Introduction to Connectivity Analyses

1. Introduction to Connectivity Analyses Jennie NewtonMarieke Schölvinck

2. Experimentally designed input Functional integration • How does one region influence another (coupling b/w regions)? • How is coupling effected by experimental manipulation (e.g. attention)? • Multivariate analyses of regional interactions Functional segregation • Where are regional responses to experimental input? • Univariate analyses of regionally specific effects Functional architecture of the brain

3. Functional integration Functional integration can be further subdivided into: Functional connectivity different ways of summarising patterns of correlations among brain systems operational/observational definition Effective connectivity the influence one neuronal system exerts upon others mechanistic/model-based definition

4. Overview • Functional Connectivity • Basic concepts • Eigenimages • Singular Value Decomposition • Limitations • Effective connectivity • Basic concepts • Regression-based models: PPIs – Psycho-Physiological Interactions SEM – Structural Equation Modelling • Limitations • Dynamic Causal Modelling

5. Functional Connectivity: Basics • Aims • 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 (e.g. several scans in multiple voxels) • Procedure • Select those voxels whose activation levels show a significant difference between the conditions of interest • From the time series of those voxels, extract the most important components which describe the intercorrelations between them • We do this by using Eigenimage / Principal Component Analysis………

6. Functional Connectivity: Eigenimages Time (scans) Extracted voxels time-series of 1D images: 128 fMRI scans of 32 voxels Eigenvariates: time-dependent profiles associated with each eigenimage Spectral decomposition: shows that only few eigenvariates are required to explain most of observed variance Eigenimages:show contribution of each eigenvariate to time series of each individual voxel Reconstruction: time-series are reconstructed from only 3 principal components

7. Functional Connectivity: Singular Value Decomposition V1 V2 voxels APPROX. OF Y by P1 APPROX. OF Y by P2 time s1 + s2 + … U1 U2 = Y (DATA) Y = USVT = s1U1V1T + s2U2V2T + ... (p < n!) U : “Eigenvariates” Expression of p patterns in n scans S : “Singular Values” or “Eigenvalues” (2) Variance the p patterns account for V : “Eigenimages” Expression of p patterns in m voxels Data reduction: components explain less and less variance

8. Functional Connectivity: example from PET 5 subjects, each scanned 12 times Alternated b/w two tasks: (1) repeat a letter presented aurally (2) generate a word beginning with letter Voxels with significant differences between the two conditions were extracted Singular Value Decomposition (SVD) used to extract eigenimages and eigenvariates Spectral decomposition shows only 2 eigenimages are required to explain most of the variance; 1st eigenimage accounts for 64.4 % 2nd eigenimage accounts for 16.0 % Friston et al. Functional connectivity; the principal component analysis of large (PET) data sets. J. Cereb. Blood Flow Metab. 1993

9. Functional Connectivity: example from PET temporal eigenvariate reflecting the expression of the first eigenimage over the 12 conditions SPMs of the positive and negative components of the first eigenimage

10. Functional Connectivity: limitations • Data-driven method • Covariation of patterns with experimental conditions not always dominant  functional interpretation not always possible • Patterns need to be orthogonal • Biologically implausible because of interactions among the different systems • Correlations can arise from many sources • May not reflect meaningful connectivity between cortical areas example: thalamus can send projections to multiple cortical regions, leading to highly correlated brain activity between these areas, despite fact they are not directly connected