1. Rosalyn Moran Wellcome Trust Centre for Neuroimaging Institute of Neurology University College London With thanks to the FIL Methods Group for slides and images Introduction to Connectivity SPM Course, Virginia Tech 25 th Jan 2012

2. Principles of Organisation Functional Specialization ? ? How do regions influence each other? + Functional Integration

3. Overview Brain connectivity: types & definitions Functional connectivity Effective connectivity - Psycho-physiological Interactions - Structural Equation Modelling

4. Overview Brain connectivity: types & definitions Functional connectivity Effective connectivity - Psycho-physiological Interactions - Structural Equation Modelling

5. Structural, functional & effective connectivity anatomical/structural connectivity = presence of axonal connections functional connectivity =statistical dependencies between regional time series effective connectivity =causal (directed) influences between neurons or neuronal populations Sporns 2007, Scholarpedia

6. Anatomical connectivity Definition: presence of axonal connections - Measured with - tracing techniques - Diffusion tensor imaging (DTI) –Neuronal communication via synaptic contacts, long range connections employ glutamate –Regions arranged hierarchically: useful prior see later –Presence of anatomical connection a necessary but not sufficient condition for functional integration –Though some transmitters employ diffuse mechanisms; volume transmission

7. Knowing anatomical connectivity is not enough... Context-dependent recruiting of connections : –Local functions depend on network activity Connections show synaptic plasticity –change in the structure and transmission properties of a synapse –even at short timescales  Look at functional and effective connectivity

8. Overview Brain connectivity: types & definitions Functional connectivity Effective connectivity - Psycho-physiological Interactions - Structural Equation Modelling

9. Definition: statistical dependencies between regional time series Seed voxel correlation analysis Coherence analysis Eigen-decomposition (PCA, SVD) Independent component analysis (ICA) Any technique describing statistical dependencies amongst regional time series Functional connectivity

10. Eg. 1 Seed-voxel correlation analyses hypothesis-driven choice of a seed voxel extract reference time series voxel-wise correlation with time series from all other voxels in the brain seed voxel

11. Eg. 1 Seed-voxel correlation analyses Task Driven Activations (finger tapping) Identification of VxOI Resting State Correlations ~0.0-1 Hz RSNs: Resting State Networks

12. Eg 2. Melodic Algorithm (>ICA) ICA separates a multivariate signal into additive subcomponents assuming independence in mixing vectors which are non-Gaussian Tensor ICA separates multi-subject data into sets of vectors characterizing underlying signals in the temporal, spatial and subject domain Bayesian Algorithm: MELODIC determines the number of independent components at rest using a Laplace approximation to the Bayesian evidence of the model order (FSL Christian F. Beckmann) Pyka et al. 2009 The time course of the DMN revealed increased activation at rest after 1-back and 2-back blocks compared to the activation after a 0-back block

13. Summary of functional connectivity analysis Pros: –useful when we have no experimental control over the system of interest and no model of what caused the data (e.g. sleep, hallucinations, resting state: DMNs) –Large scale network characterisations available eg. Through graph theoretic metrics –Anatomical parsellation based on resting state asymmetries Cons: –interpretation of resulting pairwise patterns is difficult –no mechanistic insight –usually suboptimal for data with priori knowledge / experimental control  Effective connectivity

14. Overview Brain connectivity: types & definitions Functional connectivity Effective connectivity - Psycho-physiological Interactions - Structural Equation Modelling

15. Effective connectivity Definition: causal (directed) influences between neurons or neuronal populations i.e. the effect one brain region has on another In vivo and in vitro stimulation and recording Models of causal interactions among neuronal populations –explain regional effects in terms of interregional connectivity

16. Some models for computing effective connectivity from fMRI data Regression models (e.g. psycho-physiological interactions, PPIs) Friston et al. 1997 Structural Equation Models (SEM) McIntosh et al. 1991, 1994; Büchel & Friston 1997; Bullmore et al. 2000 Volterra kernels Friston & Büchel 2000 Time series models (e.g. MAR, Granger causality) Harrison et al. 2003, Goebel et al. 2003 Dynamic Causal Models (DCM) bilinear: Friston et al. 2003; nonlinear: Stephan et al. 2008

