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Introduction to Connectivity: PPI and SEM
Carmen Tur
Maria Joao Rosa
Methods for Dummies 2009/10
24th February, UCL, London
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Functional localization
Functional integration
Gall – 19th centuryA certain function was localised in a certain anatomic region in the cortex
Goltz – 19th century
Critizied Gall’s theory of functional localization
Evidence provided by dysconnection syndromesA certain function was carried
out by certain areas/cells in the cortex but they could be anatomically separated
“Connectionism”
Networks: Interactions among specialised areas
Specialised areas exist in the cortex
Functional specialization
Functional segregation
I. Origins of connectivity
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Functional segregation Functional integration
Functional connectivityEffective connectivity
No model-based
Simple correlations between areas
Its study allows us to speak about temporal correlations among activation of different anatomic areas
These correlations do not reflect teleologically meaningful interactions
Model-based
It allows us to speak about the influence that one neuronal system exerts over another
It attempts to disambiguate correlations of a spurious sort from those mediated by direct or indirect neuronal interactions
Networks -connectivity
II. Different approaches to connectivity
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II. Different approaches of connectivity – Functional connectivity
βik ~ Functional connectivity
What? Relationship between the activity of 2 different areas
How? Principle Component Analysis (PCA), which is done by Singular Value Decomposition (SVD) eigenvariates and eigenvalues obtained
Why? To summarise patterns of correlations among brain systems Find those spatio-temporal patterns of activity which explain most of the variance in a series of repeated measurements.
Time
Region k
Region i
stimulus
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xkβik ~ Effective connectivity
What? Real amount of contribution of one area (contribution of the activity of one area) to another.
How? It takes into account functional connectivity (correlations between areas), the whole activation in one region and interactions between different factors
Types of analysis to assess effective connectivity: 1. PPI – psychophysiological interactions2. SEM – structural equation modeling3. DCM – dynamic causal model
II. Different approaches of connectivity – Effective connectivity
Time
Region k
Region i
stimulus
A known pathway is tested
STATIC MODELS
DYNAMIC MODEL
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Study design where two or more factors are involved within a task
Aim: to look at the interaction between these factors to look at the effect that one factor has on the responses due to another factor
III. Interactions a. FACTORIAL DESIGN
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TYPES OF INTERACTIONS
III. Interactions a. FACTORIAL DESIGN
PSYCHOLOGICAL PHYSIOLOGICAL
Cognitive task BOLD signal
Distracting taskDuring the memory task
V5 PP
PFC
PSYCHOPHYSIOLOGICAL
V2 V1
Psychological context
Attention – No attention
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III. Interactions a. FACTORIAL DESIGN
PSYCHOLOGICAL INTERACTIONS
Memory taskPET signal
Regional cerebral
blood flow
Distracting taskDuring the memory task
Fletcher et al. Brain 1995
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An example: Dual-task interference paradigms (Fletcher et al. 1995)
III. Interactions a. FACTORIAL DESIGN
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Memory task
To remember 15 pairs of words (word category + example) previously shown
Control task
To listen to 15 pair of words
Difficult distracting taskTo move a cursor pointing at
rectangular boxes appearing randomly in one of four positions around the screen
Easy distracting taskTo move a cursor pointing at
rectangular boxes appearing in a predictable way, i.e. appearing clockwise around the four positions on the screen
III. Interactions a. FACTORIAL DESIGN
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III. Interactions a. FACTORIAL DESIGN
A B
C D
Difficult task
Distraction
Easy task
Memory
Memory task Control task
A B C D
[1 -1 -1 1]
Interaction term:
Is activation during memory task greater under difficult distraction task?
We pose the question…
Is (A – B) > (C – D)?
Then we test:
(A – B) – (C – D)
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Studies where we try to explain the physiological response in one part of the brain in terms of an interaction between prevalence of a sensorimotor or cognitive process and activity in another part of the brain
An example: interaction between activity in region V2 and some psychological parameter (e.g. attention vs no attention) in explaining the variation in activity in region V5
III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
V2 V1
Psychological context
Attention – No attention
Buchel and Friston Cerebral cortex 1997
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Attention
No attention
Activation in region i
(e.g. V1 activity)
Activation in region k (e.g. V2 activity)
?
