Communication dynamics in complex brain networks.

Neuronal signalling and communication underpin virtually all aspects of brain activity and function. Network science approaches to modelling and analysing the dynamics of communication on networks have proved useful for simulating functional brain connectivity and predicting emergent network states. This Review surveys important aspects of communication dynamics in brain networks. We begin by sketching a conceptual framework that views communication dynamics as a necessary link between the empirical domains of structural and functional connectivity. We then consider how different local and global topological attributes of structural networks support potential patterns of network communication, and how the interactions between network topology and dynamic models can provide additional insights and constraints. We end by proposing that communication dynamics may act as potential generative models of effective connectivity and can offer insight into the mechanisms by which brain networks transform and process information.

A spectrum of routing strategies for brain networks.

Communication of signals among nodes in a complex network poses fundamental problems of efficiency and cost. Routing of messages along shortest paths requires global information about the topology, while spreading by diffusion, which operates according to local topological features, is informationally "cheap" but inefficient. We introduce a stochastic model for network communication that combines local and global information about the network topology to generate biased random walks on the network. The model generates a continuous spectrum of dynamics that converge onto shortest-path and random-walk (diffusion) communication processes at the limiting extremes. We implement the model on two cohorts of human connectome networks and investigate the effects of varying the global information bias on the network's communication cost. We identify routing strategies that approach a (highly efficient) shortest-path communication process with a relatively small global information bias on the system's dynamics. Moreover, we show that the cost of routing messages from and to hub nodes varies as a function of the global information bias driving the system's dynamics. Finally, we implement the model to identify individual subject differences from a communication dynamics point of view. The present framework departs from the classical shortest paths vs. diffusion dichotomy, unifying both models under a single family of dynamical processes that differ by the extent to which global information about the network topology influences the routing patterns of neural signals traversing the network.

Age differences in specific neural connections within the Default Mode Network underlie theory of mind.

Theory of mind (i.e., the ability to infer others' mental states) - a fundamental social cognitive ability - declines with increasing age. Prior investigations have focused on identifying task-evoked differences in neural activation that underlie these performance declines. However, these declines could also be related to dysregulation of the baseline, or 'intrinsic', functional connectivity of the brain. If so, age differences in intrinsic connectivity may provide novel insight into the mechanisms that contribute to poorer theory of mind in older adults. To examine this possibility, we assessed younger and older adults' theory of mind while they underwent task-based fMRI, as well as the intrinsic functional connectivity measured during resting-state within the (task-defined) theory of mind network. Older adults exhibited poorer theory of mind behavioral performance and weaker intrinsic connectivity within this network compared to younger adults. Intrinsic connectivity between the right temporoparietal junction and the right temporal pole mediated age differences in theory of mind. Specifically, older adults had weaker intrinsic connectivity between right temporoparietal junction and right temporal pole that explained their poorer theory of mind behavioral performance. These findings broaden our understanding of aging and social cognition and reveal more specific mechanisms of how aging impacts theory of mind.

Spatiotemporal Network Markers of Individual Variability in the Human Functional Connectome.

Functional connectivity (FC) analysis has revealed stable and reproducible features of brain network organization, as well as their variations across individuals. Here, we localize network markers of individual variability in FC and track their dynamical expression across time. First, we determine the minimal set of network components required to identify individual subjects. Among specific resting-state networks, we find that the FC pattern of the frontoparietal network allows for the most reliable identification of individuals. Looking across the whole brain, an optimization approach designed to identify a minimal node set converges on distributed portions of the frontoparietal system. Second, we track the expression of these network markers across time. We find that the FC fingerprint is most clearly expressed at times when FC patterns exhibit low modularity. In summary, our study reveals distributed network markers of individual variability that are localized in both space and time.

Resting-brain functional connectivity predicted by analytic measures of network communication.

