The human brain is a complex system with high metabolic demands and extensive connectivity that requires control to balance energy consumption and functional efficiency over time. How this control is manifested on a whole-brain scale is largely unexplored, particularly what the associated costs are. Using the network control theory, here, we introduce a novel concept, time-averaged control energy (TCE), to quantify the cost of controlling human brain dynamics at rest, as measured from functional and diffusion MRI. Importantly, TCE spatially correlates with oxygen metabolism measures from the positron emission tomography, providing insight into the bioenergetic footing of resting-state control. Examining the temporal dimension of control costs, we find that brain state transitions along a hierarchical axis from sensory to association areas are more efficient in terms of control costs and more frequent within hierarchical groups than between. This inverse correlation between temporal control costs and state visits suggests a mechanism for maintaining functional diversity while minimizing energy expenditure. By unpacking the temporal dimension of control costs, we contribute to the neuroscientific understanding of how the brain governs its functionality while managing energy expenses. Author Summary Understanding how the brain balances functional efficiency with energy conservation is a central question in neuroscience. The network control theory (NCT) views this question from a network perspective where the brain manages signal propagations along its structural connections to transition across desired activity states. Our study thus presents a novel framework based on the NCT to analyze the costs associated with transitioning across resting states, revealing that regions with high control costs on average are also metabolically demanding in terms of oxygen use. Our findings further show that transitions between sensory and association states are infrequent due to high control costs, while transitions within these states are more common. This suggests that the brain employs a mechanism to preserve functional diversity while minimizing energy costs.

A central goal in neuroscience is the development of a comprehensive mapping between structural and functional brain features, which facilitates mechanistic interpretation of brain function. However, the interpretability of structure-function brain models remains limited by a lack of biological detail. Here, we characterize human structural brain networks weighted by multiple white matter microstructural features including total intra-axonal cross-sectional area and myelin content. We report edge-weight-dependent spatial distributions, variance, small-worldness, rich club, hubs, as well as relationships with function, edge length, and myelin. Contrasting networks weighted by the total intra-axonal cross-sectional area and myelin content of white matter tracts, we find opposite relationships with functional connectivity, an edge-length-independent inverse relationship with each other, and the lack of a canonical rich club in myelin-weighted networks. When controlling for edge length, networks weighted by either fractional anisotropy, radial diffusivity, or neurite density show no relationship with whole-brain functional connectivity. We conclude that the co-utilization of structural networks weighted by total intra-axonal cross-sectional area and myelin content could improve our understanding of the mechanisms mediating the structure-function brain relationship. Author Summary For computational network models to provide mechanistic links between brain structure and function, they must be informed by networks in which edge weights quantify structural features relevant to brain function. Here, we characterized several weighted structural networks capturing multiscale features of white matter connectivity including total intra-axonal cross-sectional area and myelin density. We describe these networks in terms of edge weight distribution, variance, and network topology, as well as their relationships with each other, edge length, and function. Overall, these findings support the joint use of structural networks weighted by the total intra-axonal cross-sectional area and myelin content of white matter tracts in structure-function models. This thorough characterization serves as a benchmark for future investigations of weighted structural brain networks.

