Control theory illustrates the energy efficiency in the dynamic reconfiguration of functional connectivity

Abstract

The brain’s functional connectivity fluctuates over time instead of remaining steady in a stationary mode even during the resting state. This fluctuation establishes the dynamical functional connectivity that transitions in a non-random order between multiple modes. Yet it remains unexplored how the transition facilitates the entire brain network as a dynamical system and what utility this mechanism for dynamic reconfiguration can bring over the widely used graph theoretical measurements. To address these questions, we propose to conduct an energetic analysis of functional brain networks using resting-state fMRI and behavioral measurements from the Human Connectome Project. Through comparing the state transition energy under distinct adjacent matrices, we justify that dynamic functional connectivity leads to 60% less energy cost to support the resting state dynamics than static connectivity when driving the transition through default mode network. Moreover, we demonstrate that combining graph theoretical measurements and our energy-based control measurements as the feature vector can provide complementary prediction power for the behavioral scores (Combination vs. Control: t = 9.41, p = 1.64e−13; Combination vs. Graph: t = 4.92, p = 3.81e−6). Our approach integrates statistical inference and dynamical system inspection towards understanding brain networks.

Thalamic network controllability changes and cognitive impairment in multiple sclerosis

“…Specifically, average controllability identifies regions that contribute more to brain transitions towards easy-to-reach states like the resting state. 21,22,37 Functional hubs with denser or stronger connections typically exhibit higher average controllability. These regions have close connection with multiple regions throughout the brain and contribute to transition between states that require lower energy costs.…”

“…Following previous studies 21,22 , we constructed a simplified linear time-invariant control system to characterize the controllability of large scale functional brain networks.…”

“…To calculate A , we used a modified Laplacian normalization of the functional connectivity matrix F to ensure the stability of the dynamic system as described in a previous study. 22 Specifically, we calculated the Laplacian matrix as: where F ij is the ( i , j ) element of the functional matrix; K is the total number of nodes in the network; δ ij is the Kronecker delta ( δ ij = 1 if i = j and δ ij = 0 otherwise). The functional connectivity matrix was then normalized into the system matrix as: with λ max ( L ) denoting the maximum absolute eigenvalue of the Laplacian matrix.…”

Controllability of Functional Brain Networks and Its Clinical Significance in First-Episode Schizophrenia

“… 9 Functional hub nodes, preferentially located in the default mode network (DMN), tend to have higher average controllability. 10 These hub nodes have dense connections with other brain regions, thus can drive the transition of brain states with lower energy input. Modal controllability evaluates the ability of nodes to drive shifts into difficult-to-reach brain states.…”

Upgrading Voxel-wise Encoding Model via Integrated Integration over Features and Brain Networks

“…23,24,26,27 However, two important challenges have limited the prediction performance of these models. First, the brain is an interconnected network with different areas dynamically reconfigured and involved in different modules during cognitive tasks, [28][29][30][31][32] while the prevalent voxel-wise encoding models treat each voxel static and independently. Second, by using pretrained task optimized DNN models, it is often assumed that there is a single optimal set of representation features aligned with a specific neural population along the network hierarchy.…”