Formalizing psychological interventions through network control theory.

Despite the growing deployment of network representation to comprehend psychological phenomena, the question of whether and how networks can effectively describe the effects of psychological interventions remains elusive. Network control theory, the engineering study of networked interventions, has recently emerged as a viable methodology to characterize and guide interventions. However, there is a scarcity of empirical studies testing the extent to which it can be useful within a psychological context. In this paper, we investigate a representative psychological intervention experiment, use network control theory to model the intervention and predict its effect. Using this data, we showed that: (1) the observed psychological effect, in terms of sensitivity and specificity, relates to the regional network control theoretic metrics (average and modal controllability), (2) the size of change following intervention negatively correlates with a whole-network topology that quantifies the "ease" of change as described by control theory (control energy), and (3) responses after intervention can be predicted based on formal results from control theory. These insights assert that network control theory has significant potential as a tool for investigating psychological interventions. Drawing on this specific example and the overarching framework of network control theory, we further elaborate on the conceptualization of psychological interventions, methodological considerations, and future directions in this burgeoning field.

Network controllability measures of subnetworks: implications for neurosciences.

Objective:Recent progress in network sciences has made it possible to apply key findings from control theory to the study of networks. Referred to as network control theory, this framework describes how the interactions between interconnected system elements and external energy sources, potentially constrained by different optimality criteria, result in complex network behavior. A typical example is the quantification of the functional role certain brain regions or symptoms play in shaping the temporal dynamics of brain activity or the clinical course of a disease, a property that is quantified in terms of the so-called controllability metrics. Critically though, contrary to the engineering context in which control theory was originally developed, a mathematical understanding of the network nodes and connections in neurosciences cannot be assumed. For instance, in the case of psychological systems such as those studied to understand psychiatric disorders, a potentially large set of related variables are unknown. As such, while the measures offered by network control theory would be mathematically correct, in that they can be calculated with high precision, they could have little translational values with respect to their putative role suggested by controllability metrics. It is therefore critical to understand if and how the controllability metrics estimated over subnetworks would deviate, if access to the complete set of variables, as is common in neurosciences, cannot be taken for granted.Approach:In this paper, we use a host of simulations based on synthetic as well as structural magnetic resonance imaging (MRI) data to study the potential deviation of controllability metrics in sub- compared to the full networks. Specifically, we estimate average- and modal-controllability, two of the most widely used controllability measures in neurosciences, in a large number of settings where we systematically vary network type, network size, and edge density.Main results:We find out, across all network types we test, that average and modal controllability are systematically, over- or underestimated depending on the number of nodes in the sub- and full network and the edge density.Significance:Finally, we provide formal theoretical proof that our observations generalize to any network type and discuss the ramifications of this systematic bias and potential solutions to alleviate the problem.