17. Some models for computing effective connectivity from fMRI data Regression models (e.g. psycho-physiological interactions, PPIs) Friston et al. 1997 Structural Equation Models (SEM) McIntosh et al. 1991, 1994; Büchel & Friston 1997; Bullmore et al. 2000 Volterra kernels Friston & Büchel 2000 Time series models (e.g. MAR, Granger causality) Harrison et al. 2003, Goebel et al. 2003 Dynamic Causal Models (DCM) bilinear: Friston et al. 2003; nonlinear: Stephan et al. 2008

18. Psycho-physiological interaction: Friston et al 1997(PPI) GLM of a 2x2 factorial design: main effect of task main effect of stim. type interaction The idea is to explain responses in one cortical area, in terms of an interaction between the influence of another area and some experimental (sensory or task-related) parameter. We refer to these effects as psychophysiological interactions. As opposed to interactions based solely on experimental factors (i.e., psychological interactions) Task factor Task A Task B Stim 1 Stim 2 Stimulus factor T A /S 1 T B /S 1 T A /S 2 T B /S 2

19. Psycho-physiological interaction (PPI) Task factor Task A Task B Stim 1 Stim 2 Stimulus factor T A /S 1 T B /S 1 T A /S 2 T B /S 2 GLM of a 2x2 factorial design: main effect of task main effect of stim. type interaction Interactions based solely on experimental factors (i.e., psychological interactions)

20. Psycho-physiological interaction (PPI) Task factor Task A Task B Stim 1 Stim 2 Stimulus factor T A /S 1 T B /S 1 T A /S 2 T B /S 2 GLM of a 2x2 factorial design: main effect of task main effect of stim. type interaction The idea is to explain responses in one cortical area, in terms of an interaction between the influence of another area and some experimental (sensory or task-related) parameter. Replace one main effect in the GLM by the deconvolved time series of an area that shows this main effect. E.g. let's say V1 showed a main effect of stimulus type

21. Psycho-physiological interaction (PPI) Task factor Task A Task B Stim 1 Stim 2 Stimulus factor T A /S 1 T B /S 1 T A /S 2 T B /S 2 GLM of a 2x2 factorial design: main effect of task Psycho- physiological interaction The idea is to explain responses in one cortical area, in terms of an interaction between the influence of another area and some experimental (sensory or task-related) parameter. V1 time series  main effect of stim. type Replace one main effect in the GLM by the deconvolved time series of an area that shows this main effect. E.g. let's say V1 showed a main effect of stimulus type

22. Psycho-physiological interaction (PPI) Task factor Task A Task B Stim 1 Stim 2 Stimulus factor T A /S 1 T B /S 1 T A /S 2 T B /S 2 GLM of a 2x2 factorial design: main effect of task Psycho- physiological interaction The idea is to explain responses in one cortical area, in terms of an interaction between the influence of another area and some experimental (sensory or task-related) parameter. V1 time series  main effect of stim. type Test using reconstructed Design Matrix as usual

23. Büchel & Friston 1997, Cereb. Cortex Büchel et al. 1998, Brain Example: Attention to motion in the visual system Task factor Task A Task B Stim 1 Dots Stimulus factor T A /S 1 T B /S 1 T A /S 2 T B /S 2 Task factor Attend Passive Static Moving T A /S 1 T B /S 1 T A /S 2 T B /S 2

24. Example: Attention to motion in the visual system Task factor Task A Task B Stim 1 Dots Stimulus factor T A /S 1 T B /S 1 T A /S 2 T B /S 2 Task factor Attend Passive Static Moving T A /S 1 T B /S 1 T A /S 2 T B /S 2 main effect of attention: V5 (and SPC) main effect of motion in V1 and V5 Psychological Main Effects Does any region in the brain exhibit a modulation of motion related activity in V1, dependent on attention? Eg V5? (Can Mask)

25. Hypothesis: ‘Bottom-up’ attentional modulation of V1 output to V5V1→V5 Friston et al. 1997, NeuroImage 6:218-229 Büchel & Friston 1997, Cereb. Cortex 7:768-778 V1 x Att. attention no attention V1 activity V5 activity SPM{Z} time V5 activity Results β 3 : V5 ? V5 exhibits a modulation of motion related V1 activity dependent on attention

