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EEG’s Rosetta stone:

_Identifying _ phase-coupling &

metastability in the brain

The Human

Brain and Behavior

Laboratory

Emmanuelle Tognoli

06/07/2007

http://www.ccs.fau.edu/hbbl.html

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Which oscillation is a good model to

study general principles of

coordinated brain states?

Which oscillation is a good model to

study general principles of

coordinated brain states?

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The Freeman~Kelso Dialogue:

“…my evidence in the past 18 years for sustained synchrony (never antiphasic), for spatial phase gradients in intracranial EEGs

from high-density arrays,  and for phase cones with phase velocities corresponding to intracortical axonal propagation

velocities as evidence for state transitions.”

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Inspiration I: spend time to contemplate the states

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Question 1: antiphase coordination in scalp EEG?

Indeed by the plenty (too many):

Phase locking?

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Question 2: …and what about inphase?

One source and volume conduction?

Two sources coordinated inphase?

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Question 1: antiphase coordination in scalp EEG?

A priori, it is difficult to distinguish tangential patterns formed by a single source from pairs of radial patterns due to coordinated sources

(inverse problem)

Let us safely move to the case of broken symmetry for now.

= - a sin - 2b sin (2) + Qt

Question 2: …and what about inphase?

Inphase patterns cannot be directly studied neither. Distinguishing single from multiple sources will often require to address the

problem of volume conduction (inverse problem)

One source, two? (or more)

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Question 3: phase-locking viewed from a certain angle…

Broken symmetry (BS)

Desynchronization(decoupling, phase scattering)

Major frequency change for all 3 sitesReturn to “intrinsic” frequencies?

BS examples rarer/briefer than []:

-reflects true EEG synchrony with its “natural duration” (same typical length/recurrence for real inphase and antiphase)?-broken symmetry is intrinsically less stable?Questions of outstanding importance:

-how long does coordination in the brain persists (how many cycles)?-special physiological significance of inphase & antiphase?-can two areas present stability at different phases depending on context or will a given pair of areas always be coordinated with the same angle?

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Summary 1: Identifying phase-locking in real time scalp EEG: direct method

Is there antiphase coordination in scalp EEG?

Probably. We observed a variety of relative phases. While we cannot directly distinguish tangential patterns from antiphase coordination (yet), there is no reason to observe BS coordination patterns around , then a black hole atop suppressing antiphase.

Is there a preferential representation of inphase and antiphase (attractors) in scalp EEG?

Difficult to say. Raw EEG shows ample phase concentration inphase and antiphase (inflated by spurious synchrony). Because of the volume conduction bias, it is impossible to quantify relative occurrence of broken-symmetry and inphase/antiphase Physiologically, significance of inphase (spatial summation, potentiation) antiphase? (Kelso & Tognoli, 2007)

10Forward models

Question 4: Where is the true antiphase?

The same volume conduction effect that emphasizes spurious antiphase synchrony also attenuates real

antiphase synchrony.

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Question 5: scalp amplitude modulation by phase misalignment in the volume conductor.

E1=0.95*S1+0.6*S2

E2=0.95*S2+0.6*S1 E1=0.95*S1+p*S2

E2=0.95*S2+p*S1

p→0: distant sourcesp→0.60: close sourcesp→0.95: id sources Both source P2P amplitude of 2

S1S1 S2S2

E1E1 E2E2

S1

S2

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The Freeman~Kelso Dialogue:

“…my evidence in the past 18 years for sustained synchrony (never antiphasic), for spatial phase gradients in intracranial EEGs

from high-density arrays,  and for phase cones with phase velocities corresponding to intracortical axonal propagation

velocities as evidence for state transitions.”

Contribution of real antiphase to neural cell assemblies is less noticeable:

- amplitude reduction (volume conduction) is proportionate to phase

misalignment - at antiphase: maximal attenuation

- increases with spatial proximity(macroscale-mesoscale)

-at distance zero (symmetry in amplitude), is completely cancelled

The hidden truth about

real antiphase

coordination

(Amplitude-wise)

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90°

antiphase

E1=0.95*S1+0.6*S2

E2=0.95*S2+0.6*S1Red source half amplitude

Trouble ahead in Question 6: apparent relative phase

Sources inphase

Sources antiphase

Sources other phases

Same amplitudes

inphase

antiphaserelative

phase lessen toward inphaseDifferent

amplitudes

antiphase until flip to inphase

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Summary 2: forward models of coordinated states

Scalp amplitudes are not faithful

Scalp amplitudes are affected by relative phase between the sources. Inphase is inflated. Intermediate phases are diversely modulated. Antiphase has maximal attenuation.

This modulation is a function of volume conduction (in part: distance)

Most scalp relative phases are not faithful

Only sources that are inphase systematically transfer into scalp patterns inphase. Intermediate phases converge to inphase. Antiphase may suffer drastic amplitude reduction but remains faithful for a range of parameter. In cases of unequal amplitudes of the sources though, eventually it shifts to inphase.

This modulation is a function of volume conduction & amplitude asymmetry.

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Inspiration II: look at the edges of the state

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Question 7: Transitions, transients and intermittency: amplitude

Dwell time Escape timeEscape time

State Transition Transition

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REMIND SOMETHING?

