Fig 1.
Schematic representation of functional connectivity multivariate pattern analyses (fc-MVPA).
For each voxel, fc-MVPA analyses compute the functional connectivity maps between this seed/source voxel and the entire brain (Top-left; rn(x) in Eq 2) separately for each individual subject. Each subject functional connectivity map is then characterized by a lower dimensional eigenpattern scores (dots in top-right graph; sn(x) in Eq 5). This representation is chosen in a way that captures as well as possible the observed voxel-specific variability in functional connectivity maps across subjects. A multivariate test is then performed on the resulting lower-dimensional eigenpattern scores to ascertain potential between- or within- subjects effects of interest (e.g. differences between subjects or between conditions in functional connectivity at the original seed/source voxel). This process is then repeated for every source voxel to identify regions that show brain-wide between- or within- subjects differences in functional connectivity.
Fig 2.
Fc-MVPA results evaluating gender-related differences in connectivity.
Central figure shows left- and right- hemisphere medial (bottom) and lateral (top) views of the main fc-MVPA results showing areas with significant gender-related differences in functional connectivity (highlighted in yellow and black, TFCE statistics p-FWE<0.05). Among all significant results a reduced subset showing some of the strongest effects are highlighted in black, and the effect-sizes within these areas (pattern of differences in connectivity with each area between male and female subjects) are shown in the additional circular plots (yellow indicating higher connectivity in male compared to female subjects, and blue indicating higher connectivity in female compared to male subjects).
Fig 3.
Selecting different number of fc-MVPA eigenpatterns.
Difference in fc-MVPA statistic parametric maps evaluating gender differences in connectivity, when varying k, the number of fc-MVPA eigenpatterns used in the analysis, from k = 1 (left) to k = 100 (right). For reference, the original results shown in Fig 2 used k = 10 (highlighted here inside black box). Top: Statistic parametric maps with color coding showing voxel-level -log10(p) values for four different choices of k (from 5 to 20). The results show consistent statistic parametric maps across different k values. Bottom: Distribution of fc-MVPA statistics across all gray matter voxels with k ranging from 1 to 100, compared to null hypothesis distribution (shown in leftmost ‘null’ histogram). The results indicate high sensitivity across the entire range of evaluated k values, with sensitivity peaking at around k = 50 (close to a 4:1 ratio in subjects to eigenpatterns) for detecting widespread gender effects in this dataset.
Fig 4.
Percentage of total covariance associated with each fc-MVPA eigenpattern.
Top: histogram of ξk(x)|1≤i≤100 values, percentage of the total covariance explained by each of the first 100 eigenpatterns. Histograms are further broken down by the most likely tissue class (gray matter in black, CSF areas in grey, and white matter in white) at each individual voxel as defined by SPM’s tissue probability map templates. Bottom: spatial map ξ1(x) showing the proportion of the total intersubject covariance explained by each voxel’s first eigenpattern (a measure of the overall intersubject homogeneity in functional connectivity patterns at each voxel; see text for details).
Fig 5.
First 5 fc-MVPA eigenpatterns, characterizing the principal components of the local intersubject heterogeneity in functional connectivity maps.
The central display shows the cumulative total covariance in functional connectivity patterns explained by the first 5 eigenpatterns at each voxel (colormap values range between 22%/black to 50%/white). The first five eigenpatterns at 14 manually-defined example locations are shown in a circular display. In each of these plots, eigenpatterns range from first/left to fifth/right, and each eigenpattern is shown projected to a left hemisphere lateral (top plot) and medial (bottom plot) views, on a relative color scale ranging from blue (highest negative values for each eigenpattern) to yellow (highest positive values).
Fig 6.
Comparison between PCA and MVPA components.
Top: Median (dots) and 25%-75% percentile range (vertical lines) of the total covariance in functional connectivity patterns at each voxel explained cumulatively by the first k components from a functional connectivity Principal Component Analysis (black dots and lines), and by the first k fc-MVPA eigenpatterns (light gray dots and lines), from the analysis of the same sample dataset (Cambridge, n = 198 dataset). Bottom: First five principal components from PCA (first row) and from fc-MVPA (second and third row, first five eigenvariates shown only at two sample locations: posterior cingulate and anterior insula). Each row shows individual components sorted from first/left to fifth/right, projected to a left hemisphere lateral view (top image) and medial view (bottom image), on a relative color scale ranging from blue (highest negative values for each component) to yellow (highest positive values). Larger explanatory power of fc-MVPA components compared to PCA (shown on top figure) stems largely from the ability of fc-MVPA components to adapt to the specificity of the functional connectivity patterns at each individual location (as exemplified in the bottom figures by the differences and commonalities between the components describing posterior cingulate vs. anterior insula connectivity patterns).
Fig 7.
Validation of fc-MVPA voxel-level inferences.
Analysis of Receiver Operating Characteristic curves evaluating between-group differences in functional connectivity under the null hypothesis (when there are no true differences in the population). Top left: surfaces, and highlighted thick black lines, show, for a chosen combination of false positive threshold (false positive rate x-axis) and number of eigenpatterns (k y-axis), the resulting proportion of false positive results (positive rate z-axis), where the fc-MVPA procedure would falsely conclude there is a significant difference in connectivity between the groups. The red line marks the observed rate of false positives when fixing the prescribed false positive rate threshold at a fixed 5% level (graphically, the intersection of each ROC surface and a vertical plane with constant false positive rate = 0.05), matching the expected 5% level. Top Right: Observed false positive rates (y-axis) when using fc-MVPA statistical analyses controlled at a p < .05 level across the reference simulations (‘reference’) and simulations evaluating different conditions (FWHM = 0, FHWM-25, N = 10, N = 100, Nt = 10, Nt = 100). The average (black dots) and histogram (gray surfaces) of the observed false positive rates across these simulations all indicate an appropriate match to the expected/prescribed false positive level (5%). Bottom: evaluating validity under different conditions: (A) low spatial autocorrelation (FWHM = 0); (B) large spatial autocorrelation (FWHM = 25 voxels); (C) low number of subjects (N = 10); (D) high number of subjects (N = 100); (E) short scanning session (Nt = 10); (F) long scanning session (Nt = 100).
Fig 8.
Sensitivity of fc-MVPA voxel-level inferences.
Analysis of Receiver Operating Characteristic curves evaluating between-group differences in functional connectivity. Top Left: surfaces, and highlighted thick black lines, show, for a chosen combination of false positive threshold (false positive rate x-axis) and number of eigenpatterns (k y-axis), the resulting proportion of true positive results (positive rate z-axis), where the fc-MVPA procedure would correctly conclude there is a significant difference in connectivity between the groups in our reference simulations. Top Right: Observed true positive rates (y-axis) when using fc-MVPA statistical analyses controlled at a p < .05 level across the reference simulations (‘reference’) and simulations evaluating different conditions (FWHM = 0, FHWM = 25, N = 10, N = 100, Nt = 10, Nt = 100). The average (black dots) and histogram (gray surfaces) of the observed true positive rates, or proportion of significant results, across these simulations indicate that sensitivity is typically higher when using low or intermediate numbers of eigenpatterns, with poorer sensitivity when the number of timepoints for functional connectivity estimation is low (Nt = 10), or when the number of subjects included in the analysis is low (N = 10). Bottom: evaluating sensitivity under different conditions: (A) no spatial autocorrelation (FWHM = 0); (B) large spatial autocorrelation (FWHM = 25 voxels); (C) low number of subjects (N = 10); (D) high number of subjects (N = 100); (E) short scanning session (Nt = 10); (F) long scanning session (Nt = 100).