Article Figures & Data
Figures
- Figure 1.
A, Longitudinal plot: each dot represents a subject at the age of assessment. Lines represent longitudinal assessments of a subject. B, Pubertal Development Scale scores (PDS) along age. Thin lines represent individual trajectories; thick lines represent locally estimated scatterplot smoothing (LOESS) curves per sex group (with 95% confidence-interval shadow) after controlling for intraindividual trends. F, female; M, male; QC, session with excessive motion artifact. Figures were modified from Gracia-Tabuenca et al. (2021) under CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).
- Figure 2.
Betti-0 (B0) and Betti-1 (B1) for different filtration values. Illustrative example with 20 nodes, five filtration values ε, represented as the circle diameter and their corresponding B0 and B1 values. At ε = 0, the number of components (B0) equals the number of nodes, and there are no holes. As the filtration value increases, the number of components (B0) decreases until they form a single component containing all the nodes. Meanwhile, the number of holes (B1) starts at 0, increases, and finally goes back to 0 again. A hole of dimension 1 is a cycle with four or more edges (highlighted with green edges); the simplices of dimension >1 are colored in light blue for each filtration value ε.
- Figure 3.
Sample intercepts for the B0 (A) and B1 (B) curves are in blue. Average of 1000 bootstrapped connectomes with random edge-rewiring curves in gray. Every average with 95% confidence interval. The blue bars are centered at the sample intercept filtration for starting/ending values with 95% confidence interval in dashed red. Extended Data Figure 3-1 also shows that the persistence of topological holes (B1) shown in B is directly related to the number of holes.
- Figure 4.
Scatter-plots of the GAMM PDS (left) and age (right) models for the B0 (top) and B1 (bottom) area under de curve (AUC) in relation to the pubertal scale (PDS) or age (in years). Thin lines represent individual trajectories; thick black lines represent the sample curve (with 95% confidence-interval shadow). Smooth spline F statistics are depicted. GAMM-age adjustments have higher AIC than GAM-PDS, but are depicted as a reference. a.u., arbitrary units. The relationship between the PDS or Age and the TDA features residuals after regressing out average motion, head coil, and intraindividual slopes covariates is included in Figure Extended Data Figure 4-1. F, females; M, males.
- Figure 5.
Brain maps of the smooth spline’s F value of the Pubertal Development Scale (PDS) GAMM term for B0-AUC at the functional networks level. Mapping was based on ROI corresponding to the consensus area according to Power et al. (2011), using BrainNet Viewer (Xia et al., 2013; RRID:SCR_009446).
- Figure 6.
Scatter-plot of the GAMM model for the B0-AUC of the fronto-parietal network (FPN) in relation to the pubertal scale (PDS). Thin lines represent individual trajectories; thick black lines represent the sample’s smooth spline curve (with 95% confidence-interval shadow). Smooth spline F statistics are depicted. a.u., arbitrary units. The relationship between the PDS and the B0-AUC residuals after regressing out average motion, head coil, and intraindividual slopes covariates is included in Extended Data Figure 6-1. EDF, effective degrees of freedom.
Tables
- Table 1
Akaike Information Criterion (AIC), Shapiro–Wilk test (SW) for the residuals (e) and random-effects (RE) for Betti-0 (B0) and Betti-1 (B1) areas under the curve (AUC) at every developmental model
B0-AUC B1-AUC AIC e-SW(p) RE-SW(p) AIC e-SW(p) RE-SW(p) LME-Age 863 0.993 (0.71) 0.984 (0.36) 627.6 0.98 (0.04) 0.974 (0.07) LME-Age.Sex 864.9 0.994 (0.82) 0.984 (0.35) 631.3 0.98 (0.04) 0.974 (0.07) GAMM-Age 861.4 0.994 (0.79) 0.987 (0.53) 627.7 0.986 (0.18) 0.981 (0.22) GAMM-Age.Sex 862.9 0.994 (0.82) 0.986 (0.49) 630.9 0.987 (0.21) 0.981 (0.22) GAMM-PDS 858.3 0.992 (0.65) 0.983 (0.31) 625.6 0.989 (0.36) 0.988 (0.63) GAMM-PDS.Sex 859.5 0.991 (0.57) 0.979 (0.15) 633.1 0.985 (0.14) 0.984 (0.37) GAMM-AgePDS 859.4 0.994 (0.82) 0.983 (0.3) 625.9 0.991 (0.54) 0.987 (0.53) GAMM-AgePDS.Sex 862.5 0.993 (0.74) 0.983 (0.3) 631.7 0.991 (0.57) 0.979 (0.17) Developmental models: linear mixed-effects models for age (LME-Age) and age-sex interaction (LME-Age.Sex), generalized additive mixed models with smooth splines for age (GAMM-Age) and age-by-sex (GAMM-Age.Sex), PDS (GAMM-PDS) and PDS-by-sex (GAMM-PDS.Sex), and age-PDS interaction (GAMM-AgePDS) and age-PDS interaction-by-sex (GAMM-AgePDS.Sex). Akaike Information Criterion (AIC) and Shapiro–Wilk tests (SW) for the residuals (e) and random-effects (RE) of the Betti-0 (B0) and Betti-1 (B1) areas under the curve (AUC) for every developmental model.
