Generative models of brain activity as measured in functional MRI and MEGEEG

1
Generative models of brain activity as measured
in functional MRI and MEG/EEG

• Olivier David
• odavid_at_ujf-grenoble.fr
• www-nifm.ujf-grenoble.fr/people/odavid
• Inserm U594 Neuroimagerie Fonctionnelle et
  Métabolique
• Université Joseph Fourier, Grenoble, France

Networks in Cognitive Systems / Trends and
Challenges in Biomedicine From Cerebral
Process to Mathematical Tools Design, Valparaiso,
Chile December 11-15, 2006
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EEG/fMRI Program in Grenoble
Since January 2005

• Aktham Asfour Frédéric Grouiller
• Olivier David Sébastien Reyt
• Alexandre Krainik
• Christoph Segebarth
• Inserm U594 Functional Metabolic Neuroimaging

• Antoine Depaulis Agata Wozniak
• Colin Deransart
• Isabelle Guillemain
• Philippe Kahane
• Lorella Minotti
• Laurent Vercueil
• Inserm U704 Dynamics of Neural Networks

Grenoble Institute of Neuroscience (GIN)
Identification of epileptic networks fMRI EEG
Control of epileptic networks Adaptive
neurostimulation Biofeedback

• Small animal (rat, mouse)
• Patient

3

IMAGING


Neural mechanisms?
SMALL ANIMAL
HUMAN

ELECTRO- PHYSIOLOGY
4
Generative models
Forward problem Given the generative model, one
can predict the measured data

• Neuronal variables
• Synaptic time constant
• Synaptic efficacy
• Inhibition/Excitation
• Connectivity (networks)

• Macroscopic data at the brain level
• Local field potentials
• Scalp EEG/MEG
• Functional MRI

Inverse problem Given the measured data, one can
estimate the generative model
Dynamic Causal Modelling
5
Outline

• Dynamic Causal Modelling (DCM)
• Neural modelling of macroscopic brain activity
• Linear bilinear models
• Neural mass models
• Functional MRI
• Biophysics of fMRI
• Hemodynamic model
• DCM for fMRI
• EEG/MEG
• Biophysics of EEG/MEG
• Forward model
• DCM for evoked responses in EEG/MEG

6
Modelling levelsin functional neuroimaging
DCM

• How does this implementation operate (in
  mechanistic terms)?
• Models of interactions (connectivity) between
  activated regions

• Where is implemented a given cerebral process?
• Activation maps

• What does this process mean (in computational
  terms)?
• Models of neural codes

7
Dynamic Causal Modelling Concept
Friston et al., NeuroImage, 2003 David et al.,
NeuroImage, 2006
Perturbations
Model of neural interactions
Neuronal networks
Electric model
Hemodynamic model
fMRI
MEG/EEG
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Generative models
Physiological models
Neural networks
Hemodynamic parameters
Electrical parameters
EEG/MEG
fMRI
Identification of networks by estimating the
model parameters
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Dynamic Causal Modelling Formalism

• A DCM is a dynamical system.
• It is specified in terms of
• A state equation
• An output equation
• The parameters q are estimated from the data y

Neuronal input-state-output system
input
output
EEG/MEG fMRI
Stimulus
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Neural modelling of macroscopic brain activity
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Functional principles

• Functional segregation
• Local connectivity

• Functional integration
• Long range connectivity

12
Modelling levels
2
3
1
4
13
Structural Equation Modelling (SEM)
u2
u3
2
u1
a32
3
a21
Not physiological Not dynamical
1
a34
4
a41

• Residual covariance CuuT
• Measured covariance S
• Modelled covariance S
• Estimation of A to minimise S-S

u4
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Dynamical system

• System
• Set of elements which interact in a spatially and
  temporally specific fashion
• System dynamics
• Change of state vector in time
• Causal effects in the system
• Interactions between elements
• External inputs u
• System parameters ?
• Specify the nature of interactions
• General state equation for non-autonomous systems

