Brain Structure and Disease
By applying graph theory to how they model the structure of the brain, many scientists have recognized topological patterns among patients suffering from Alzheimer’s disease or schizophrenia. Most brain networks use the most simplistic model for the brain, an undirected, unweighted graph. The way the graph defines its nodes or edges depends on the scale of neuroimaging data. When analyzing the data extracted from studies on the human brain, which is on the macroscopic scale, the nodes of the graph often represent the major subcortical nuclei and cortical regions and the edges represent a statistical measure of association, either the correlation between the different parts of the brain or how much shared information two regions contain.
Studies that examined the gray matter in the brain found patterns in the topological properties of the graphs among patients with schizophrenia and among patients with Alzheimer’s disease. The graphs of the patients with schizophrenia had longer edge lengths between nodes, an attenuated hierarchial structure of the heteromodal cortex and many looked as though there were inefficient wiring. The graphs of patients with Alzheimer’s disease possessed a more lattice-like structure than the other patients, with a high cluster coefficient and long path length. The cluster coefficient measures the density of connections between a node and its neighbors which is a good indicator of densely connected regions of the brain. The path length is smallest number of edges that connects one node to another.
Other studies that constructed the model of the brain after functional magnetic resonance imaging (fMRI) data showed that there is an inverse correlation between the topological property of small worldness and how long a person suffers from schizophrenia. The “small world” property refers to networks with a high clustering coefficient and short average path length. The clustering coefficient was reduced in the graphs patients with Alzheimer’s disease.
These findings show that graph theory has revolutionized the way we look at the brain. It allows us to identify correlations between the structure of the brain and disease as described by the two examples above. There is also the potential of discovering a relationship between these models and cognitive behavior.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2902726/