26. PPI: interpretation Two possible interpretations of the PPI term: V1 Modulation of V1  V5 by attention V1 V5 Modulation of the impact of attention on V5 by V1. V1 V5 attention V1 attention V5 V5 V5

27. PPIs Pros: –given a single source region, we can test for its context- dependent connectivity across the entire brain Cons: –very simplistic model: only allows to model contributions from a single area –ignores time-series properties of data –operates at the level of BOLD time series

28. Some models for computing effective connectivity from fMRI data Regression models (e.g. psycho-physiological interactions, PPIs) Friston et al. 1997 Structural Equation Models (SEM) McIntosh et al. 1991, 1994; Büchel & Friston 1997; Bullmore et al. 2000 Volterra kernels Friston & Büchel 2000 Time series models (e.g. MAR, Granger causality) Harrison et al. 2003, Goebel et al. 2003 Dynamic Causal Models (DCM) bilinear: Friston et al. 2003; nonlinear: Stephan et al. 2008

29. Structural Equation Modelling (SEM) Static, linear model of imaging dependencies: (MacIntosh and Gonzalez-Lima, 1991) Parameters are estimated in structural equation modelling by minimizing the difference between the observed covariances and these implied by a structural or path model The parameters of the model are connection strength or path coefficients and correspond to an estimate of effective connectivity

30. SEM Generative Model After normalisation assume Zero mean innovations drive each region stochastically 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 b 12 b 13 b 32 includes only paths of interest Penny et al, 2004

31. SEM Generative Model includes only paths of interest 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 b 12 b 13 b 32 Regression Model where y appears on both sides. Rearranging see dependency of vector y on path coefficients (This is repeated for each t)

32. SEM Generative Model includes only paths of interest 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 b 12 b 13 b 32 Regression Model where y appears on both sides. Rearranging see dependency of vector y on path coefficients (This is repeated for each t) Assume data are normally generated and innovations are zero mean with Covariance R (iid)

33. SEM Generative Model Regression Model where y appears on both sides. Rearranging see dependency of vector y on path coefficients (This is repeated for each t) Then the modelled covariance of y, is a function of connection paths includes only paths of interest 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 b 12 b 13 b 32

34. includes only paths of interest 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 b 12 b 13 b 32 SEM Inversion: Estimate B Given Sample Covariance From Real Data Can estimate the connection paths & error variance

35. includes only paths of interest 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 b 12 b 13 b 32 SEM Inversion: Estimate B Given Sample Covariance Can estimate the connection paths & error variance Using Gradient Ascent on likelihood

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

37. Example: Experimental Effect of Attention: 3 regions Refined Hypothesis: Does attention effect connectivity in three region network? Approach: Partition the data set into (i) periods in which the subject was attending to moving stimuli and (ii) periods in which stimuli were moving but the subject did not attend to that movement Penny et al, 2004 Basic Model

38. Example: Experimental Effect of Attention Attention does significantly change the value of this connection (χ2 = 8.6, df = 1, p = 0.003) Penny et al, 2004 1.Null model in which path coefficients are fixed between conditions 2.Alternative Model can change between attention conditions

39. Introduction | Theory | Application | Limitations | Conclusions SEM Pros: –Multivariate causal model: Can test for >2 region connectivity Cons: –Assumes stochastic input –operates at the level of BOLD time series

40. Some models for computing effective connectivity from fMRI data Regression models (e.g. psycho-physiological interactions, PPIs) Friston et al. 1997 Structural Equation Models (SEM) McIntosh et al. 1991, 1994; Büchel & Friston 1997; Bullmore et al. 2000 Volterra kernels Friston & Büchel 2000 Time series models (e.g. MAR, Granger causality) Harrison et al. 2003, Goebel et al. 2003 Dynamic Causal Models (DCM) bilinear: Friston et al. 2003; nonlinear: Stephan et al. 2008

41. Input u(t) connectivity parameters  system state z(t) State changes of a system are dependent on: –the current state –external inputs –its connectivity –time constants System = a set of elements which interact in a spatially and temporally specific fashion A Causal Model Neural Dynamics

42. Input u(t) system state z(t) State changes of a system are dependent on: –the current state –external inputs –its connectivity –time constants System = a set of elements which interact in a spatially and temporally specific fashion State Space Model Neural Dynamics Hemodynamic Response connectivity parameters 

43. More on DCM later … Thank you