Understanding Waves

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Understanding Waves

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Title: Understanding Waves

1
Understanding Waves
An introduction to quantitative EEG assessment
David A Kaiser, Ph.D.
2
Our job is to make real what we imagined as kids
would exist

After (humans) had explored all the suns in the
universe, and all the planets of all the suns,
they realized that there was no other life in the
universe, and that they were all alone. .
And they were very happy
because then they knew it was up to them to
become all the things they had imagined they
would find."
- Schoolteacher in Lanford Wilsons 5th of July

3
Were interested in eliciting proper brain
behavior
4
Electrophysiological indices of brain behavior

single neuron recordings evoked potentials
spontaneous activity

5
Continuous EEG (Electroencephalography)
6
Amplifying scalp potentials, from cortical
sources below
7
Why amplify?

102 volts - Wall socket
10-3 volts - EKG
(millivolts)
10-5 volts EOG
10-6 volts EEG
(microvolts)

Attenuation of signal through insulating layers

9
Artifact can make everything upside down and
meaningless
10
Sources of Artifact

Non-cerebral (physiological)
Equipment-related
Computational
Cerebral (functional)
Unstable background
state transitions, transients, drowsiness
Inappropriate mental processes
Inappropriate frequency correspondence

11
Eye movement blinks
12
Muscles Heart, jaw, and neck
13
Non-biological artifacts
Impedance artifact
Referential movements
14
Computational artifactSpectral Leakage
Undersampling
E.g. heart beat of 60 bpm 60 samples/min DC 90
samples/min 15 bpm
15
Tapering windows eliminate leakage significantly,
but they produce two news forms of artifacts
1. Spectral broadening (acceptable) 2.
Sampling bias (less so)
Spectral broadening of 17 Hz signal
16
Analysis sensitive to epoch positions due to
sampling bias
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Solution
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Artifact Management
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Seaming
Seaming Delta generator
21
Leverage tapering in artifact mgmt
SKIL 3.0 uses Blackman-Harris -92db window,
better as handling artifact than Hamming window
22
Hamming vs Blackman-Harris-92db
frequency response
http//www.diracdelta.co.uk/science/source/b/l/bla
ckman-harris20window/source.html
23
Macrostate analysis generally means
stabilization, minimal state transitionsLook at
the dataMore is better
24
Power vs Magnitude

Power
Magn

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Natural Log Magnitude (or Ln Power /2)

Ln Natural log (base e, not base 10)
e 1 1/1! 1/2! 1/3! 2.718

Value Log
A 10 1
B 100 2
Avg 55 1.5 or 1.74
Nonlinear measures misbehave
26
Why analyze spectra instead of voltage?Spectra
better reflects neural coding of mental events
such as the desynchronization-behavior
relationship
27
Why comodulation (and all other spectral
parameters) are performed on magnitude (mV)
instead of power (mV2) in SKIL

Dietsch (1932) analyzed a few EEG signals using
Fourier (1831) analysis (DFT).
Fast Fourier Transform (FFT) algorithm invented
(Cooley Tukey, 1965) , allowing practical
spectral applications
Dumermuth Fluhler (1967) applied FFT to EEG

Why assume brain rhythms-to-mental activity
corresponds with a power function? (i.e., brain
behaviors are associated with larger changes in
mental behavior) More conservative to assume
linearly relationship until proven
otherwise. Small change in brain activity relate
to what size change in mental activity Change
from 10 uV to 11 uV 10 increase
or Change from 100uV2 to 121uV2 21
increase or Change from 1 log uV to 1.04 log uV
4 increase This is a scientific question,
not theoretical
28
Issues with Power Spectrum analysis (as opposed
to Magnitude spectrum)
29
Brief aside on using spectral magnitude in EEG
analysis