Here the interaction can be seen as a significant difference in the regression slopes of V1 activity on V2 activity when assessed under two attentional conditions
III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
Can we detect those areas of the brain connected to V2 whose activity changes depending on the presence or
absence of attention?
OUR QUESTION…
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We could have that V1 activity/response reflects:
A change of the contribution from V2 by attention
A modulation of attention-specific responses by V2 inputs
III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
Two possible perspectives on this interaction…
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y = b1*(x1 X x2) + b2*x1 + b3*x2 + e
III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
V1
Psychological context
Attention – No attention
V2
Physiological activity in V1
We want to test H0
Interaction term
H0: b1 is = 0
H1: b1 is ≠ 0 and p value is < 0.05
Interaction between activity in V2 and psychological context
Mathematical representation of our question
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Neurobiological process: Where these interactions occur?
Hemodynamic vs neural level
III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
But interactions occur at a NEURAL LEVEL
Hemodynamic responses – BOLD signal – reflect the underlying neural activity
Gitelman et al. Neuroimage 2003
And we know: (HRFxV2) X (HRFxAtt) ≠ HRFx(V2XAtt)
≠
HRF basic function
?
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
SOLUTION:
1- Deconvolve BOLD signal corresponding to region of interest (e.g. V2)
2- Calculate interaction term considering neural activitypsychological condition x neural activity
3- Re-convolve the interaction term using HRF
Gitelman et al. Neuroimage 2003
x
HRF basic function
BOLD signal in V2
Neural activity in V2 Psychological variable
Neurobiological process: Where these interactions occur?
Hemodynamic vs neural level
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
How can we do this in SPM?
http://www.fil.ion.ucl.ac.uk/spm/data/attention/
Practical example from SPM central page
We want to assess whether the influence that V2 exerts over other areas from visual cortex (V1) depends on the status of a certain psychological condition (presence vs. absence of attention)
V2 V1
Attention – No
attention
Att
No A
ttHow can we do this in SPM?
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
1. Estimate GLM
Y = X . β + ε
I. GLM analysis
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
2. Extract time series
Meaning? To summarise the evolution in time of the activation of a certain region
Place? At region of interest (e.g. V2) region used as explanatory variable
Procedure? Principle Component Analysis (done by Singular Value Decomposition) To find those temporal patterns of activity which explain most of the variance of our region of interest these patterns are represented by the eigenvectors the variance of these eigenvectors is represented by eigenvalues
Reason? To include (the most important) eigenvalues in the model we transform dynamic information into STATIC information we will work with this static information PPI is a STATIC MODEL
I. GLM analysis
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
2. Extract time series
Y = X.β + ε + C.V2.β
We choose the temporal pattern of activity which best explains our data (First eigenvector)
Time
V2 activity
I. GLM analysis
…
Different temporal patterns which
explain the
activity in V2
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
1. Select (from the previous equation-matrix) those parameters we are interested in, i.e.- Psychological condition: Attention vs. No attention- Activity in V2
2. Deconvolve physiological regressor (V2) transform BOLD signal into electrical activity
Y = β.X + ε + β.C.V2
β(Att-NoAtt) + βiXi ~ βc.V2
Electrical activity
BOLD signal
HRF basic function
II. PPI analysis
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
3. Calculate the interaction term V2x(Att-NoAtt)
4. Convolve the interaction term V2x(Att-NoAtt)
5. Put into the model this convolved term:
y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) + βiXi + e
H0: β1 = 0
6. Create a t-contrast [1 0 0 0] to test H0 at 0.01 of significance
Electrical activity
BOLD signal
HRF basic function
II. PPI analysis
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
7. Obtain image
V2 Fixation (V1)
Psychological context
Attention – No attention
In this example For Dummies
y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) [+ βiXi + e]
II. PPI analysis
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
7. Obtain image
Interaction between activity in V2 and psychological condition (attention vs. no attention)
BOLD activity (whole brain – V1)
y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) [+ βiXi + e]
H1: β1 is ≠ 0 and p value is < 0.05
II. PPI analysis
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III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS
The end
(of PPI…)
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Structural Equation Modelling
Maria Joao Rosa,UCL, London, 24/02/2010
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Introduction | Theory | Application | Limitations | Conclusions
A bit of history
• Since 1920s and in economics, psychology and social sciences.
