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

Region 1

Region 3

Region 2

??

Dynamic Phase CouplingDynamic Phase Coupling

( )i i jj

g PhaseInteractionFunction

One Oscillator

f1

Two Oscillators

f1

f2

Two Coupled Oscillators

f1

)sin(3.0 122 f

0.3

Different initial phases

f1

)sin(3.0 122 f

0.3

Stronger coupling

f1

)sin(3.0 122 f

0.6

Bidirectional coupling

)sin(3.0 122 f

0.30.3

)sin(3.0 211 f

Connection to Neurobiology:Septo-Hippocampal theta rhythm

Denham et al. 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

4xWilson-Cowan style model

Four-dimensional state space

Hippocampus

Septum

A

A

B

B

Hopf Bifurcation

cossin)( baz

For a generic Hopf bifurcation (Ermentrout, Mathemat. Neurosci, 2010)

See Brown et al. 04, for PRCs corresponding to other bifurcations

0

1sin( ) cos( )

2i

ij i j ij i jj

df a b

dt

3

2

1

12a

13a

Dynamic Phase Coupling Model

12b

13b

Delay activity (4-8Hz)

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 ?

Data Preprocessing

• Source reconstruct activity in areas of interest (with fewer sources than sensors and known location, then pinv will do; Baillet 01)

• Bandpass data into frequency range of interest

• Hilbert transform data to obtain instantaneous phase

• Use multiple trials per experimental condition

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

See also Rosa et al. Post-hoc Model Selection, J. Neurosci. Meth. 2011

LogEv

Model

1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450

When comparing two models, a posterior probability of 0.95 correspondsto a Bayes factor of 20. Or log Bayes factor of 3.

See also Random Effects Bayesian Model Inference to look for consistencyof model selection in a group of subjects (Stephan, Neuroimage, 2009).

Summary

• Statistical Parametric Mapping• Multivariate Analysis• Connectivity Modelling• Role of Oscillations in Memory

http://www.fil.ion.ucl.ac.uk/~wpenny

Thank you to

• Wellcome Trust• Kai Miller (WashU)• Emrah Duzel (UCL)• Gareth Barnes (UCL)• Lluis Fuentemilla (UCL)• Vladimir Litvak (UCL)• STAMLIN organisers !

fMTL-fVIS

f IFG-f

VIS

Control

fMTL-fVIS

f IFG-f

VIS

Memory

MRI MEG