Neurofeedback We train amplitude bursts
(analogous to magnitude) so assess magnitude
Science
Magnitude keeps frequency analysis in the
original measurement units (uV)
EEG power violates the parametric normality
assumption
Power is sensitive to epoch length because it
misbehaves (i.e., violates communicative laws of
algebra)
EEG is an interval scale (a differential), not a
ratio scale (an absolute) so linear
correspondences are likely
Parseval's theorem mistakenly interpreted as only
for power, but it also works for magnitude.
We derive spectral magnitudes dozens of ways,
arriving at the original measurement unit (i.e.,
without transforming the measurement by squaring
it)
Psychophysical data find a basic linearity
between neural coding and mental events
(Mountcastle, K Johnson), thus power may be
inflating Type I errors

30
Linearity of neuro-psychophysics neural coding
to mental experiences
31
Deciphering Gross Neural codingBrainwave
frequencies and approximate mentation

0.1 4 Hz DELTA Slow wave sleep
4-7 Hz THETA Inward focus, daydream
8-12 Hz ALPHA Sensory quiescence,
preparatory recruitment
12-15 Hz SMR Motoric quiescence
stage 2 sleep
spindle
12 Hz BETA Active external attention
30 Hz GAMMA Muscle, anxiety, time-
binding

32
Eyes Closed Eyes Open
Rest Baselines
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Activation and thalamocortical network
34
Steriade et al
35
Low information High informationState
36
Inhibitory networks produce population rhythmicity
37
Idling rhythm ? responsive quiescence

Actively turned off so easier to recruit
neurons in such states than active processing
states

38
When is theta alpha? Dominant frequency
determination
39
Dominant Frequency
4-8 Hz
8-12 Hz
Healthy Adult
Healthy Child
40
Untailored Dominant Frequency

IAF individuals alpha frequency

41
1 Hz Brain Maps
42
One goal is to identify greatest brain clot
specific source of greatest dysfunction -- for
Crux training (why we need laplacian
techniques)
43

What if the clot is in a network?

44
Connectivity is key to intelligent behavior
White matter increases with development
45
Myelination across lifespan
46
Detecting networks through shared energies
(amount or timing of energies)
47
Defining my terms

Raw EEGs are voltages across time
In time domain, we estimate
amplitude (positive negative values)
at a sample rate (only positive)
In frequency domain, we estimate
magnitude (only positive)
phase (positive and negative)
at a frequency
Spectral power is the square of spectral
magnitude
(power is nonlinear, so where squaring occurs
can vary results depending upon if squaring
occurs at epoch level, at condition level, or at
sampling point)

48
How similar are two signals in frequency content?

Phase consistency coherence
(Goodman, 1957 Walter, 1961)
Magnitude consistency comodulation
(Pearson, 1896 Kaiser, 1994)

Coh range from 0.0 to 1.0 Comod range
from -1.0 to 1.0
49
History of EEG phase magnitude investigations
Early phase descriptions Adrian EDK Yamagiwa
(1935) The origin of the Berger rhythm, Brain, 58
323-351. Motokawa K Tuziguti K (1944). Alpha
phases in EEG activity. Japanese Journal of
Medical Sciences, 10, 23-38. Computation of
Coherence Goodman, N.R. (1957, diss.). On the
joint estimation of the spectra, cospectrum and
quadrature spectrum of a two-dimensional
stationary Gaussian process. Princeton Univ. JW
Tukey advisor Walter DO. (1961).Spectral
analysis for electroencephalograms mathematical
determination of neurophysiological relationships
from records of limited duration. Experimental
Neurology, 8, 151-181.
Early magnitude descriptions Berger H. (1929).
Ueber das Elektroenkephalogramm des Menschen.
Archiv Psy Nerv, 87, 527-570. Dietsch, G.
(1932). Fourier-analyse von Elektrenkephalog. des
Menschen. Pflüger's Arch. Ges. Physiol., 230,
106-112. Computation of Comodulation Kaiser,
DA. (1994, diss.). Interest in Films as Measured
by Subjective Behavioral Ratings and
Topographic EEG. UCLA. MB Sterman,
advisor Sterman, M.B. Kaiser, D.A. (1999).
Topographic analysis of spectral density
co-variation normative database and clinical
assessment. Clinical Neurophysiology, 110 (S1),
S80.
50
Comodulation was invented to examine low spatial
resolution concerns of EEG topography (e.g.,
volume conduction, Nunez, 1990)
Does surface EEG reflect cortical potentials
well? - if not, all neighbors will be equally
correlated with each other - if so, correlations
will be stronger within functionally-related areas
51
Signals are

