Metastability in the BrainMetastability in the Brain

J.A.S. Kelso E. TognoliJ.A.S. Kelso E. Tognoli

Human Brain and Behavior Human Brain and Behavior LaboratoryLaboratoryCenter for Complex Center for Complex

Systems Systems and Brain Sciencesand Brain Sciences

kelso@ccs.fau.edu tognoli@ccs.fau.edukelso@ccs.fau.edu tognoli@ccs.fau.edu

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

• What are the coordination laws at work in the brain to organize the activity of its numerous and heterogeneous components?

• Kelso’s approach: Coordination Dynamics transcends levels of behavior, brain and groups of brains (societies)

• Our essay today: The principle of metastability observed in the extended HKB model applies to brain dynamics (Kelso, 1995; Friston, 1997; Bressler and Kelso,

2001; Fingelkurts & Fingelkurts, 2004; Perez-Velazquez & Wennberg, 2004; Werner, 2006).

Metastability: from L. meta- beyond and -stabilis able to stand

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

Initial HKB model:Initial HKB model:

Symmetry of the Symmetry of the componentscomponents

Extended HKB model:Extended HKB model:

Symmetry-breakingSymmetry-breaking

2 stable fixed points,

2 unstable fixed points

multistability

1 stable fixed point,

1 unstable fixed point

Notice the transient inflexion at the ghost of the annihilated

fixed point

Metastability

End of states, only transients and tendenciesThe control parameter The control parameter did notdid not change at predefined change at predefined

times to create a succession of states and times to create a succession of states and transitions. transitions.

This metastable regime corresponds to fixed This metastable regime corresponds to fixed parameters of the model.parameters of the model.

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

segregate, reminiscent of transition) is inherent.segregate, reminiscent of transition) is inherent.

segregation

integration

segregation integration

info

rmat

ion

Awake resting state

Epilepsy

Cognition

Schizophrenia Autism

Cn

• Symmetry breaking. Heterogeneity of the coordinating elements.

• Disappearance of fixed points

• Dynamical exploration of various regions in the attractor landscape.

Symmetry Symmetry

BrokenBrokenSymmetry Symmetry

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

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

Metastability in the BrainMetastability in the Brain

empirical evidence - predictionsempirical evidence - predictions

Measuring metastability in the brain

Segregation

Integration

Metastability

Dwell time

Escape time

Escape time

“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.

0

-

-2

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

0

-

-2

Escape time

Provided the ability to measure accuratelythe oscillations of the coordinating elements

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

How to distinguish metastabilitymetastability from

state/transitionstate/transition

Bressler & Kelso, TICS, 2001

[LFP, Coherence]

Rodriguez et al, Nature, 1999

[EEG, PLV]

Phase Phase scatteringscattering

0

-

-2

0

-

-2

Stationarity not metDwell and escape

times

Advantages arising from a Advantages arising from a metastable regimemetastable regime

1.Coordination extended to a larger range of applicable 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 be visited dynamically over the time course of the

Coordination Variable

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

Metastability in the BrainMetastability in the BrainAcknowledgments:Acknowledgments:

GC. De GuzmanGC. De Guzman

Gautam VallabhaGautam Vallabha