1 EEG’s Rosetta stone: _ Identifying _ phase-coupling & metastability in the brain The Human Brain and Behavior Laboratory Emmanuelle Tognoli 06/07/ ?

2 Which oscillation is a good model to study general principles of coordinated brain states?

3 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.”

4 Inspiration I: spend time to contemplate the states

5 Question 1: antiphase coordination in scalp EEG? Indeed by the plenty (too many): Phase locking?

6 Question 2: …and what about inphase? One source and volume conduction? Two sources coordinated inphase?

7 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  ) +  Q  t 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)   

8 Question 3: phase-locking viewed from a certain angle… Broken symmetry (BS) Desynchronization (decoupling, phase scattering) Major frequency change for all 3 sites Return 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?

9 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)

10 Forward models Question 4: Where is the true antiphase? The same volume conduction effect that emphasizes spurious antiphase synchrony also attenuates real antiphase synchrony.

11 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 sources p→0.60: close sources p→0.95: id sources Both source P2P amplitude of 2 S1 S2 E1 E2 S1 S2

12 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 Both source unit B2P amplitude E1=0.95*S1+0.6*S2 E2=0.95*S2+0.6*S1 Red source half amplitude Broken symmetry in amplitude of the sources

13 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)

14 90° antiphase E1=0.95*S1+0.6*S2 E2=0.95*S2+0.6*S1 Red source half amplitude Trouble ahead in Question 6: apparent relative phase Sources inphase Sources antiphase Sources other phases Same amplitudes inphase antiphase relative phase lessen toward inphase Different amplitudes antiphase until flip to inphase

15 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.

16 Inspiration II: look at the edges of the state

17 Question 7: Transitions, transients and intermittency: amplitude Dwell time Escape time State Transition

18 REMIND SOMETHING? Intermittency Local patterns of phase cancellation due to volume conductor Dynamics of phase misalignment AMPLITUDE MODULATION

19 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

20 “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)

21 Summary 3: forward models of transitions/intermittency Scalp amplitudes are dynamically modulated at transition At 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 transition Relative 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.

22 p

24 Significance

25 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?

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

27 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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29 Procedures and recipes

30 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 + +

31 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?

32 Modeling: what do we know about the sources? E1: A E1 : amplitude at location 1 f E1 :frequency at location 1  E1 : phase at location 1 E2: A E2 : amplitude at location 1 f E2 : frequency at location 1  E2 : phase at location 1 Coordination Variable: rp E S1: A S1 : amplitude at location 1 f S1 :frequency at location 1  S1 : phase at location 1 S2: A S2 : amplitude at location 1 f S2 : frequency at location 1  S2 : phase at location 1 Coordination Variable: rp S A E1, f E1,  E1 =f(A S1,  S1, A S2,  S2, VC) A E2, f E2,  E2 =f(A S1,  S1, A S2,  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)

34 Question 6: Data driven estimation of volume conduction? p

CP4

36 Expands channels pairs Compresses time Classical phase-coupling methods transposed to source estimates (inverse problem). Sequencing/modeling approach Expands time Compresses sensors For n channels, consider n.(n-1)/2 pair-wise comparisons. 64 channels → channels → channels → channels → True EEG synchronization methods On computationally-intensive phase-coupling approaches

37 More about metastability

38 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.”

39 Next critical step: -differentiate phase-transition and metastable regimes (statistical indices of (non-)transition)

40 The end ~beginning