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

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

Functional segregation Functional 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

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

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

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

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

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

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

A B C D Difficult task Distraction Easy task Memory Memory task Control task A B C D [ ] 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 Psychological context Attention – No attention 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 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…

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…

y = b 1 *(x1 X x2) + b 2 *x1 + b 3 *x2 + e III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS V1 Psychological context Attention – No attention V2 Physiological activity in V1 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 Mathematical representation of our question

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 ?

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 Neurobiological process: Where these interactions occur? Hemodynamic vs neural level

III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 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) V2 V1 Attention – No attention Att No Att How can we do this in SPM?

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

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

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

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 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 [ ] to test H 0 at 0.01 of significance Electrical activity BOLD signal HRF basic function 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] 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 – V1) y = β1[V2x(Att-NoAtt)] + β2V2 + β3(Att-No-Att) [+ βiXi + e] H 1 : β 1 is ≠ 0 and p value is < 0.05 II. PPI analysis

III. Interactions – b. PSYCHOPHYSIOLOGICAL INTERACTIONS 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)

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.

To start with… y 1 y 3 y 2 y 3 y 2 y 1 Introduction | Theory | Application | Limitations | Conclusions 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 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 Introduction | Theory | Application | Limitations | Conclusions

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

- assumed some value of the innovations - implied covariance Estimate path coefficients (b 12,13,32 ) using a standard estimation algorithm Introduction | Theory | Application | Limitations | Conclusions

Alternative models y 1 y 3 y 2 Model comparison: likelihood ratio (chi-squared test)

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

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

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

Further reading 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, 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, Friston KJ, Buechel C, Fink GR et al. Psychophysiological and Modulatory Interactions in Neuroimaging. Neuroimage (1997) 6, Buchel C & Friston KJ. Modulation of connectivity in visual pathways by attention: Cortical interactions evaluated with structural equation modelling & fMRI. Cerebral Cortex (1997) 7, Buchel C & Friston KJ. Assessing interactions among neuronal systems using functional neuroimaging. Neural Networks (2000) 13; Ashburner J, Friston KJ, Penny W. Human Brain Function 2nd EDITION (2003) Chap Gitelman DR, Penny WD, Ashburner J et al. Modeling regional and neuropsychologic interactions in fMRI: The importance of hemodynamic deconvolution. Neuroimage (2003) 19; Slides from previous years

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