Resting brain dynamics at different timescales capture distinct aspects of human behavior

Linking human behavior to resting-state brain function is a central question in systems neuroscience. In particular, the functional timescales at which different types of behavioral factors are encoded remain largely unexplored. The behavioral counterparts of static functional connectivity (FC), at the resolution of several minutes, have been studied but behavioral correlates of dynamic measures of FC at the resolution of a few seconds remain unclear. Here, using resting-state fMRI and 58 phenotypic measures from the Human Connectome Project, we find that dynamic FC captures task-based phenotypes (e.g., processing speed or fluid intelligence scores), whereas self-reported measures (e.g., loneliness or life satisfaction) are equally well explained by static and dynamic FC. Furthermore, behaviorally relevant dynamic FC emerges from the interconnections across all resting-state networks, rather than within or between pairs of networks. Our findings shed new light on the timescales of cognitive processes involved in distinct facets of behavior.

where Y , C and E are 419 × 58 matrices. Y contains the 58 processed behavioral measures for all 419 subjects. V ec(C) ∼ N (0, Σ c ⊗ F ) and V ec(E) ∼ N (0, Σ e ⊗ I), where V ec(.) is the matrix vectorization operator, ⊗ is the Kronecker product of matrices, and I is the identity matrix. F is a similarity matrix such that F (i, j) encodes the (static or dynamic) FC similarity between subjects i and j, and is defined as the correlation between the static FC (or dynamic FC) matrices of the two subjects. Σ c and Σ e are unknown 58 × 58 matrices to be estimated from F and Y . Estimates of Σ c and Σ e are obtained using a moment-matching method [1]: where τ = T r(F )/N , κ = T r(F 2 )/N , and ν F = N (κ − τ 2 ). The variance explained by (static or dynamic) FC markers, denoted M , then writes: Variance explained for a single behavioral measure is given by M i = Σ c (i, i)/(Σ c (i, i) + Σ e (i, i)).
If more than one kernel is used in the analysis (e.g., if one wants to explore the variance explained when static and dynamic FC are combined), Supplementary Eq. (1) generalizes as follows: where V ec(C l ) ∼ N (0, Σ c l ⊗ F l ) and V ec(E) ∼ N (0, Σ e ⊗ I). The variance explained by all components is defined as: The variance explained by a particular component C l 0 is defined as: and the variance explained for a single behavioral measure i is computed as: (7) Estimates of Σ C l and Σ e are now computed as follows. Denoting the (r, s)-element of Σ C l as σ C l ,rs and the (r, s)-element of Σ e as σ e,rs , we have: cov(y r , y s ) = l σ C l ,rs F l + σ e,rs I.
We then regress V ec(y r y T s ) onto V ec(F l ) and V ec(I) which leads to the following linear system: T r(F 1 F 1 ) . . . T r(F 1 F L ) T r(F 1 ) . . . . . . . . . . . .
T r(F L F 1 ) . . . T r(F L F L ) T r(F L ) where σ rs = (σ C 1 ,rs , . . . , σ C L ,rs , σ e,rs ) T . Solving the linear system gives the (r, s)-element in each of the variance component matrices, and Σ c and Σ e are estimated by repeating this for all r and s. Note that when only one kernel is used, a closed-form estimator can be derived, which is Supplementary Eq. (2).
The mean and standard deviation (SD) of the behavioral variance explained by -static or dynamic-FC patterns are then computed using the Jackknife method (Equations (4) and (5); [2]).
Importantly, the estimated SD of the 'delete-1' estimates is not the SD of the behavioral variance represented by error bars in Figures 1-4, as can be seen from Equation (5). More precisely, the SD of the delete-1 estimates is (much) smaller than the SD of the explained variance. This is explained by the fact that the delete-1 estimates are computed from subsets of size (N − 1) sharing all but one subject, and hence the delete-1 estimates are close to each other. This redundancy is taken into account in Equation (5) (5).

Identifying patterns of interactions contributing to the overall explained variance
The contribution of pairwise interactions to the overall explained variance is obtained from the following model: where y is a vector encoding one behavioral measure for the N subjects, u is a random-effects vector of length P , the number of entries in the FC matrices, W is an N × P matrix with centered and unit-variance lines, and e is the normally distributed residual with variance σ e . Assuming each element of u is independent and follows a normal distribution with variance σ c /P , then the model can be turned into the variance component model of Equation (2) we used: where F = W · W T /P is the similarity matrix of the connectome between pairs of individuals.
Then, using the best linear unbiased predictor of u following Yang et al.  Figure 4).

Accounting for covariates
Age, gender, race, education and motion (mean FD) were regressed from the 58 phenotypic measures which were then quantile normalized. To do so, each behavioral measure distribution was sorted and mapped to a linear spacing of the ]0, 1[ interval. Each behavioral measure was then replaced by the inverse normal cdf of its mapped value, leading to a rank-preserving Gaussian redistribution of the behavioral measures [4]. This normalization was motivated by the fact that Gaussianity is an assumption of the multidimensional variance component model. Quantile An alternative way of including covariates would have been to explicitly account for them in the variance component model: where X is an N × Q matrix of Q covariates and B a matrix of fixed effects. Again, using this alternative approach did not significantly affect our results.

Supplementary Results
Variance explained for additional behavioral measures

Exploring subcategories of task-based measures
To test whether the advantage of dynamic FC in explaining task-based behavioral measures was shared across different types of task-based measures, we computed the behavioral variance explained by dynamic and static FC in subcategories of task-based measures. These categories were determined based on the the expected cognitive domains recruited by the tasks [5]. We

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In t e r f e r e n c e S u r v e y

Supplementary Table 1 reports the p-values of the statistical tests (two-tailed t-tests) performed
in Figures 1-4 (original dataset) and the corresponding tests in the replication dataset (Supplementary Figures 5-9). The p-values marked with an asterix are the ones surviving an FDR correction at the level q < 0.05, when correcting for the 16 tests reported in Supplementary Table 1.

Additional control analyses
We performed four control analyses to evaluate the impact of different processing steps included in our baseline analysis: 1. Including the variance of the mean grayordinate signal as a covariate in the variance component model (Supplementary Figure 10B).
2. Computing the static and dynamic FC matrices from fMRI time series on which no mean grayordinate signal was performed (Supplementary Figure 10C).

Including head motion metrics (mean FWD, max FWD and number of volumes scrubbed)
as covariates of the variance component model (Supplementary Figure 10D).

4.
Computing the static and dynamic FC matrices from full (i.e., uncensored) fMRI time series (Supplementary Figure 10E).
In each variant, the main results are reproduced.  Figures 11D-F).

Static and dynamic contribution in the combined model
We present the relative contributions of static and dynamic FC variance in the combined model used in Figure 4. It can be seen that as in the case of individual models, dynamic FC captures more behavioral variance than static FC within the combined model: out of the average 45% explained by the combined model, 12% are attributed to static FC and 33% to dynamic FC (Supplementary Figure 12A). Note that as the combined explained variance (45%) is smaller than the sum of individual static (18%) and dynamic (37%) explained variances, there is shared variance between the static and dynamic contributions. Further work is required to determine how this shared variance is distributed among various contributions from a theoretical point of view and hence this result should be considered with caution.   Table 2: List of the 58 behavioral measures from the Human Connectome Project used in the present work. These measures were selected so as to span cognitive, emotion and social behavioral aspects and were classified as task performance measures (TA), self-reported measures (SR), or left unclassified (UC).