Effective Connectivity Lee Harrison Wellcome Department of Imaging Neuroscience, University College London, UK SPM Short Course, May 2004
Outline Motivation & concepts Models of effective connectivity An example
Outline Motivation & concepts Models of effective connectivity An example
Functional Specialization Q. In what areas does the ‘motion’ factor change activity ? Univariate Analysis
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 Z2 Z4 Z3 Z5
Concepts Brain as a physical system System identification Evoked response to input System identification Parameterised models In terms of connectivity Classification of models Black box & hidden states
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 22 factorial design
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 22 factorial design
Model of Neuronal Activity Z2 Z1 Z4 Z3 Z5 Stimuli u1 Set u2 Nonlinear, systems-level model
Bilinear Dynamics Z4 Z2 Psycho-physiological interaction Z5 Z1 Z3 Set Stimuli u1 Set u2 Psycho-physiological interaction
Bilinear Dynamics a53 Psycho-physiological interaction Set Stimuli u2
Bilinear Dynamics: Positive transients Stimuli u1 Set u2 u 1 Z 2 - + Z1 - + + Z2 - -
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 22 factorial design
Outline Motivation & concepts Models of effective connectivity An example
Practical steps 1) Standard Analysis of fMRI Data 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 Z2 Z4 Z3 Z5
Outline Motivation & concepts Models of effective connectivity Linear regression Convolution State-Space An example
Outline Motivation & concepts Models of effective connectivity Linear regression Convolution State-Space An example
Structural Equation Modelling y1 y2 y3
Inference in SEMs V1 V5 PPC V1 V5 PPC V1 V5 PPC 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
Outline Motivation & concepts Models of effective connectivity Linear regression Convolution State-Space An example
Bilinear Convolution Model
Outline Motivation & concepts Models of effective connectivity Linear regression Convolution State-Space An example
Outline Motivation & concepts Models of effective connectivity Linear regression Convolution State-Space Dynamic Causal Modelling An example
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) y y y Hemodynamic model
The hemodynamic model y
Overview Models of Constraints on Bayesian estimation Hemodynamics in a single region Neuronal interactions Constraints on Connections Hemodynamic parameters Bayesian estimation
Practical steps 1) Standard Analysis of fMRI Data 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 Z2 Z4 Z3 Z5
Outline Motivation & concepts Models of effective connectivity Linear regression Convolution State-Space An example DCM for visual motion processing
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
1) Hierarchical architecture V1 IFG V5 SPC Motion Photic Attention .92 .43 .62 .40 .53 .35 .73 .49 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
Summary Studies of functional integration look at experimentally induced changes in connectivity Neurodynamics and hemodynamics DCM Inferences about large-scale neuronal networks