Introduction to Connectivity: PPI and SEM Carmen Tur Maria Joao Rosa Methods for Dummies 2009/10 24 th February, UCL, London

Introduction to Connectivity: PPI and SEM

Carmen Tur

Maria Joao Rosa

Methods for Dummies 2009/10

24th February, UCL, London

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

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

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

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

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

TYPES OF INTERACTIONS


PSYCHOLOGICAL PHYSIOLOGICAL

Cognitive task BOLD signal

Distracting taskDuring the memory task

V5 PP

PFC

PSYCHOPHYSIOLOGICAL

V2 V1

Psychological context

Attention – No attention


PSYCHOLOGICAL INTERACTIONS

Memory taskPET signal

Regional cerebral

blood flow

Distracting taskDuring the memory task

Fletcher et al. Brain 1995

An example: Dual-task interference paradigms (Fletcher et al. 1995)


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



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)

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



Buchel and Friston Cerebral cortex 1997

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


Can we detect those areas of the brain connected to V2 whose activity changes depending on the presence or

absence of attention?

OUR QUESTION…

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


Two possible perspectives on this interaction…

y = b1*(x1 X x2) + b2*x1 + b3*x2 + e


V1



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

Neurobiological process: Where these interactions occur?

Hemodynamic vs neural level


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

?


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


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?


1. Estimate GLM

Y = X . β + ε

I. GLM analysis


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


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


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


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


7. Obtain image

V2 Fixation (V1)



In this example For Dummies

y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) [+ βiXi + e]

II. PPI analysis


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


The end

(of PPI…)

Structural Equation Modelling

Maria Joao Rosa,UCL, London, 24/02/2010

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)


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.

To start with…

y 1

y 3

y 2

y 3

y 2y 1


Question: are these regions functionally related to each other?

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


includes only paths of interest


- assumed some value of the innovations

- implied covariance

Estimate path coefficients (b12,13,32 ) using a standard

estimation algorithm



Alternative models

y 1

y 3

y 2

Model comparison: likelihood ratio (chi-squared test)


Application to fMRI

[Penny 2004]


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


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

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

SPECIAL THANKS TO

ANDRE MARREIROS

Thanks for your attentionLondon, February 24th, 2010

Documents

Introduction to Connectivity: PPI and SEM Carmen Tur Maria Joao Rosa Methods for Dummies 2009/10 24 th February, UCL, London