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Brain-wide connectome inferences using functional connectivity MultiVariate Pattern Analyses (fc-MVPA) [1]

['Alfonso Nieto-Castanon', 'Department Of Speech', 'Language', 'Hearing Sciences', 'Boston University', 'Boston', 'Massachusetts', 'United States Of America', 'Department Of Brain', 'Cognitive Sciences']

Date: 2022-11 

Fc-MVPA brain-wide connectome inferences: interpretation and examples

Group-level analyses of the eigenpattern scores s n (x) enable statistical inferences at the level of individual searchlight voxels evaluating the form or shape of the connectivity patterns with each voxel. In particular, for any individual hypothesis (e.g. group A = group B) the fc-MVPA procedure will produce a statistical parametric map F(x) evaluating that hypothesis separately at each individual searchlight voxel x. In order to test brain-wide connectome hypotheses it is still necessary to control the resulting maps F(x) for multiple comparisons across the total number of tests evaluated (one test per voxel). Fortunately, this can be done using the same nonparametric cluster-level inferential procedures that are common in standard analyses of functional activation, such as cluster-mass or TFCE statistics based on permutation / randomization analyses [5,6,53]. These approaches allow us to compute statistics as well as associated familywise error corrected p-values for individual clusters of contiguous searchlight voxels in the statistical parametric map F(x), supporting cluster-level inferences with meaningful false positive control (e.g. controlling the likelihood of observing or more false positive clusters across the entire brain below 5%, for a familywise control procedure, or controlling the rate of false positive clusters below 5% among all significant clusters, for a False Discovery Rate control procedure).

Another important choice that remains when using fc-MVPA in the context of brain-wide connectome inferences is to select k, the dimensionality of s n (x) or the number of eigenpattern scores used to represent functional connectivity at each voxel. As it will be discussed in more detail in the Simulations section below, there is no “correct” choice of this parameter, and fc-MVPA inferences remain valid for all possible values of this parameter. Nevertheless it is important that this choice is made a priori and justified (e.g. from prior literature), and, if different values are tested/evaluated, the results of all these different evaluations should be reported (rather than reporting only the value that produces the best results for a particular analysis, which would inflate the chance of false positives). Regarding the sensitivity of fc-MVPA inferences, choosing a low value of k can be expected to improve sensitivity to detect relatively large or widespread effects of interest such as inter-network connectivity differences, while choosing a higher value of k can improve our ability to detect relatively smaller or marginal effects such as connectivity with smaller areas or subnetworks. In the absence of assumptions about the extent of the expected effects, a reasonable balance is to scale the choice of k with the dataset size (e.g. suggested 5:1, 10:1, or 20:1 ratio between N:k, the number of subjects in the analysis and the number of eigenpattern scores retained [54–56]), in order to maintain a reasonable sensitivity to identify large effects in small samples, and comparatively finer details in the analysis of larger samples. As with any other preprocessing or analysis choices, as long as the choice of k is made a priori, statistical inferences will remain valid. If, on the other hand, the value of k is selected a posteriori as the one that produced the “best” results among several possible values evaluated, an appropriate multiple-comparison correction should be used for statistical inferences (e.g. using a Bonferroni corrected cluster-level threshold p-FWE<0.05/10 if the results were selected among 10 different choices of k values, or using split or cross-validation procedures such as choosing k as the value that produces the “best” results in one half of the subjects and then basing statistical inferences on the analysis of the other half using the selected k value). For new analyses, and in the absence of any other rationale (e.g. based on prior literature, N:k ratios, or expected extent of effects) we recommend using a value of k = 10, as that seems to suffice to cover a large proportion of the intersubject variability in functional connectivity profiles (e.g. see fc-MVPA eigenpatterns section below). In all cases we encourage researchers to evaluate and report the robustness of their results to different choices of this parameter (e.g. as exploratory post-hoc analyses, without a need for additional multiple comparison corrections), as that will help other researchers build upon those results in future analyses and the field converge toward useful conventions.

Last, regarding the interpretation of fc-MVPA results, when reporting statistical inferences from fc-MVPA brain-wide connectome analyses, those inferences should be if possible framed regarding the patterns of connectivity between each voxel or cluster and the rest of the brain. For example, when using fc-MVPA to evaluate the difference in connectivity between two groups of subjects, if the fc-MVPA procedure above produces one supra-threshold cluster with corrected significance level below p < .05 that should be interpreted as indicating that the pattern of connectivity between this cluster and the rest of the brain is (significantly) different between the two groups. The fc-MVPA method does not afford further spatial specificity in the resulting statistical inferences, but it is still useful to report measures of effect-size characterizing the patterns of connectivity within each individual significant cluster, as a way to suggest possible interpretations and future analyses.

