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Effective Connectivity

Explore models of effective connectivity in neural systems including concepts like evoked response, system identification, and bilinear dynamics. Learn practical steps in fMRI data analysis and inference of model parameters.

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Effective Connectivity

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  1. Effective Connectivity Lee Harrison Wellcome Department of Imaging Neuroscience, University College London, UK SPM Short Course, May 2003

  2. Outline • Motivation & concepts • Models of effective connectivity • An example

  3. Outline • Motivation & concepts • Models of effective connectivity • An example

  4. Functional Specialization Q. In what areas does the ‘motion’ factor change activity ? Univariate Analysis

  5. Z4 Z5 Z2 Z3 Functional Integration • To estimate and make inferences about • the influence that one neural system exerts over another • (2) how this is affected by the experimental context

  6. Concepts • Brain as a physical system • Evoked response to input • System identification • Parameterised models • In terms of connectivity • Classification of models • Black box & hidden states

  7. Concepts (continued) • Linear vs nonlinear systems • Balance mathematical tractability and biological plausibility • Generalization of General Linear Model • Bilinear models • Inputs • Perturbing & contextual • Stochastic & deterministic • use of design matrix • Experimental design • 22 factorial design

  8. Concepts (continued) • Linear vs nonlinear systems • Balance mathematical tractability and biological plausibility • Generalization of General Linear Model • Bilinear models • Inputs • Perturbing & contextual • Stochastic & deterministic • use of design matrix • Experimental design • 22 factorial design

  9. Z2 Set u2 Stimuli u1 Z4 Z5 Z1 Z2 Z3 Model of Neuronal Activity Nonlinear, systems-level model

  10. Z2 Set u2 Stimuli u1 Z4 Z5 Z1 Z2 Z3 Bilinear Dynamics Psycho-physiological interaction

  11. Bilinear Dynamics a53 Set u2 Stimuli u1 Psycho-physiological interaction

  12. u 1 u 2 Z 1 Z 2 Bilinear Dynamics: Positive transients Stimuli u1 Set u2 - + Z1 - + + Z2 - -

  13. Concepts (continued) • Linear vs nonlinear systems • Balance mathematical tractability and biological plausibility • Generalization of General Linear Model • Bilinear models • Inputs • Perturbing & contextual • Stochastic & deterministic • use of design matrix • Experimental design • 22 factorial design

  14. Outline • Motivation & concepts • Models of effective connectivity • An example

  15. Z4 Z5 Z2 Z3 Practical steps Design matrix 1) Standard Analysis of fMRI Data 2) Statistical Parametric Maps 3) Anatomical model 4) Connectivity model 5) Estimation & inference of model parameters SPMs

  16. Outline • Motivation & concepts • Models of effective connectivity • Linear regression • Convolution • State-Space • An example

  17. Outline • Motivation & concepts • Models of effective connectivity • Linear regression • Convolution • State-Space • An example

  18. Structural Equation Modelling y1 y2 y3

  19. Inference in SEMs V1 V5 PPC V1 V5 PPC vs V1 V5 PPC V1 V5 PPC V1 V5 PPC PFC V1 V5 PPC PFC vs PPIV5xPFC PPIV5xPFC Attentional set Attentional set

  20. Outline • Motivation & concepts • Models of effective connectivity • Linear regression • Convolution • State-Space • An example

  21. Bilinear Convolution Model

  22. Outline • Motivation & concepts • Models of effective connectivity • Linear regression • Convolution • State-Space • An example

  23. Outline • Motivation & concepts • Models of effective connectivity • Linear regression • Convolution • State-Space • Dynamic Causal Modelling • An example

  24. y y y The DCM and its bilinear approximation neuronal changes intrinsic connectivity induced connectivity induced response Input u(t) The bilinear model activity z2(t) activity z3(t) activity z1(t) Hemodynamic model

  25. y The hemodynamic model

  26. Overview • Models of • Hemodynamics in a single region • Neuronal interactions • Constraints on • Connections • Hemodynamic parameters Bayesian estimation

  27. Z4 Z5 Z2 Z3 Practical steps Design matrix 1) Standard Analysis of fMRI Data 2) Statistical Parametric Maps 3) Anatomical model 4) Connectivity model 5) Estimation & inference of model parameters SPMs

  28. Outline • Motivation & concepts • Models of effective connectivity • Linear regression • Convolution • State-Space • An example • DCM for visual motion processing

  29. A fMRI study of attentional modulation Stimuli 250 radially moving dots at 4.7 degrees/s Pre-Scanning 5 x 30s trials with 5 speed changes (reducing to 1%) Task - detect change in radial velocity Scanning (no speed changes) 6 normal subjects, 4 100 scan sessions; each session comprising 10 scans of 4 different condition F A F N F A F N S ................. F - fixation point only A - motion stimuli with attention (detect changes) N - motion stimuli without attention S - no motion PPC V5+ Buchel et al 1999

  30. Attention Photic SPC .43 .53 .40 V1 IFG .49 .62 .92 .35 .53 V5 Motion .73 1) Hierarchical architecture 3) Attentional modulation of prefrontal connections That is sufficient to explain regionally specific attentional effects 2) Segregation of motion information to V5

  31. Summary • Studies of functional integration look at experimentally induced changes in connectivity • Neurodynamics and hemodynamics • DCM • Inferences about large-scale neuronal networks

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