dynamic causal modelling will penny wellcome department of imaging neuroscience, university college...
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Dynamic Causal ModellingDynamic Causal Modelling
Will Penny
Wellcome Department of Imaging Neuroscience, University College London, UK
FMRIB, Oxford, May 28 2003
Outline
Functional specialisation and integration
DCM theory
Attention Data
Model comparison
Outline
Functional specialisation and integration
DCM theory
Attention Data
Model comparison
Attention to Visual MotionAttention to Visual Motion
StimuliStimuli
250 radially moving dots at 4.7 degrees/s250 radially moving dots at 4.7 degrees/s
Pre-ScanningPre-Scanning
5 x 30s trials with 5 speed changes (reducing to 1%)5 x 30s trials with 5 speed changes (reducing to 1%)
Task - detect change in radial velocityTask - detect change in radial velocity
ScanningScanning (no speed changes) (no speed changes)
6 normal subjects, 4 100 scan sessions;6 normal subjects, 4 100 scan sessions;
each session comprising 10 scans of 4 different conditioneach session comprising 10 scans of 4 different condition
e.g. F A F N F A F N S .................e.g. F A F N F A F N S .................
F – fixationF – fixation
S – stationary dots S – stationary dots
N – moving dotsN – moving dots
A – attended moving dotsA – attended moving dots
1. Photic Stimulation, S,N,A2. Motion, N,A3. Attention, A
Experimental Factors
Buchel et al. 1997
Functional Specialisation
Q. In what areas does the ‘motion’ factor change activity ?
Univariate Analysis
AttentionAttention
V2V2
attention
no attention
V2 activity
V5
acti
vity
SPM{Z}
time
V5
acti
vity
Functional Integration
Q. In what areas is activity correlated with activity in V2 ?
Q. In what areas does the ‘attention’ factor change this correlation ?
Multivariate Analysis
Functional Integration
Q. In what areas is activity correlated with activity in V2 ?
Q. In what areas does the ‘attention’ factor change this correlation ?
Q. In what areas is activityrelated to the correlation betweenV2 and V5 ?
Psycho-Physiological (PPI)Interaction
Physio-Physiological (PPI)Interaction
Physiological correlation
Larger networks
Structural Equation Modelling (SEM)
Multivariate Autoregressive (MAR)
Dynamic Causal Modelling (DCM)
Connections = ‘Hemodynamic’ (SEM/MAR) = ‘Neuronal’ (PPI/DCM)
Z2
Z4
Z3
Z5
Outline
Functional specialisation and integration
DCM theory
Attention Data
Model comparison
To estimate and make inferences about
(1) the influence that one neural system exerts over another (i.e. effective connectivity)
(2) how this is affected by the experimental context
Aim of DCM
Z2
Z4
Z3
Z5
DCM Theory
A Model of Neuronal ActivityA Model of Hemodynamic ActivityFitting the ModelMaking inferencesModel Comparison
Model of Neuronal Activity
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Nonlinear,systems-levelmodel
Bilinear Dynamics
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Bilinear Dynamics: Oscillatory transients
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Bilinear Dynamics: Positive transients
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DCM: A model for fMRI
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Causality: set of differential equations relatingchange in one areato change inanother
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signal BOLD
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The hemodynamic model
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F lo w in d u c in g s ig n a l
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State Equations
Buxton,Mandeville,Hoge,Mayhew.
Hemodynamics
Impulseresponse
BOLD is sluggish
Neuronal Transients and BOLD: I
300ms 500ms
More enduring transients produce bigger BOLD signals
SecondsSeconds
Neuronal Transients and BOLD: II
BOLD is sensitive to frequencycontent of transients
Seconds
Seconds
Seconds
Relative timings of transients areamplified in BOLD
Model estimation and inference
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Unknown neural parameters, N={A,B,C}Unknown hemodynamic parameters, HVague priors and stability priors, p(N) Informative priors, p(H)Observed BOLD time series, B.Data likelihood, p(B|H,N) = Gauss (B-Y)
Bayesian inference p(N|B) p(B|N) p(N)
LaplaceApproximation
Posterior Distributions
CuuBzAzz
A1 A2 WA
C
P(A(ij)) = N (A(i,j),ij))
P(B(ij)) = N (B(i,j),ij))
P(C(ij)) = N (C(i,j),Cij))
Show connections for which A(i,j) > Threshwith probability > 90%
Outline
Functional specialisation and integration
DCM theory
Attention Data
Model comparison
Attention to Visual MotionAttention to Visual Motion
StimuliStimuli
250 radially moving dots at 4.7 degrees/s250 radially moving dots at 4.7 degrees/s
Pre-ScanningPre-Scanning
5 x 30s trials with 5 speed changes (reducing to 1%)5 x 30s trials with 5 speed changes (reducing to 1%)
Task - detect change in radial velocityTask - detect change in radial velocity
ScanningScanning (no speed changes) (no speed changes)
6 normal subjects, 4 100 scan sessions;6 normal subjects, 4 100 scan sessions;
each session comprising 10 scans of 4 different conditioneach session comprising 10 scans of 4 different condition
e.g. F A F N F A F N S .................e.g. F A F N F A F N S .................