• In functional imaging since early 1990s:
– Animal autoradiographic data
– Human PET data (McIntosh and Gonzalez-Lima, 1991)
– fMRI (Büchel and Friston, 1997)
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Introduction | Theory | Application | Limitations | Conclusions
Definition
• Structural Equation Moldelling (SEM) or ‘path analysis’:
multivariate tool that is used to test hypotheses regarding the influences among interacting variables.
• Neuro-SEM:
– Connections between brain areas are based on known neuroanatomy.
– Interregional covariances of activity are used to calculate the path coefficients representing the magnitude of the influence or directional path.
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To start with…
y 1
y 3
y 2
y 3
y 2y 1
Introduction | Theory | Application | Limitations | Conclusions
Question: are these regions functionally related to each other?
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Innovations - independent residuals, driving the region stochastically
To start with…
y 1
y 3
y 2
y1 = z1 y2 = b12y1 + b32y3 + z2
y3 = b13y1 + z3
y2 = f (y1 y3) + z
b12
b13 b32
Introduction | Theory | Application | Limitations | Conclusions
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includes only paths of interest
Introduction | Theory | Application | Limitations | Conclusions
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- assumed some value of the innovations
- implied covariance
Estimate path coefficients (b12,13,32 ) using a standard
estimation algorithm
Introduction | Theory | Application | Limitations | Conclusions
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Introduction | Theory | Application | Limitations | Conclusions
Alternative models
y 1
y 3
y 2
Model comparison: likelihood ratio (chi-squared test)
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Introduction | Theory | Application | Limitations | Conclusions
Application to fMRI
[Penny 2004]
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Introduction | Theory | Application | Limitations | Conclusions
Limitations
• Static model (average effect) – DCM dynamic model
• Inference about the parameters is obtained by iteratively constraining the model
• Need to separate data – no need in DCM
• The causality is inferred at the hemodynamic level – neuronal level in DCM
• No input to model (stochastic innovations) – DCM
• Software: LISREL, EQS and AMOS
• SPM toolbox for SEM: check website
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Introduction | Theory | Application | Limitations | Conclusions
Conclusions
• Functional segregation vs. functional integration
• Functional connectivity vs. effective connectivity
• Three main types of analysis to study effective connectivity
– PPI STATIC MODEL
– SEM STATIC MODEL
– DCM DYNAMIC MODEL
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Further readinghttp://www.fil.ion.ucl.ac.uk/mfd/page2/page2.html
http://en.wikibooks.org/wiki/SPM
http://www.fil.ion.ucl.ac.uk/spm/data/attention/
Friston KJ, Frith CD, Passingham RE, et al (1992). Motor practice and neuropsychological adaptation in the cerebellum: a positron tomography study. Proc R Soc Lond B (1992) 248, 223-228.
Friston KJ, Frith CD, Liddle, PF & Frackowiak, RSJ. Functional Connectivity: The principle-component analysis of large data sets, J Cereb Blood Flow & Metab (1993) 13, 5-14
Fletcher PC, Frith CD, Grasby PM et al. Brain systems for encoding and retrieval of auditory-verbal memory. An in vivo study in humans. Brain (1995) 118, 401-416
Friston KJ, Buechel C, Fink GR et al. Psychophysiological and Modulatory Interactions in Neuroimaging. Neuroimage (1997) 6, 218-229
Buchel C & Friston KJ. Modulation of connectivity in visual pathways by attention: Cortical interactions evaluated with structural equation modelling & fMRI. Cerebral Cortex (1997) 7, 768-778
Buchel C & Friston KJ. Assessing interactions among neuronal systems using functional neuroimaging. Neural Networks (2000) 13; 871-882.
Ashburner J, Friston KJ, Penny W. Human Brain Function 2nd EDITION (2003) Chap 18-20
Gitelman DR, Penny WD, Ashburner J et al. Modeling regional and neuropsychologic interactions in fMRI: The importance of hemodynamic deconvolution. Neuroimage (2003) 19; 200-207.
Slides from previous years
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SPECIAL THANKS TO
ANDRE MARREIROS
Thanks for your attentionLondon, February 24th, 2010