The effect size (i.e., partial correlation
r) of the age effect of control energy at the whole-brain level and in the fronto-parietal system (
a) with 100 different initial states, in which the activation value of regions in fronto-parietal follow the Gaussian distribution with a mean value of 0 and standard deviation of 0.1, and (
b) with 100 different target states, in which the activation value of regions in fronto-parietal system follow the Gaussian distribution with a mean value of 1 and standard deviation of 0.1. (
c) The distribution of the age effect of average control energy of whole-brain and fronto-parietal systems when using null model networks, which preserve the degree and strength distribution. The null networks were created by brain connectivity toolbox (
Rubinov and Sporns, 2010). The red arrow indicates the actual age effect estimated using the data from the real brain network. (
d), The whole-brain control energy cost to activate the fronto-parietal system when constraining the whole brain was highly significantly correlated with the energy cost when only the fronto-parietal system was constrained (
r = 0.94, p<2 × 10
−16). (
e), Left: the energy required to reach a motor activation state was significantly higher for null networks than real networks. Right: the whole brain average control energy did not change over the age range studied.