SPM short course SPM short course
Functional integration and connectivityFunctional integration and connectivitySPM short course SPM short course
Functional integration and connectivityFunctional integration and connectivity
Christian BüchelChristian Büchel
Karl FristonKarl Friston
The Wellcome Department of Cognitive Neurology, UCLThe Wellcome Department of Cognitive Neurology, UCL
London UK http//:www.fil.ion.ucl.ac.uk/spmLondon UK http//:www.fil.ion.ucl.ac.uk/spm
Data analysisData analysis
RealignmentRealignment SmoothingSmoothing
NormalisationNormalisation
General linear modelGeneral linear model
fMRI time-seriesfMRI time-series
Parameter estimatesParameter estimates
Design matrixDesign matrix
TemplateTemplate
KernelKernel
p <0.05p <0.05
Inference with Gaussian Inference with Gaussian field theoryfield theory
Adjusted regional dataAdjusted regional data
spatial modes and spatial modes and effective connectivityeffective connectivity
Functional brain architecturesFunctional brain architecturesFunctional brain architecturesFunctional brain architectures
Functional segregationFunctional segregationUnivariate analyses of regionally Univariate analyses of regionally specific effectsspecific effects
Functional segregationFunctional segregationUnivariate analyses of regionally Univariate analyses of regionally specific effectsspecific effects
Functional integrationFunctional integrationMultivariate analyses of Multivariate analyses of regional interactionsregional interactions
Functional integrationFunctional integrationMultivariate analyses of Multivariate analyses of regional interactionsregional interactions
Functional connectivityFunctional connectivity““the temporal correlation between the temporal correlation between neurophysiological events”neurophysiological events”
an operational definitionan operational definition
Functional connectivityFunctional connectivity““the temporal correlation between the temporal correlation between neurophysiological events”neurophysiological events”
an operational definitionan operational definition
Effective connectivityEffective connectivity““the influence one neuronal system the influence one neuronal system exerts over another”exerts over another”
a model-dependent definitiona model-dependent definition
Effective connectivityEffective connectivity““the influence one neuronal system the influence one neuronal system exerts over another”exerts over another”
a model-dependent definitiona model-dependent definition
Issues in functional integrationIssues in functional integrationIssues in functional integrationIssues in functional integration
• Functional ConnectivityFunctional ConnectivityEigenimage analysis and PCAEigenimage analysis and PCA
• Effective ConnectivityEffective ConnectivityPsychophysiological InteractionsPsychophysiological InteractionsState space Models (Variable parameter regression)State space Models (Variable parameter regression)Structural Equation ModellingStructural Equation ModellingVolterra seriesVolterra series
Effective vs. functional connectivityEffective vs. functional connectivityEffective vs. functional connectivityEffective vs. functional connectivity
Model: A = V1 fMRI time-seriesB = 0.5 * A + e1C = 0.3 * A + e2
Model: A = V1 fMRI time-seriesB = 0.5 * A + e1C = 0.3 * A + e2
Correlations:
A B C10.49 10.30 0.12 1
Correlations:
A B C10.49 10.30 0.12 1
A
B
C
0.49
0.31
-0.02
2=0.5, ns.
Correct model
Correct model
Eigenimages - the basic conceptEigenimages - the basic conceptEigenimages - the basic conceptEigenimages - the basic concept
A time-series of 1D imagesA time-series of 1D images128 scans of 40 “voxels”128 scans of 40 “voxels”
Expression of 1st 3 “eigenimages”Expression of 1st 3 “eigenimages”
Eigenvalues and spatial “modes”Eigenvalues and spatial “modes”
The time-series ‘reconstituted’The time-series ‘reconstituted’
Eigenimages and SVDEigenimages and SVDEigenimages and SVDEigenimages and SVD
Y Y (DATA)(DATA)
timetime
voxelsvoxels
Y = USVY = USVTT = = ss11UU11VV11TT + + ss22UU22VV22
T T + ... + ...
APPROX. APPROX. OF YOF Y
UU11
==APPROX. APPROX.
OF YOF YAPPROX. APPROX.
OF YOF Y
+ + ss22 + + ss33 + ...+ ...ss11
UU22 UU33
VV11 VV22 VV33
An example from PETAn example from PETAn example from PETAn example from PET
Eigenimage analysis of aEigenimage analysis of aPET word generation studyPET word generation study
Word generation Word generation GGWord repetitionWord repetition RR
R G R G R G.........R G R G R G.........
