Macroscopic resting-state brain dynamics are best described by linear models.

It is typically assumed that large networks of neurons exhibit a large repertoire of nonlinear behaviours. Here we challenge this assumption by leveraging mathematical models derived from measurements of local field potentials via intracranial electroencephalography and of whole-brain blood-oxygen-level-dependent brain activity via functional magnetic resonance imaging. We used state-of-the-art linear and nonlinear families of models to describe spontaneous resting-state activity of 700 participants in the Human Connectome Project and 122 participants in the Restoring Active Memory project. We found that linear autoregressive models provide the best fit across both data types and three performance metrics: predictive power, computational complexity and the extent of the residual dynamics unexplained by the model. To explain this observation, we show that microscopic nonlinear dynamics can be counteracted or masked by four factors associated with macroscopic dynamics: averaging over space and over time, which are inherent to aggregated macroscopic brain activity, and observation noise and limited data samples, which stem from technological limitations. We therefore argue that easier-to-interpret linear models can faithfully describe macroscopic brain dynamics during resting-state conditions.

Models of communication and control for brain networks: distinctions, convergence, and future outlook.

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

Model-based design for seizure control by stimulation.

OBJECTIVE: Current brain stimulation paradigms are largely empirical rather than theoretical. An opportunity exists to improve upon their modest effectiveness in closed-loop control strategies with the development of theoretically grounded, model-based designs. APPROACH: Inspired by this need, here we couple experimental data and mathematical modeling with a control-theoretic strategy for seizure termination. We begin by exercising a dynamical systems approach to model seizures (n = 94) recorded using intracranial EEG (iEEG) from 21 patients with medication-resistant, localization-related epilepsy. MAIN RESULTS: Although each patient's seizures displayed unique spatial and temporal patterns, their evolution can be parsimoniously characterized by the same model form. Idiosyncracies of the model can inform individualized intervention strategies, specifically in iEEG samples with well-localized seizure onset zones. Temporal fluctuations in the spatial profiles of the oscillatory modes show that seizure onset marks a transition into a regime in which the underlying system supports prolonged rhythmic and focal activity. Based on these observations, we propose a control-theoretic strategy that aims to stabilize ictal activity using static output feedback for linear time-invariant switching systems. Finally, we demonstrate in silico that our proposed strategy allows us to dampen the emerging focal oscillatory sources using only a small set of electrodes. SIGNIFICANCE: Our integrative study informs the development of modulation and control algorithms for neurostimulation that could improve the effectiveness of implantable, closed-loop anti-epileptic devices.

Spectral mapping of brain functional connectivity from diffusion imaging.

Understanding the relationship between the dynamics of neural processes and the anatomical substrate of the brain is a central question in neuroscience. On the one hand, modern neuroimaging technologies, such as diffusion tensor imaging, can be used to construct structural graphs representing the architecture of white matter streamlines linking cortical and subcortical structures. On the other hand, temporal patterns of neural activity can be used to construct functional graphs representing temporal correlations between brain regions. Although some studies provide evidence that whole-brain functional connectivity is shaped by the underlying anatomy, the observed relationship between function and structure is weak, and the rules by which anatomy constrains brain dynamics remain elusive. In this article, we introduce a methodology to map the functional connectivity of a subject at rest from his or her structural graph. Using our methodology, we are able to systematically account for the role of structural walks in the formation of functional correlations. Furthermore, in our empirical evaluations, we observe that the eigenmodes of the mapped functional connectivity are associated with activity patterns associated with different cognitive systems.

Trade-offs between driving nodes and time-to-control in complex networks.

Recent advances in control theory provide us with efficient tools to determine the minimum number of driving (or driven) nodes to steer a complex network towards a desired state. Furthermore, we often need to do it within a given time window, so it is of practical importance to understand the trade-offs between the minimum number of driving/driven nodes and the minimum time required to reach a desired state. Therefore, we introduce the notion of actuation spectrum to capture such trade-offs, which we used to find that in many complex networks only a small fraction of driving (or driven) nodes is required to steer the network to a desired state within a relatively small time window. Furthermore, our empirical studies reveal that, even though synthetic network models are designed to present structural properties similar to those observed in real networks, their actuation spectra can be dramatically different. Thus, it supports the need to develop new synthetic network models able to replicate controllability properties of real-world networks.