Age‐related changes in the ease of dynamical transitions in human brain activity

Abstract Executive functions, a set of cognitive processes that enable flexible behavioral control, are known to decay with aging. Because such complex mental functions are considered to rely on the dynamic coordination of functionally different neural systems, the age‐related decline in executive functions should be underpinned by alteration of large‐scale neural dynamics. However, the effects of age on brain dynamics have not been firmly formulated. Here, we investigate such age‐related changes in brain dynamics by applying “energy landscape analysis” to publicly available functional magnetic resonance imaging data from healthy younger and older human adults. We quantified the ease of dynamical transitions between different major patterns of brain activity, and estimated it for the default mode network (DMN) and the cingulo‐opercular network (CON) separately. We found that the two age groups shared qualitatively the same trajectories of brain dynamics in both the DMN and CON. However, in both of networks, the ease of transitions was significantly smaller in the older than the younger group. Moreover, the ease of transitions was associated with the performance in executive function tasks in a doubly dissociated manner: for the younger adults, the ability of executive functions was mainly correlated with the ease of transitions in the CON, whereas that for the older adults was specifically associated with the ease of transitions in the DMN. These results provide direct biological evidence for age‐related changes in macroscopic brain dynamics and suggest that such neural dynamics play key roles when individuals carry out cognitively demanding tasks.

The disconnectivity graphs for the right and left FPNs showed similar patterns to those for the DMN, except for the right FPN of the younger group (Fig. S6A). The disconnectivity graph for the right FPN of the younger group had more branches and local minimums than those of the DMN and CON. However, in all the FPNs, s+ and s-were the local minimums with almost the largest frequency of being visited. Therefore, we continued to use the categorization of the activity patterns into the four groups (s+, s-, b+, and b-) or five groups (s+, s-, b+, b-, and bother) depending on whether there were only two local minimums (which were the synchronized activity patterns) or more than two local minimums. Figure S2 shows the rate of transitions between s+ and s-and that of peripheral transitions.
The difference between the age groups was less significant than that for the DMN and CON reported in the main text. In addition, the efficiency score for the FPN of the individual participants was not significantly correlated with the executive score ( Fig. S3). Thus, the ease of dynamical transitions in the FPN was not related to aging.

Results for the auditory network
As a negative control, we conducted the same analysis on the auditory network (Aud) whose coordinates of the ROIs were defined in a previous study (Power et al., 2011). We selected this brain system because its number of ROIs (i.e., NROI = 13) is similar to that of the DMN (i.e., NROI = 12) and the Aud is considered to be less relevant to executive functions than the other systems investigated in the present study. As we did for the DMN and FPN, we separately analyzed the right (NROI = 6) and left (NROI = 7) hemispheres of the Aud. The accuracy of fitting of the pairwise MEM was equal to (0.981, 0.958) and (0.972, 0.962) for the right and left hemispheric Aud, respectively, where the first and second values in the parentheses are the accuracy for the younger and older groups, respectively.
The disconnectivity graphs for the right and left Aud were similar to those for the DMN and FPN (Fig. S6B). For the right Aud of the older group, an activity pattern adjacent to s+ and an activity pattern adjacent to s-(denoted by and , respectively) were the local minima. Because their deviation from s+ or s-was small, we computed the efficiency score based on the basins of and transitions between and . Figure S2 shows the rate of transitions between s+ and s-( and in the case of the right Aud of the older group) and that of peripheral transi- Second, all native gray matter images were non-linearly registered to this study-specific template and "modulated" to correct for local expansion (or contraction) due to the non-linear component of the spatial transformation. Finally, the average gray matter volume (GMV) at each ROI were averaged over the ROIs in each system (i.e., DMN and CON) for each individual.
We then regressed out the effect of the GMV of each participant on the efficiency score.
The correlation values between the efficiency score after the removal of the effect of the GMV and the executive score were similar to those reported in the main text (DMN, younger: r 2 = .23, p = .27; CON, younger: r = .49, p < .012; DMN, older: r = .60, p < .01; CON, older: r = -.18, p = .41; uncorrected p values). Therefore, we conclude that our main results are not confounded by the age-related strucutural differences in the brain.
Additional results with robust linear regression To confirm that our main results were not influenced by the choice of a method of outlier exclusion, we tested another method, robust linear regression (Yohai, 1987;Koller and Stahel, 2011), and examined the correlation between the executive score and the efficiency score. We used the lmrob function in

Results for seed-based analysis
In the current study, we defined brain systems based on previ- (B) CON. The P value is that for the significance test for the correlation coefficient. For the Aud, the MNI coordinate of each ROI is shown.

Figure S8
Results of the seed-based functional connectivity analysis for (A) CON, (B) DMN, and (c) FPN. Spatial maps that represent brain regions that were positively correlated with the seed region were shown in blue for the younger adults and red for the older adults.
Green dots represent the ROIs used in the current study. Table S1. Each subtest in D-KEFS and its factor loading score on the executive score.

Factor loading
Verbal