Introduction to Connectivity: PPI and SEM

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

2. I. Origins of connectivity Functional localization “Connectionism” Gall – 19th century A 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 syndromes Functional segregation A certain function was carried out by certain areas/cells in the cortex but they could be anatomically separated Functional specialization Functional integration Specialised areas exist in the cortex Networks: Interactions among specialised areas

3. II. Different approaches to connectivity Functional integration Functional segregation Networks -connectivity Functional connectivity Effective 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

4. II. Different approaches of connectivity – Functionalconnectivity Region i Region k stimulus Time 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.

5. II. Different approaches of connectivity – Effective connectivity STATIC MODELS DYNAMIC MODEL A known pathway is tested Region i Region k stimulus Time • 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 functionalconnectivity (correlations between areas), the whole activation in one region and interactions between different factors • Types of analysis to assess effective connectivity: • PPI – psychophysiological interactions • SEM – structural equation modeling • DCM – dynamic causal model

6. III. Interactions a. FACTORIAL DESIGN • 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

7. III. Interactions a. FACTORIAL DESIGN Cognitive task BOLD signal Distracting task During the memory task PP PSYCHOPHYSIOLOGICAL V5 V1 V2 PFC Psychological context Attention – No attention TYPES OF INTERACTIONS PHYSIOLOGICAL PSYCHOLOGICAL

8. III. Interactions a. FACTORIAL DESIGN Memory task PET signal Regional cerebral blood flow Distracting task During the memory task Fletcher et al. Brain 1995 PSYCHOLOGICAL INTERACTIONS

9. III. Interactions a. FACTORIAL DESIGN An example: Dual-task interference paradigms (Fletcher et al. 1995)

10. Memory task To remember 15 pairs of words (word category + example) previously shown Control task To listen to 15 pair of words Difficult distracting task To move a cursor pointing at rectangular boxes appearing randomly in one of four positions around the screen Easy distracting task To 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

11. III. Interactions a. FACTORIAL DESIGN 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) Memory Memory task Control task A B C D Difficult task Distraction Easy task A B C D [1 -1 -1 1]

12. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS V1 V2 Psychological context Attention – No attention Buchel and Friston Cerebral cortex 1997 • Studies where we try to explain the physiological responsein 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

13. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS OUR QUESTION… Activation in region i (e.g. V1 activity) Attention ? No attention Can we detect those areas of the brain connected to V2 whose activity changes depending on the presence or absence of attention? 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

14. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS Two possible perspectives on this interaction… • 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

15. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS V1 V2 Psychological context Attention – No attention H0: b1is = 0 H1: b1is ≠ 0 and p value is < 0.05 y = b1*(x1 X x2)+b2*x1 + b3*x2 + e Interaction term Physiological activity in V1 Mathematical representation of our question Interaction between activity in V2 and psychological context We want to test H0

16. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS HRF basic function Neurobiological process: Where these interactions occur? Hemodynamic vs neural level Hemodynamic responses – BOLD signal – reflect the underlying neural activity ? But interactions occur at a NEURAL LEVEL And we know: (HRFxV2) X (HRFxAtt) ≠ HRFx(V2XAtt) ≠ Gitelman et al. Neuroimage 2003

17. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS BOLD signal in V2 HRF basic function Neural activity in V2 Psychological variable x Gitelman et al. Neuroimage 2003 Neurobiological process: Where these interactions occur? Hemodynamic vs neural level SOLUTION: 1- Deconvolve BOLD signal corresponding to region of interest (e.g. V2) 2- Calculate interaction term considering neural activity psychological condition x neural activity 3- Re-convolve the interaction term using HRF

18. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS V2 Attention – No attention Att No Att How can we do this in SPM? How can we do this in SPM? 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) V1 http://www.fil.ion.ucl.ac.uk/spm/data/attention/

19. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS I. GLM analysis 1. Estimate GLM Y= X. β+ ε

20. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 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

21. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS I. GLM analysis 2. Extract time series Y= X.β+ ε+ C.V2.β V2 activity Different temporal patterns which explain the activity in V2 … Time We choose the temporal pattern of activity which best explains our data (First eigenvector)

22. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS Y= β.X+ ε+β.C.V2 β(Att-NoAtt) + βiXi ~ βc.V2 Electrical activity HRF basic function BOLD signal II. PPI analysis • 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

23. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS Electrical activity HRF basic function BOLD signal 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

24. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS Fixation (V1) Psychological context Attention – No attention II. PPI analysis 7. Obtain image V2 In this example For Dummies y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) [+ βiXi + e]

25. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS II. PPI analysis 7. Obtain image BOLD activity (whole brain – V1) H1: β1is ≠ 0 and p value is < 0.05 Interaction between activity in V2 and psychological condition (attention vs. no attention) y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) [+ βiXi + e]

26. III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS The end (of PPI…)

27. Structural Equation Modelling Maria Joao Rosa, UCL, London, 24/02/2010

28. 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)

29. 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.

30. y 1 y 2 y y 1 2 y 3 y 3 Introduction | Theory | Application | Limitations | Conclusions To start with… Question: are these regions functionally related to each other?

31. y 1 y 2 y 3 Innovations - independent residuals, driving the region stochastically Introduction | Theory | Application | Limitations | Conclusions To start with… y1 = z1 y2 = b12y1 + b32y3 + z2 b12 b13 b32 y3 = b13y1 + z3 y2 = f (y1 y3) + z

32. includes only paths of interest Introduction | Theory | Application | Limitations | Conclusions

33. Introduction | Theory | Application | Limitations | Conclusions Estimate path coefficients (b12,13,32 ) using a standard estimation algorithm • assumed some value of the innovations • implied covariance

34. y 1 y 2 y 3 Introduction | Theory | Application | Limitations | Conclusions Alternative models Model comparison: likelihood ratio (chi-squared test)

35. Introduction | Theory | Application | Limitations | Conclusions Application to fMRI [Penny 2004]

36. 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

37. 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

38. Further reading http://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

39. SPECIAL THANKS TO ANDRE MARREIROS Thanks for your attention London, February 24th, 2010