The discovery of resting-state networks shifted the focus from the role of local regions in cognitive tasks to the ongoing spontaneous dynamics in global networks. Recently, efforts have been invested to reduce the complexity of brain activity recordings through the application of nonlinear dimensionality reduction algorithms. Here, we investigate how the interaction between these networks emerges as an organising principle in human cognition. We combine deep variational autoencoders with computational modelling to construct a dynamical model of brain networks fitted to the whole-brain dynamics measured with functional magnetic resonance imaging (fMRI). Crucially, this allows us to infer the interaction between these networks in resting state and seven different cognitive tasks by determining the effective functional connectivity between networks. We found a high flexible reconfiguration of task-driven network interaction patterns and we demonstrate that it can be used to classify different cognitive tasks. Importantly, compared with using all the nodes in a parcellation, we obtain better results by modelling the dynamics of interacting networks in both model and classification performance. These findings show the key causal role of manifolds as a fundamental organising principle of brain function, providing evidence that interacting networks are the computational engines’ brain during cognitive tasks. Author Summary The discovery of resting-state networks has greatly influenced the investigation of brain functioning, shifting the focus from local regions involved in cognitive tasks to the ongoing spontaneous dynamics in global networks. This research goes beyond that shift and proposes investigating how human cognition is shaped by the interactions between whole-brain networks embedded in a low-dimensional manifold space. To achieve this, a combination of deep variational autoencoders with computational modelling is used to construct a dynamic model of brain networks, fitted to whole-brain dynamics measured with functional magnetic resonance imaging (fMRI). The results show that during cognitive tasks, highly flexible reconfigurations of task-driven network interaction patterns occur, and these patterns, in turn, can be used to accurately classify different cognitive tasks. Importantly, using this low-dimensional whole-brain network model provides significantly better results than working in the conventional brain space.

Networks in neuroscience determine how brain function unfolds, and their perturbations lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual, particle-wave, perspective, integrate time delays due to finite transmission speeds, and derive a normalization of the connectome. When applied to the database of the Human Connectome Project, it explains the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects ( N = 100) and are a fundamental network property within the wave picture. The normalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms. These two perspectives are orthogonal, but not incommensurable, when understood within the novel, here-proposed, generalized framework of structural connectivity. Author Summary All networks are composed of nodes and links, forming the structural frame, in which communication occurs. We demonstrate that graph theoretical tools make the implicit assumption of information transmission via exchange of bits, suggesting that the stronger connected nodes have greater impact upon the remainder of the network. This corollary does not extend to communication via oscillations, which is the prominent information carrier in brain networks. We extend traditional network analysis to the oscillatory domain and derive a novel network normalization complete with descriptive metrics. Along the prototypical example of the brain as a network, we illustrate the consequences of this novel approach and demonstrate that the normalization robustly explains the emergence of the prominent frequency-specific network cores, which cannot be understood within the traditional framework.

Resting-state functional networks such as the default mode network (DMN) dominate spontaneous brain dynamics. To date, the mechanisms linking brain structure and brain dynamics and functions in cognition, perception, and action remain unknown, mainly due to the uncontrolled and erratic nature of the resting state. Here we used a stimulation paradigm to probe the brain’s resting behavior, providing insights on state-space stability and multiplicity of network trajectories after stimulation. We performed explorations on a mouse model to map spatiotemporal brain dynamics as a function of the stimulation site. We demonstrated the emergence of known functional networks in brain responses. Several responses heavily relied on the DMN and were suggestive of the DMN playing a mechanistic role between functional networks. We probed the simulated brain responses to the stimulation of regions along the information processing chains of sensory systems from periphery up to primary sensory cortices. Moreover, we compared simulated dynamics against in vivo brain responses to optogenetic stimulation. Our results underwrite the importance of anatomical connectivity in the functional organization of brain networks and demonstrate how functionally differentiated information processing chains arise from the same system. Author Summary We demonstrate how functionally differentiated information processing chains arise from the same anatomical network. The main result of the in-silico mouse brain simulations is the emergence of specific functional networks based on structural data from the mouse brain. When the brain is stimulated, for example, by sensory inputs or direct electrical stimulation, the brain initially responds with activities in specific regions. The brain’s anatomical connectivity constrains the subsequent pattern formation. We built a high-resolution mouse brain network model. The model structure originated from experimental data. We systematically explored the mouse model and investigated the simulated brain dynamics after stimulation. Known functional networks emerged in the simulated brain responses. The default mode network occurred in almost all characteristic response patterns. Simulated brain response dynamics and in-vivo response dynamics of the mouse brain to optogenetic stimulation showed similarities even without parameter tuning. Anatomical connectivity and dynamics shape the functional organization of brain networks.

While numerous studies of ephaptic interactions have focused on either axons of peripheral nerves or on cortical structures, no attention has been given to the possibility of ephaptic interactions in white matter tracts. Inspired by the highly organized, tightly packed geometry of axons in fiber pathways, we aim to investigate the potential effects of ephaptic interactions along these structures that are resilient to experimental probing. We use axonal cable theory to derive a minimal model of a sheet of N ephaptically coupled axons. Numerical solutions of the proposed model are explored as ephaptic coupling is varied. We demonstrate that ephaptic interactions can lead to local phase locking between adjacent traveling impulses and that, as coupling is increased, traveling impulses trigger new impulses along adjacent axons, resulting in finite size traveling fronts. For strong enough coupling, impulses propagate laterally and backwards, resulting in complex spatiotemporal patterns. While common large-scale brain network models often model fiber pathways as simple relays of signals between different brain regions, our work calls for a closer reexamination of the validity of such a view. The results suggest that in the presence of significant ephaptic interactions, the brain fiber tracts can act as a dynamic active medium. Author Summary Starting from the FitzHugh-Nagumo cable model, we derive a system of nonlinear coupled partial differential equations (PDEs) to model a sheet of N ephaptically coupled axons. We also present a continuous limit approximation transforming the model into a two-dimensional field equation. We numerically solve the equations exploring the dynamics as coupling strength is varied. We observe phase locking of adjacent impulses and coordination of subthreshold dynamics. Strong enough coupling generates complex spatiotemporal patterns as new impulses form traveling fronts propagating laterally and backwards. The transition between different dynamic regimes happens abruptly at critical values of parameter. The results put into question the validity of assuming the role of fiber pathways to be that of mere interneuronal transmission and call for further investigation of the matter.

The purpose of this paper is to describe a framework for the understanding of rules that govern how neural system dynamics are coordinated to produce behavior. The framework, structured flows on manifolds (SFM), posits that neural processes are flows depicting system interactions that occur on relatively low-dimension manifolds, which constrain possible functional configurations. Although this is a general framework, we focus on the application to brain disorders. We first explain the Epileptor, a phenomenological computational model showing fast and slow dynamics, but also a hidden repertoire whose expression is similar to refractory status epilepticus . We suggest that epilepsy represents an innate brain state whose potential may be realized only under certain circumstances. Conversely, deficits from damage or disease processes, such as stroke or dementia, may reflect both the disease process per se and the adaptation of the brain. SFM uniquely captures both scenarios. Finally, we link neuromodulation effects and switches in functional network configurations to fast and slow dynamics that coordinate the expression of SFM in the context of cognition. The tools to measure and model SFM already exist, giving researchers access to the dynamics of neural processes that support the concomitant dynamics of the cognitive and behavioral processes.