Effect-sizes in GLM analyses are typically represented by linear combinations of the estimated regressor coefficients B, and, specifically in the context of hypothesis testing, linear combinations of the form c∙B, as these measures quantify the extent of the observed departures from the null hypothesis (c∙B = 0). The interpretation of effect-sizes in GLM depends naturally on the choice of hypothesis being evaluated. For example, for a GLM two-sample t-test comparing connectivity between two groups, effect-sizes of the form c∙B would represent the difference in connectivity (e.g. average differences in r- values) between the two groups, while for a GLM regression analysis evaluating the association between some behavioral measure and connectivity strength, effect-sizes of the form c∙B would represent the slope of the regression line approximating the observed associations. Note that in both cases an effect-size of zero would represent the null hypothesis (of no differences or no associations, respectively). In the analysis of the statistical parametric map F(x), for any significant cluster Ω (group of contiguous suprathreshold voxels with a cluster-level corrected p-value below the chosen family-wise error threshold), we recommend reporting the effect-sizes separately for each meaningful between-subjects contrast c j (e.g. individual rows of the contrast matrix C). Effect sizes can be reported as a vector of eigenpattern weights (h eig (Ω)), or as a whole-brain projected map (h map (Ω)):

fc-MVPA effect-sizes at location Ω

(9)

The effect-size measure h eig (Ω) is a vector, with one element per eigenpattern, estimated separately at each location Ω. It represents the effect-size of a group-level analysis contrast of interest evaluated separately for each individual eigenpattern (columns of ). For example, if the group-level analysis was a two-sample t-test comparing connectivity between two subject groups, then the k-th element in the h eig (Ω) effect-size vector will evaluate what is the difference in the k-th eigenpattern scores at location Ω between these two groups.

Similarly, and perhaps more directly interpretable, the effect-size measure h map (Ω) represents the same contrast but is now evaluated separately at each individual voxel. In the example above, the value of h map (Ω) at a particular voxel will represent the difference in functional connectivity between Ω and this voxel between the two subject groups analyzed. It should be noted that a very similar whole-brain projected map of effect-sizes h map (Ω) can also be computed from the voxel-level effect-sizes of a post hoc analysis that would evaluate the same group-level model as in Eq 7 but this time focusing on the seed-based connectivity maps (SBC) associated with seeds defined from each individual significant cluster Ω. As in any post-hoc analysis, p-values derived from these SBC post-hoc analyses will be partially inflated due to selection bias and should not to be used to make secondary inferences regarding individual connections within the reported patterns. Despite this limitation, post-hoc SBC analyses on the same dataset offer a simple and perfectly valid alternative approach for reporting fc-MVPA effect sizes within each significant cluster, while, when performed on an independent dataset, they also offer a natural method to further probe specific aspects of these connectivity patterns. For those interested, the resulting h map (Ω) effect-sizes following this approach can be shown to be equal to those derived from Eq 9 in the limit when the number of eigenpatterns retained equals the total number of subjects in the study, simplifying the variable h scores (Ω) to a constant vector independent of the location Ω: (10)

Effect-size measures such as those described in Eqs 9 and 10 represent post-hoc estimates, and as such they should always be understood to contain a certain amount of bias. Their application is mainly for interpretation purposes and for hypothesis building. In other contexts, when the accuracy of these estimates may be essential, a cross-validation approach may be used where, for example, the clusters Ω may be computed from an initial General Linear Model (Eqs 7 and 8) that includes only data from a subset of subjects, while the effect-size estimates (Eqs 9 and 10) may be computed using a second GLM that includes data from a separate/independent subset of subjects.

As an illustration of fc-MVPA brain-wide connectome inferences, we analyzed gender differences in resting state functional connectivity using the Cambridge 1000-connectomes dataset (n = 198, see S2 Appendix for a description of this dataset preprocessing and fc-MVPA analysis methods [57–66]). The question that these analyses ask is whether there are any differences across the entire voxel-to-voxel functional connectome between male and female subjects. To answer this question, we performed fc-MVPA analyses focusing on the first 10 eigenpatterns (an approximate 20:1 subjects to eigenpattern ratio), entering the corresponding eigenpattern scores into a second-level group analysis evaluating a multivariate ANCOVA test with gender as a between-subjects factor and subject motion (average framewise displacement) as a control variable. The resulting statistical parametric maps were thresholded using Threshold Free Cluster Enhancement [6] (TFCE, with default H = 1, E = 0.5 values) at a familywise error corrected 5% false positive level.

The results, shown in Fig 2 show a large number of areas with significant gender-related differences in connectivity (p-FWE < .05, shown as yellow and black areas in the center image). Given the abundance of areas showing significant gender effects, for illustration purposes we focused our description only on a subset of cortical regions showing some of the strongest effects (TFCE>200; p-FWE < .001, highlighted in black in Fig 2 center image). For each cluster in this reduced subset, we computed effect-size maps h map (Ω) characterizing the pattern of gender-related differences in connectivity with each cluster (displayed in Fig 2 as a circular array of brain displays), with yellow indicating higher connectivity with this cluster in male compared to female subjects, and blue indicating higher connectivity in female compared to male subjects.

