Recent research of persistent homology in algebraic topology has shown that the altered network organization of human brain provides a promising indicator of many neuropsychiatric disorders and neurodegenerative diseases. However, the current slope-based approach may not accurately characterize changes of persistent features over graph filtration because such curves are not strictly linear. Moreover, our previous integrated persistent feature (IPF) works well on an rs-fMRI cohort while it has not yet been studied on metabolic brain networks. To address these issues, we propose a novel univariate network measurement, kernel-based IPF (KBI), based on the prior IPF, to quantify the difference between IPF curves. In our experiments, we apply the KBI index to study fluorodeoxyglucose positron emission tomography (FDG-PET) imaging data from 140 subjects with Alzheimer's disease (AD), 280 subjects with mild cognitive impairment (MCI), and 280 healthy normal controls (NC). The results show the disruption of network integration in the progress of AD. Compared to previous persistent homology-based measures, as well as other standard graph-based measures that characterize small-world organization and modular structure, our proposed network index KBI possesses more significant group difference and better classification performance, suggesting that it may be used as an effective preclinical AD imaging biomarker.
Keywords: Alzheimer’s disease (AD); brain network; graph theory; network measure; persistent homology; positron emission tomography (PET).