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Linear dynamical system
FG right
FG left
LG lingual gyrus FG fusiform gyrus
z4
z3
a13
a12
Visual input in the left visual field (LVF) and
right visual field (RVF)
c12
LG left
LG right
z1
z2
RVF
LVF
u2
u1
a11
state changes
effective connectivity
system state
Input parameters
extrinsic inputs
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Bilinear dynamical system
FG right
FG left
z4
z3
LG left
LG right
z1
z2
RVF
LVF
u2
u1
CONTEXT
u3
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State equation of a bilinear system
state changes
intrinsic connectivity
m extrinsic inputs
system state
input connectivity
modulation of connectivity
Neuronal model used in Dynamic Causal Modelling
for fMRI
18
Modelling levels
2
3
1
4
19
Structure of a cortical area
Jones, PNAS, 2000
Interneuron
Pyramidal cell
Cortical minicolumn (400 pyramidal cells)
50 mm
Cortical area
Cortical macrocolumn
900 mm
20
Neural mass model
Jansen Rit, Biol. Cybern., 1995
Neuronal population
Mean firing rate m(t)
Mean firing rate m(t)
Mean membrane potential v(t)
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Neural mass modelof a cortical area
Jansen Rit, Biol. Cybern., 1995
E x t r i n s i c i n p u t s
Excitatory interneurones He, te
g1
g2
Pyramidal cells He, te
MEG/EEG signal
g3
g4
Inhibitory interneurones Hi, ti
Excitation
Inhibition

• te, ti synaptic time constants (excitation
  inhibition)
• He, Hi synaptic efficacies (excitation
  inhibition)
• g1,,4 connectivity constants

Parameters
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Neural mass modelof a cortical area
David et al., Neuroimage, 2005
Extrinsic lateral connections
inhibitory interneurons
Extrinsic forward connections
spiny stellate cells
Intrinsic connections
pyramidal cells
Extrinsic backward connections
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Rules of cortical connectivity
Felleman Van Essen, Cereb. Cortex, 1991 David
et al., NeuroImage, 2005
1
2
Forward
Backward
Lateral
Supra granular
Cortex
Layer IV (granular)
Infra granular
1
2
1
2
1
2
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Hierarchical cortical networks
inhibitory interneurons
2
3
spiny stellate cells
1
pyramidal cells
Intrinsic Forward Backward Lateral
Input u
Neuronal model used in Dynamic Causal Modelling
for EEG/MEG
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Neural coupling and synchronisation in EEG/MEG
David Friston, NeuroImage, 2003
abu10
1
2
atd
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fMRI
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Generative model of fMRI
fMRI signal
Neuronal activity (LFP)
Stimulus
Hemodynamic model
Neuronal model
Bilinear model of neural interactions
Hemodynamic balloon model
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Summary of DCM for fMRI
Neuronal state equation
Bilinear model
Effective connectivity
Modulation of connectivity
Input u(t)
Extrinsic inputs
c1
b23
Integration of differential equations
Neural states
a12
x2(t)
x3(t)
Hemodynamic model
x1(t)
y
y
y
BOLD
29
Modelled neural signals
stimuli u1
context u2
u1
-

-
u2
x1

x1

x2
x2
-
-
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Biophysics of fMRI
Raichle, Sc. American, April 1994

• Indirect effects of neuronal activation
• Variations of blood volume
• Variations of blood flow
• Variations of deoxyhemoglobin concentration

Dt
fMRI signal
0
20
Time (s)
31
The hemodynamic Balloon model
Friston et al., Neuroimage, 2000

• 5 hemodynamic parameters
• Empirically determineda priori distributions
• Computed separately for each area (like the
  neural parameters)

32
Friston et al., Neuroimage, 2000
The hemodynamic Balloon model
Neuronal activity x
s
y
0
v
q
f
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Parameter estimation
stimulus function u

• Combining the neural and hemodynamic states gives
  the complete forward model.
• An observation model includes measurement error
  e and confounds X (e.g. drift).
• Bayesian parameter estimation by means of a
  Levenberg-Marquardt gradient ascent, embedded
  into an Expectation-Maximisation (EM) algorithm.
• Result Gaussian a posteriori parameter
  distributions, characterised by mean ??y and
  covariance C?y.

neuronal state equation
parameters
hidden variables
state equation
BOLD response
observation model
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Model comparison
Pitt Miyung, TICS, 2002

• Given some hypotheses on the structure and
  functional mechanisms of a system, which model is
  the best?
• Find the model mi with the largest evidence
  p(ymi).
• Which model represents the best trade-off between
  the data fit and the model complexity?