Dynamic changes in effective connectivityDynamic changes in effective connectivity Attentional modulation of V5 responses to visual motionAttentional modulation of V5 responses to visual motion
Dynamic changes in effective connectivityDynamic changes in effective connectivity Attentional modulation of V5 responses to visual motionAttentional modulation of V5 responses to visual motion
• Psychophysiological interactionsPsychophysiological interactions
Attentional modulation of V2 to V5 connectionsAttentional modulation of V2 to V5 connections
• State space models and variable parameter regressionState space models and variable parameter regressionAttentional modulation of V5 to PPC connectionsAttentional modulation of V5 to PPC connections
• Models of effective connectivityModels of effective connectivity
The mediating role of posterior parietal cortexThe mediating role of posterior parietal cortex
in attentional modulationin attentional modulation
Structural Equation modellingStructural Equation modelling
Volterra formulationVolterra formulation
The fMRI studyThe fMRI study
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
Scanning (no speed changes)Scanning (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 - fixation point onlyF - fixation point only
A - motion stimuli with attention (detect changes)A - motion stimuli with attention (detect changes)
N - motion stimuli without attentionN - motion stimuli without attention
S - no motionS - no motion
PsychophysiologicalPsychophysiological interactions:interactions:
Attentional modulation ofAttentional modulation ofV2 -> V5 influencesV2 -> V5 influences
AttentionAttention
V2V2
V5V5
attention
no attention
V2 activity
V5
acti
vity
SPM{Z}
time
V5
acti
vity
Regression with time-varying coefficientsRegression with time-varying coefficients
Fixed regression model (one coefficient for entire time-series)Fixed regression model (one coefficient for entire time-series)
y = x*b + ey = x*b + e
Time varying regression model (coefficient changes over time) Time varying regression model (coefficient changes over time)
yyt t = x= xtt..bbtt + e + ett
bbtt = b = bt-1t-1+h+htt
Coefficient b of the explanatory variable (V5) is modelledCoefficient b of the explanatory variable (V5) is modelled
as a time-varying random walk. Estimation by Kalman filter.as a time-varying random walk. Estimation by Kalman filter.
AttentionFixation No attention
bbtt
x = V5x = V5y = PPy = PP
Time (scans)regr
essi
on c
oeff
icie
nt0.5
0.8
The source of modulatory afferentsThe source of modulatory afferentsThe source of modulatory afferentsThe source of modulatory afferents
p<0.05 correctedp<0.05 corrected
RR
RR
““Modulatory” sources Modulatory” sources identified as regions identified as regions correlated with correlated with bbtt
Anterior cingulate Dorsolateral prefrontal cortexAnterior cingulate Dorsolateral prefrontal cortex
Minimise the difference between the observed (Minimise the difference between the observed (SS) and implied () and implied () covariances by adjusting the path ) covariances by adjusting the path coefficients (a, b, c) coefficients (a, b, c)
The implied covariance structure: The implied covariance structure:
xx = x.B + z= x.B + zxx = z.(I - B)= z.(I - B)-1-1
x : matrix of time-series of regions U, V and Wx : matrix of time-series of regions U, V and W
B: matrix of unidirectional path coefficients (a,b,c)B: matrix of unidirectional path coefficients (a,b,c)
Variance-covariance structure:Variance-covariance structure:
xxT T . x = . x = = (I-B)= (I-B)-T-T. C.(I-B). C.(I-B)-1-1
where Cwhere C = z= zTT z z
xxTT.x is the implied variance covariance structure .x is the implied variance covariance structure C contains the residual variances (u,v,w) and covariancesC contains the residual variances (u,v,w) and covariances
The free parameters are estimated by minimising a [maximum likelihood] function of The free parameters are estimated by minimising a [maximum likelihood] function of SS and and
Structural equation modelling (SEM)Structural equation modelling (SEM)Structural equation modelling (SEM)Structural equation modelling (SEM)
U
W
Va
bc
u v
w
Attention - No attentionAttention - No attentionAttention - No attentionAttention - No attention
AttentionNo attention
0.760.47
