Transcript Document

Spatial analysis of human EEG recorded
from multiple electrodes located on the
scalp or intracranially on the pial
surface of cortex.
A tutorial
The olfactory system
Walter J Freeman
Walter J Freeman
University
of California
http://sulcus.berkeley.edu
OUTLINE
1. Review of temporal spectral analysis and spatial
spectral analysis of human scalp EEG
2. High resolution spatial pattern discovery using
dense arrays of electrodes for EEG scalp recording
3. High resolution spatiotemporal pattern discovery
using the Hilbert transform to extract the analytic
phase and the instantaneous gamma frequency
Walter J Freeman
University of California at Berkeley
Time Ensemble Averaging, Evoked potentials
In TEA the EEG traces are aligned with the stimulus time marker and
summed over N trials at each time point. The amplitude and phase
patterns are determined by the stimulus site and the afferent axons.
Walter J Freeman
University of California at Berkeley
In SEA the amplitude and phase are endogenously determined.
Phase is defined with respect to the spatial ensemble average wave.
Walter J Freeman
University of California at Berkeley
From Freeman et al. 2003
Walter J Freeman
University of California at Berkeley
1 cm
10x10 cm
1.25 mm
1x1 cm
8x8
0.5 mm
32 mm
Walter J Freeman
1x64
8x8
University of California at Berkeley
Step One in Spatial EEG Analysis: Electrode design
The standard clinical montages are designed to give a spatial
sample from the cortex. They are intended to display signals
from discrete generators, normal or pathological. Analysis is by
Laplacian operators that improve the isolation of the signals.
An alternative approach is to search for spatial patterns of EEG
activity generated by broad areas of cortex. A different type of
array is required: high-density by close spacing of electrodes.
The method is implemented by fixing all available electrodes in
a line, with spacing that is close enough together to measure the
texture of patterns. This procedure is called “over-sampling”.
The method is applied to scalp EEG with 64 electrodes spaced
at intervals of 3 mm, giving an array that is 189 mm long.
Walter J Freeman
University of California at Berkeley
A photo montage shows the pial surface of a human brain, projected to
the scalp - gyri are light, sulci are dark. EEG were from 64 electrodes.
Representative traces are shown of EEG and muscle potentials (EMG).
From Freeman et al. 2003
Walter J Freeman
University of California at Berkeley
Step Two in Spatial EEG Analysis: Temporal spectra
Signal analysis in the time domain proceeds by calculation of the
power spectral density (PSDt) of the signal, most often by means
of the Fast Fourier Transform (FFT). This transformation from
the time domain into the temporal frequency domain enables
clinicians to detect periodic signals by the peaks they cause in the
PSDt.
The FFT also helps to determine the optimal rate at which to
sample the EEG in analog to digital conversion. The usual
criterion is to look for the peaks in the PSDt and choose a cut-off
just above the peak with the highest frequency. That cut-off is
called the Nyquist frequency. The sample rate must be at least
twice the Nyquist frequency and preferably three times higher The practical Nyquist frequency (Barlow, 1993).
Walter J Freeman
University of California at Berkeley
The most common display of the
power spectral density (PSDt) of
EEG time series is in linear
coordinates: power vs. frequency.
This prevents visualization of the
beta and gamma ranges.
The display of PSDt as log10 power
Vs. log10 frequency shows the form
as 1/fa: linear fall-off in log power
with increasing log frequency in Hz.
The real power is proportional to the
square of the frequency. Activity in
the gamma band needs substantial
metabolic energy.
Walter J Freeman
University of California at Berkeley
The conventional subdivisions of the EEG spectrum are based on
empirical observations, not on brain theory or neurodynamics.
From Freeman et al. 2003
Walter J Freeman
University of California at Berkeley
Step Three in spatial EEG analysis: Spatial spectral analysis
Calculation of the spatial power spectral density PSDx from a
curvilinear electrode array is by means of the same mathematical
algorithm in space as in time. The interval between electrodes
corresponds to the digitizing step in time series signal analysis.
The FFT is applied to the 64 amplitudes of EEG at each time
step.
In practice, the FFT is taken over a 5 s window with 1000 time
steps at a sample rate of 200/s (5 ms interval), and the average is
computed for the 64 PSDt.
Then the FFT is taken over the 189 mm window with 64 samples
at a sample rate of 3.33/cm (3 mm interval) and averaged over the
1000 time steps in the same time window.
Walter J Freeman
University of California at Berkeley
From Freeman et al. 2003
Walter J Freeman
University of California at Berkeley
Examples from nine subjects show the variability of spatial spectra.