Intermittency Local patterns of phase cancellation due to volume conductorDynamics of phase

misalignment

AMPLITUDE MODULATION

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Question 8: Dephasing: transitions, transients and intermittency

E1=0.95*S1+0.6*S2

E2=0.95*S2+0.6*S1

Scalp frequencies of unlocked regimes are not faithful

During transitions/transients/intermittent regimes, scalp frequencies undulate around their true value (dynamics of relative phase shift seen in state). Undershoot at inphase and overshoot at antiphase.

p

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“Coordination in the brain is like a Balanchine ballet. Neural groups briefly couple, some join as others leave, new groups form and dissolve, creating fleeting dynamical coordination patterns of mind that are always meaningful but don’t stick around for very long.”

Kelso & Engstrøm (2006) The Complementary Nature.

Question 9: and what next… when another area enters the ballet

Recruitment of new neural groups is accompanied by shift in space of preexisting pattern. Or in other words transition in

space does not imply the replacement of the current pattern by a new pattern.

Waltz of the patterns over the scalp depends on instantaneous polarities (movement toward or away) & amplitudes (distance

shift).

(it was Inspiration III)

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Summary 3: forward models of transitions/intermittency

Scalp amplitudes are dynamically modulated at transitionAt transition, scalp signals loose the coupling of the source but maintain the coupling of VC. Frequencies split apart but amplitudes may stay correlated (with typical signature max-inphase min-antiphase).Scalp frequencies and phases are dynamically modulated at transitionRelative phase’s dwelling increases with volume conduction. Dwelling is also prolonged but less recurrent with smaller (different time scale; rp concentration not affected)

Frequencies undulate around their true value for small VCs. For higher VCs and amplitude difference, scalp signal above the weak source looses its own frequency and undulate around the frequency of the strong source.Persisting areas’ scalp topographies glide with incoming/outgoing areas

Smooth spatial transition is not pertinent (sufficient) to call for the dissolution of a pair of coupled areas.

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Significance

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Question 1: antiphase coordination in the scalp EEG?

Question 2: …and what about inphase?

Time has come to address the separation of true and spurious synchrony

A priori, it is difficult to distinguish tangential patterns formed by a single source from pairs of

radial patterns due to coordinated sources (inverse problem)

Inphase patterns cannot be directly studied neither. Distinguishing single from multiple

sources will often require to address the problem of volume conduction (inverse

problem)

Brain Coordination

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26 Bias example 1

An experiment compares EEG coherence between task A and B.

Tasks engage the same networks, with the same coupling, same amplitudes, same duration… except that B recruits the left

intraparietal sulcus which is not active in task A.

This situation is sufficient to elicit significant change in coherence.

A B

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Bias example 2

An experiment compares EEG coherence between task A and B.

Tasks engaged the same networks, with the same coupling, same amplitudes, same duration… except that B disengages the

fusiform gyrus.

Oh yes! even this can affect synchrony.

A B

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Procedures and recipes

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Sequencing approach (genome):- start identifying patterns in simple cases (where superposition is understandable)

- identify succession probability (pattern … is frequently followed by pattern…)

- characterize their task dependence (a step toward behavioral/cognitive significance)

STRATEGY: Understand the multitude of objects (patterns) that constitute the real-time EEG.

Identify their occurrence, rules of succession

Selective modeling:- detect primary & secondary indices

-mathematical reconstruction of sources’ coordination dynamics

+ +

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Even less are modulated by the task under investigation

Selective modeling: how much data concerned?

Frequency stabilization is the primary sign of phase locking

Even less represent the activity for which this electrode pair is at maximum

Metastability?

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Modeling: what do we know about the sources?

E1: AE1: amplitude at location 1fE1:frequency at location 1E1: phase at location 1

E2: AE2: amplitude at

location 1fE2: frequency at location

1E2: phase at location 1

Coordination Variable: rpE

S1: AS1: amplitude at location 1fS1:frequency at location 1S1: phase at location 1

S2: AS2: amplitude at

location 1fS2: frequency at location

1S2: phase at location 1

Coordination Variable: rpS

AE1, fE1, E1 =f(AS1, S1, AS2, S2, VC)

AE2, fE2, E2 =f(AS1, S1, AS2, S2, VC)

S1 S2?

Approximations of volume conductor

• Standard values in the literature (e.g. distance). • Non specific VC values can be derived directly from the data over long periods of time (distribution of relative phase), • Specific values could probably be modeled from phase-dependent distribution of amplitude attenuation.

State at relative phase ≠ [0, ]

State antiphase

State inphase

Dwell near inphase

Real coupling

Real coupling antiphase (terminated)

Tangential source Both maxima decay, replaced by VC from

other sources

Transition shows drifting frequencies

Real coupling

Radial source

Spatial discontinuity resolved

Spatial discontinuity not resolved

Amplitudes different

Amplitudes similar

Close sources

New area grows amplitude (rotates)

No new source growth

Real coupling antiphase

Real coupling inphase

Phase attraction by volume conductor

Metastable regime

Centered at zero

Off zero (BS)

Dwell near antiphase Phase attraction by

volume conductor

Metastable regime

Frequencies in odds of Arnold’s tongue (exact antiphase conjunction)

Frequencies with no notable ratio relationship

No frequency drift before source dies out

Phase coordination’s decision tree (v.1): primary & secondary indices

Real coupling antiphase (ongoing)

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The end

The end~beginning~beginning