Optimization of energy state transition trajectory supports the development of executive function during youth
- Departments of Psychiatry, University of Pennsylvania, United States
- Departments of Bioengineering, University of Pennsylvania, United States
- Department of Psychological and Brain Sciences, Indiana University, United States
- Department of Computer Science, University of Electronic Science and Technology, China
- Departments of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, United States
- Departments of Electrical and Systems Engineering, University of Pennsylvania, United States
- Department of Mechanical Engineering, University of California, United States
- Departments of Physics and Astronomy and Neurology, University of Pennsylvania, United States
- Departments of Neurology, University of Pennsylvania, United States
- Santa Fe Institute, United States
Figures
Figure 1 with 3 supplements
Schematic of the network control approach and the estimation of control energy.
(a) From a baseline state, we calculated the control energy required to reach a fronto-parietal activation target state. This transition was calculated for each subject based on their structural …
Figure 1—figure supplement 1
Sample construction.
The cross-sectional sample of the Philadelphia Neurodevelopmental Cohort (PNC) has 1601 participants in total. 340 subjects were excluded owing to clinical factors, such as medical disorders. Then, …
Figure 1—figure supplement 2
Functional brain networks defined by Yeo et al. (2011).
Each parcel was mapped to one of these networks.
Figure 1—figure supplement 3
Relationship between trajectory distance and control energy.
(a) The activation profiles of all 27 brain regions of the fronto-parietal system during an optimal trajectory from the baseline state to the final state. We define the final state to be a vector in …
Figure 2 with 4 supplements
Control energy evolves with age in youth.
(a) The mean whole-brain control energy required to reach the fronto-parietal activation target declines with age. (b) Control energy declines significantly with age in the fronto-parietal, visual, …
Figure 2—figure supplement 1
Scatter plots of significant age effects of control energy at the system scale.
The control energy of (a) visual, (b) motor, and (f) subcortical systems decline significantly with age, while that of (c) ventral attention, (d) limbic and (e) default mode systems increase …
Figure 2—figure supplement 2
Specificity and sensitivity analyses provide convergent results.
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 …
Figure 2—figure supplement 3
Age effects at the whole brain, cognitive system, and nodal levels remain after controlling for the (a) modal controllability and (b) network modularity.
For each system with a significant association, the effect size is reported (in each bar) as the partial correlation between system-level control energy and age while controlling for the covariates. …
Figure 2—figure supplement 4
Convergent results from a target state defined by a working memory task that recruits the fronto-parietal system.
(a) Alternative target state, defined by the 2-back >0-back contrast on the fractal n-back working memory task (see Satterthwaite et al., 2013). (b) As in the main results, the control energy cost …
Figure 3 with 2 supplements
The whole-brain control energy pattern contains sufficient information to predict brain maturity in unseen individuals.
(a) The predicted brain maturity index was significantly related to the chronological age in a multivariate ridge regression model that used 2-fold cross validation (2F-CV) with nested parameter …
Figure 3—figure supplement 1
Schematic overview of one outer loop of the nested 2-fold cross-validation (2F-CV) prediction framework.
All subjects were divided into 2 halves according to age rank, with the first half used as a training set and the second half used as a testing set. Each feature was linearly scaled between zero and …
Figure 3—figure supplement 2
The histograms of the permutation distribution of the (a) correlation r and (b) MAE with the first subset used as a training set and the second subset used as a testing set, and (c) correlation r and (d) MAE with the first subset used as the testing set and the second subset used as training set.
The red arrow represents the actual prediction accuracy (i.e., r or MAE). The actual correlation r was significantly higher than expected by chance (p<0.001) and the actual MAE was significantly …
Figure 4
Reduced control energy in both the a, left and b, right mid-cingulate cortex was associated with higher executive performance.
Of all brain regions examined, only the left and right mid-cingulate cortex survived FDR correction. Data points represent each subject (n = 944), the bold line indicates the best linear fit, and …