F – fixationF – fixation
S – stationary dots S – stationary dots
N – moving dotsN – moving dots
A – attended moving dotsA – attended moving dots
1. Photic Stimulation, S,N,A2. Motion, N,A3. Attention, A
Experimental Factors
Buchel et al. 1997
V1
IFG
V5
SPC
Motion
Photic Attention
..82(100%)
.42(100%)
.37(90%)
.69 (100%).47(100%)
.65 (100%)
.52 (98%)
.56(99%)
Motion modulates bottom-upV1-V5 connection
Attention modulates top-downIFG-SPC and SPC-V5 connections
Friston et al. 2003
Outline
Functional specialisation and integration
DCM theory
Attention Data
Model comparison
First level of Bayesian Inference
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pypyp
First level of Inference: What are the best parameters ?
We have data, y, and some parameters,
Parameters are of model, M, ….
First and Second Levels
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MpMypMyp
The first level again, writing in dependence on M:
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Second level of Inference: What’s the best model ?
Model Comparison
We need to compute the Bayesian Evidence:
dpypMyp )()|()|(
We can’t always compute it exactly, but we can approximate it: Log p(y|M) ~ F(M)
Evidence = Accuracy - Complexity
m=1
V1 PFC
V5
PPC
MotionPhotic
Attention MotionPhotic
Attention
MotionPhotic
Attention
MotionPhotic
Attention
m=2
V1 PFC
V5
PPC
Motion
Photic
Attention
V1 PFC
V5
PPC
Motion
Photic
Attention
V1 PFC
V5
PPC
Motion
Photic
Attention
m=3
m=4
m=1
V1 PFC
V5
PPC
MotionPhotic
Attention MotionPhotic
Attention
MotionPhotic
Attention
MotionPhotic
Attention
m=2
V1 PFC
V5
PPC
Motion
Photic
Attention
V1 PFC
V5
PPC
Motion
Photic
Attention
V1 PFC
V5
PPC
Motion
Photic
Attention
m=3
m=4
Summary
Studies of functional integration look at
experimentally induced changes in connectivityIn PPI’s and DCM this connectivity is at the
neuronal levelDCM: Neurodynamics and hemodynamicsInferences about large-scale neuronal networksModel comparison/averaging
Single word processing at different rates
SPM{F}
“Dog”
“Mountain”
“Gate”
Functional localisation of primary and secondary auditory cortex and Wernicke’s area
Friston et al.2003
Time Series
A1
WA
A2Auditory stimulus, u1
Adaptation variable, u2
Dynamic Causal Model
A2
WA
A1
.
.
Auditory stimulus, u1
Model allows forfull intrinsicconnectivity
u1 Adaptation variable, u2
u1 enters A1 and is also allowed to affect all intrinsic self-connections
CuuBzAzz
u2 is allowed to affect all intrinsic connections betweenregions
Inferred Neural Network
A2
WA
A1
.92(100%)
.38(94%)
.47(98%)
.37 (91%)
-.62 (99%)
-.51 (99%)
.37 (100%)
Intrinsic connectionsare feed-forward
Neuronal saturationwith increasing stimulus frequencyin A1 & WA
Time-dependentchange in A1-WAconnectivity
Two central problems
The problem of the hidden level
We measure hemodynamics but wish
to make inferences about neurodynamics
The problem of the hidden variable
Association between A and B can be
mediated by causal influence from C