Parkinson’s disease is a progressive neurodegenerative disorder characterized by accumulation of abnormal isoforms of alpha-synuclein. Alpha-synuclein is proposed to act as a prion in Parkinson’s disease: In its misfolded pathologic state, it favors the misfolding of normal alpha-synuclein molecules, spreads trans-neuronally, and causes neuronal damage as it accumulates. This theory remains controversial. We have previously developed a Susceptible-Infected-Removed (SIR) computational model that simulates the templating, propagation, and toxicity of alpha-synuclein molecules in the brain. In this study, we test this model with longitudinal MRI collected over 4 years from the Parkinson’s Progression Markers Initiative (1,068 T1 MRI scans, 790 Parkinson’s disease scans, and 278 matched control scans). We find that brain deformation progresses in subcortical and cortical regions. The SIR model recapitulates the spatiotemporal distribution of brain atrophy observed in Parkinson’s disease. We show that connectome topology and geometry significantly contribute to model fit. We also show that the spatial expression of two genes implicated in alpha-synuclein synthesis and clearance, SNCA and GBA , also influences the atrophy pattern. We conclude that the progression of atrophy in Parkinson’s disease is consistent with the prion-like hypothesis and that the SIR model is a promising tool to investigate multifactorial neurodegenerative diseases over time. Author Summary It has been suggested that neurodegenerative diseases are caused by abnormal generation, propagation, and accumulation of neurotoxic protein isoforms. In the case of Parkinson’s disease, the culprit is alpha-synuclein, which has been shown in animal models to exhibit prion-like properties. We devised a Susceptible-Infected-Removed agent-based model of synucleinopathy, in which we simulate the fates of normal and misfolded alpha-synuclein molecules moving along a brain network. We show that the progression of brain atrophy in Parkinson’s disease over the first 2 years following diagnosis can be simulated by our model. We conclude that the pattern of brain atrophy in Parkinson’s disease is shaped by a combination of the connectome and regional expression of genes that control the clearance and synthesis of alpha-synuclein. Our work supports the prion-like model of neurodegeneration in Parkinson’s disease.

Systematic changes have been observed in the functional architecture of the human brain with advancing age. However, functional connectivity (FC) is also a powerful feature to detect unique “connectome fingerprints,” allowing identification of individuals among their peers. Although fingerprinting has been robustly observed in samples of young adults, the reliability of this approach has not been demonstrated across the lifespan. We applied the fingerprinting framework to the Cambridge Centre for Ageing and Neuroscience cohort ( n = 483 aged 18 to 89 years). We found that individuals are “fingerprintable” (i.e., identifiable) across independent functional MRI scans throughout the lifespan. We observed a U-shape distribution in the strength of “self-identifiability” (within-individual correlation across modalities), and “others-identifiability” (between-individual correlation across modalities), with a decrease from early adulthood into middle age, before improving in older age. FC edges contributing to self-identifiability were not restricted to specific brain networks and were different between individuals across the lifespan sample. Self-identifiability was additionally associated with regional brain volume. These findings indicate that individual participant-level identification is preserved across the lifespan despite the fact that its components are changing nonlinearly. Author Summary Important interindividual differences are increasingly identified in functional connectivity studies. However, most of the work to date has focused on samples of younger adults, ignoring older individuals in which brains undergo significant transformation. Here, we examine individual-level patterns of functional connectivity—that is, connectome fingerprints—across the adult lifespan. Our results suggest that connectome fingerprints can reliably predict individuals from independent brain scans across the lifespan. Additionally, regions contributing to fingerprints differed from person to person, emphasizing the extent of interindividual differences in the brain. Specific patterns of brain volume, associated with normative age-related atrophy, may impact the identification of individual-specific functional connectivity patterns. Our findings highlight the importance of interindividual variability in functional connectivity, regardless of participant age, when assessing individual differences in brain function.

Applications of graph theory to the connectome have inspired several models of how neural signaling unfolds atop its structure. Analytic measures derived from these communication models have mainly been used to extract global characteristics of brain networks, obscuring potentially informative inter-regional relationships. Here we develop a simple standardization method to investigate polysynaptic communication pathways between pairs of cortical regions. This procedure allows us to determine which pairs of nodes are topologically closer and which are further than expected on the basis of their degree. We find that communication pathways delineate canonical functional systems. Relating nodal communication capacity to meta-analytic probabilistic patterns of functional specialization, we also show that areas that are most closely integrated within the network are associated with higher order cognitive functions. We find that these regions’ proclivity towards functional integration could naturally arise from the brain’s anatomical configuration through evenly distributed connections among multiple specialized communities. Throughout, we consider two increasingly constrained null models to disentangle the effects of the network’s topology from those passively endowed by spatial embedding. Altogether, the present findings uncover relationships between polysynaptic communication pathways and the brain’s functional organization across multiple topological levels of analysis and demonstrate that network integration facilitates cognitive integration. Author Summary Several mathematical models describe how neural signaling unfolds atop the structure of the brain. These communication models have mainly been used to characterize brain networks at a global scale. Here, using a simple standardization procedure, we benchmark inter-regional measures of communication capacity to determine which pairs of brain regions show a higher or lower propensity to communicate than expected by chance. We identify relationships between communication pathways and the brain’s functional organization across multiple network levels and show that network integration facilitates cognitive integration. Throughout, we consider the effect of spatial proximity on inter-regional communication relationships.

