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