Understanding Waves

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Understanding Waves
An introduction to quantitative EEG assessment
David A Kaiser, Ph.D.
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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

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

• single neuron recordings evoked potentials
  spontaneous activity

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

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

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• Attenuation of signal through insulating layers

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Artifact can make everything upside down and
meaningless
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Sources of Artifact

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

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Eye movement blinks
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Muscles Heart, jaw, and neck
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Non-biological artifacts
Impedance artifact
Referential movements
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Computational artifactSpectral Leakage
Undersampling
E.g. heart beat of 60 bpm 60 samples/min DC 90
samples/min 15 bpm
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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
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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
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Leverage tapering in artifact mgmt
SKIL 3.0 uses Blackman-Harris -92db window,
better as handling artifact than Hamming window
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Hamming vs Blackman-Harris-92db
frequency response
http//www.diracdelta.co.uk/science/source/b/l/bla
ckman-harris20window/source.html
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Macrostate analysis generally means
stabilization, minimal state transitionsLook at
the dataMore is better
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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
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Why analyze spectra instead of voltage?Spectra
better reflects neural coding of mental events
such as the desynchronization-behavior
relationship
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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
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Issues with Power Spectrum analysis (as opposed
to Magnitude spectrum)
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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

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Linearity of neuro-psychophysics neural coding
to mental experiences
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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

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

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

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

• IAF individuals alpha frequency

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1 Hz Brain Maps
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One goal is to identify greatest brain clot
specific source of greatest dysfunction -- for
Crux training (why we need laplacian
techniques)
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• What if the clot is in a network?

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Connectivity is key to intelligent behavior
White matter increases with development
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Myelination across lifespan
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Detecting networks through shared energies
(amount or timing of energies)
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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)

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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
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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.
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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
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Signals are

• coherent if phase relationship is stable

• comodulated if magnitude relationship
  is stable

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Coherence indicates functional relatedness, not
just proximity
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• Coherence analysis provides
• Coherence (Coh)
• Phase delay (/-180o)
• Comodulation analysis provides
• Comodulation (Comod)
• Unity1.0 Diff/Sum

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Smoke test test of orthogonality

• For 2000 signal pairs, correlation between values
  was rho 0.10

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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

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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

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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
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Data (rho) and Statistical (z) values
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Orient ones reading by the fixed points each
site is compared to itself in each head
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College students generally show frontal
plasticity and immaturity (esp. in comodulation)
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Effect of Guitar playing on motor strip (C3 Cz C4)
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Hypermodulation of depression
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Network Maps (anterior callosotomy case)
Comod
Coh
Unity
Phase
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Referential vs Laplacian
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No intervention vs Neurofeedback (focal seizure)
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Autism as functional fragmentation (global
disconnectivity) replicated
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Autism as functional fragmentation (global
disconnectivity) -rep
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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

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Higher left brain integration in Asperger
compared to normals
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Greater interhemispheric integration in normal
children (comod only)
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In Asperger, lower right anterior (Fp2 F4 F8) and
higher left posterior (T5 P3 O1)
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Global Connectivity n by age19-site mean of 18
comparisons each site
Life is about making connections...
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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
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SKIL Source ImagingBrodmann Map estimations
based on brain heterogeneity
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Hidden revealed by Remontaging
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Montage Differences
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Brodmann complete (BA 55)
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BA by Primary function

• BA AREA RIGHT
• 1 Perception.Audition
• 2 Action.Imagination
• 3,4 Action.Execution.Speech
• 5 Cognition.Language.Orthography
• 6 Action.Observation
• 7 Cognition.Space
• 8 Perception.Vision.Color
• 9 Action.Motor Learning
• 10 Sexuality
• 11 Perception.Somesthesis.Pain
• 17 Perception.Vision.Color
• 18 Perception.Vision.Color Hunger
• 19 Cognition.Language
• 20 Emotion.Sadness
• 21 Action.Observation
• 22 Perception.Olfaction
• 23 Perception.Vision
• 24 Action.Motor Learning

• 1,2 Perception.Somesthesis
• 3,4 Action.Motor Learning
• 5 Cognition.Space
• 6 Cognition.Time
• 7 Cognition.Time Motor Learning
• 8 Emotion.Happiness
• 9 Cognition.Time
• 10 Interoception.Sexuality
• 11 Emotion.Sadness
• 17,19 Perception.Vision.Color
• 18 Perception.Vision.Color Hunger
• 20 Cognition.Language.Speech
• 21 Action.Motor Learning
• 22 Emotion.Anger.Music
• 23 Emotion.Fear
• 24 Action.Imagination
• 31 Perception.Olfaction Sexuality
• 32 Interoception.Hunger
• 37 Emotion.Anxiety

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Based on 1,000 fMRI studies
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Dominant Frequency by Area