脑电和脑磁研究中的动态因果模型

Parameters
e,i
H e,i
Within-area parameters Between-area parameters
C F ,B ,L
G

Input parameters Spatial parameters
g 1,,4
1,2 ,
c
mom , loc
Dynamic causal modelling
Dynamic Causal Modelling of Evoked Responses in EEG/MEG
Stefan Kiebel
Wellcome Dept. of Imaging Neuroscience University College London
Principles of organisation
h
m
Time [ms]
v [mV]
Jansen‘s model for a cortical area
E x t r i n s i c Excitatory Interneurons He, e
g1
Pyramidal Cells He, e
g2
MEG/EEG signal
i n p u t s
Connectivity between areas
1
2
Bottom-up
Top-Down
Lateral Supra granular
Cortex
Layer IV Infra granular
1 2 1 2 1 2
Felleman & Van Essen, Cereb. Cortex, 1991
Connectivity between areas
-Numerical solution (Mosher 1999) -2D meshes -Isotropy and homogeneity
-Numerical solution (Marin 1998) -3D meshes
Linear equation
=
x
+
e
data
=
Forward model K
Sensor data
Current density
Neuronal activity
Generative model
Dynamics f Spatial forward model g
f ( x , u, ) x
states x
parameters θ ERP/ERF
y g ( x, )
Functional segregation Functional integration
来自百度文库
Varela et al. 2001, Nature Rev Neuroscience
Power of signal, source localisation
Interactions between distant brain areas
EEG and MEG
EEG
- ~1929 (Hans Berger) - Neurophysiologists - From 10-20 clinical system to 64, 127, 256 sensors - Potential V: ~10 µ V
MEG
- ~1968 (David Cohen) - Physicists - From ~ 30 to more than 150 sensors - Magnetic field B: ~10-13 T
Cortex
Pyramidal cells Inhibitory interneurons
Supra granular
Layer IV Infra granular Lateral
Excitatory interneurons
Pyramidal cells Inhibitory interneurons
g4
Inhibitory Interneurons Hi, i
g3
Excitatory connection Inhibitory connection
Parameters:
e, i : synaptic time constant (excitatory and inhibitory) He, Hi:synaptic efficacy (excitatory and inhibitory) g1,…,g4: connectivity constants
x
Sources J
(over time)
+
Error
e
Spatiotemporal characterization of the sensor data in terms of brain sources Question: How to solve for sources J?
Spherical model
0 x5 x6 x 2 x5 x
Pyramidal cells
5 x
He
e
((C B C L ) S ( x0 ) g 2 S ( x1 ))
2 x5
e

e2
x2
3 x6 x 6 x Hi
i
g 4 S ( x7 )
2 x6
i

i2
x3
u(t ) b(t,1 ,2 ) cos(2 (i 1)t )
c i
Gamma function
Low-frequent change in input
Propagation delays
There is short delay within-area between subareas (~2 ms).

mom
,
loc
One area - one dipole
PC
OF
OF
STG
Left A1
Right A1
A1
A1
Left OF
Right OF
input
PC Right STG
Forward Backward Lateral
Modulation by context
Different responses for two auditory stimuli
e
((C B C L g 3 I ) S ( x0 ))
2 x8
e

e2
x7
C
F ,B ,L
Input
Input is modelled by an impulse at peri-stimulus time t=0 convolved with some input kernel.
Jansen & Rit, Biol. Cybern., 1995
Jansen‘s model for a cortical area
MEG/EEG signal = dendritic signal of pyramidal cells
Output : y(t)=v1-v2
3 x
He
e
S 3 (v1 v2 ) 3 x3 v
Input u
data y
Neural mass model
Neuronal assembly
Mean firing rate m(t)
v(t ) m(t ) h(t )
Mean membrane potential v(t)
Mean firing rate m(t)
H t exp( t ) t 0 p(t ) 0 t0
2
e
x3
1

2 e
v3
v1
1 x He
e
( p S1 (v2 )) 1 x1 v
2
e
x1
1

2 e
v1
v2
2 x2 1 v2
v3
Input : p(t) cortical noise
2 x
Hi
i
S 2 (v 3 )
i

2 i
2 x2 v
Jansen & Rit, Biol. Cybern., 1995
Exc. Inter. Pyr. Cells
abu
atd
ala
Inh. Inter.
Inh. Inter.
Inh. Inter.
Inh. Inter.
Area 1
Area 2
Area 1
Area 2
Area 1
Area 2
David et al., NeuroImage, 2005
Connectivity model (no delay)
Excitatory Interneurons He, e
g1
Pyramidal Cells He, e
g2
There is delay between areas. We found that these delays are important parameters (~10-30 ms).
g4
Inhibitory Interneurons Hi, i
g3
1
2
Delayed differential equations
Connectivity parameters
e,i
H e,i
Within-area parameters Between-area parameters
C F ,B ,L
Example data
MEG experiment
Faces (F) vs. Scrambled faces (S)
M170
fT
S F
L
R
150-190ms
ERP/ERF
single trials
...
average estimated event-related potential/field (ERP/ERF)
Bottom-up
Exc. Inter. Pyr. Cells Inh. Inter. Exc. Inter. Pyr. Cells Inh. Inter.
Top-Down
Exc. Inter. Pyr. Cells Exc. Inter. Pyr. Cells Exc. Inter. Pyr. Cells
Network of areas
MEG/EEG scalp data

g 1,,4
Input parameters
1,2 ,
c
Spatial forward model
f ( x, u, ) x
Depolarisation of pyramidal cells Sensor data
K
Spatial model
y Kx0 g ( x0 , )
Forward model
Magnetic field
Interactions between areas
Sensor data
Current density
Neuronal activity
Inverse problems
Source reconstruction
Effective connectivity
MMN Mismatch negativity (MMN)
Model: Explain 2nd ERP/ERF by modulation of connectivity between areas
ERP standards ERP deviants deviants - standards
G
Gain modulation matrix
Idea: Each area is spatially modelled by one equivalent current dipole.
Advantages of spherical model:
-Analytic solution (fast) -Easy to use -Good model for MEG (said to be less so for EEG) -Easy to parameterise -Seems to explains data well for early to medium latencies Spatial parameters
jth state for all areas
1 x4 x
Excit. IN
4 x
He
e
((C F C L g 1 I ) S ( x0 ) CU u)
2 x4
e

e2
x1
xj
Connectivity matrices
Inhib. IN
7 x8 x 8 x He
Forward modelling
3 main approaches lead to forward model
Spherical model
2D realistic model
3D realistic model
-Analytic solution (Sarvas 1987) -Isotropy and homogeneity