35
Model comparison
Penny et al., NeuroImage, 2004

• Which model is the best among a set of competing
  models?
• Bayes law
• Model evidence

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Modulation of attention
Büchel et al., Cereb. Cortex, 1997

• Stimulus
• 250 radially moving dots (4.7 degrees/sec).
• Pre-acquisition
• 5 x 30s blocks avec 5 changes of speed (reduction
  of 1).
• Task to detect speed changes.
• Acquisition
• No change in speed.
• F A F N F A F N S .............
• F fixation dot only.
• A - stimulus with attention (detection of change
  in speed).
• N - stimulus without attention.
• S no movement.

LGN
PPC
PFC
V1
V5
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Modulation of attention
Friston et al., Neuroimage, 2003
Attentional modulation of prefontal connections
Photic stimulation
.43
.53 (97)
SPC
.40
.49 (97)
.62
V1
IFG
.92
.35
.53
-.05
V5
Segregation of movement information in V5
.73
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Comparaison of 3 models
Penny et al., Neuroimage, 2004
Model 1modulation by attention of V1?V5
Model 2modulation by attention of SPC?V5
Model 3modulation by attention of V1?V5 and
SPC?V5
Attention
Attention
Photic
Photic
Photic
SPC
0.55
0.03
0.85
0.86
0.85
0.70
0.70
0.75
1.36
0.84
1.42
1.36
0.89
0.85
V1
-0.02
-0.02
-0.02
0.56
0.57
0.57
V5
Movement
Movement
Movement
0.23
0.23
Attention
Attention

• Bayesian model selection
• Model 1 better than model 2
• Model 1 model 3 equivalent
• Decision for model 1, because attention modulates
  mainly V1?V5

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EEG/MEG
40
EEG MEG
Marin et al., Hum. Brain Mapp., 1998
MEG
EEG
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Generative model of EEG/MEG
Dynamics f
Spatial forward model g
ERP/ERF
states x
Input u
parameters ?
data y
42
Somatosensory evoked potential
mode 1
3.57 (99)
SII
SII
0.95 (53)
Forward Backward Lateral
mode 2
27.68 (100)
2.67 (100)
SI
input
mode 3
43
Perception of faces vs. houses
Haxby et al., Science, 2001
N170 Visage-Maison
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David et al., Neuroimage , 2006
mode 1
40
20
PPA
PPA
0
STS
-20
-40
5.56 (100)
FFA
-60
0.61 (100)
0
200
400
40
mode 2
RS
RS
20
IOG
0.11 (100)
0
0.55 (100)
-20
-40
-60
0
200
400
V1
V1
40
mode 3
20
0
-20
input
-40
0
-60
0
200
400
0
200
400
time (ms)
Time ms
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Auditory oddball andmismatch negativity (MMN)

• 600 stimuli, 100 ms duration
• Frequent event (80) tone 1000 Hz
• Rare event (20) tone 2000 Hz
• 128 EEG channels

Rare-Frequent
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Mismatch negativity (MMN)
Näätänen, Int. J. Psychophysiol., 2003

• Negative component of the ERP to any
  discriminative change in some repetitive aspect
  of auditory stimulation
• Based on the presence of a memory trace formed by
  the preceding sound stimuli
• Duration of the traces involved 10 sec
• Bilateral auditory and bilateral (right )
  frontal cortex

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Auditory oddballmodel comparaison
PC
OF
OF
STG
200
4.22
150
A1
A1
100
input
50
Forward Backward Lateral
0
F
B
FB
FBL
48
30
mode 1
PC
20
10
0
-10
OF
OF
-20
0
200
400
30
mode 2
20
10
2.74 (98)
2.17 (95)
3.58 (100)
STG
4.09 (100)
0
-10
3.23 (97)
-20
0
200
400
A1
A1
30
1.93 (100)
mode 3
20
10
0
-10
input
-20
600
0
200
400
0
time (ms)
0
200
400
49
Implanted epileptic patientDCM / 1 Hz electrical
stimulation
50
Implanted epileptic patient
Electrode showing first ictal patterns
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Spontaneous seizure
52
1 Hz neurostimulation
Electrode showing first ictal patterns
Electrode of stimulation
53
Induced seizure
54
Short-term plasticity
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DCM location
Stimulation of amygdala

• Amygdala
• Temporal pole
• Anterior hippocampus
• Insula

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DCM time series

• Amygdala
• Temporal pole
• Anterior hippocampus
• Insula

57
DCM model
0.98
42 / 59
4.3
(x1.4)
Amyg
Temp Pole
Hippo
Insula
52 / 59
27 / 26
49
(x1.1)
(x0.96)
0.29
Fit
Measurement
50 ms
Beginning of stim
End of stim
58
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