Temporal and spatial analysis of electroencephalographic signals


Walter J Freeman and Rodrigo Quian Quiroga


Consciousness for most of us is realized in a rapid sequence of thoughts, feelings, perceptions and mental images, since few of us are Zen masters.  Instead of seeking measures of the state or level of consciousness in subjects, as in evaluating surgical anesthesia or sleepiness, we propose to make images of the neural activity patterns in subjects who give verbal, instrumental or behavioral feedback on their mental states. Making such images is a challenging task that can be addressed with recent advances in EEG analysis.  The objective of this tutorial is to describe these advanced methods of analysis of single and multichannel electroencephalogram (EEG) recordings.  These new algorithms can be applied in any clinical facility with standard equipment at no great expense.  They have applications to the study of attention, intention, expectancy, sensory processing, formation of meaning, learning, habituation, sensitization, epilepsy, etc.

In the first part of the tutorial we will review conventional as well as advanced methods of analysis of EEGs in the temporal and frequency domains. One of the most distinctive features of the EEGs is the appearance of oscillations in different frequency bands, which reflect the synchronized activity of a large group of neurons. Brain oscillations have been correlated with different brain processes and its power is usually quantified by means of the Fourier Transform. The Fourier Transform is so far the most used tool for the analysis of EEGs, but it assumes stationarity of the signal and it does not give any time information. It is therefore not appropriate when frequency patterns change over time. For these cases, ‘time-frequency’ representations such as the one given by the Short Time Fourier Transform are more suitable. In particular, we will describe relatively new time-frequency decomposition, namely, the Wavelet Transform, and stress its advantages in the analysis of EEG data. Brain processes involving larger neuronal assemblies or interactions between distant sites are represented in correlations between EEG electrodes. In this respect, we will describe recently proposed measures of synchronization and compare them to conventional approaches.

In the second part we will review recent advances in EEG spatial pattern imaging, with emphasis on techniques for analysis of multichannel scalp recordings from normal human volunteers. We will begin by describing the advantages of spatial analysis with 1-D arrays preparatory to 2-D recording.  We will describe reformulation of the 1-D FFT for display in log-log coordinates.  This display is useful to distinguish among various noise spectra and the “1/f” scaling that distinguishes EEGs from muscle potentials [electromyograms, EMGs].  We will show the application of the 1-D FFT to EEGs from curvilinear scalp electrode arrays to discuss temporal and spatial sampling, aliasing, the Nyquist frequencies, and the spectral distortions caused by the impedance barriers of the scalp and skull, and the sulci and gyri of cortex.  We will demonstrate the subdivision of the temporal and spatial spectra into the classical ranges by use of temporal and spatial band pass filters. We will discuss in detail a form of nonstationarity in brain dynamics, in which cortical states occur as brief stable EEG amplitude patterns, like frames in a movie film.  Each window is bracketed by sudden changes in EEG phase patterns. We will introduce the Hilbert transform, as a complement to the Fourier transform, in order to get the high temporal resolution needed to document the phase jumps.  We will conclude with discussion of the criteria for the temporal and spatial filtering that is necessary for effective use of the Hilbert transform.


Walter J Freeman                                                                    dfreeman@berkeley.edu

Professor of the Graduate School                                        tel 1-510-642-4220

Dept Molecular & Cell Biology                               fax 1-510-643-9290

University of California, Donner 101                                   http://sulcus.berkeley.edu

Berkeley CA 94720-3206

Rodrigo Quian Quiroga                                             rodri@vis.caltech.edu

Lecturer in Bioengineering.                                                    Tel: +44 116 252 2314

Dept. of Engineering                                                               http://www.vis.caltech.edu/~rodri

University of Leicester

LE1 7RH Leicester U.K.