coherent if phase relationship is stable

comodulated if magnitude relationship
is stable

52
Coherence indicates functional relatedness, not
just proximity
53

Coherence analysis provides
Coherence (Coh)
Phase delay (/-180o)
Comodulation analysis provides
Comodulation (Comod)
Unity1.0 Diff/Sum

54
Smoke test test of orthogonality

For 2000 signal pairs, correlation between values
was rho 0.10

55
Additional definitions

Coherence is stability of phase1
Such shared timing indicates a common origin
(df0, matter, globality restraining locally)
Comodulation is stability of amplitude1
Such shared energy indicates functional unity2
Energy is freedom, freedom of representation
(df up to infinity, locality advancing
globally)
Both are calculated across time.
Coherence averages across time (sameness)
Comodulation evaluates changes across time
(differences).
Coherence quantifies the degree of similar
influences
Comodulation quantifies the degree of similar
autonomy
1 stability of phase difference, or amplitude
difference, between signals
2 stability or consistency, conformity,
congruity, correspondence, similarity,
stationarity, harmony whatever metaphor you
choose

56
Comodulation is most prominent in the dominant
frequency activity.Coh? Likely the same, not yet
calculated
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Focality Magn/Comod or like Activity/Connectivit
y
Corticality comod/coh

61
Focality Local events dissociated from
(precede, lag) network responses
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Functional model for dominant frequency
...suggests distributed generator Complex
recruitment Coordination Feedback system -
Modulators Corticothalamic projections Slow,
diffuse, weak

...suggests focal generator (pacemaker) Primitive
recruitment Synchronization Fastforward system -
Drivers Thalamocortical projections Fast, focal,
strong
64
Data (rho) and Statistical (z) values
65
Orient ones reading by the fixed points each
site is compared to itself in each head
66
College students generally show frontal
plasticity and immaturity (esp. in comodulation)
67
Effect of Guitar playing on motor strip (C3 Cz C4)
68
Hypermodulation of depression
69
Network Maps (anterior callosotomy case)
Comod
Coh
Unity
Phase
70
Referential vs Laplacian
71
No intervention vs Neurofeedback (focal seizure)
72
Autism as functional fragmentation (global
disconnectivity) replicated
73
Autism as functional fragmentation (global
disconnectivity) -rep
74
EEG Comod and Coh values are often very similar
generally
Eyes Closed Replications Within subject, n20
EC1 v 2 r .91 Coh r .84 Comod Being more
reliable also can mean less sensitive to state
differences

Dark bars Comod Red/green bars Coherence

75
Higher left brain integration in Asperger
compared to normals
76
Greater interhemispheric integration in normal
children (comod only)
77
In Asperger, lower right anterior (Fp2 F4 F8) and
higher left posterior (T5 P3 O1)
78
Global Connectivity n by age19-site mean of 18
comparisons each site
Life is about making connections...
79
in fact, slowing down the rate of connections at
some times in your life may even do you some
good!Intelligence resists the natural neural
integration trajectory
Neural behavioral indices of neoteny
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Fisher Z transformation for high values
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LORETA Low resolution EEG tomographical array
(based on maximal smoothness)presumes singular
source in isomorphic volume
Source Imaging
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Associated MRI slices to 21 sites
85
SKIL Source ImagingBrodmann Map estimations
based on brain heterogeneity
86
Hidden revealed by Remontaging
87
Montage Differences
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Brodmann complete (BA 55)
89
BA by Primary function