Network neuroscience is an approach to understanding the structure and function of the human brain through an approach of network science, through the paradigm of graph theory. A network is a connection of many brain regions that interact with each other to give rise to a particular function. Network Neuroscience is a broad field that studies the brain in an integrative way by recording, analyzing, and mapping the brain in various ways. The field studies the brain at multiple scales of analysis to ultimately explain brain systems, behavior, and dysfunction of behavior in psychiatric and neurological diseases. Network neuroscience provides an important theoretical base for understanding neurobiological systems at multiple scales of analysis.
Multiple scales of analysis for the brain
Microscale On the microscale (nanometer to micrometer), network analysis is performed on individual neurons and synapses. Due to the incredible number of neurons in a brain network, it is extremely difficult to construct a complete network at the microscale. Specifically, data collection is too slow to resolve all of the billions of neurons, machine vision tools to annotate the collected data are insufficient, and we lack the mathematical algorithms to properly analyze the resulting networks. Mapping the brain at the cellular level in vertebrates currently requires post-mortem (after death) microscopic analysis of limited portions of brain tissue. Non-optical techniques that rely on high-throughput DNA sequencing have been proposed recently by Anthony Zador (CSHL).
Mesoscale On the mesoscopic scale (micrometer to millimeter), mesoscale analysis seeks to capture anatomically distinct populations of typically 80-120 neurons (e.g. cortical columns) across different brain regions. Mesoscale analysis allows integration of both microscale and macroscale studies, and thus allows multiscale and structural-functional integration. This scale still presents a very ambitious technical challenge at this time and can only be probed on a small scale with invasive techniques or very high field magnetic resonance imaging (MRI) on a local scale.
Macroscale On the macroscale (millimeter), large brain areas can be analyzed for anatomical distinctions, their structure and interactions. The macroscopic scale is best suited for mapping and annotating human connectomes, a comprehensive map of neural connections, with cognitive and behavioral associations since in vivo imaging of the human connectome is only available at the macroscale. Additionally, macroscale analysis permits more compact and comprehensive mapping. Magnetic resonance imaging, functional magnetic resonance imaging (fMRI), and diffusion-weighted magnetic resonance imaging (DW-MRI) are the most popular tools for building macroscale data sets due to their availability and resolution, among fMRI's and dMRI's abilities to parce structural and functional connectivities, respectively.
Mapping brain networks Brain networks can be mapped at multiple scales using both structural connectivity and functional connectivity imaging techniques. Structural descriptions of the components of neuronal networks are described as the connectome.
Structural connectivity Structural connectivity describes how regions in the brain can communicate through anatomical pathways such as synaptic coupling between cells and axonal projections between neurons at the micro-scale and meso-scale and white matter fiber bundles at the macro scale. Diffusion-weighted MRI data is used to measure white-matter bundles.
Functional connectivity Functional connectivity measures the commonality in function between anatomically separated brain regions and is usually measured at the macroscopic level. This commonality of function is inferred from similar activation patterns in imaging techniques such as functional magnetic resonance imaging (fMRI). Many of these fMRI experiments are known as resting-state experiments and measure spontaneous brain activity when the participant is told to relax. Similar (Blood-Oxygen Level Dependent) BOLD signals between different regions represent co-activation between these regions. There are many new methods that have emerged for extracting functional connectivity from fMRI data including Granger causality and dynamic causal modeling (DCM).
Even though fMRI is the preferred method for measuring large-scale functional networks, electroencephalography (EEG) has also shown some progress in measuring resting state functional brain networks. In a simultaneous fMRI-EEG study, a statistically significant correlation was observed between the fMRI data and the EEG data thus showing that EEG can be a new and promising method to measure functional brain networks. The advantage of using EEG over fMRI includes its large temporal resolution.
There are novel methods to study functional connectivity. Polarized Light Imaging (PLI) allows high-resolution quantitative analysis of fiber orientations and can be used to bridge the microscopic and macroscopic levels of analysis. Optogenetic functional MRI (ofMRI) allows selective mapping of brain regions based on genetic markers, anatomic location, and axonal projections. Optogenetics can connect cellular activity with BOLD fMRI signals.
Functional networks differ from structural networks in that they have additional properties not evident by studying the structural network alone. There are new methods using linear algebra such as the eignenmode approach that seek to explain the complicated connection between functional and structural networks.
