Preprocessing of images. SPM8 software (Wellcome Trust Center for Neuroimaging, UK) was used for preprocessing, including slice timing correction, motion correction by realignment, coregistration of the functional image to a structural brain image, and spatial normalization of the functional data. After head motion correction, the functional volumes were normalized to template image, which are coregistered to the mouse brain atlas (55), using the default nonlinear registration algorithm implemented in SPM8. The data were then processed using ICA-AROMA to correct for any remaining head movement (40).

Odor stimulation task-based fMRI. Following preprocessing, the normalized images were smoothed with a Gaussian filter [full width at half maximum (FWHM) = 0.6 mm]. Statistical analyses for odor stimulation were conducted using SPM8. The smoothed images were high pass–filtered for 100 s. The regressor was constructed by convolving the hemodynamic response function to the box-car model (on/off stimulation). Framewise displacement (41) was computed and regressed at the first-level analysis to control for head motion. A threshold of P < 0.05 (FDR-corrected at the cluster-wise level) was used to identify regional activation patterns associated with odor stimulation. To perform group inference, second-level (random effect) analyses were conducted by using the results of the first level analysis P < 0.05 (FDR-corrected at the cluster-wise level).

Resting-state functional connectivity. Framewise displacement (41) and time series derived from white matter, ventricles, and all gray matter were regressed because global signal is correlated with spontaneous, nonneuronal fluctuation of the blood flow. The residuals from this regression were used for all subsequent analyses. Detrending and bandpass filtering (0.01 to 0.1 Hz) were performed to exclude high-frequency components. Then, the processed images were smoothed with a Gaussian filter (FWHM = 0.6 mm). The Pearson correlation coefficient was computed between preprocessed and regionally averaged (32 regions) BOLD signals to yield a connectivity matrix for each mouse. The regions spanned the entire cortex and were drawn manually on the basis of the structural image corresponding to the mouse brain atlas (55). These 32 regions were selected on the basis of the regions related to the odor recognition and cognitive function.

Network-based statistic. The NBS (20) was used to identify functional connections (pairs of regions) that significantly differed in connectivity strength (Pearson correlation) between groups. We considered six independent comparisons among WT-saline, WT-DCS, 15q dup-saline, 15q dup-DCS. To correct for the three independent comparisons, a significance threshold of α = 0.05/6 = 0.008 was enforced. For each comparison, a two-sample t test was performed independently for each distinct pair of regions (496 pairs) to test the null hypothesis of equality between groups in the mean Pearson correlation coefficient. This yielded a 32 × 32 matrix of t statistics. Connections with a t statistic threshold exceeding 3 were admitted to a suprathreshold graph, and connected components, referred to as subnetworks, were identified in this graph. The size of each subnetwork was measured as the number of suprathreshold connections that it comprised. To determine a familywise error–corrected P value for each subnetwork, permutation testing (5000 permutations) was used to generate a null distribution for the maximal subnetwork size. The P value for an observed subnetwork of the given size was estimated as the proportion of permutations for which the maximal subnetwork exceeded or equaled this size. To isolate subnetworks comprising the strongest effects, the t statistic threshold was increased from 3 to 6 in cases where widespread subnetworks were found for the lower threshold (Fig. 2B). The NBS provides control of the familywise error rate in the weak sense across the whole network; namely, the set of all connections. The P value associated with each subnetwork identified with the NBS was thus corrected for familywise errors across the whole network.

Modularity. Network modules were delineated in the 32 × 32 functional connectivity matrices constructed for each mouse. A consensus modular decomposition was also delineated for all mice (WT-saline, WT-DCS, 15q dup-saline, and 15q dup-DCS). The Louvain algorithm was used to identify modules, with the resolution parameter set to unity (56). To account for degeneracy in the solution space, the Louvain algorithm was implemented for 100 independent trials for each mouse, and a consensus matrix across these trials was generated. Because of the stochastic nature of the algorithm, decompositions varied across trials. Each cell in the consensus matrix stored the proportion of trials for which a given pair of regions belonged to a common module. Elements in the consensus matrix that were below a value of 0.4 were set to zero. The Louvain algorithm was applied to the thresholded matrix (100 trials) to yield a consensus modular decomposition (28). This process was iterated until the consensus matrices converged between successive iterations. To determine a modular decomposition for all mice, a consensus matrix was first constructed across all mice, where each cell in this matrix stored the proportion of mice for which a given pair of nodes belonged to a common module. The Louvain algorithm was then applied to this consensus matrix. The modularity Q score (57) was used to quantify the extent to which each functional network was segregated into distinct modules. Higher Q scores indicate greater modular structure.

Dual-regression analysis. The REST toolkit (REST v1.8) and SPM8 were used to delineate the DMN. First, the preprocessed fMRI data were temporally detrended and bandpass-filtered (0.01 to 0.1 Hz). We used FMRIB Software Library (FSL) Multivariate Exploratory Linear Optimized Decomposition into Independent Components (MELODIC) for probabilistic ICA. The multisession temporal ICA concatenated approach was used for all mice in a temporally concatenated fashion for the ICA analysis. A total of 70 independent components were extracted from each analysis group (30, 58). Of the 70 independent components in each group, a representative network from a previous study was extracted, i.e., local cortical network, associated cortical network, subcortical network, limbic network, DMN, ThN, and cerebellum (fig. S5) (30, 48, 58). DMN was selected for comparison using dual regression. We used dual-regression program (FSL 5.0.2.2) for between-subject analysis, allowing for voxel-wise comparisons of rsfMRI data (30, 58). We used unpaired t tests to test for differences between groups.

FA map and structural connectivity in DTI. FA maps were calculated from the diffusion-weighted images using ParaVision 5.1 (Bruker BioSpin, Billerica, CA, USA). The FA maps were normalized to the template images using SPM 8. Normalization was performed via the T2 image (b = 0 s/mm2), which had a contrast that better resembled the template image than the FA maps. Regionally averaged FA values were determined for 18 gray matter regions by averaging FA values across all voxels comprising each region. FA values were compared between WT and 15q dup groups using a two-way ANOVA.

Structural connectivity strength was quantified using two measures, mean FA and EW using DSI Studio software (http://dsi-studio.labsolver.org). FA at a given tracking point, measuring the degree of organization of the underlying white matter at each point, was computed and averaged over all tracked points on the fiber bundles. EW, which takes into account the number of fibers, the length of the fibers, and the ROI size, was computed as the following equation (59)EW(i,j)=2Si+SjfF(i,j)1L(f)where F(i,j) is the set of fibers connecting ROIs i and j, Si and Sj are the sizes of the two ROIs, f is each individual fiber within F(i,j), and L(f) is the length of fiber f.

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