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Weakly Coupled Oscillators Will Penny Will Penny Wellcome Trust Centre for Neuroimaging, Wellcome Trust Centre for Neuroimaging, University College London, UK University College London, UK IMN Workshop on Interacting with Brain IMN Workshop on Interacting with Brain Oscillations, Oscillations, 33 Queen Square, London. Friday 12 33 Queen Square, London. Friday 12 th th March 2010 March 2010
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Weakly Coupled Oscillators

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Weakly Coupled Oscillators. Will Penny. Wellcome Trust Centre for Neuroimaging , University College London, UK. IMN Workshop on Interacting with Brain Oscillations, 33 Queen Square, London. Friday 12 th March 2010. For studying synchronization among brain regions - PowerPoint PPT Presentation
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Page 1: Weakly Coupled Oscillators

Weakly Coupled OscillatorsWeakly Coupled Oscillators

Will PennyWill Penny

Wellcome Trust Centre for Neuroimaging,Wellcome Trust Centre for Neuroimaging,University College London, UKUniversity College London, UK

IMN Workshop on Interacting with Brain Oscillations,IMN Workshop on Interacting with Brain Oscillations,33 Queen Square, London. Friday 1233 Queen Square, London. Friday 12thth March 2010 March 2010

Page 2: Weakly Coupled Oscillators

For studying synchronization among brain regions Relate change of phase in one region to phase in others

Region 1

Region 3

Region 2

??

( )i i jj

g

Page 3: Weakly Coupled Oscillators

Connection to Neurobiology:Septo-Hippocampal theta rhythm

Denham et al. Hippocampus. 2000:Hippocampus

Septum

11 1 1 13 3 3

22 2 2 21 1

13 3 3 34 4 3

44 4 4 42 2

( ) ( )

( ) ( )

( ) ( )

( ) ( )

e e CA

i i

i e CA

i i S

dxx k x z w x P

dtdx

x k x z w xdtdx

x k x z w x Pdtdx

x k x z w x Pdt

1x

2x 3x

Wilson-Cowan style model

Page 4: Weakly Coupled Oscillators
Page 5: Weakly Coupled Oscillators

Four-dimensional state space

Page 6: Weakly Coupled Oscillators

Hippocampus

Septum

A

A

B

B

Hopf Bifurcation

Page 7: Weakly Coupled Oscillators

cossin)( baz

For a generic Hopf bifurcation (Ermentrout & Kopell, SIAM Appl Math, 1990)

See Brown et al. Neural Computation, 2004 for PRCs corresponding to other bifurcations

Page 8: Weakly Coupled Oscillators

0

1sin( ) cos( )

2i

ij i j ij i jj

df a b

dt

3

2

1

12a

13a

DCM for Phase Coupling – SPM8

12b

13b

Page 9: Weakly Coupled Oscillators

MEG Example Fuentemilla et al, Current Biology, 2009

+

+

+

1 sec 3 sec 5 sec 5 sec

1) No retention (control condition): Discrimination task

2) Retention I (Easy condition): Non-configural task

3) Retention II (Hard condition): Configural task

ENCODING MAINTENANCE PROBE

Page 10: Weakly Coupled Oscillators

Delay activity (4-8Hz)

Friston et al. Multiple Sparse Priors. Neuroimage, 2008

Page 11: Weakly Coupled Oscillators

Difference in theta power between conditions

Page 12: Weakly Coupled Oscillators

Questions

• Duzel et al. find different patterns of theta-coupling in the delay period dependent on task.

• Pick 3 regions based on [previous source reconstruction]

1. Right MTL [27,-18,-27] mm2. Right VIS [10,-100,0] mm3. Right IFG [39,28,-12] mm

• Fit models to control data (10 trials) and hard data (10 trials). Each trial comprises first 1sec of delay period.

• Find out if structure of network dynamics is Master-Slave (MS) or (Partial/Total) Mutual Entrainment (ME)

• Which connections are modulated by (hard) memory task ?

Page 13: Weakly Coupled Oscillators

Data Preprocessing

• Source reconstruct activity in areas of interest (with fewer sources than sensors and known location, then pinv will do; Baillet et al, IEEE SP, 2001)

• Bandpass data into frequency range of interest

• Hilbert transform data to obtain instantaneous phase

• Use multiple trials per experimental condition

Page 14: Weakly Coupled Oscillators

MTL

VISIFG

MTL

VISIFG

MTL

VISIFG

MTL

VISIFG

MTL

VISIFG

MTL

VISIFG1

MTL

VISIFG2

3

4

5

6

7

Master-Slave

PartialMutualEntrainment

TotalMutualEntrainment

MTL Master VIS Master IFG Master

Page 15: Weakly Coupled Oscillators

LogEv

Model

1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450

Bayesian Model Comparison

Penny et al, Comparing Dynamic Causal Models, Neuroimage, 2004

Page 16: Weakly Coupled Oscillators

MTL

VISIFG

2.89

2.46

0.89

0.77

Estimated parameter values:

Page 17: Weakly Coupled Oscillators

MTL-VIS

IF

G-

VIS

Control

Page 18: Weakly Coupled Oscillators

MTL-VIS

IF

G-

VIS

Memory

Page 19: Weakly Coupled Oscillators

In agreement with spike-LFP recordings by Jones & Wilson, PLoS Biol 2005

Page 20: Weakly Coupled Oscillators