Concerning the developmental effects at the functional network level, the PDS term showed strong effects in the fronto-parietal (FPN) and moderate effects in the auditory (AUD), sensorimotor-hand (SMH), and subcortical (SUB) networks for the B0-AUC (Fig. 5). Only the FPN had a significant effect after FDR correction (F = 6.84; EDF = 2.09; p = 0.001), which shows a nonlinear trend similar to the whole brain network (Fig. 6). No effects (even uncorrected) were found for the B1-AUC.
- Table 2
Model performance at the RSN, effective degrees of freedom (EDF), F and p values for the development component
B0-AUC B1-AUC EDF F p EDF F p AUD 1 0.47 0.493 1.93 1.82 0.156 CBL 1 0.04 0.838 1 1.16 0.283 CON 1.91 2.38 0.067 1 0.44 0.506 DMN 1 0.37 0.543 1 0.02 0.896 DAN 1.78 1.57 0.203 1 0.01 0.904 FPN 2.09 6.84 0.001* 1 3.21 0.076 MEM 1 0.07 0.794 1 2.03 0.157 SAL 1 4.09 0.045 1 0.82 0.368 SMH 1 2.74 0.1 1 0.04 0.839 SMM 1 1.83 0.178 1 0.26 0.611 SUB 1 1.98 0.162 1 0.24 0.628 VAN 1 0.16 0.691 1 1.12 0.291 VIS 1 3.81 0.053 1 4.01 0.047 Auditory (AUD), cerebellar (CBL), cingulo-opercular (CON), default mode (DMN), dorsal attention (DAN), fronto-parietal (FPN), memory-retrieval (MEM), salience (Sal), sensomotor-hand (SMH), sensomotor-mouth (SMM), subcortical (Sub), ventral attention (VAN), and visual (VIS) networks.
* Significant after FDR-corrected at q < 0.05.
Extended Data Figure 3-1
Scatter-plot of Betti-1 area under the curve (B1-AUC) against the number (#) of topological holes, the red line corresponds to the fitted line with its corresponding 95% confidence interval in gray. Intercept at 60.16 and slope of 14.7, R2 = 0.89 (p < 2.2e-16). Intrasubject random-effects were regressed-out from both variables. Download Figure 3-1, TIF file.
Extended Data 1
Code and materials. Download Extended Data 1 ZIP file
Extended Data Figure 4-1
Scatter-plots of the GAMM PDS (left) and age (right) models for the B0 (top) and B1 (bottom) area under de curve (AUC) residuals (e) in relation to the pubertal scale (PDS) or age (in years). Average motion, head coil, and intraindividual slopes were regress-out from the dependent variable. Thin lines represent individual trajectories; thick black lines represent the sample curve (with 95% confidence-interval shadow). Smooth spline F statistics are depicted. GAMM-age adjustments have higher AIC than GAM-PDS, but are depicted as a reference. Download Figure 4-1, TIF file.
Extended Data Figure 6-1
Scatter-plot of the GAMM model for the B0-AUC residuals (e), after regressing out in-scanner motion and head-coil, of the fronto-parietal network (FPN) in relation to the pubertal scale (PDS). Thin lines represent individual trajectories; thick black lines represent the sample’s smooth spline curve (with 95% confidence-interval shadow). Smooth spline F statistics are depicted. Download Figure 6-1, TIF file.
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