Metastability in the Brain J.A.S. Kelso E. Tognoli Human Brain and Behavior Laboratory Center for...
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Transcript of Metastability in the Brain J.A.S. Kelso E. Tognoli Human Brain and Behavior Laboratory Center for...
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 LaboratoryLaboratory
Center for Complex Center for Complex Systems Systems
and Brain Sciencesand Brain Sciences
[email protected] [email protected]@ccs.fau.edu [email protected]
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
Awake resting state
Epilepsy Epilepsy
CognitionCognition
Schizophrenia Autism
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 Symmetry Symmetry
BrokenBrokenSymmetry 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
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
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 metStationarity not metDwell and escape
timesDwell 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
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 BrainMetastability in the BrainMetastability in the Brain
Acknowledgments:Acknowledgments:
GC. De GuzmanGC. De Guzman
Gautam VallabhaGautam Vallabha