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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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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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

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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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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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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:

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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

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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