Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Applied Mathematics

First Advisor

Danielle S. Bassett


The brain is a complex system with complicated structures and entangled dynamics. Among the various approaches to investigating the brain's mechanics, the graphical method provides a successful framework for understanding the topology of both the

structural and functional networks, and discovering efficient diagnostic biomarkers for cognitive behaviors, brain disorders and diseases. Yet it cannot explain how the structure affects the functionality and how the brain tunes its transition among multiple states to manipulate the cognitive control. In my dissertation, I propose a novel framework of modeling the mechanics of the cognitive control, which involves in applying control theory to analyzing the brain networks and conceptually connecting the cognitive control with the engineering control. First, I examine the energy distribution among different states via combining the energetic and structural constraints of the brain's state transition in a free energy model, where the interaction between regions is explicitly informed by structural connectivity. This work enables the possibility of achieving a whole view of the brain's energy landscape and preliminarily indicates the feasibility of control theory to model the dynamics of cognitive control. In the following work, I exploit the network control theory to address two questions about how the large-scale circuitry of the human brain constrains its dynamics. First, is the human brain theoretically controllable? Second, which areas of the brain are most influential in constraining or facilitating changes in brain state trajectories? Further, I seek to examine the structural effect on the control actions through solving the optimal control problem under different boundary conditions. I quantify the efficiency of regions in terms of the energy cost for the brain state transition from the default mode to task modes. This analysis is extended to the perturbation analysis of trajectories and is applied to the comparison between the group with mild traumatic brain injury(mTBI) and the healthy group. My research is the first to demonstrate how control theory can be used to analyze human brain networks.

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