Analyzing brain networks
Graph theory The utilization of graph theory in neuroscience studies has been actively applied after the discovery of functional brain networks. In graph theory, an N × N adjacency matrix (also called a connection matrix) with the elements of zero or non-zero indicates the absence or presence of a relationship between the vertices of a network with N nodes. By analyzing different metrics from these connection matrices from the network, one can obtain a topological analysis of the desired graph; and this is referred to as the human brain network in the field of neuroscience.
One of the core architectures in brain network models is the "small-world" architecture. It interprets models to be regular networks, while they occasionally experience random activity. In small-world networks, the clustering coefficient (i.e., transitivity) is high, and the average path distance is short. These two characteristics reflect the central maxim in the natural biological process: the balance between minimizing the resource cost and maximizing the flow of information among the network components. Given the complex structure of the human brain, measures that can represent the small-world properties of the brain network are of great importance since it simplifies the systems and becomes decipherable.
Graph theoretical approaches have set up a mathematical framework to model the pairwise communications between elements of a network. In human neuroscience, graph theory is generally applied to either functional or effective connectivity. Graph theory methods, when applied properly, can offer important new insights into the structure and function of networked brain systems, including their architecture, evolution, development, and clinical disorders. It describes meaningful information about the topological architecture of human brain networks, such as small-worldness, modular organization, and highly connected or centralized hubs. For example, in a study hypothesizing that aging processes modulate brain connectivity networks, 170 healthy elderly volunteers were submitted to EEG recordings in order to define age-related normative limits. Graph theory functions were applied to exact low-resolution electromagnetic tomography on cortical sources in order to evaluate the small-world parameter as a representative model of network architecture. It is based on the strength of synchronization in the time-varying oscillatory electromagnetic activity of different brain regions as measured by EEG or MEG.
Key components of network analysis
Key components include:
Node degree, distribution and assortativity The degree of a node is the number of connections that link with the rest of the network, which is one of the fundamental measures for defining the model. The degrees of all the network's nodes form a degree distribution. In random networks, all connections are equally probable, resulting in a Gaussian and symmetrically centered degree distribution. Complex networks generally have non-Gaussian degree distributions. By convention, the degree distributions of scale-free networks follow a power law. Lastly, assortativity is the correlation between the degrees of connected nodes. Positive assortativity indicates that high-degree nodes tend to connect to each other.
Clustering coefficients and motifs The clustering coefficient is a measure of the degree to which each node in a graph tends to cluster together. Random networks have low average clustering whereas complex networks have high clustering (associated with high local efficiency of information transfer and robustness). Interactions between neighboring nodes can also be quantified by counting the occurrence of small motifs of interconnected nodes. The distribution of different motifs in a network provides information about the types of local interactions that the network can support.
Path length and efficiency Path length is the minimum number of edges that must be traversed between two nodes. Random and complex networks have short mean path lengths (high global efficiency of parallel information transfer) whereas regular lattices have long mean path lengths. Efficiency is the inversely related metric related to the path length. It is more actively utilized than the path length due to its easier numerical use and interpretation - for instance, estimating topological distances between elements of disconnected graphs.
Connection density or cost Connection density is the actual number of edges in the graph as a proportion of the total number of possible edges. It is the simplest estimator of the physical cost of a network — for example, the energy or other resource requirements.
Hubs, centrality, and robustness Hubs are nodes with high degree, or high centrality. The centrality of a node measures how many of the shortest paths between all other node pairs in the network pass through it. A node with high centrality is thus crucial to efficient communication. The importance of an individual node to network efficiency can be evaluated by deleting (i.e., lesioning) the certain hubs and estimating the efficiency of that 'lesioned' network. Robustness refers either to the structural integrity of the network following deletion of nodes or edges or to the effects of perturbations on local or global network states.
Modularity Many complex networks consist of a number of modules. There are various algorithms that estimate the modularity of a network, and one of the widely utilized algorithms is based on hierarchical clustering. Each module contains several densely interconnected nodes, and there are relatively few connections between nodes in different modules. Hubs can therefore be described in terms of their roles in this community structure. Provincial hubs are connected mainly to nodes in their own modules, whereas connector hubs are connected to nodes in other modules.
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