked potentials, oscillations at the frequency of the mammalian alpha rhythm and non-stationary epileptic spikes.

Robust chaos in a model of the electroencephalogram: Implications for brain dynamics

Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling. (c) 2001 American Institute of Physics.

Measurement processes and spatial principal components analysis

SummarySpatial principal components analysis (SPCA) applied to the ongoing EEG yields factor loadings which, when mapped, consistently reveal symmetrical patterns resembling the spherical harmonics. In this paper, we consider the mechanisms responsible for these characteristic patterns. In doing so, we demonstrate that volume conduction is one of a family of processes capable of generating such patterns with SPCA. It is shown that any series of measurements on a sphere in which the covariance is only a function of measurement site angular separation (shift invariant processes) will yield the spherical harmonics as the eigenvectors or factor loadings of the covariance matrix. Simulations further indicate that this effect is robust and not determined by the geometry of the measurement sites. In situations where shift invariant signals coexist with those generated at specific sites (anatomically specific processes), such as evoked potentials and some artifacts, it is shown that the anatomically specific signals do not influence the eigenvectors of the covariance matrix in a uniform or random fashion. The factors most influenced are those whose symmetry is similar to that of the site specific signal.

Laser exposure of gold nanorods can induce intracellular calcium transients

Uncoated and poly(styrene sulphonate) (PSS)-coated gold nanorods were taken up by NG108-15 neuronal cells. Exposure to 780 nm laser light at the plasmon resonance wavelength of the gold nanorods was found to induce intracellular Ca(2+) transients. The higher Ca(2+) peaks were observed at lower laser doses, with the highest levels obtained at a radiant exposure of 0.33 J/cm(2) . In contrast, the cells without nanoparticles showed a consistently small response, independent of the laser dose. These initial results open up new opportunities for peripheral nerve regeneration treatments and for more efficient optical stimulation techniques.

Comparison of high resolution EEG methods having different theoretical bases

SummaryMathematically simulated data is used to obtain direct comparisons of the accuracies of spline/Laplacian and cortical imaging algorithms in predicting cortical potential. Even though the two approaches have quite different theoretical bases, the two methods provide nearly identical estimates of cortical activity at scales greater than about 2 or 3 cm when 64 electrodes are used.