Network neuroscience

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.

Multiple scales of analysis for the brain

Microscale

• Microscale - nanometer to micrometer scale.

On the microscale, 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

• Mesoscale - micrometer to millimeter scale.

A brain network measured at the level of hundreds of micrometers is considered to be at the mesoscale. 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

• Macroscale - millimeter to centimeter scale.

A brain network measured at the millimeter scale is considered to be at the macroscale. At the macroscopic scale, 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 in Network Analysis

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.

Key Components of Network Analysis

Node degree, 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.

Models

Dynamic networks

Brain networks are not immutable, static constructs; rather those networks are highly variable based on multiple time scales. Data on time-varying brain graphs generally takes the form of time series (or stacks) of graphs that form an ordered series of snapshots, for example data recorded in the course of learning or across developmental stages. This dynamicity can be represented through tracking the changes in network topology utilizing the graph measures on each time point.

Multilayer networks

The arrival of multi-omic data has enabled the joint analysis of networks between elements of neurobiological systems at different levels of organization. Prime examples are recent studies that combine maps of anatomical and functional networks, as well as studies that combine large-scale brain connectivity data with spatially registered data on patterns of gene expression.

Algebraic topology

Network science is largely built on the tools of graph theory, which focuses on the dyad (a single connection between two nodes) as the fundamental unit of interest. However, recent evidence suggests that sensor networks, technological networks, and even neural networks display higher-order interactions that simply cannot be reduced to pairwise relationships. To address this, network science started to incorporate algebraic topology. Algebraic topology reframes the problem of relational data in terms of simplices or collections of vertices, rather than pairs. IN other words, simplices represent the relational data in terms of collections of vertices: a 0-simplex is a node, a 1-simplex is an edge, and a 2-simplex is a filled (connected) triangle. Due to the macroscopic scale to re-define the network systems through “simplicies”, topological data analysis can detect, quantify and compare mesoscale structure present in complex network data.

Network of Network through Model Comparison Methods (Graph Distance Measures)  

Analyzing similarity between brain networks - also referred to as the network of network -  can be useful for several applications in cognitive and clinical neuroscience. In cognitive neuroscience experiments, similarity analysis of brain networks can be used to build a “semantic map”: nodes represent the estimated networks of visual/auditory objects, and edges denote the similarity between these networks. In clinical neuroscience, a potential application of network distance measures is the mapping of a “disease network”. Here, the nodes may represent each brain disease and the edges can represent the similarity between the different networks associated with each disease - for example, Parkinson’s, Alzheimer’s, and epilepsy. Another potential application of the network of networks approach is to construct a similarity network across species connectomes, in which nodes can denote species and edges the similarity between them. However, the major difficulty of this cross-species network analysis is devising the measure to access the different connectome data from a range of species as each specimen has a unique biological baseline or structure. Yet, this may help to better understand cross-species communalities and differences in terms of brain structure and function.

Large-scale Brain Networks

When Blood-Oxygen-Level-Dependent (BOLD) signal activity in different areas of our brains co-occur, during tasks or rest, those areas are considered to have varying degrees of functional connectivity between them. Large Scale Brain Networks occur when various different areas in the brain are showing co-activation and functional connectivity with each other, either during rest or when a certain task is performed. Current large scale brain networks include the Default Mode Network, the Salience Network, the FrontoParietal Network, the Attention Network, the Sensorimotor Network, the Visual Network and the Cingulo-Opercular Network.

Default Mode Network

The Default Mode Network (DMN) is a large-scale brain network that is active while the brain is at wakeful rest. It was initially noticed to be deactivated during external goal oriented tasks, specifically tasks involving visual attention or cognitive working memory. Because of this, it was referred to as a task-negative network. However, when tasks are internally goal-oriented, the default mode network is activated and positively correlated with other brain networks. Similarly, this network has also been shown to be active when individuals are focused on their internal mental-state processes. Internal mental-state processes can include daydreaming, thinking of the future, remembering past memories, thinking of others and ourselves, mind wandering and introspection.

Some of the main anatomical features of this network include the medial prefrontal cortex, posterior cingulate cortex and areas of the inferior parietal lobule, such as the angular gyrus. Abnormalities in the DMN have been associated with Autism Spectrum Disorders, Alzheimer’s and Schizophrenia.

Salience Network

The Salience Network is thought to be made up of primarily the anterior insula and the anterior cingulate cortex. This network functions not only to complete bottom-up recognition of salient stimuli, such as sensory and emotional occurrences, but also aids in switching between various other large scale brain networks such as the Default Mode Network and the Frontal-Parietal Network. In this way, the Salience Network allows us to generate and perform the correct behavioral response to a given salient stimuli.The salience network also integrates the ventral attention network in its function to respond to unexpected salient behavioral stimuli.Salience Network dysfunction has been associated with schizophrenia, anxiety disorders, and Autism Spectrum Disorders.

Attention Network

During tasks that require attention, certain regions become more active while others become less active. This is because there are different networks in the brain that are responsible for different types of activity and are activated by different types of stimuli. There are two main systems that modulate different aspects of attention: the dorsal frontoparietal system and the ventral frontoparietal system.

The Dorsal frontoparietal system primarily functions in goal-oriented control over visuospatial attention. This network increases activity with attention-demanding tasks; it guides “top-down voluntary allocation of attention to locations or features.” It is composed primarily of the intraparietal sulcus (IPS) and the frontal eye fields (FEF). Researchers have used tools such as fMRI and MRI to locate these regions by monitoring the brain while people perform various cognitive tasks. The Ventral frontoparietal system, on the other hand, is responsible for triggering shifts of attentions. The system is implicated in detecting unexpected stimuli and guiding where attention should be directed.

While there are two relatively distinct systems involved in attention, they must interact in a dynamic way to give rise to flexible and fluid attention. The way they interact is thought to be determined by the type of task that is at hand.

Frontoparietal Network

The frontoparietal network, also known as the Central Executive Network, is one of the large-scale brain networks involved in manipulating and maintaining information in working memory. It also plays a role in decision making and problem solving regarding goal-directed behavior. The major anatomical parts of this network are the dorsolateral prefrontal cortex and the posterior parietal cortex. Brain imaging research has shown this network becomes more active during cognitively demanding tasks, unlike other networks such as the Default Mode Network, which reduces activity during cognitive tasks. Despite the distinct network systems in terms of cognitive tasks, these two networks are theorised to interact via the Salience Network. The Salience Network, which is involved in bottom-up processing, modulates between the Default Mode Network and the Frontoparietal Network.

See also

• Quantitative psychology
• Talairach coordinates