From Freeman et al. 2003
Walter J Freeman
University of California at Berkeley
The pial PSDx is 1/f, but the scalp PSDx is not, due to impedance of
dura, skull and scalp, yet a prominent peak persists @ .1-.3 c/cm.
From Freeman et al. 2003
Walter J Freeman
University of California at Berkeley
A peak can appear in the spatial PSDx of the scalp EEG only if
the oscillations over the temporal PSDt are synchronous
everywhere in neighboring gyri facing across the sulci.
Walter J Freeman
University of California at Berkeley
The spatial spectrum is calculated for narrow temporal bands in order
to test the hypothesis that oscillations with high temporal frequency
are smoothed at high spatial frequency. This dispersion relation is
disproved. Instead, the spatial peak in the range of gyral frequency is
found in all temporal bands. This implies that an aperiodic temporal
pulse with a periodic spatial frequency exists in the scalp EEG. How
can it be demonstrated?
From Freeman et al. 2003
Walter J Freeman
University of California at Berkeley
Step Four: An introduction to cortical state transitions
Fourier analysis was not appropriate in a search for an event that was
temporally aperiodic although it was spatially periodic.
The gyral peak was most pronounced when alpha or theta was also
present in the unfiltered EEG, that is, when the EEG was also nearly
temporally periodic.
However, the broad distribution of the spatial spectral spike across
the temporal spectrum indicated that the periodic spatial event was a
temporal spike, usually occurring aperiodically, but sometimes
nearly periodically at alpha-theta rates.
The most likely candidate for this occult event was a global,
hemisphere-wide state transition, by which cortical dynamics
changed abruptly and unpredictably - as in cognition.
Walter J Freeman
University of California at Berkeley
Step Five: An introduction to the Hilbert transform
The most important characteristic of a cortical state transition is the
re-initialization of the phase of the on-going oscillations in the beta
and gamma ranges of the EEG. Because state transitions may occupy
the entire hemisphere, the change in phase can be observed in the
scalp EEG, which reflects broad, non-local spatial patterns.
Fourier analysis lacks temporal resolution, because it requires the
measurement of frequency before phase.
The Hilbert transform gives the analytic phase, from which the rate
of change in phase gives the instantaneous analytic frequency.
Therefore the method of choice for detecting state transitions in the
cortical EEG is the Hilbert transform.
Walter J Freeman
University of California at Berkeley
Walter J Freeman
University of California at Berkeley
The Hilbert transform cannot be used without band pass temporal
filtering. The identification of optimal high-pass and low-pass
settings is by constructing tuning curves to maximize the peak of
the cospectrum in the alpha range.
From Freeman, Burke & Holmes, 2003
Walter J Freeman
University of California at Berkeley
From Freeman, Burke & Holmes, 2003
Walter J Freeman
University of California at Berkeley
From Freeman, Burke & Holmes, 2003
Walter J Freeman
University of California at Berkeley
From Freeman, Burke & Holmes, 2003
Walter J Freeman
University of California at Berkeley
From Freeman, Burke & Holmes, 2003
Walter J Freeman
University of California at Berkeley
References
Freeman, W. J. [2000] Neurodynamics. Springer-Verlag.
Freeman, W. J. [2001] How Brains Make Up Their Minds.
Columbia University Press.
Freeman, W. J. [2003] A neurobiological theory of meaning,
International Journal of Bifurcation & Chaos, September.
Freeman, W. J., Burke, B C., Holmes, M. D. & Vanhatalo, S.
[2003] Clinical Neurophysiology 114(6): 1055-1066.
Freeman, W. J., Burke, B. C. & Holmes, M. D. [2003]
Human Brain Mapping 19: in press.
http://sulcus.berkeley.edu
Acknowledgments
This work was supported by grants to Prof. Robert
Kozma from NASA (NCC2-1244) and from NSF
(EIA-0130352). EEG and EMG data were collected
and edited by Dr. Mark D. Holmes and Dr. Sampsa
Vanhatalo, the EEG Clinic of Harborview Hospital,
University ofThe
Washington,
olfactory systemSeattle, and analyzed in
the Department of Molecular & Cell Biology, the
University of California at Berkeley. Programs
were by Linda Rogers and Brian Burke. Prior
Walter J Freeman
animal data were collected in collaboration
with John Barrie, Mark Lenhart, and
Gyöngyi Gaál, and with support
by grants from NIMH (MH06686)
and ONR (N00014-93-1-09380.