A concise and persistent feature to study brain resting‐state network dynamics: Findings from the Alzheimer's Disease Neuroimaging Initiative

Alzheimer's disease (AD) is the most common type of dementia in the elderly with no effective treatment currently. Recent studies of noninvasive neuroimaging, resting‐state functional magnetic resonance imaging (rs‐fMRI) with graph theoretical analysis have shown that patients with AD and mild cognitive impairment (MCI) exhibit disrupted topological organization in large‐scale brain networks. In previous work, it is a common practice to threshold such networks. However, it is not only difficult to make a principled choice of threshold values, but also worse is the discard of potential important information. To address this issue, we propose a threshold‐free feature by integrating a prior persistent homology‐based topological feature (the zeroth Betti number) and a newly defined connected component aggregation cost feature to model brain networks over all possible scales. We show that the induced topological feature (Integrated Persistent Feature) follows a monotonically decreasing convergence function and further propose to use its slope as a concise and persistent brain network topological measure. We apply this measure to study rs‐fMRI data from the Alzheimer's Disease Neuroimaging Initiative and compare our approach with five other widely used graph measures across five parcellation schemes ranging from 90 to 1,024 region‐of‐interests. The experimental results demonstrate that the proposed network measure shows more statistical power and stronger robustness in group difference studies in that the absolute values of the proposed measure of AD are lower than MCI and much lower than normal controls, providing empirical evidence for decreased functional integration in AD dementia and MCI.