The brain’s structural connectivity supports the propagation of electrical impulses, manifesting as patterns of coactivation, termed functional connectivity. Functional connectivity emerges from the underlying sparse structural connections, particularly through polysynaptic communication. As a result, functional connections between brain regions without direct structural links are numerous, but their organization is not completely understood. Here we investigate the organization of functional connections without direct structural links. We develop a simple, data-driven method to benchmark functional connections with respect to their underlying structural and geometric embedding. We then use this method to reweigh and reexpress functional connectivity. We find evidence of unexpectedly strong functional connectivity among distal brain regions and within the default mode network. We also find unexpectedly strong functional connectivity at the apex of the unimodal-transmodal hierarchy. Our results suggest that both phenomena—functional modules and functional hierarchies—emerge from functional interactions that transcend the underlying structure and geometry. These findings also potentially explain recent reports that structural and functional connectivity gradually diverge in transmodal cortex. Collectively, we show how structural connectivity and geometry can be used as a natural frame of reference with which to study functional connectivity patterns in the brain. Author Summary The structural connectivity of the brain supports interregional signaling, manifesting as highly organized patterns of functional connectivity. Importantly, structural and functional connectivity are fundamentally constrained by the spatial embedding of brain regions, such that proximal regions are more likely to exhibit stronger connectivity. Here we develop a simple method that uses robust relationships between geometry, structure, and function as the baseline to reweigh and reexpress functional connectivity. We use the method to identify functional connections that are greater than expected given their structural and geometric embedding. We then show that the arrangement of these connections systematically follows the functional modules and the putative unimodal-transmodal hierarchy of the brain. Collectively, our findings demonstrate highly organized patterns of polysynaptic functional connections that support the emergence of canonical features of functional connectivity networks, including modules and hierarchies.

The brain is a frustrated system that contains conflictual link arrangements named frustration. The frustration as a source of disorder prevents the system from settling into low-energy states and provides flexibility for brain network organization. In this research, we tried to identify the pattern of frustration formation in the brain at the levels of region, connection, canonical network, and hemisphere. We found that frustration formation has no uniform pattern. Some subcortical elements have an active role in frustration formation, despite low contributions from many cortical elements. Frustrating connections are mostly between-network connections, and triadic frustrations are mainly formed between three regions from three distinct canonical networks. We did not find any significant differences between brain hemispheres or any robust differences between the frustration formation patterns of various life-span stages. Our results may be interesting for those who study the organization of brain links and promising for those who want to manipulate brain networks. Author Summary Brain network analysis approaches commonly ignore the signs of links. Frustration is a fascinating phenomenon referring to the conflictual arrangements of signed links. As a source of instability, it can give valuable information on altering components of a network. It can specify which brain network elements intend to drive brain network alterations. Accordingly, we tried to identify the pattern of frustration formation in the brain network, which brain network elements are more frustrated and which ones are less frustrated. We provided some maps for frustration formation in the levels of region, connection, canonical network, and hemisphere. The introduced concept of frustration and our results may be interesting for brain network scientists.

