New developments in
EEG research
Part 2. Spatial analysis
in four steps
Walter J Freeman
University of California
at Berkeley
http://sulcus.berkeley.edu
Steps in spatial EEG Analysis:
1. Electrode design
2. Spatial spectral analysis
3. Spatial pattern classification
4. Location of frames in time
Early on I.T. was repudiated
by the key designer of the
serial digital computer:
“Whatever the language of
the brain is, it cannot fail to
differ considerably from
what we consciously and
explicitly consider as
mathematics.”
The Computer and the Brain
Jancsi von Neumann New Haven: Yale UP, 1952
1904-1958
“Brains lack the arithmetic
and logical depth that
characterize our
computations… .”
“We require exquisite
numerical precision over
many logical steps to
achieve what brains
accomplish in very few
short steps.”
John von Neumann
Step One in spatial EEG Analysis: Electrode design
Clinical arrays give spatial samples;
Widely spaced.
Sparse sampling gives temporal modular signals.
High-density arrays give spatial patterns:
Closely spaced.
High resolution gives access to spatial patterns.
Walter J Freeman
University of California at Berkeley
Scalp EEG
Blink artifact
Standard 10-20 montage for clinical scalp EEG recording
Referential
Bipolar
Structural MRI with 64 electrodes
WJF courtesy of Jeff Duyn at NIH and Thomas Witzel at MIT
Extracranial arrays
This photographic montage shows the
pial surface of my ‘brain in a vat’, projected to the scalp. Gyri are light, sulci
dark. EEG were from 64 electrodes.
Walter J Freeman
From Freeman et al. 2003
University of California at Berkeley
Step Two in spatial EEG analysis: Spatial spectra
The electrode spacing corresponds to the digitizing step
in time: 3 ms gives practical Nyquist frequency = 125 Hz.
A sample rate of 3.33/cm (3 mm interval) on the scalp
gives the practical Nyquist frequency: 1.0 cycle/cm.
The spatial power spectral density PSDx gives the basis
for choosing the optimal spatial sample interval.
The PSDt is from 1000 steps, averaged over 64 EEGs.
The PSDx is from 64 channels, averaged over 1000 steps.
Walter J Freeman
University of California at Berkeley
Temporal spectra from frontal scalp
From Freeman et al. 2003
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 impedances
of dura, skull and scalp, yet a prominent peak persists @ .1-.3 c/cm.
From Freeman et al. 2003
A peak appears only if the beta-gamma waves
are synchronous over long distances (to 19 cm).
From Freeman et al. 2003
Decomposition of spatial spectrum by temporal pass band
From Freeman et al. 2003
A temporal pulse has the spatial frequency of the gyri.
• The Hilbert transform is needed to detect and
measure the temporal pulse in EEG activity.
• A wide electrode array is needed to detect pulses.
• Temporal band pass filtering is needed to reduce
spurious phase slip.
• An objective criterion is needed to set the filter in
the beta or gamma range.
A tuning curve is constructed using the cospectrum
between unfiltered alpha and the SDx of the phase.
Noise and nonlinearity in broad-spectrum signals
give the appearance of random walk or a Markov
process known as ‘phase slip’. Band pass temporal
filtering is essential to make sense of the data.
Co-spectra of raw EEG vs. phase SDx
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
Band 12-30 Hz
From Freeman, Burke & Holmes, 2003
Walter J Freeman
University of California at Berkeley
Step Three in spatial EEG analysis:
Pattern classification
• Analysis of olfactory bulbar EEGs reveals repeated
state transitions induced by respiration.
• The gamma activity is generated by global
interactions, so that the same wave form appears on
all channels with intracranial recording.
• The spatial patterns of amplitude modulation of
the carrier wave form are modified by training.
An inhalation triggers a state transition to an attractor
in a landscape. A stimulus selects a category of input.
Cognitive-related EEG information is in the spatial domain.
Left hemisphere of the rabbit brain.
Squares show 8x8 electrode arrays.
Circles show modal and 95% diameter activity domains.
Each new pattern of neural activity has the form of
amplitude modulation (AM) of an aperiodic carrier wave
in the beta or gamma range. AM patterns change under
classical and operant conditioning.
Each frame gives a point in 64-space. Multiple frames are
projected into 2-space for classification, here by stepwise
discriminant analysis. Similar patterns give clusters of points.
Classificatory information is spatially distributed.
Correct classification depends on the number of channels,
not their locations. No channel is more or less important
than any other. The spatial density of information is
uniform, despite variation in content.
Lashley’s Dilemma
‘Generalization is one of the most
primitive basic functions of
organized nervous tissue.’ …
‘Here is the dilemma. Nerve
impulses are transmitted through
definite cell-to-cell connections.
Yet all behavior is determined by
masses of excitation. … The
Karl Lashley (1942) problem is universal in activities
of the nervous system.’
His dilemma is resolved by neurodynamics.
AM pattern classification in serial conditioning.
AM patterns lack invariance with respect to stimuli.