The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structural connectivity of the human brain and explore the capacity of these measures to predict resting-state functional connectivity across three independently acquired datasets. We focus on the layout of shortest paths across the network and on two communication measures--search information and path transitivity--which account for how these paths are embedded in the rest of the network. Search information is an existing measure of information needed to access or trace shortest paths; we introduce path transitivity to measure the density of local detours along the shortest path. We find that both search information and path transitivity predict the strength of functional connectivity among both connected and unconnected node pairs. They do so at levels that match or significantly exceed path length measures, Euclidean distance, as well as computational models of neural dynamics. This capacity suggests that dynamic couplings due to interactions among neural elements in brain networks are substantially influenced by the broader network context adjacent to the shortest communication pathways.

Generative models of the human connectome.

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to different wiring rules combining geometric and a broad range of topological factors. We find that a combination of geometric constraints with a homophilic attachment mechanism can create synthetic networks that closely match many topological characteristics of individual human connectomes, including features that were not included in the optimization of the generative model itself. We use these models to investigate a lifespan dataset and show that, with age, the model parameters undergo progressive changes, suggesting a rebalancing of the generative factors underlying the connectome across the lifespan.

Greater ventral striatal functional connectivity in cigarette smokers relative to non-smokers across a spectrum of alcohol consumption.

Cigarette smoking is associated with elevated risk of disease and mortality and contributes to heavy healthcare-related economic burdens. The nucleus accumbens is implicated in numerous reward-related behaviors, including reinforcement learning and incentive salience. The established functional connectivity of the accumbens includes regions associated with motivation, valuation, and affective processing. Although the high comorbidity of cigarette smoking with drinking behaviors may collectively affect brain activity, there could be independent effects of smoking in alcohol use disorder that impact brain function and behavior. We hypothesized that smoking status, independent of alcohol use, would be associated with aberrations of nucleus accumbens functional connectivity to brain regions that facilitate reward processing, salience attribution, and inhibitory control. Resting state functional magnetic resonance imaging data from thirty-one nonsmokers and nineteen smoking individuals were analyzed using seed-based correlations of the bilateral accumbens with all other brain voxels. Statistical models accounted for drinks consumed per week. The smoking group demonstrated significantly higher functional connectivity between the left accumbens and the bilateral insula and anterior cingulate cortex, as well as hyperconnectivity between the right accumbens and the insula. Confirmatory analyses using the insula and cingulate clusters generated from the original analysis as seed regions reproduced the hyperconnectivity in smokers between the bilateral insular regions and the accumbens. In conclusion, smoking status had distinct effects on neural activity; hyperconnectivity between the accumbens and insula in smokers may reflect enhanced encoding of the reinforcing effects of smoking and greater orientation toward smoking-associated stimuli.

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility.

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the gray matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9-0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease-course longitudinal studies.

Editorial: Network Communication in the Brain.

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.

Resting state network modularity along the prodromal late onset Alzheimer's disease continuum.

Alzheimer's disease is considered a disconnection syndrome, motivating the use of brain network measures to detect changes in whole-brain resting state functional connectivity (FC). We investigated changes in FC within and among resting state networks (RSN) across four different stages in the Alzheimer's disease continuum. FC changes were examined in two independent cohorts of individuals (84 and 58 individuals, respectively) each comprising control, subjective cognitive decline, mild cognitive impairment and Alzheimer's dementia groups. For each participant, FC was computed as a matrix of Pearson correlations between pairs of time series from 278 gray matter brain regions. We determined significant differences in FC modular organization with two distinct approaches, network contingency analysis and multiresolution consensus clustering. Network contingency analysis identified RSN sub-blocks that differed significantly across clinical groups. Multiresolution consensus clustering identified differences in the stability of modules across multiple spatial scales. Significant modules were further tested for statistical association with memory and executive function cognitive domain scores. Across both analytic approaches and in both participant cohorts, the findings converged on a pattern of FC that varied systematically with diagnosis within the frontoparietal network (FP) and between the FP network and default mode network (DMN). Disturbances of modular organization were manifest as greater internal coherence of the FP network and stronger coupling between FP and DMN, resulting in less segregation of these two networks. Our findings suggest that the pattern of interactions within and between specific RSNs offers new insight into the functional disruption that occurs across the Alzheimer's disease spectrum.

