The Human
Brain and Behavior
Laboratory
http://www.ccs.fau.edu/hbbl.html
Emmanuelle Tognoli
06/07/2007
EEG’s Rosetta stone:
_
_
Identifying
?
phase-coupling & metastability
in the brain
1
Which oscillation is a
good model to study
general principles of
coordinated brain
states?
2
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.”
3
Inspiration I: spend time to contemplate the states
4
Question 1: antiphase coordination in scalp EEG?
Indeed by the plenty (too many):
Phase locking?
5
Question 2: …and what about inphase?
One source and
volume conduction?
Two sources
coordinated inphase?
6
One source, two? (or more)
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)
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)
2p
Let us safely move to the case of
broken symmetry for now.
p
f = dw - a sinf - 2b sin (2f) + Qxt
7
0
Question 3: phase-locking viewed from a certain angle…
Broken symmetry (BS)
BS examples rarer/briefer than [0,p]:
Desynchronization
(decoupling, phase scattering)
-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:
Major frequency
change for all 3 sites
Return to “intrinsic” frequencies?
8
-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?
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 p, then a black hole atop p 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)
9
Question 4: Where is the true antiphase?
The same volume conduction effect that
emphasizes spurious antiphase synchrony also
attenuates real antiphase synchrony.
10
Forward models
Question 5: scalp amplitude modulation by phase
misalignment in the volume conductor.
E1
E2
S1
S2
S1
E1=0.95*S1+0.6*S2
S2
E2=0.95*S2+0.6*S1
11 Both source P2P amplitude of 2
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
Contribution of real antiphase to neural cell
assemblies is less noticeable:
- amplitude reduction (volume conduction) is
proportionate to phase misalignment
- at antiphase: maximal attenuation
The hidden
- increases
with spatial
proximityreal
truth
about
-at distance zero
, is completely
antiphase
cancelled
coordination
(macroscale-mesoscale)
(symmetry in amplitude)
The Freeman~Kelso Dialogue:
(Amplitude-wise)
“…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.”
13
Trouble ahead in Question 6: apparent relative phase
E1=0.95*S1+0.6*S2
Red source half amplitude
Sources
inphase
Sources
antiphase
E2=0.95*S2+0.6*S1
Sources
other phases
antiphase
Same
amplitudes
antiphase
inphase
Different
amplitudes
14
antiphase
until flip to
inphase
relative
90°
phase lessen
toward
inphase
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.
15
Inspiration II: look at the edges of the state
16
Question 7: Transitions, transients and intermittency: amplitude
17
Escape time
Dwell time
Escape time
Transition
State
Transition
Intermittency
AMPLITUDE MODULATION
Dynamics of phase
misalignment
REMIND SOMETHING?
18
Local patterns of phase
cancellation due to
volume conductor
p
Question 8: Dephasing: transitions, transients and
intermittency
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.
19
E1=0.95*S1+0.6*S2
E2=0.95*S2+0.6*S1
Question 9: and what next… when another area enters the
ballet
“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)
Recruitment of new neural groups is
accompanied
by shift in space
of
The
Complementary
Nature.
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
(it(movement
was Inspiration
III)& amplitudes (distance shift).
toward or away)
20
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 dw (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.
21
Significance
24
Question 1: antiphase coordination in the
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)
Brain
Coordination?
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)
Time has come to address the separation of true and spurious synchrony
25
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
26
Bias example 1
B
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
27
B
28
Procedures and recipes
29
STRATEGY: Understand the multitude of objects (patterns) that constitute the realtime EEG.
Identify their occurrence, rules of succession
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)
Selective modeling:
- detect primary & secondary indices
-mathematical reconstruction of sources’ coordination dynamics
+
30
+
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
Even less are modulated by the task under investigation
31
Metastability?
Modeling: what do we know about the sources?
Coordination Variable: rpE
E2:
AE2: amplitude at location 1
fE2: frequency at location 1
fE2: phase at location 1
E1:
AE1: amplitude at location 1
fE1:frequency at location 1
fE1: phase at location 1
AE1, fE1, fE1 =f(AS1, fS1, AS2, fS2, VC)
AE2, fE2, fE2 =f(AS1, fS1, AS2, fS2, VC)
fS1 fS2?
S1:
AS1: amplitude at location 1
fS1:frequency at location 1
fS1: phase at location 1
32
Coordination Variable: rpS
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.
S2:
AS2: amplitude at location 1
fS2: frequency at location 1
fS2: phase at location 1
Phase coordination’s decision tree (v.1):
State at relative phase ≠ [0, p]
State antiphase
primary & secondary indices
Real coupling
Transition shows
drifting frequencies
No new source growth
Real coupling antiphase (terminated)
New area grows
amplitude (rotates)
Real coupling antiphase (ongoing)
Both maxima decay,
replaced by VC from
other sources
No frequency drift
before source dies out
Spatial discontinuity
not resolved
Radial source
Tangential source
Real coupling antiphase
Close sources
State inphase
Spatial discontinuity
resolved
Amplitudes different
Real coupling
Real coupling inphase
Amplitudes similar
Off zero (BS)
Dwell near
inphase
Centered at zero
Dwell near
antiphase
Metastable regime
Phase attraction by
volume conductor
Frequencies with no
notable ratio relationship
Frequencies in odds of Arnold’s tongue
(exact antiphase conjunction)
Metastable regime
Phase attraction by
volume conductor
The end
~beginning
40