Using network control theory to study the dynamics of the structural connectome

Abstract

Network control theory (NCT) is a simple and powerful tool for studying how network topology informs and constrains dynamics. Compared to other structure-function coupling approaches, the strength of NCT lies in its capacity to predict the patterns of external control signals that may alter dynamics in a desired way. We have extensively developed and validated the application of NCT to the human structural connectome. Through these efforts, we have studied (i) how different aspects of connectome topology affect neural dynamics, (ii) whether NCT outputs cohere with empirical data on brain function and stimulation, and (iii) how NCT outputs vary across development and correlate with behavior and mental health symptoms. In this protocol, we introduce a framework for applying NCT to structural connectomes following two main pathways. Our primary pathway focuses on computing the control energy associated with transitioning between specific neural activity states. Our second pathway focuses on computing average controllability, which indexes nodes' general capacity to control dynamics. We also provide recommendations for comparing NCT outputs against null network models. Finally, we support this protocol with a Python-based software package called network control theory for python (https://github.com/BassettLab/nctpy)

The control costs of human brain dynamics

“…Such costs are subject to anatomical constrains imposed by the individual's connectome. In other words, we quantify the effort required in each region to change its current activity to a desired state, with other connected regions also contributing to its change [33,39,60]. To maintain biological plausibility, we set our simulated path to follow an optimal trajectory that balances the energy required to enable a transition with the proximity to the desired target state [33].…”

“…Network control theory is a powerful tool to investigate the emergence of dynamics from the structural scaffold of the brain [60]. Its application in neuroscience has yielded valuable insights, e.g., into individual differences in psychiatric conditions [48,62] or developmental changes in youth [17,80].…”

“…Drawing inspiration from engineering principles, network control theory (NCT) offers a novel perspective on this problem by conceptualizing the brain as a networked control system in order to explain its dynamics [33]. In its most basic form, NCT considers brain dynamics as a composite outcome of a region's connectivity profile and the necessary control inputs to guide neural activity toward a desired state [33,39,60] (Fig. 1a).…”

“…In other words, the changes in brain activity of a particular region are modelled as depending on its connectivity profile and an "activation" that spreads out along such profile, but also spreads in from other regions. Such activation is referred to control input and is fitted to represent an optimal bridge between the brain's current and next state [60]. (b) Before employing a control model, we define what a brain state is, i.e., how maps of brain activity are represented.…”

Altered structural connectivity and functional brain dynamics in individuals with heavy alcohol use

“…We utilized each individual's cluster centroids from Section 2.3 as brain-states to quantify state transition energies using NCT. Transition energy here is defined as the minimum energy input into a network-here, the structural connectomerequired to move from one state to another [14,33,34]. To model neural dynamics, we used a linear time-invariant model:…”