Myelin plays a crucial role in how well information travels between brain regions. Complementing the structural connectome, obtained with diffusion MRI tractography, with a myelin-sensitive measure could result in a more complete model of structural brain connectivity and give better insight into white-matter myeloarchitecture. In this work we weight the connectome by the longitudinal relaxation rate (R1), a measure sensitive to myelin, and then we assess its added value by comparing it with connectomes weighted by the number of streamlines (NOS). Our analysis reveals differences between the two connectomes both in the distribution of their weights and the modular organization. Additionally, the rank-based analysis shows that R1 can be used to separate transmodal regions (responsible for higher-order functions) from unimodal regions (responsible for low-order functions). Overall, the R1-weighted connectome provides a different perspective on structural connectivity taking into account white matter myeloarchitecture. Author Summary In the present work, we show that by using a myelin-sensitive measure we can complement the diffusion MRI-based connectivity and provide a different picture of the brain organization. We show that the R1-weighted average distribution does not follow the same trend as the number of streamlines strength distribution, and the two connectomes exhibit different modular organization. We also show that unimodal cortical regions tend to be connected by more streamlines, but the connections exhibit a lower R1-weighted average, while the transmodal regions have higher R1-weighted average but fewer streamlines. This could imply that the unimodal regions require more connections with lower myelination, whereas the transmodal regions rely on connections with higher myelination.

The brain is a complex network of interconnected and interacting neuronal populations. Global efforts to understand the emergence of behavior and the effect of perturbations depend on accurate reconstruction of white matter pathways, both in humans and in model organisms. An emerging animal model for next-generation applied neuroscience is the common marmoset ( Callithrix jacchus ). A recent open respository of retrograde and anterograde tract tracing presents an opportunity to systematically study the network architecture of the marmoset brain (Marmoset Brain Architecture Project; http://www.marmosetbrain.org ). Here we comprehensively chart the topological organization of the mesoscale marmoset cortico-cortical connectome. The network possesses multiple nonrandom attributes that promote a balance between segregation and integration, including near-minimal path length, multiscale community structure, a connective core, a unique motif composition, and multiple cavities. Altogether, these structural attributes suggest a link between network architecture and function. Our findings are consistent with previous reports across a range of species, scales, and reconstruction technologies, suggesting a small set of organizational principles universal across phylogeny. Collectively, these results provide a foundation for future anatomical, functional, and behavioral studies in this model organism. Author Summary Emerging research points to network connectivity as a fundamental feature of brains, influencing interregional signaling, cognition, and behavior. Global efforts are under way to map, image, and trace cellular connection patterns in humans and in a variety of model organisms. The common marmoset is increasingly becoming the most used nonhuman primate model for neuroimaging, genomics, and behavioral research. Here we provide a comprehensive characterization of the marmoset brain connectome using a recently published cortico-cortical tract tracing atlas. We find evidence of nonrandom organization across multiple scales, including near-minimal path length, multiscale community structure, densely interconnected hubs, a unique motif fingerprint, and the existence of topological cavities. Collectively, these features suggest that the network is configured to support the coexistence of segregation and integration of information.

Communication models describe the flow of signals among nodes of a network. In neural systems, communication models are increasingly applied to investigate network dynamics across the whole brain, with the ultimate aim to understand how signal flow gives rise to brain function. Communication models range from diffusion-like processes to those related to infectious disease transmission and those inspired by engineered communication systems like the internet. This Focus Feature brings together novel investigations of a diverse range of mechanisms and strategies that could shape communication in mammal whole-brain networks.

