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