Graph Theoretical Measures for Alzheimer’s, MCI, and Normal Controls: A Comparative Study Using MRI Data

The Graph theory provides the platform that could be used to model complex brain networks mathematically, and it could play a significant role in the diagnosis of various neurodegenerative diseases such as Alzheimer’s. The main aim of our study is to perform a comparative analysis in terms of various graph theoretic measures of structural brain networks. In particular, the paper evaluates graph theoretical measures by first forming graphs using magnetic resonance imaging (MRI) data. In this paper, we study and evaluate graph theoretical measures using MRI data, namely characteristic path length, global efficiency, strength, and clustering coefficient, in a cohort of normal controls ( N = 30), a cohort of mild cognitive impairment (MCI) ( N = 30), and a cohort of Alzheimer’s disease (AD) ( N = 30). In our work, MRI data is preprocessed and cortical thickness is extracted for each brain region. The connectivity matrix is obtained, and thus a graph is formed. We have also performed receiver operating characteristic (ROC) and area under the ROC analyses of all graph theoretical measures to better elucidate and validate the results. It is observed that these measures may be used to differentiate Alzheimer’s from normal. In our study, we observed that a very random and disrupted network is obtained in the case of Alzheimer’s in comparison with the normal and MCI cases. The other observations in terms of graph theoretic measures are an increase in characteristic path length, a decrease in global efficiency, a decrease in strength, and a reduction in values of the clustering coefficient in the case of Alzheimer’s. The findings suggest that graph theoretical measures and alterations in network topology could be used as quantitative biomarkers of AD.