0.750.43
PPPP
==
The use of moderator or interaction variablesThe use of moderator or interaction variablesThe use of moderator or interaction variablesThe use of moderator or interaction variables
V5V5
V1V1
V1xPPV1xPP
V5V5
2 =11, p<0.01
0.14
Modulatory influence of parietal cortex on V1 to V5Modulatory influence of parietal cortex on V1 to V5
Hierarchical architecturesHierarchical architecturesHierarchical architecturesHierarchical architectures
V1V1
V5V5PPPP
PFCPFC
LGNLGN
22=13.6, p<0.01=13.6, p<0.01
22=5.9, p<0.01=5.9, p<0.010.1
0.2
Changes in effective connectivity over time: LearningChanges in effective connectivity over time: Learning Changes in effective connectivity over time: LearningChanges in effective connectivity over time: Learning
• Paired associates learningPaired associates learning
• Pairing Pairing – Object (Snodgrass) withObject (Snodgrass) with
– LocationLocation
• fMRI, 48 axial slices, TR 4.1s, 8 scans/condfMRI, 48 axial slices, TR 4.1s, 8 scans/cond
• 8 cycles (E)ncoding (C)ontrol (R)etrieval8 cycles (E)ncoding (C)ontrol (R)etrieval
• 3 sessions (each with new objects & locations)3 sessions (each with new objects & locations)
C C C
E R E R
V1
ITp ITaPP
LP
V1
ITp
DE
SEM: Encoding Early vs. Late SEM: Encoding Early vs. Late SEM: Encoding Early vs. Late SEM: Encoding Early vs. Late
V1
DE
PPLP
ITpITa
Early
0.57
0.45
0.35
0.15
0.410.61
-0.03
V1
DE
PPLP
ITpITa
Late
0.46
0.38
0.27
0.26
0.370.59
0.132 =6.3p<0.05diff. = 0.16
Single subjects: +0.27*, +0.21, +0.37*, +0.24*, +0.19, +0.31*
* p < 0.05
Changes in effective connectivity Changes in effective connectivity predict learningpredict learning
Changes in effective connectivity Changes in effective connectivity predict learningpredict learning
Length of EARLY (in learning blocks) that maximised the EARLY vs. LATE difference in connectivity (PP -> ITP)
lear
nin
g r
ate
k
r = 0.64
1
0.4
1 2 3 4 5 6 7
learning block
k = .35 k = .60
k = .63 k=.95
k = .71k =.44
% c
orr
ect
Volterra series - Volterra series - a general nonlinear input-output modela general nonlinear input-output model
y(t)y(t) = = 11[u(t)] + [u(t)] + 22[u(t)] + .... + [u(t)] + .... + nn[u(t)] + ....[u(t)] + ....
nn[u(t)] = [u(t)] = .... .... h hnn(t(t11,..., t,..., tnn)u(t - t)u(t - t11) .... u(t - t) .... u(t - tnn)d t)d t1 1 .... d t.... d tnn
[u(t)] response y(t)response y(t)input[s] u(t)input[s] u(t)
kernels (h)kernels (h)
Regional activitiesRegional activities
estimateestimate
Volterra series approximationVolterra series approximationVolterra series approximationVolterra series approximation
• Trying to explain activity in region Trying to explain activity in region AA by by
– past and present activity in other regions (1st order)past and present activity in other regions (1st order)
• direct effects (eg. effect of B on direct effects (eg. effect of B on AA))
– past and present activity in other regions (pairwise = 2nd order)past and present activity in other regions (pairwise = 2nd order)
• non-linear (eg. effect of Bnon-linear (eg. effect of B22 on on AA))
• modulatory (eg. effect of AB on modulatory (eg. effect of AB on AA) )
– AA = a = a11B + aB + a22C + aC + a33AA + aAA + a44BB + aBB + a55CC + aCC + a66AB + aAB + a77AC + aAC + a88BCBC
– All terms can be seen as regressors and their impact can be tested with the general linear All terms can be seen as regressors and their impact can be tested with the general linear modelmodel
– directdirect effect of B on effect of B on AA : B and BB as covariates of interests, others confounds : B and BB as covariates of interests, others confounds
– modulatorymodulatory effect of B on effect of B on AA : AB and BC as covariates of interest, others confounds : AB and BC as covariates of interest, others confounds
V3aV3a
PPCPPC
FEFFEF
V5V5
IFSIFS
PPCPPC
V5V5
PulPul
V1/V2V1/V2
PPCPPC
areas showing attentional effectsareas showing attentional effects
regional interactions examinedregional interactions examined
Changes in V5 response to V2 Changes in V5 response to V2 inputs with PPC activityinputs with PPC activity
i.e. a modulatory (activity-dependent)i.e. a modulatory (activity-dependent)component of V5 responsescomponent of V5 responses
SPM{F}
PPC activity = 1
PPC activity = 0
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