Path ensembles and a tradeoff between communication efficiency and resilience in the human connectome.

Computational analysis of communication efficiency of brain networks often relies on graph-theoretic measures based on the shortest paths between network nodes. Here, we explore a communication scheme that relaxes the assumption that information travels exclusively through optimally short paths. The scheme assumes that communication between a pair of brain regions may take place through a path ensemble comprising the k-shortest paths between those regions. To explore this approach, we map path ensembles in a set of anatomical brain networks derived from diffusion imaging and tractography. We show that while considering optimally short paths excludes a significant fraction of network connections from participating in communication, considering k-shortest path ensembles allows all connections in the network to contribute. Path ensembles enable us to assess the resilience of communication pathways between brain regions, by measuring the number of alternative, disjoint paths within the ensemble, and to compare generalized measures of path length and betweenness centrality to those that result when considering only the single shortest path between node pairs. Furthermore, we find a significant correlation, indicative of a trade-off, between communication efficiency and resilience of communication pathways in structural brain networks. Finally, we use k-shortest path ensembles to demonstrate hemispherical lateralization of efficiency and resilience.

Stochastic resonance at criticality in a network model of the human cortex.

Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good candidate to take advantage of stochastic resonance. In this work, we aim to identify the optimal levels of noise that promote signal transmission through a simple network model of the human brain. Specifically, using a dynamic model implemented on an anatomical brain network (connectome), we investigate the similarity between an input signal and a signal that has traveled across the network while the system is subject to different noise levels. We find that non-zero levels of noise enhance the similarity between the input signal and the signal that has traveled through the system. The optimal noise level is not unique; rather, there is a set of parameter values at which the information is transmitted with greater precision, this set corresponds to the parameter values that place the system in a critical regime. The multiplicity of critical points in our model allows it to adapt to different noise situations and remain at criticality.

Routes Obey Hierarchy in Complex Networks.

The last two decades of network science have discovered stunning similarities in the topological characteristics of real life networks (many biological, social, transportation and organizational networks) on a strong empirical basis. However our knowledge about the operational paths used in these networks is very limited, which prohibits the proper understanding of the principles of their functioning. Today, the most widely adopted hypothesis about the structure of the operational paths is the shortest path assumption. Here we present a striking result that the paths in various networks are significantly stretched compared to their shortest counterparts. Stretch distributions are also found to be extremely similar. This phenomenon is empirically confirmed on four networks from diverse areas of life. We also identify the high-level path selection rules nature seems to use when picking its paths.

Network morphospace.

The structure of complex networks has attracted much attention in recent years. It has been noted that many real-world examples of networked systems share a set of common architectural features. This raises important questions about their origin, for example whether such network attributes reflect common design principles or constraints imposed by selectional forces that have shaped the evolution of network topology. Is it possible to place the many patterns and forms of complex networks into a common space that reveals their relations, and what are the main rules and driving forces that determine which positions in such a space are occupied by systems that have actually evolved? We suggest that these questions can be addressed by combining concepts from two currently relatively unconnected fields. One is theoretical morphology, which has conceptualized the relations between morphological traits defined by mathematical models of biological form. The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems. Here, we explore a new theoretical concept that lies at the intersection between both fields, the 'network morphospace'. Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common 'morphological' characteristics related to aspects of their connectivity. Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.

Using Pareto optimality to explore the topology and dynamics of the human connectome.

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Exploring the morphospace of communication efficiency in complex networks.

Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system's dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network ("routing"), we define analytic measures directed at characterizing network communication when signals flow in a random walk process ("diffusion"). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology.