Connectivity analyses for task-based fMRI

Abstract

Functional connectivity is conventionally defined by measuring the similarity between brain signals from two regions. The technique has become widely adopted in the analysis of functional magnetic resonance imaging (fMRI) data, where it has provided cognitive neuroscientists with abundant information on how brain regions interact to support complex cognition. However, in the past decade the notion of "connectivity" has expanded in both the complexity and heterogeneity of its application to cognitive neuroscience, resulting in greater difficulty of interpretation, replication, and cross-study comparisons. In this paper, we begin with the canonical notions of functional connectivity and then introduce recent methodological developments that either estimate some alternative form of connectivity or extend the analytical framework, with the hope of bringing better clarity for cognitive neuroscience researchers.

Keywords: Functional connectivity; Graph theory; Multivariate pattern analysis; Representational similarity analysis; fMRI.

Fig. 1.. Common visualizations of task fMRI-based brain connectivity.

All visualizations were created using synthetic data. A) Statistic map of seed-based thresholded connectivity on anatomical brain slices, with the seed region (medial prefrontal cortex) indicated by the green circle. B) Graph representation of thresholded connections on glass brain slices, with dots indicating the center of regions of interests and edge colors reflecting connection strength. C) Chord diagram of the same connections shown in (B). Networks were assigned based on the Schaefer 7network-and-200-parcel atlas (Schaefer et al., 2018). D) Heatmap of the full connectivity matrix with cells color-coded to indicate connection strength. The following software programs were used to create these visualizations: A and B, Nilearn (Abraham et al., 2014). C, NiChord (Bogdan et al., 2023). D, Matplotlib (Hunter, 2007). For a more comprehensive and detailed discussion on visualizations of brain networks of all kinds, readers are referred to (Margulies et al., 2013).

Fig. 2.. Psychophysiological interaction (PPI) analysis.

A) Physiological activity time courses from the target region (y) and the seed region (x). B) In standard PPI, a single task variable C_A−B codes the contrast condition A - condition B. C) The psychological variable H(C_A−B) is the expected BOLD response according to the task, which is obtained by convolving the task variable with the hemodynamic response function. D) The PPI term is computed as the element-wise product of the seed physiological activity x and the psychological variable H(C_A−B). E) In generalized PPI, task conditions A and B are coded in separate task variables, C_A and C_B, which are then used to create F) two psychological variables, H(C_A) and H(C_B), and subsequently G) two Separate PPI terms.

Fig. 3.. Beta series correlation (BSC).

A) The least squares - all (LSA) modeling approach constructs one general linear model (GLM) that contains N regressors, each of which models a single trial, and simultaneously estimates N regression coefficients (β₁, … , β_N). Task conditions are color-coded (orange vs. purple). B) The least squares - separate (LSS) modeling approach constructs N GLMs in parallel. Each model contains one regressor for a single trial i of interest (color-coded by condition), as well as a regressor for all other trials across conditions (gray). Regression coefficients β₁, …, β_N are collected across models. Of note, for both LSA and LSS approaches, nuisance covariates such as motion parameters are commonly included in practice but omitted in the figure for simplicity. C) Regression coefficients or β values are split by task conditions to form beta series, which are then correlated between regions of interest (ROIs) to generate condition-specific functional connectivity.

Fig. 4.. Seed partial least squares (seed PLS) analysis.

A. Synthetic trial-level activity series extracted from one seed and two target regions, organized by participant and task condition. Participant-and-condition-level activity can be estimated as the mean of relevant trial-level activities. B. Condition-wise cross-correlations for all seeds and targets are computed either across-participant (using participant-level activity) or within-participant (using trial-level activity). Correlation matrices are stacked vertically to form a correlation structure R, which is factorized by singular value decomposition to extract latent variables.

Fig. 5.

A) Pattern discriminability series from decoding analysis. The multi-voxel activity patterns are organized by voxel and trial. The training set is used to train the classifier and will determine its decision criterion. The trained classifier is applied to the test set trials and generates a pattern discriminability series (red) indicating the magnitude of classifier evidence (e.g., probability) of individual trials belonging to the correct class. B) Representational strength series from representational similarity analysis. Representational dissimilarity matrices (RDMs) indicate the dissimilarity structure of the stimuli based on some hypothesis or model (model RDM) and their multi-voxel activity pattern (neural RDM). A row-wise correlation of these RDMs generates a representational strength series (red) which reflects the second-order correspondence between stimulus property and brain activity. The pattern discriminability series or representational strength series from distinct brain regions are correlated to compute informational connectivity or (model-based) representational connectivity, respectively.

Fig. 6.

Various statistical relationships between two random variables with 50 observations. r, Pearson correlation coefficient; MI, mutual information.