Sex differences in multilayer functional network topology over the course of aging in 37543 UK Biobank participants

Abstract Aging is a major risk factor for cardiovascular and neurodegenerative disorders, with considerable societal and economic implications. Healthy aging is accompanied by changes in functional connectivity between and within resting-state functional networks, which have been associated with cognitive decline. However, there is no consensus on the impact of sex on these age-related functional trajectories. Here, we show that multilayer measures provide crucial information on the interaction between sex and age on network topology, allowing for better assessment of cognitive, structural, and cardiovascular risk factors that have been shown to differ between men and women, as well as providing additional insights into the genetic influences on changes in functional connectivity that occur during aging. In a large cross-sectional sample of 37,543 individuals from the UK Biobank cohort, we demonstrate that such multilayer measures that capture the relationship between positive and negative connections are more sensitive to sex-related changes in the whole-brain connectivity patterns and their topological architecture throughout aging, when compared to standard connectivity and topological measures. Our findings indicate that multilayer measures contain previously unknown information on the relationship between sex and age, which opens up new avenues for research into functional brain connectivity in aging.

A. Difference between men and women in different parameters.
FIG. S2. Differences between men and women in cognition, vascular and structural measures. Plots showing the differences between men and women (calculated as women -men) in the a) attention, b) memory, c) executive and d) visuospatial cogntive domains. Differences between the prevalence of e) high blood pressure, f) heart attack, g) angina and h) stroke in men and women are also shown. Figure i-k show the observed sex differences in average cortical thickness, average subcortical volumes and white matter hyperintensities. The areas show the upper and lower bounds of the 95% confidence intervals (CI), and the differences in the corresponding measures between groups in blue circles as a function of individual's age. The differences are considered statistically significant if they fall outside the CIs. In particular, the orange circles show the differences that remained significant after applying a correction for multiple comparisons across the different age groups (FDR at q < 0.05). CIs. In particular, the orange circles show the differences that remained significant after applying a correction for multiple comparisons across the different age groups (FDR at q < 0.05)

IV. MULTILAYER MEASURES AS FUNCTION OF INTER-LAYER WEIGHT.
FIG. S5. Differences between men and women in multilayer clustering. Plots showing the differences between men and women (calculated as women -men) in the multilayer clustering for different values of inter-layer weight, ranging from a) σ = 0.05 to t) σ = 1. The areas show the upper and lower bounds of the 95% confidence intervals (CI), and the differences in the corresponding measures between groups in blue circles as a function of individual's age. The differences are considered statistically significant if they fall outside the CIs. In particular, the orange circles show the differences that remained significant after applying a correction for multiple comparisons across the different age groups (FDR at q < 0.05).

FIG. S6. Differences between men and women in multilayer global efficiency. Plots
showing the differences between men and women (calculated as women -men) in the multilayer global efficiency for different values of inter-layer weight, ranging from a) σ = 0.05 to t) σ = 1. The areas show the upper and lower bounds of the 95% confidence intervals (CI), and the differences in the corresponding measures between groups in blue circles as a function of individual's age.
The differences are considered statistically significant if they fall outside the CIs. In particular, the orange circles show the differences that remained significant after applying a correction for multiple comparisons across the different age groups (FDR at q < 0.05).

VII. MULTILAYER MEASURES UNCOVER SIMILAR PATTERNS OF BETWEEN-SEX DIFFERENCES FOR DIFFERENT SAMPLE SIZES.
We assessed the reproducibility of the multilayer measures as a function of sample size, by calculating sub-samples of men and women at each age, across a range of 40%-95% of the individuals included in the original sample. For each sub-sample, we randomly drew 100 sets of men and women, which were compared using permutation testing. The reproducibility was assessed as the percentage of the sets where we were able to detect between-sex differences that were also significant in the original sample. These results are shown in Supplementary   Figs. S9 and S10 and they indicate that, at most ages, more than 90% of the sub-sampled sets with sizes as low as 55%-60% can also detect the differences identified in the original sample. and women were drawn from the original sample (range 40% to 95%) at each age, and compared between each other. For each sub-sample size, the comparison was drawn between 100 sets; the dark gray bars show the percentage of sets that were able to detect the between-sex differences that were significant in the original sample.
Age ( We assessed whether our results were replicable at individual network densities (Supplementary Fig. S11). These analyses showed that the multilayer measures are less able to detect between-sex differences at low densities. However, we obtained highly reproducible results for all densities larger than 15%. Each weighted connectivity network was binarized at a density range 6% to 33% in steps of 1%. We calculated each functional connectivity measure at all densities within this range and plotted the measure as a function of density (solid black line). For each measure, we integrated the total area under the curve (gray area). Calculated in this way, the AUC measure summarizes the behavior of the corresponding measure over the complete density range considered, and as such, it is less sensitive to the thresholding process.