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. 2024 Dec 30;14(1):32032.
doi: 10.1038/s41598-024-83696-7.

The brain selectively allocates energy to functional brain networks under cognitive control

Majid Saberi  1   2 , Jenny R Rieck  3 , Shamim Golafshan  4 , Cheryl L Grady  3   5   6 , Bratislav Misic  7   8 , Benjamin T Dunkley  9   10   11 , Ali Khatibi  12   13
Affiliations

The brain selectively allocates energy to functional brain networks under cognitive control

Majid Saberi et al. Sci Rep. .

Abstract

Network energy has been conceptualized based on structural balance theory in the physics of complex networks. We utilized this framework to assess the energy of functional brain networks under cognitive control and to understand how energy is allocated across canonical functional networks during various cognitive control tasks. We extracted network energy from functional connectivity patterns of subjects who underwent fMRI scans during cognitive tasks involving working memory, inhibitory control, and cognitive flexibility, in addition to task-free scans. We found that the energy of the whole-brain network increases when exposed to cognitive control tasks compared to the task-free resting state, which serves as a reference point. The brain selectively allocates this elevated energy to canonical functional networks; sensory networks receive more energy to support flexibility for processing sensory stimuli, while cognitive networks relevant to the task, functioning efficiently, require less energy. Furthermore, employing network energy, as a global network measure, improves the performance of predictive modeling, particularly in classifying cognitive control tasks and predicting chronological age. Our results highlight the robustness of this framework and the utility of network energy in understanding brain and cognitive mechanisms, including its promising potential as a biomarker for mental conditions and neurological disorders.

Keywords: Brain biomarker; Canonical functional networks; Cognitive control; Executive functions; Functional connectivity; Network energy; Predictive modeling; Structural balance theory.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests. Conflict of interest: The authors declare that there are no conflicts of interest regarding the publication of this paper.

Figures

Fig. 1
Fig. 1
Schematic representation of the brain network’s energy landscape, network states, and state transitions, as well as the calculation of network energy. Brain functional network exhibits different levels of energy, corresponding to the configuration of functional connections. The arrangement of positive (red) and negative (blue) functional connections influences the stability or instability and the level of energy. Triangles formed by functional connections between three brain regions are categorized as either balanced (stable) or imbalanced (unstable), depending on the positive or negative nature of their connections. The intensity of balanced and imbalanced triangles determines the energy level. Network energy is calculated by multiplying the connection weights for each triangle and summing across all triangles in the functional network. Blue and red lines represent negative and positive functional connections, respectively, with the line width indicating the strength of coactivation between two regions. Further details about the formula are provided in the text. (Created with BioRender.com).
Fig. 2
Fig. 2
Whole-brain network energy during cognitive control tasks and resting state. Horizontal lines represent group-level medians, while notches on the boxes indicate the 95% confidence interval for the median. Individual subjects are linked by lines, with task conditions distinguished by color. Colored asterisks above the respective conditions denote significant corrected p-values for non-parametric pairwise comparisons between cognitive task conditions.
Fig. 3
Fig. 3
(A) Energy levels of canonical functional networks during resting state and cognitive control task conditions, shown as group-level medians. The color code on the right differentiates between cognitive task conditions and canonical networks. The radar chart displays energy values ranging between − 0.45 and − 0.05. (B) Energy levels of canonical networks during task-free resting state, with horizontal lines indicating group-level medians and notches representing the 95% confidence intervals for these medians. (C) Changes in network energy during the transition from rest to task state for each canonical network and cognitive task condition. Dots represent group-level medians of energy changes, with different networks indicated by colors. (D) A schematic representation of energy shifts during the transition from rest to task state. Abbreviations: AUD: auditory; COP: cingulo-opercular; DAN: dorsal attention; DMN: default mode; FPC: frontoparietal; SAL: salience; SM: somatomotor; SC: subcortical; VAN: ventral attention; VIS: visual; U: network energy; ΔU: network energy alteration.
Fig. 4
Fig. 4
Classification of cognitive control task states. (A) Bar plots display the classifier’s accuracy for each cognitive task state (class) individually, along with the balanced accuracy for the overall classification model. The colors of the bars represent different subsets of input features. The horizontal dotted line marks the chance level of classification. (B) Confusion matrix for the classification model using all network measure types as input features during training. The numbers indicate the percentage of actual values that were predicted for each class, with darker cell colors representing higher values. (C) Bar plot illustrates the importance of different features in cognitive task state classification. The colors of the bars represent various canonical networks. Asterisks on the x-axis labels denote network energy features extracted from functional networks. Abbreviations: NE: network energy; GCC: global clustering coefficient; GE: global efficiency; GM: global modularity; GLOB: all global network measure types; AUD: auditory; COP: cingulo-opercular; DAN: dorsal attention; DMN: default mode; FPC: frontoparietal; SAL: salience; SM: somatomotor; SC: subcortical; VAN: ventral attention; VIS: visual.
Fig. 5
Fig. 5
Regression modeling of chronological age. (A) Bar plots show the performance and error in age prediction for various subsets of network measures utilized as input features. (B) Scatter plot demonstrates actual versus predicted age using the full set of input features obtained from all network measures, with each dot representing an individual subject and the fitted line showing the linear relationship. (C) Bar plot illustrates the importance of different features in predicting chronological age when we trained the model using all network measure types. The colors of the bars represent various canonical networks, with features related to network energy marked by asterisks on the x-axis labels. Abbreviations: R²: coefficient of determination; MAE: mean absolute error; NE: network energy; GCC: global clustering coefficient; GE: global efficiency; GM: global modularity; GLOB: all global network measure types; AUD: auditory; COP: cingulo-opercular; DAN: dorsal attention; DMN: default mode; FPC: frontoparietal; SAL: salience; SM: somatomotor; SC: subcortical; VAN: ventral attention; VIS: visual.
Fig. 6
Fig. 6
Validity and reliability of network energy. (A) Energy comparison between actual whole-brain networks and their corresponding null networks with random topologies. Horizontal lines in the box plots denote group-level medians of energy levels, and notches represent the 95% confidence intervals. Actual networks corresponding to cognitive task conditions are color-coded, while the related null networks are shown in gray, adjacent to each task condition. Lines connect each subject’s network to its corresponding null network. (B) Intraclass correlation of whole-brain network energies between networks formed using Power’s atlas and Schaefer’s parcellation atlas for each cognitive task condition. The height of the bar plots indicates the average fixed raters’ ICC values, with error bars representing the corresponding 95% confidence intervals. Colors distinguish between task conditions.
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