Brain Connectivity and Model Comparison
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Brain Connectivity and Model Comparison Will Penny Will Penny Wellcome Trust Centre for Neuroimaging, Wellcome Trust Centre for Neuroimaging, University College London, UK University College London, UK 26 26 th th November November 20 20 10 10
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Brain Connectivity and Model Comparison. Will Penny. Wellcome Trust Centre for Neuroimaging, University College London, UK. 26 th November 20 10. Dynamic Causal Models. Neural state equation :. inputs. Dynamic Causal Models. Neural state equation :. MEG. Neural model: - PowerPoint PPT Presentation
Transcript of Brain Connectivity and Model Comparison
Brain Connectivity and Model Comparison
Will PennyWill Penny
Wellcome Trust Centre for Neuroimaging,Wellcome Trust Centre for Neuroimaging,University College London, UKUniversity College London, UK
2626thth November November 20 201010
),,( uxFx Neural state equation:
inputs
Dynamic Causal Models
),,( uxFx Neural state equation:
Neural model:8 state variables per region
nonlinear state equationpropagation delays
MEG
inputs
Dynamic Causal Models
),,( uxFx Neural state equation:
Electric/magneticforward model:
neural activityEEGMEGLFP
(linear)
Neural model:8 state variables per region
nonlinear state equationpropagation delays
MEG
inputs
Dynamic Causal Models
),,( uxFx Neural state equation:
Electric/magneticforward model:
neural activityEEGMEGLFP
(linear)
Neural model:1 state variable per regionbilinear state equationno propagation delays
Neural model:8 state variables per region
nonlinear state equationpropagation delays
fMRI MEG
inputs
Dynamic Causal Models
),,( uxFx Neural state equation:
Electric/magneticforward model:
neural activityEEGMEGLFP
(linear)
Neural model:1 state variable per regionbilinear state equationno propagation delays
Neural model:8 state variables per region
nonlinear state equationpropagation delays
fMRI MEG
inputs
Hemodynamicforward model:neural activityBOLD(nonlinear)
Dynamic Causal Models
Dynamic Causal Models
DCM for ERP/ERFDCM for Steady State Spectra
DCM for fMRI
DCM for Time Varying SpectraDCM for Phase Coupling
Synchronization
Gamma sync synaptic plasticity, forming ensembles
Theta sync system-wide distributed control (phase coding)
Pathological (epilepsy, Parkinsons)
Phase Locking Indices, Phase Lag etc are useful characterising systems in their steady state
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
Weakly Coupled Oscillators
One Oscillator
f1
Two Oscillators
f1
f2
Two Coupled Oscillators
f1
)sin(3.0 122 f
0.3
Stronger coupling
f1
)sin(6.0 122 f
0.6
Mutual Entrainment
)sin(3.0 122 f
0.30.3
)sin(3.0 211 f
3
2
1
DCM for Phase Coupling
)sin( jij
ijii af
3
2
1
DCM for Phase Coupling
)sin( jij
ijii af
])[sin( jij
ijkk
ii kaf
3
2
1
DCM for Phase Coupling
)sin( jij
ijii af
])[sin( jij
ijkk
ii kaf
])[cos(])[sin( jij
ijkk
jij
ijkk
ii kbkaf
Phase interaction function is an arbitrary order Fourier series
MEG Example
Fuentemilla et al, Current Biology, 2010
Delay activity (4-8Hz)
Duzel et al. (2005) find different patterns of sensor-space theta-coupling in the delay period dependent on task. We are now looking at source space and how this coupling evolves.
Data Preprocessing
Pick 3 regions based on source reconstruction
1. Right MTL [27,-18,-27] mm2. Right VIS [10,-100,0] mm3. Right IFG [39,28,-12] mm
Project MEG sensor activity onto 3 regions with fewer sources than sensors and known location, then pinv will do (Baillet et al., 2001)
Data Preprocessing
Pick 3 regions based on source reconstruction
1. Right MTL [27,-18,-27] mm2. Right VIS [10,-100,0] mm3. Right IFG [39,28,-12] mm
Project MEG sensor activity onto 3 regions with fewer sources than sensors and known location, then pinv will do (Baillet et al., 2001)
Bandpass data into frequency range of interest
Hilbert transform data to obtain instantaneous phase
Data Preprocessing
Pick 3 regions based on source reconstruction
1. Right MTL [27,-18,-27] mm2. Right VIS [10,-100,0] mm3. Right IFG [39,28,-12] mm
Project MEG sensor activity onto 3 regions with fewer sources than sensors and known location, then pinv will do (Baillet et al., 2001)
Bandpass data into frequency range of interest
Hilbert transform data to obtain instantaneous phase
Fit models to control data (10 trials) and memory data (10 trials).
Each trial comprises first 1sec of delay period.
QuestionWhich connections are modulated by memory task?
MTL
VISIFG
2.89
2.46
?
?
This question can be answered using Bayesian parameter inference
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
Q. How do we compare these hypotheses ? A. Bayesian Model Comparison
LogEv
Model
1 2 3 4 5 6 70
50
100
150
200
250
300
350
400
450
LogBF model 3 versus model 1 > 20
MTL
VISIFG
2.89
2.46
0.89
0.77
Model 3
MTL-VIS
IFG
-V
IS
Control
MTL-VIS
IFG
-V
IS
Memory
Jones and Wilson, PLoS B, 2005
Recordings from rats doing spatial memory task:
Summary
Differential equation models of brain connectivity
Bayesian inference over parameters and models
DCM for Phase Coupling
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
dx x k x z w x Pdtdx 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 (Erm & Kopell…)
See Brown et al. 04, for PRCs corresponding to other bifurcations