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TIFF original image Download: 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). https://doi.org/10.1371/journal.pcbi.1010634.g002

Some of the strongest effects were visible in the bilateral Occipital Pole visual areas. A left hemisphere cluster centered at MNI coordinates (-22,-94,+4) mm showed a pattern of increased connectivity with Default Mode Network (DMN) and increased anticorrelations with Salience Network (SN) areas in male subjects (see Fig 2 Occipital Pole plot). A similar pattern (not shown) was present in another cluster in right hemisphere Occipital Pole areas (+28,-82,+2). Similarly, there were significant gender effects in several DMN areas, such as Medial Prefrontal Cortex (+6,+54,-12) and Precuneus (+18,-72,+32), showing a similar pattern of stronger connectivity with visual and sensorimotor areas (shown in yellow in Fig 2 Medial Frontal Cortex and Precuneus plots) in male subjects compared to stronger connectivity (weaker anticorrelations) with SN and attention areas in female subjects (shown in blue in same plots).

In the left hemisphere, Inferior Frontal Gyrus pars triangularis (-54,+22,+14) showed a pattern of stronger connectivity in female subjects with frontoparietal network areas and with Inferior Temporal Cortex (shown in blue in Fig 2 Inferior Frontal Gyrus plot).

In the right hemisphere, there was a cluster of regions in the Temporal Parietal Occipital Junction that also showed strong gender-related differences in connectivity. Lateral superior Postcentral Gyrus (+36,-32,+48) showed a mixed pattern of increased integration with other Dorsal Attention areas in female subjects, compared to increased connectivity with Central Sulcus, including somatosensory and motor areas in male subjects. A cluster in superior Angular Gyrus centered at coordinates (+50,-54,+42) mm showed increased integration with medial prefrontal and posterior cingulate areas in female subjects, and increased integration with lateral prefrontal and reduced anticorrelations with insular areas in male subjects. Relatedly, a cluster in the mid Insular Cortex (+38,+10,+2) showed a similar pattern of higher connectivity with angular Gyrus and other DMN areas in male subjects. Another relatively proximal cluster in the Anterior Supramarginal Gyrus (+60,-26,+30) also showed increased local associations with superior postcentral areas in male subjects. Posterior Superior Temporal Gyrus (+48,-26,-2) showed a pattern of higher connectivity (mixed with reduced anticorrelations) with frontoparietal areas in female subjects (shown in blue in Fig 2 Superior Temporal Gyrus plot), compared to a similar pattern of stronger local connectivity in male subjects (shown in yellow in same plot).

Last, Medial Precentral Gyrus areas (+16,-26,+40) showed relatively higher integration with SN or ventral attention network in female subjects. In contrast, lateral Precentral Gyrus areas (+54,-4,+22) showed higher integration with the same networks in male subjects, while in female subjects this area showed stronger local correlations (shown in blue in Fig 2 Precentral Gyrus plot).

From a validation and generalization perspective, it is interesting to question whether the same or similar results would have been observed if, instead of using 10 eigenpattern scores, based on a conservative suggestion to maintain an approximately 20:1 ratio between subjects and eigenpatterns, we would have chosen a different number. To that end we repeated the previous group-level analyses evaluating gender differences in connectivity but now using different number of eigenpattern scores, ranging from 1 to 100, and compared the resulting fc-MVPA statistic parametric maps F(x).

The results (Fig 3 top) show very similar F(x) statistics when varying the number of eigenpatterns around the k = 10 value selected for our original analyses. In addition, the distribution of resulting statistics across the entire brain (Fig 3 bottom) shows high sensitivity across the entire range of evaluated k values, consistent with the sensitivity simulations in the sections below, and with average sensitivity peaking at k = 50 (approximately a 4:1 ratio in subjects to eigenpatterns) for detecting gender effects in this dataset. While there were several areas like superior Postcentral Gyrus where the statistics peaked at relatively low number of eigenpatterns, suggesting that the effects in these areas may be best represented by the first few fc-MVPA eigenpatterns (i.e. they may be better described in terms of common/large sources of variability across subjects), there were also many areas where the F(x) statistics peaked when using a large number of eigenpatterns (e.g. 50 or above), suggesting that there may still be widespread gender differences in functional connectivity beyond those highlighted in our original analyses and described in Fig 2 that are better expressed in some of the higher-order fc-MVPA eigenpatterns (i.e. representing more subtle or less common sources of intersubject variability).

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[1] Url: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1010634

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