Understanding complexity in the human brain

Abstract

Although the ultimate aim of neuroscientific enquiry is to gain an understanding of the brain and how its workings relate to the mind, the majority of current efforts are largely focused on small questions using increasingly detailed data. However, it might be possible to successfully address the larger question of mind-brain mechanisms if the cumulative findings from these neuroscientific studies are coupled with complementary approaches from physics and philosophy. The brain, we argue, can be understood as a complex system or network, in which mental states emerge from the interaction between multiple physical and functional levels. Achieving further conceptual progress will crucially depend on broad-scale discussions regarding the properties of cognition and the tools that are currently available or must be developed in order to study mind-brain mechanisms.

Figure 1. Brain graph construction

One of the recent applications of complex network theory in neuroscience has been in the creation of brain graphs from neuroimaging data [30,79,80]. In this process, brain regions are represented by nodes in a graph and connections between those regions, whether anatomical (using diffusion imaging) or functional (using fMRI, electroencephalography or magnetoelectroencephalography), are represented by edges between those nodes. In this way a graph can be constructed that characterizes the entire brain system according to its components (nodes) and their relations with one another (edges).

Figure 2

Spatial scaling indicates that an organizational principle characterizes the structure of the human cortex over multiple spatial scales. An example of spatial scaling is the mathematical principle of network hierarchy [8]. Hierarchical structure is defined as a relation between network nodes whereby hubs (or highly connected nodes) are connected to nodes that are not otherwise connected to one another; in other words, the neighbors of a hub are not clustered together. This structure facilitates global communication and is thought to play a role in the modular organization of connectivity in the cortex [33,78]. Hierarchical network structure is consistently displayed at increasing spatial resolutions in which the brain is parcellated into more and more regions of interest (ROIs).

Figure 3. Modularity

The general concept of modularity is that the components of a system can be categorized according to their functions. Components that subserve a similar function are said to belong to a single module, whereas components that subserve a second function are said to belong to another module. Modularity can also be defined mathematically in terms of network organization [30,33,70]. Nodes that share many common links are said to belong to a module, whereas nodes that do not share many links are likely to be assigned to different modules. The categorization of nodes into partitions is a process known as ‘community detection’ because – rather appropriately – it detects communities or modules composed of highly connected nodes and delineates the boundaries between those communities. This categorization procedure is an important current area of network science research.

Figure 4. Wiring diagram of Caenorhabditis elegans

The wiring diagram of the nematode worm, C. elegans, is composed of nodes (neurons) and connections between those nodes (electrical and chemical synapses). The worm is known to contain 302 neurons and here only a small fraction of the connections known to exist between these neurons are displayed (the full connectivity would be too dense to visualize clearly in this way). The color of each node represents the number of connections emanating from that node (red indicating many and blue indicating few). The analysis of wiring diagrams can be used to assess important organizational principles of biological system structure and might provide insight into system function [46].