Comparison of EEGs from paleocortex and neocortex
Visual cortical EEGs give 1/f
power spectral densities.
From Barrie, Freeman & Lenhart, 1996
Spatial patterns, visual cortex
Above: 64 EEGs unfiltered.
Right: Contour plots of
gamma amplitude at three
latencies.
Algorithm for binary classification by Euclidean distance
1. Collect 40 trials artifact-free:
20 reinforced = CS+; 20 not reinforced = CS-.
2. Divide into 10 each training cases and test cases and
calculate centers of gravity of training cases in 64-space.
3. Find the distance of each test case to the nearest centroid,
and tabulate which cases are correct or incorrect.
4. Cross-validate by reversing test and training sets.
5. Estimate the binomial probability of the level of correct
classification having occurred by chance.
Classification of AM patterns by Euclidean distances
Classification of AM patterns in the gamma range
p = .01
p = .05
Classification of AM patterns in the beta range
Define a new measure for pattern stability:
De is the Euclidean distance between
successive points in N-space given by the
square of the analytic amplitude, after
normalization of frame amplitude to
unit variance at each step.
De tends to maintain low values during
high values of analytic amplitude.
Increased amplitude follows pattern stabilization.
A new measure of synchrony is the ratio of variances
Frequency = 23.4 Hz
Pass band = 20-50 Hz
Window = 2 cycles, 86 ms
1/Re = Mean of the SDt / SDt of the mean
Pattern stability follows onset of phase synchrony.
The sequence of a cortical state transition
• Step 1: The phase of gamma oscillation is re-set,
as shown by the jump and plateau in SDt.
• Step 2: The cortical oscillations are re-synchronized,
as shown by the rise in Re (fall in 1/Re).
• Step 3: The rate of change in spatial pattern falls
rapidly, as shown by the decrease in De.
• Step 4: The analytic amplitude increases to a peak,
as shown by the rise in A2(t).
Step Four in spatial EEG analysis: Location of frames
The Hilbert transform provides two forms of useful
information.
• Analytic phase locates frames in time, in which
linearity and stationarity hold to good approximation;
• Analytic amplitude gives:
1. Evidence for the level of stability of AM patterns,
2. The identity of AM patterns within frames,
3. The intensity of cortical transmission.
Peaks in stabilized AM patterns in the gamma carrier range
Peaks in stabilized AM patterns in the beta carrier range
Nonlinear mapping [Sammon, 1969]
• Define an initial plane by the 2 axes with largest variance by PCA
• Calculate the N(N - 1)/2 Euclidean distances between the points in
64-space and between the points in 2-space
• Define an error function by the normalized differences between the
two sets of distances
• Minimize the error by steepest gradient descent
Classification [Barrie, Holcman and Freeman [1999]
• Define the number of clusters; label the N points by membership
• Calculate the center of gravity for the points in each cluster
• For every point find the Euclidean distance to closest center of
gravity
• Classify as 'correct' or 'incorrect'
• Display the points and draw a line between clusters
Classification using tuning curve and 3x64 frames
An optimal threshold for selecting frames based on some
measure of amplitude is found by systematic change in
threshold while re-calculating goodness of classification.
Pairwise evaluation after 6-way nonlinear mapping
Criterion of linear separability
Unsolved problems for the future
• Classification and measurement of frames with
beta and gamma carrier waves in human EEG:
size, duration, and locations in space and time
• Classification of spatial AM patterns in scalp EEG
with respect to categories of cognitive contents
• Relations of EEG to unit data and fMRI data
• Development of brain theory that is competent to
explain the properties of EEG
What theory will you test by analyzing EEG?
If you believe that cortex maintains:
A mosaic of modules
Overlapping global fields
your metaphor for neural activity is:
Cocktail party
Double, triple exposures
You treat the background activity as:
Noise
Signal
and choose your dimension for averaging:
Time
Space
You place your electrodes in arrays:
As far apart as possible
Close to avoid aliasing
to sample the modules
and under-sampling
You choose electrode diameter for spatial resolution:
Small (microelectrode)
Large (for low noise)
Your preferred spatial filter:
High-pass to localize Low-pass for reference
values
Your preferred temporal pass band:
Narrow to get frequencies
Broad to get phases
What are your sites of localization?
Areas of cortex
and basal ganglia
Project active areas
onto fMRI of lobes,
gyri and Broca’s areas
and nuclei.
Regions of brain
state space
Project infinite brain
state space into N-space,
where N is the number
of channels of EEG/MEG.
Outcomes:
Connectionist networks,
Modular operations
Attractor landscapes,
Itinerant trajectories
Conclusions
Most of the techniques illustrated in this tutorial –
FFT, Hilbert transform, wavelets,
temporal (FIR) filters, spatial (Gaussian) filters,
stepwise discriminant analysis, Euclidean distance –
are standard tools of linear analysis.
Guidance by differing brain theories leads to diametrically
opposed pictures of what EEGs look like, or should look like.
Consciousness studies need more attention
to brain theory.