(A) The full similarity matrix (FSM) containing normalized mutual information (NMI) metrics between every possible pair of independent components (ICs) from different subjects. The purple lines separate ICs from different subjects, forming subject blocks in the FSM. ICs from different subjects are labeled using different colors. (B) The NMI metrics in the FSM are standardized into Z-scores within each row in each subject block. The resultant matrix, Zrow, is an asymmetric matrix. (C) The maximal values within each row in each subject block are identified, and all other values are set to zeros, forming a matrix Zmax. (D) Zmax is multiplied by its transpose, yielding a matrix W. In this step, the NMI values are set to zero in uni-directional correspondence cases, such as IC3 of subject 1 has the maximal similarity to IC3 among all components in subject 2, but the IC3 of subject 2 has the maximal similarity to IC2 among all from subject 1, as demonstrated in (C). The symmetric matrix W reflects only bi-directional correspondence between ICs from different subjects. Summing up the values in W along each row gives a value of popularity for each component, indicating its consistency across all subjects in terms of strength of bi-directional correspondence. The ICs from all subjects are ranked according to this popularity value. (E) The Zrow matrix in (B) is added to its own transpose to yield the matrix in (E), which contains (A) standardized NMI (SNMI), a metric reflecting the specificity of each NMI similarity value within all values within a subject block. The component with top popularity from (D), which is represented using a red line in this SNMI matrix, is used to align ICs from different subjects. (F) The local maximum in each subject block along the red line (top ranked component) is identified, as indicated by orange lines. The ICs corresponding to the local maxima are labeled at the edges of the matrix, with each color indicating a different subject. (G) The SNMI between every pair of the matched ICs is found in the cross between red and orange lines. (H) The SNMI values between the identified ICs are collected in the matrix, generating a maximal similarity matrix for the current group-level aligned component (AC). The selected ICs are then removed from the rank in (D) and the SNMI matrix in (E). The search continues from (E), until the component popularity rank is empty.

(A) The PCU-dPCC network dominated by the dorsal and ventral precuneus and the dorsal posterior cingulate cortex; (B) the DMN consisting of the ventral posterior cingulate cortex, ventral precuneus, left and right inferior parietal cortex, and medial prefrontal cortex. In both (A) and (B), the group level spatial maps representing the intrinsic connectivity networks are shown on the top-left corners. The maps are thresholded at |Z| > 2 (i.e., the weighted average score from the Z scores of the individual spatial maps). The reproducibility matrices depicting the inter-subject consistency are shown on the bottom-left corners, where the subjects represented in both horizontal and vertical axes are sorted according to age. While the PCU-dPCC network shows decreasing consistency with age, the DMN does not show such a tendency. The subject centrality metrics are plotted against age (top-right), where the horizontal axis indicates age. Compared to the PCU-dPCC network, the DMN shows a stable subject centrality with increasing age. The lifespan is then divided into five age groups. The within age-group mean similarity plots are shown in the right-middle panels, and the within age-group ratios of significant subjects (RSS) are shown in the bottom-right corners in (A) and (B). These two metrics reflect age-dependency in the PCU-dPCC network, but not in the DMN. (C) The locations of the clusters defined in the DMN and in the PCU-dPCC network are rendered and color-coded. The clusters are identified using a thresholded at |Z| > 2 and cluster size > 540 mm³. The two networks overlap at the ventral precuneus (the yellow region). The right panel of (C) summarizes the memberships of these clusters.

In panels A-B, red color renders clusters whose contribution to the DMN spatial map exhibit significantly positive correlation with age. Regions in purple represent the PCU and dPCC clusters identified in the PCU-dPCC network. Yellow color indicates the overlap between the red clusters and purple regions. Clusters overlap with the PCU-dPCC regions are circled and labeled. Panels C and D plot the linear fittings between the mean Z scores in these two clusters and age.

(A) Maximal correlation coefficients for the DMN network; (B) maximal correlation coefficients for the PCU-dPCC network. The horizontal axes represent individual subjects sorted by ascending age, and the vertical axes indicate different choices for the number of components in the individual ICA. The reference spatial templates are defined by applying gRAICAR to 11 subjects between 30 and 40 years old with the number of components set to 60 for the individual subject ICA. The black rectangles around ‘REF’ indicate the subjects used to generate the gRAICAR reference template. The maximal correlation coefficients for the DMN network are consistent across all subjects and across different settings for the number of components, while those for the PCU-dPCC network showed a decreasing trend with age. This tendency is preserved with different choices of number of components when they are larger than 30.

The colors in the matrix indicate Fisher’s Z-scores for correlation coefficients. Since the Z scores are all positive here, the negative range is not shown here. Each row or column in the matrices represents a voxel (total voxels = 811). The white dashed lines segment voxels from different clusters. Abbreviations in the cluster labels are: dPCU, dorsal precuneus; vPCU, ventral precuneus; vPCC, ventral posterior cingulate cortex; dPCC, dorsal posterior cingulate cortex; vmPFC, ventral medial prefrontal cortex; l-IP, left inferior parietal cortex; and r-IP, right inferior parietal cortex. The partitions representing the interNFC, the intraNFC of PCU-dPCC network, and the intraNFC of DMN are highlighted with labels and solid lines.

The black dots represent functional connectivity measured from individual subjects. The red lines indicate linear fitting of age effects, taking into account the nuisance effects from head micromovements (meanFD) and sex. The green dashed curves indicate the 95% confidence interval of the fitted line. The significance of the beta values and goodness of fitting statistics are marked at the bottom of the plots. The plots for the PCU-dPCC network are shown in the top row (A, B), and the bottom row shows the plots for the DMN (C, D). Panels (A) and (C) show the intraNFC, and panels (B) and (D) show the relative intraNFC. The values are first converted to Fisher’s Z values and further standardized into Z scores (mean=0, standard deviation=1) for easier comparisons. For both dependent variables (intraNFC and relative intraNFC), the PCU-dPCC network shows a stronger negative relationship with age compared with the DMN.