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Introduction to Connectivity

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

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Introduction to Connectivity

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

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

  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/structuralconnectivity= presenceofaxonalconnections • functionalconnectivity= statisticaldependenciesbetween regional time series • effectiveconnectivity= causal (directed) influencesbetweenneuronsor 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. Functional connectivity Definition: statisticaldependenciesbetween 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

  10. Eg. 1 Seed-voxelcorrelationanalyses • 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-voxelcorrelationanalyses 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) 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 Pykaet al. 2009

  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 CausalModels (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 CausalModels (DCM)bilinear: Friston et al. 2003; nonlinear: Stephan et al. 2008

  18. Task factor GLM of a 2x2 factorial design: Task B Task A main effect of task TA/S1 TB/S1 Stim 1 main effect of stim. type Stimulus factor interaction Stim 2 TB/S2 TA/S2 Psycho-physiologicalinteraction: Friston et al 1997(PPI) 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)

  19. Task factor GLM of a 2x2 factorial design: Task B Task A main effect of task TA/S1 TB/S1 Stim 1 main effect of stim. type Stimulus factor interaction Stim 2 TB/S2 TA/S2 Psycho-physiological interaction (PPI) Interactions based solely on experimental factors (i.e., psychological interactions)

  20. Task factor GLM of a 2x2 factorial design: Task B Task A main effect of task TA/S1 TB/S1 Stim 1 main effect of stim. type Stimulus factor interaction Stim 2 TB/S2 TA/S2 Psycho-physiological interaction (PPI) 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. Task factor GLM of a 2x2 factorial design: Task B Task A main effect of task TA/S1 TB/S1 Stim 1 Stimulus factor Stim 2 TB/S2 TA/S2 Psycho-physiological interaction Psycho-physiological interaction (PPI) 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 V1 time series  main effect of stim. type

  22. Task factor GLM of a 2x2 factorial design: Task B Task A main effect of task TA/S1 TB/S1 Stim 1 Stimulus factor Stim 2 TB/S2 TA/S2 Psycho-physiological interaction Psycho-physiological interaction (PPI) 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. Test using reconstructed Design Matrix as usual V1 time series  main effect of stim. type

  23. Task factor Task factor Task B Passive Task A Attend TA/S1 TA/S1 TB/S1 TB/S1 Static Stim 1 Dots Stimulus factor Moving TB/S2 TB/S2 TA/S2 TA/S2 Example: Attention to motion in the visual system Büchel & Friston 1997, Cereb. Cortex Büchel et al.1998, Brain

  24. Task factor Task factor Task B Passive Attend Task A TA/S1 TA/S1 TB/S1 TB/S1 Static Stim 1 Dots Stimulus factor Moving TB/S2 TB/S2 TA/S2 TA/S2 Example: Attention to motion in the visual system Psychological Main Effects main effect of attention: V5 (and SPC) main effect of motion in V1 and V5 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’ attentionalmodulation of V1 output to V5V1→V5 Results β3: SPM{Z} V5 activity V1 x Att. time V5 attention V5 activity no attention V1 activity Friston et al. 1997, NeuroImage 6:218-229 Büchel & Friston 1997, Cereb. Cortex 7:768-778 V5 exhibits a modulation of motion related V1 activity dependent on attention

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

  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 CausalModels (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. y 1 y 2 y 3 SEM Generative Model y2 = b12 y1 + b32 y3+ z2 y1 = z1 b12 b13 b32 includes only paths of interest y3 = b13 y1+ z3 After normalisationassume Zero mean innovations drive each region stochastically Penny et al, 2004

  31. y 1 y 2 y 3 SEM Generative Model y1 = z1 y2 = b12y1 + b32y3 + z2 includes only paths of interest b12 b13 b32 y3 = b13y1 + z3 Regression Model where y appears on both sides. Rearranging see dependency of vector y on path coefficients (This is repeated for each t)

  32. y 1 y 2 y 3 SEM Generative Model y1 = z1 y2 = b12y1 + b32y3 + z2 includes only paths of interest b12 b13 b32 y3 = b13y1 + z3 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. y 1 y 2 y 3 SEM Generative Model y1 = z1 y2 = b12y1 + b32y3 + z2 includes only paths of interest b12 b13 b32 y3 = b13y1 + z3 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

  34. y 1 y 2 y 3 SEMInversion: Estimate B y1 = z1 y2 = b12y1 + b32y3 + z2 includes only paths of interest b12 b13 b32 y3 = b13y1 + z3 Given Sample Covariance From Real Data Can estimate the connection paths & error variance

  35. y 1 y 2 y 3 • SEM Inversion: Estimate B y1 = z1 y2 = b12y1 + b32y3 + z2 includes only paths of interest b12 b13 b32 y3 = b13y1 + z3 Given Sample Covariance Can estimate the connection paths & error variance Using Gradient Ascent on likelihood

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

  37. Example: Experimental Effect of Attention: 3 regions Basic Model SPC V1 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 V5 Penny et al, 2004

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

  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 CausalModels (DCM)bilinear: Friston et al. 2003; nonlinear: Stephan et al. 2008

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

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

  43. More on DCM later … Thank you

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