1: Tutorial for ASSC9 24 June 2005 Part 2

56
New developments in EEG research Part 2. Spatial analysis in four steps Walter J Freeman University of California at Berkeley http://sulcus.berkeley.edu

description

1: Tutorial for ASSC9 24 June 2005 Part 2. New developments in EEG research Part 2. Spatial analysis in four steps. Walter J Freeman University of California at Berkeley http://sulcus.berkeley.edu. 2: Steps in spatial EEG Analysis. Steps in spatial EEG Analysis: - PowerPoint PPT Presentation

Transcript of 1: Tutorial for ASSC9 24 June 2005 Part 2

Page 1: 1: Tutorial for ASSC9 24 June 2005 Part 2

New developments in EEG research

Part 2. Spatial analysisin four steps

Walter J FreemanUniversity of California at Berkeleyhttp://sulcus.berkeley.edu

1: Tutorial for ASSC9 24 June 2005 Part 2

Page 2: 1: Tutorial for ASSC9 24 June 2005 Part 2

Steps in spatial EEG Analysis:

1. Electrode design

2. Spatial spectral analysis

3. Spatial pattern classification

4. Location of frames in time

2: Steps in spatial EEG Analysis

Page 3: 1: Tutorial for ASSC9 24 June 2005 Part 2

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 New Haven: Yale UP, 1952Jancsi von Neumann

1904-1958

Page 4: 1: Tutorial for ASSC9 24 June 2005 Part 2

“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

Page 5: 1: Tutorial for ASSC9 24 June 2005 Part 2

Step One: Spatial sampling vs. spatial function

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.

Step One in spatial EEG Analysis: Electrode design

Walter J Freeman University of California at Berkeley

Page 6: 1: Tutorial for ASSC9 24 June 2005 Part 2

Scalp EEG

Blink artifact

Page 7: 1: Tutorial for ASSC9 24 June 2005 Part 2

Standard 10-20 montage for clinical scalp EEG recording

Referential Bipolar

Page 8: 1: Tutorial for ASSC9 24 June 2005 Part 2

Structural MRI with 64 electrodes

WJF courtesy of Jeff Duyn at NIH and Thomas Witzel at MIT

Page 9: 1: Tutorial for ASSC9 24 June 2005 Part 2

This photographic montage shows the pial surface of my ‘brain in a vat’, pro-jected to the scalp. Gyri are light, sulci dark. EEG were from 64 electrodes.

Scalp recording with high density linear array

Walter J Freeman University of California at Berkeley

From Freeman et al. 2003

Extracranial arrays

Page 10: 1: Tutorial for ASSC9 24 June 2005 Part 2

Step Three: Spatial spectral analysis

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 scalpgives 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

Page 11: 1: Tutorial for ASSC9 24 June 2005 Part 2

Temporal spectra from frontal scalp

From Freeman et al. 2003

Page 12: 1: Tutorial for ASSC9 24 June 2005 Part 2

Spatial spectrum of the gyri-sulci & EEG

Walter J Freeman University of California at Berkeley

From Freeman et al. 2003

Page 13: 1: Tutorial for ASSC9 24 June 2005 Part 2

Illustration of intracranial arrays From Menon et al 1996

Page 14: 1: Tutorial for ASSC9 24 June 2005 Part 2

EEG awake intracranial

Page 15: 1: Tutorial for ASSC9 24 June 2005 Part 2

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

Page 16: 1: Tutorial for ASSC9 24 June 2005 Part 2

A peak appears only if the beta-gamma waves are synchronous over long distances (to 19 cm).

Explain the spatial spectral peak at the frequency of gyri

Page 17: 1: Tutorial for ASSC9 24 June 2005 Part 2

Decomposition of spatial spectrum by temporal pass bandFrom Freeman et al. 2003

Page 18: 1: Tutorial for ASSC9 24 June 2005 Part 2

A temporal pulse has the spatial frequency of the gyri.

From Freeman et al. 2003

Page 19: 1: Tutorial for ASSC9 24 June 2005 Part 2

• 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.

Needs to be met by use of the Hilbert transform

Page 20: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Numerical instability of Hilbert transform without filtering

Page 21: 1: Tutorial for ASSC9 24 June 2005 Part 2

Construction of tuning curves for optimized band pass filters

Page 22: 1: Tutorial for ASSC9 24 June 2005 Part 2

Walter J Freeman University of California at Berkeley

Partial synchronization across the frontal area

From Freeman, Burke & Holmes, 2003Co-spectra of raw EEG vs. phase SDx

Page 23: 1: Tutorial for ASSC9 24 June 2005 Part 2

Walter J Freeman University of California at Berkeley

Comparison of CAPD in the beta and gamma ranges

From Freeman, Burke & Holmes, 2003

Page 24: 1: Tutorial for ASSC9 24 June 2005 Part 2

Walter J Freeman University of California at Berkeley

Spatial filtering to clarify analytic phase differences

From Freeman, Burke & Holmes, 2003

Band 12-30 Hz

Page 25: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Step Three: pattern classification

Page 26: 1: Tutorial for ASSC9 24 June 2005 Part 2

An inhalation triggers a state transition to an attractor in a landscape. A stimulus selects a category of input.

