K T Metastability

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Metastability in the Brain

J.A.S. Kelso E. Tognoli

Human Brain and Behavior Laboratory

Center for Complex Systems

and Brain Sciences

[email protected] [email protected]

http://www.ccs.fau.edu/section_links/HBBLv2/


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What are the coordination laws at work in thebrain to organize the activity of its numerous and

heterogeneous components?

Kelso

s approach: Coordination Dynamics transcends levels of behavior, brain and groupsof brains (societies)

Our essay today: The principle of metastabilityobserved in the extended HKB model applies tobrain dynamics (Kelso, 1995; Friston, 1997; Bressler and Kelso,2001; Fingelkurts & Fingelkurts, 2004; Perez-Velazquez & Wennberg, 2004; Werner, 2006) .


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Metastability: from L.meta- beyondand -stabilis able to stand

f = dw - a sin f - 2b sin (2 f ) + Qxt

Initial HKB model:

Symmetry of thecomponents

Extended HKB model:

Symmetry-breaking


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2 stable fixed points,

2 unstable fixed points

multistability

1 stable fixed point,

1 unstable fixed pointNotice the transient inflexion

at the ghost of the annihilatedfixed point

Metastability

End of states,

only transientsand tendencies

The control parameter did not change at predefinedtimes to create a succession of states and

transitions.

This metastable regime corresponds to fixedparameters of the model.

The tendency of the trajectoryto bend to horizontal (tendency to integrate,reminiscent of state) or vertical (tendency to

segregate, reminiscent of transition) is inherent.


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segregation

integration


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segregation integration

i n f o r m a

t i o n

Awakerestingstate

Epilepsy

Cognition

Schizophrenia Autism

Cn


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Symmetry breaking. Heterogeneity ofthe coordinating elements.

Disappearance of fixed points

Dynamical exploration of variousregions in the attractor landscape .

Symmetry

BrokenSymmetry

f = dw - a sin f - 2b sin (2 f )

f = - a sin f - 2b sin (2 f )


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empirical evidence - predictions


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Measuring metastability in the brain


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Segregation


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Integration


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Metastability

Dwelltime

Escapetime

Escapetime


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Coordination in the brain is like aBalanchine ballet. Neural groups brieflycouple, some join as others leave, newgroups form and dissolve, creating fleetingdynamical coordination patterns of mindthat are always meaningful but don

t stickaround for very long.

Kelso & Engstrm (2006)The Complementary Nature.
http://mitpress.mit.edu/catalog/item/default.asp?tid=10684&ttype=2


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p0

-p

-2p

How to recognize metastability? Associated signs

Level of coordinating elements:

-Frequency altered by the coupling: shift/broadening of the spectrum

Level of the system:

-Increased phase coherence between the coordinating elements

Collective variable proper -Relative phase between the coordinating elements

Dwell time

p0

-p

-2pEscape time

Provided the ability to measure accuratelythe oscillations of the coordinating elements

(spatial resolution, identification of stationary segments, idling vs active coupling)


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How to distinguishmetastability from state/transition

Bressler & Kelso,TICS, 2001

[LFP, Coherence]

Rodriguez et al,Nature , 1999

[EEG, PLV]

Phasescattering

p0

-p

-2p

p0

-p

-2pStationarity not met

Dwell and escapetimes


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Advantages arising from ametastable regime

1. Coordination extended to a larger range ofapplicable systems: broken symmetry,

heterogeneity of the components

2. Speed: no need for a disengagement mechanism(phase scattering) to leave the attractor( s ghost)

3. Flexibility: a series of attracting tendencies can bevisited dynamically over the time course of the

Coordination Variable

4. Balance integration~segregation: situates thesystem in the range of maximal information


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Acknowledgments:

GC. De Guzman

Gautam Vallabha

K T Metastability

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