1. PSYCHOPHYSIOLOGICAL INTERACTIONS STRUCTURAL EQUATION MODELLING Karine Gazarian and Carmen Tur London, February 11th, 2009 Introduction to connectivity Methods for Dummies 2008-9

2. 0. Preface I. Origins of connectivity II. Different approaches of connectivity a. Functional connectivity b. Effective connectivity III. Interactions a.Factorial design b.Psychophysiological interactions IV. Structural Equation Modelling V. Conclusions Index

3. Preface Wish of doing a talk about connectivity Level of the Talk Physicist Clinician ?

4. Functional localization Functional integration 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 A 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

5. Functional segregationFunctional integration 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 Networks Connectivity II. Different approaches to connectivity

6. II. Different approaches of connectivity – Functional connectivity Time Region k Region i stimulus β ik ~ 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.

7. x k β ik ~ 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 interactions 2.SEM – structural equation modeling 3.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

8. 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 III. Interactions a. FACTORIAL DESIGN

9. An example: Investigation of interaction between motor activation and time (Friston et al. 1992) III. Interactions a. FACTORIAL DESIGN

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

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

12. 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 V1 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 V5 Psychological context Attention – No attention Buchel and Friston Cerebral cortex 1997

13. Attention No attention Activation in region i (e.g. V5 activity) Activation in region k (e.g. V2 activity) ? Here the interaction can be seen as a significant difference in the regression slopes of V5 activity on V2 activity when assessed under two attentional conditions III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS

14. We could have that V5 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…

15. Mathematical explanation y = b 1 *(x1 X x2) + b 2 *x1 + b 3 *x2 + e III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS V5 Psychological context Attention – No attention V2 Physiological activity in V5 We want to test H 0 Interaction term H 0 : b 1 is = 0 H 1 : b 1 is ≠ 0 and p value is < 0.05 Interaction between activity in V2 and psychological context

16. 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 ?

17. Neurobiological process: Where these interactions occur? Hemodynamic vs neural level III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 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 Gitelman et al. Neuroimage 2003 x HRF basic function BOLD signal in V2 Neural activity in V2Psychological variable

18. 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 (V5) depends on the status of a certain psychological condition (presence vs. absence of attention) V2 V5 Attention – No attention Att No Att

19. How can we do this in SPM? I. GLM analysis III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 1. Estimate GLM Y = X. β + ε

20. How can we do this in SPM? I. GLM analysis III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 2. Extract time series Meaning? To summarise the evolution in time and space 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 spatio-temporal patterns of activity which explain most of the variance of our dataset (i.e. activity in V1 over time)  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 (movement in time & space) into STATIC information (saved as a new matrix)  we will work with this static information  PPI is a STATIC MODEL

21. How can we do this in SPM? I. GLM analysis III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 2. Extract time series Y = X.β + ε + C.V2.β We add information about spatio-temporal patterns of activity which best explains our data into the previous model x y z Time x y z x y z x y z V2 activity

22. How can we do this in SPM? II. PPI analysis 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) + β i X i ~ β c.V2 Electrical activity BOLD signal HRF basic function

23. How can we do this in SPM? II. PPI analysis 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 = β 1 [V2x(Att-NoAtt)] + β 2 V2 + β 3 (Att-No-Att) + β i Xi + e H 0 : β 1 = 0 6. Create a t-contrast [1 0 0 0] to test H 0 at 0.01 of significance Electrical activity BOLD signal HRF basic function

24. How can we do this in SPM? II. PPI analysis 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]

25. How can we do this in SPM? II. PPI analysis III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 7. Obtain image Interaction between activity in V2 and psychological condition (attention vs. no attention) BOLD activity (whole brain) y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) [+ βiXi + e] H 1 : β 1 is ≠ 0 and p value is < 0.05

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

27. SEM Structural Equation Modelling Karine Gazarian

28. Definition Structural Equation Moldelling (SEM) or otherwise called ‘path analysis’ is a multivariate tool that is used to test hypotheses regarding the influences among interacting variables. –Unlike PPI, combines an anatomical model and the inter-regional covariances of activity. –Uses estimation of parameters that define the strength of connections between brain areas in question (path coefficients), rather than activity in individual variables.

29. 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)

30. To start with… y 1 y 3 y 2 y 3 y 2 y 1

31. Innovations - independent residuals, driving the region stochastically To start with… y 1 y 3 y 2 y 1 = z 1 y 2 = b 12 y 1 + b 32 y 3 + z 2 y 3 = b 13 y 1 + z 3 y 2 = f (y 1 y 3 ) + z b 12 b 13 b 32

32. includes only paths of interest

33. - assumed some value of the innovations - implied covariance Estimate path coefficients (b 12,13,32 ) using a standard estimation algorithm

34. Alternative models y 1 y 3 y 2

35. Limitations Static model Inference about the parameters is obtained by iteratively constraining the model (As opposed to DCM - good example of a dynamic causal model, which allows to infer the connectivity parameters in one step) The causality is inferred at the hemodynamic level, rather than at the more realistic neuronal level (DCM)

36. 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

37. 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 FURTHER READING…

38. SPECIAL THANKS TO ANDRE MARREIROS Thanks for your attention London, February 11 th, 2009 Introduction to connectivity