Page 27: 1: Tutorial for ASSC9 24 June 2005 Part 2

Electrode arrays on rabbit neocortex and olfactory parts

Left hemisphere of the rabbit brain. Squares show 8x8 electrode arrays.

Circles show modal and 95% diameter activity domains.

Cognitive-related EEG information is in the spatial domain.

Page 28: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Spatial patterns of EEG

Page 29: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Stepwise discriminant analysis

Page 30: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Classificatory information is spatially distributed.Distribution of classificatory information

Page 31: 1: Tutorial for ASSC9 24 June 2005 Part 2

Karl LashleyLashley’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 problem is universal in activities

of the nervous system.’Karl Lashley (1942)

His dilemma is resolved by neurodynamics.

Page 32: 1: Tutorial for ASSC9 24 June 2005 Part 2

AM pattern classification in serial conditioning.

AM patterns lack invariance with respect to stimuli.

Page 33: 1: Tutorial for ASSC9 24 June 2005 Part 2

John Dewey on Representationalism

Page 34: 1: Tutorial for ASSC9 24 June 2005 Part 2

Visual cortical EEGs give 1/f power spectral densities.

From Barrie, Freeman & Lenhart, 1996

Comparison of EEGs from paleocortex and neocortex

Page 35: 1: Tutorial for ASSC9 24 June 2005 Part 2

Spatial patterns, visual cortex

Above: 64 EEGs unfiltered. Right: Contour plots of

gamma amplitude at three latencies.

Page 36: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Page 37: 1: Tutorial for ASSC9 24 June 2005 Part 2

Classification of AM patterns by Euclidean distances

Page 38: 1: Tutorial for ASSC9 24 June 2005 Part 2

Classification of AM patterns in the gamma range

Page 39: 1: Tutorial for ASSC9 24 June 2005 Part 2

Classification of AM patterns in the beta range

p = .01

p = .05

Page 40: 1: Tutorial for ASSC9 24 June 2005 Part 2

Define a new measure for pattern stability

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.

Page 41: 1: Tutorial for ASSC9 24 June 2005 Part 2

Relation of De to analytic amplitude

Increased amplitude follows pattern stabilization.

Page 42: 1: Tutorial for ASSC9 24 June 2005 Part 2

A new measure of synchrony is the ratio of variances

1/Re = Mean of the SDt / SDt of the mean

Frequency = 23.4 HzPass band = 20-50 Hz Window = 2 cycles, 86 ms

Page 43: 1: Tutorial for ASSC9 24 June 2005 Part 2

Pattern stability follows onset of phase synchrony.

Page 44: 1: Tutorial for ASSC9 24 June 2005 Part 2

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).

Page 45: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Step Four: location of frames

Page 46: 1: Tutorial for ASSC9 24 June 2005 Part 2

Peaks in stabilized AM patterns in the gamma carrier range

Page 47: 1: Tutorial for ASSC9 24 June 2005 Part 2

Peaks in stabilized AM patterns in the beta carrier range

Page 48: 1: Tutorial for ASSC9 24 June 2005 Part 2

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

Page 49: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.

Page 50: 1: Tutorial for ASSC9 24 June 2005 Part 2

Pairwise evaluation after 6-way nonlinear mapping

Page 51: 1: Tutorial for ASSC9 24 June 2005 Part 2

Criterion of linear separability

Page 52: 1: Tutorial for ASSC9 24 June 2005 Part 2

•  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

Unsolved problems for the future

Page 53: 1: Tutorial for ASSC9 24 June 2005 Part 2

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

What theory will you test?

Page 54: 1: Tutorial for ASSC9 24 June 2005 Part 2

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

Experimental determinations

Page 55: 1: Tutorial for ASSC9 24 June 2005 Part 2

What are your sites of localization?

Areas of cortex Regions of brain and basal ganglia state space

Project active areas Project infinite brain onto fMRI of lobes, state space into N-space, gyri and Broca’s areas where N is the number and nuclei. of channels of EEG/MEG.

Outcomes:

Connectionist networks, Attractor landscapes,Modular operations Itinerant trajectories

What are your sites of localization?

Page 56: 1: Tutorial for ASSC9 24 June 2005 Part 2

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.