Emerging Frontiers of Neuroengineering: A Network Science of Brain Connectivity

Abstract

Neuroengineering is faced with unique challenges in repairing or replacing complex neural systems that are composed of many interacting parts. These interactions form intricate patterns over large spatiotemporal scales and produce emergent behaviors that are difficult to predict from individual elements. Network science provides a particularly appropriate framework in which to study and intervene in such systems by treating neural elements (cells, volumes) as nodes in a graph and neural interactions (synapses, white matter tracts) as edges in that graph. Here, we review the emerging discipline of network neuroscience, which uses and develops tools from graph theory to better understand and manipulate neural systems from micro- to macroscales. We present examples of how human brain imaging data are being modeled with network analysis and underscore potential pitfalls. We then highlight current computational and theoretical frontiers and emphasize their utility in informing diagnosis and monitoring, brain-machine interfaces, and brain stimulation. A flexible and rapidly evolving enterprise, network neuroscience provides a set of powerful approaches and fundamental insights that are critical for the neuroengineer's tool kit.

Keywords: control theory; graph theory; network neuroscience; neuroengineering; neuroimaging.

Figure 1

Relational data in biological systems. Repeating genotypic and phenotypic patterns emerge frequently in the study of biological systems. These biological patterns are expressed across multiple scales of granularity. Illustrated here are three different scales of biological elements (behavioral, structural, and genetic) in different animal species, with lines representing conceptual relationships between elements. At the macroscale, we observe behavioral similarities across different species, such as the ability to fly in birds and fruit flies. However, a closer lens on the neurological substrate of this behavior may tell a different story: that mesoscale structural brain architecture differs significantly between birds and fruit flies, and is more similar between insects (e.g., fruit flies and ants) and between mammals (e.g., mice and cats). Despite differences in structural brain architecture, we might find that animals of different species share commonalities in genetic code that manifest similarly in physical attributes. Although differences in each element reveal unique qualities of each individual animal species, examining relational data can provide a more comprehensive view of the functional role of each element ecologically.

Figure 2

Multiscale topology in brain networks. Brain networks express fundamental organizing principles across multiple spatial scales. Brain networks are modeled as a collection of nodes (representing regions of interest with presumably coherent functional responsibilities) and edges (structural connections or functional interactions between brain regions). (a) Node centrality describes the importance of individual nodes in terms of their connectivity relative to other nodes in the network. Nodes with more connections or stronger edges tend to be hubs (red ), whereas nodes with fewer connections tend to be isolated (blue). (b) Clustering coefficient, a measure of connectivity between the neighbors of a node, is another local measure of network topology. Unlike network topologies with strong hubness qualities, as in panel a, networks with strong clustering coefficient demonstrate a high density of triangles that is believed to facilitate local information processing. (c) Modularity is a mesoscale topological property that captures communities of nodes that are tightly connected to one another and weakly connected to nodes in other communities. Modular organization underlies a rich functional specialization within individual communities. Here, nodes of different communities are colored red, blue, or purple. (d ) Networks with core–periphery structure exhibit a set of tightly connected nodes (core, red ) sparsely connected to a set of isolated nodes (periphery, blue). This organization is in stark contrast to the modular organization in panel c. The core–periphery architecture is characteristic of networks that integrate information from isolated regions in a central area.

Figure 3

Constructing connectomes from magnetic resonance imaging (MRI) data. To generate human connectomes with MRI, an anatomic scan delineating gray matter is partitioned into a set of nodes. This scan is combined with either diffusion scans of white matter structural connections or time series of brain activity measured by functional MRI, resulting in a weighted connectivity matrix.

Figure 4

Tools for higher-order interactions from algebraic topology. (a) The human connectome is a complex network architecture that contains both dyadic and higher-order interactions. Graph representations of the human connectome encode only dyadic relationships, leaving higher-order interactions unaccounted for. A natural way in which to encode higher-order interactions is in the language of algebraic topology, which defines building blocks called simplices (176): A 0-simplex is a node, a 1-simplex is an edge between two nodes, a 2-simplex is a filled triangle, and so on. (b) These building blocks enable the description of two distinct structural motifs that are thought to play very different roles in neural computations (178): Cliques, which are all-to-all connected subgraphs, are thought to facilitate integrated computations, and cycles or cavities, which are collections of n-simplices arranged to have an empty geometric boundary, are thought to facilitate segregated codes and computations. (c) Additional tools available to the investigator include filtrations and persistent homology. Filtrations represent weighted simplicial complexes as a series of unweighted simplicial complexes, and can be used to study networks that change over time or display hierarchical structure across edge weights. Filtrations allow one to follow cycles from one complex to another and quantify how long they live (via the number of complexes in which they are consecutively present). Because this is a study of the persistence of a cycle, it is referred to as the persistent homology of the weighted simplicial complex.

Figure 5

Brain network regulation and control can help navigate dynamical states. To accomplish behavioral and cognitive goals, brain networks internally navigate a complex space of dynamical states. Putative brain states may be situated in various peaks and troughs of an energy landscape, requiring the brain to expend metabolic energy to move from the current state to the next state. Within the space of possible dynamical states, there are easily accessible states and harder-to-reach states; in some cases, the accessible states are healthy, whereas in other cases, they may contribute to dysfunction, and similarly for the harder-to-reach states. Two commonly observed control strategies that are quantifiable in brain networks are average control and modal control. In average control, highly central nodes navigate the brain towards easy-to-reach states. In contrast, modal control nodes tend to be isolated brain regions that navigate the brain toward hard-to-reach states that may require additional energy expenditure (185). As a self-regulation mechanism for preventing transitions towards damaging states, the brain may employ cooperative and antagonistic push–pull control strategies (80). In such a framework, the propensity for the brain to transition toward a damaging state might be competitively limited by opposing modal and average controllers whose goal would be to pull the brain toward less damaging states.

Figure 6

Clinical translation of network neuroscience tools. Network neuroscience offers a natural framework for improving tools to diagnose and treat brain network disorders. (a) For drug-resistant epilepsy patients, invasive monitoring of brain activity to localize brain tissue where seizures originate and to plan resective surgery is challenging, because the neural processes generating seizures are poorly understood. Epileptic brain signals, electrical fields produced by the firing of neuron populations, are sensed by electrodes that rest on the surface of the brain, beneath the dura, and are recorded by a digital acquisition system. Shown is a three-dimensional reconstruction of a patient’s brain (red ) with electrodes colocalized ( green) to anatomical features. (b) Recorded brain signals are studied by clinical practitioners to characterize spatial and temporal behavior of the patient’s seizure activity. Each line represents a time-varying voltage fluctuation from each electrode sensor. (c) Inferred functional connections from a single time slice during the patient’s recorded seizure demonstrates rich relationships in neural dynamics between brain regions and are not visually evident in panel b (nodes, blue; strong connections, red links; weak connections, yellow links). Functional connectivity patterns demonstrate strong interactions around the brain regions in which seizures begin and weak projections to the brain regions in which seizures spread. Objective tools in network neuroscience can usher in an era of personalized algorithms capable of mapping epileptic network architecture from neural signals and pinpointing implantable neurostimulation devices to specific brain regions for intervention (79, 80, 192).