Author Summary In the present report we asked how signals travel on brain networks and what types of nodes they potentially visit en route. We traced individual path motifs to investigate the propensity of communication paths to explore the putative unimodal-transmodal cortical hierarchy. We find that the architecture of the network promotes signaling via the hierarchy, suggesting a link between the structure and function of the network. Importantly, we also find instances where detours are promoted, particularly as paths traverse attention-related networks. Finally, information about hierarchical position aids navigation in some parts of the network, over and above spatial location. Altogether, the present results touch on several emerging themes in network neuroscience, including the nature of structure-function relationships, network communication and the role of cortical hierarchies. Abstract The wiring of the brain is organized around a putative unimodal-transmodal hierarchy. Here we investigate how this intrinsic hierarchical organization of the brain shapes the transmission of information among regions. The hierarchical positioning of individual regions was quantified by applying diffusion map embedding to resting-state functional MRI networks. Structural networks were reconstructed from diffusion spectrum imaging and topological shortest paths among all brain regions were computed. Sequences of nodes encountered along a path were then labeled by their hierarchical position, tracing out path motifs. We find that the cortical hierarchy guides communication in the network. Specifically, nodes are more likely to forward signals to nodes closer in the hierarchy and cover a range of unimodal and transmodal regions, potentially enriching or diversifying signals en route. We also find evidence of systematic detours, particularly in attention networks, where communication is rerouted. Altogether, the present work highlights how the cortical hierarchy shapes signal exchange and imparts behaviorally relevant communication patterns in brain networks.

Author Summary Sparse structural connectivity data from many subjects can be succinctly represented using appropriate averaging procedures. We show, however, that several popular procedures for doing so generate group-averaged networks with statistics that are dissimilar from the subject-level networks they are intended to represent. These dissimilarities, we argue, arise from the over- and underexpression of short-range and long-distance connections, respectively, in the group-averaged matrix. We present a distance-dependent thresholding procedure that preserves connection length distributions and consequently better matches subject-level networks and their statistics. These findings inform data-driven exploratory analyses of connectomes. Abstract Large-scale structural brain networks encode white matter connectivity patterns among distributed brain areas. These connection patterns are believed to support cognitive processes and, when compromised, can lead to neurocognitive deficits and maladaptive behavior. A powerful approach for studying the organizing principles of brain networks is to construct group-representative networks from multisubject cohorts. Doing so amplifies signal to noise ratios and provides a clearer picture of brain network organization. Here, we show that current approaches for generating sparse group-representative networks overestimate the proportion of short-range connections present in a network and, as a result, fail to match subject-level networks along a wide range of network statistics. We present an alternative approach that preserves the connection-length distribution of individual subjects. We have used this method in previous papers to generate group-representative networks, though to date its performance has not been appropriately benchmarked and compared against other methods. As a result of this simple modification, the networks generated using this approach successfully recapitulate subject-level properties, outperforming similar approaches by better preserving features that promote integrative brain function rather than segregative. The method developed here holds promise for future studies investigating basic organizational principles and features of large-scale structural brain networks.

The intricate connectivity patterns of neural circuits support a wide repertoire of communication processes and functional interactions. Here we systematically investigate how neural signaling is constrained by anatomical connectivity in the mesoscale Drosophila (fruit fly) brain network. We use a spreading model that describes how local perturbations, such as external stimuli, trigger global signaling cascades that spread through the network. Through a series of simple biological scenarios we demonstrate that anatomical embedding potentiates sensory-motor integration. We find that signal spreading is faster from nodes associated with sensory transduction (sensors) to nodes associated with motor output (effectors). Signal propagation was accelerated if sensor nodes were activated simultaneously, suggesting a topologically mediated synergy among sensors. In addition, the organization of the network increases the likelihood of convergence of multiple cascades towards effector nodes, thereby facilitating integration prior to motor output. Moreover, effector nodes tend to coactivate more frequently than other pairs of nodes, suggesting an anatomically enhanced coordination of motor output. Altogether, our results show that the organization of the mesoscale Drosophila connectome imparts privileged, behaviorally relevant communication patterns among sensors and effectors, shaping their capacity to collectively integrate information. Author Summary The complex network spanned by neurons and their axonal projections promotes a diverse set of functions. In the present report, we study how the topological organization of the fruit fly brain supports sensory-motor integration. Using a simple communication model, we demonstrate that the topology of this network allows efficient coordination among sensory and motor neurons. Our results suggest that brain network organization may profoundly shape the functional repertoire of this simple organism.