Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool from the physical and engineering sciences that can provide insights regarding that relationship; it formalizes the study of how the dynamics of a complex system can arise from its underlying structure of interconnected units. Given the recent use of network control theory in neuroscience, it is now timely to offer a practical guide to methodological considerations in the controllability of structural brain networks. Here we provide a systematic overview of the framework, examine the impact of modeling choices on frequently studied control metrics, and suggest potentially useful theoretical extensions. We ground our discussions, numerical demonstrations, and theoretical advances in a dataset of high-resolution diffusion imaging with 730 diffusion directions acquired over approximately 1 hour of scanning from ten healthy young adults. Following a didactic introduction of the theory, we probe how a selection of modeling choices affects four common statistics: average controllability, modal controllability, minimum control energy, and optimal control energy. Next, we extend the current state of the art in two ways: first, by developing an alternative measure of structural connectivity that accounts for radial propagation of activity through abutting tissue, and second, by defining a complementary metric quantifying the complexity of the energy landscape of a system. We close with specific modeling recommendations and a discussion of methodological constraints. Our hope is that this accessible account will inspire the neuroimaging community to more fully exploit the potential of network control theory in tackling pressing questions in cognitive, developmental, and clinical neuroscience.Recent advances in network control theory offer a formal means to study how the temporal dynamics of a complex system emerges from its underlying network structure [9][10][11]. Applying this theory to the brain requires that one first builds a network model in which brain regions (nodes) are anatomically connected to one another (edges) [12,13]. The state of the brain network system is then reflected in the pattern of neurophysiological activity across network nodes, and state trajectories represent the temporal sequence of brain states that the system traverses [14,15]. With definitions of the network and its state in hand, we can consider the problem of network controllability, which in essence amounts to asking how the system can be driven to specific target states by means of internal or external control input [16]. In the context of the brain, such input can intuitively take the form of electrical stimulation [17-21], task modulation [22][23][24], or other perturbations from the world or from different portions of the body [25,26]. Practically, network control theory and its associated toolkit e...

SUMMARY Optimizing direct electrical stimulation for the treatment of neurological disease remains difficult due to an incomplete understanding of its physical propagation through brain tissue. Here, we use network control theory to predict how stimulation spreads through white matter to influence spatially distributed dynamics. We test the theory’s predictions using a unique dataset comprising diffusion weighted imaging and electrocorticography in epilepsy patients undergoing grid stimulation. We find statistically significant shared variance between the predicted activity state transitions and the observed activity state transitions. We then use an optimal control framework to posit testable hypotheses regarding which brain states and structural properties will efficiently improve memory encoding when stimulated. Our work quantifies the role that white matter architecture plays in guiding the dynamics of direct electrical stimulation and offers empirical support for the utility of network control theory in explaining the brain’s response to stimulation.

Discrimination against racial and ethnic minority groups exists in the academy, and the associated biases impact hiring and promotion, publication rates, grant funding, and awards. Precisely how racial and ethnic bias impacts the manner in which the scientific community engages with the ideas of academics in minority groups has yet to be fully elucidated. Citations are a marker of such community engagement, as well as a currency used to attain career milestones. Here we assess the extent and drivers of racial and ethnic imbalance in the reference lists of papers published in five top neuroscience journals over the last 25 years. We find that reference lists tend to include more papers with a White person as first and last author than would be expected if race and ethnicity were unrelated to referencing. We show that this imbalance is driven largely by the citation practices of White authors, and is increasing over time even as the field diversifies. To further explain our findings, we examine co-authorship networks and find that while the network has become markedly more integrated in general, the current degree of segregation by race/ethnicity is greater now than it has been in the past. Citing further from oneself on the network is associated with greater balance, but White authors' preferential citation of White authors remains even at high levels of network exploration. We also quantify the effects of intersecting identities, determining the relative costs of gender and race/ethnicity, and their combination in women of color. Our findings represent a call to scientists and journal editors of all disciplines to consider the ethics of citation practices, and actions to be taken in support of an equitable future.

Executive function develops during adolescence, yet it remains unknown how structural brain networks mature to facilitate activation of the fronto-parietal system, which is critical for executive function. In a sample of 946 human youths (ages 8-23y) who completed diffusion imaging, we capitalized upon recent advances in linear dynamical network control theory to calculate the energetic cost necessary to activate the fronto-parietal system through the control of multiple brain regions given existing structural network topology. We found that the energy required to activate the fronto-parietal system declined with development, and the pattern of regional energetic cost predicts unseen individuals’ brain maturity. Finally, energetic requirements of the cingulate cortex were negatively correlated with executive performance, and partially mediated the development of executive performance with age. Our results reveal a mechanism by which structural networks develop during adolescence to reduce the theoretical energetic costs of transitions to activation states necessary for executive function.

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Network control theory is increasingly used to profile the brain’s energy landscape via simulations of neural dynamics. This approach estimates the control energy required to simulate the activation of brain circuits based on structural connectome measured using diffusion magnetic resonance imaging, thereby quantifying those circuits’ energetic efficiency. The biological basis of control energy, however, remains unknown, hampering its further application. To fill this gap, investigating temporal lobe epilepsy as a lesion model, we show that patients require higher control energy to activate the limbic network than healthy volunteers, especially ipsilateral to the seizure focus. The energetic imbalance between ipsilateral and contralateral temporolimbic regions is tracked by asymmetric patterns of glucose metabolism measured using positron emission tomography, which, in turn, may be selectively explained by asymmetric gray matter loss as evidenced in the hippocampus. Our investigation provides the first theoretical framework unifying gray matter integrity, metabolism, and energetic generation of neural dynamics.