Graph Signal Entropy for Analyzing Functional Brain Abnormalities of Alzheimer's Disease Patients

A majority of research shows that the brain complexity of Alzheimer's disease (AD) patients is smaller than that of healthy controls (HCs). In this paper, we propose a novel method based on graph signal entropy to investigate the complexity of functional brain networks in AD patients. By using a spectral graph wavelet filter to decompose the subjects' BOLD signal, we generate distinct functional brain networks for each graph frequency band. We then use the multivariate dispersion entropy to examine the abnormal complexity of AD patients across different graph frequency bands. Experimental results reveal that in the low and mid-frequency bands, the brain complexity of AD patients is generally larger than that of HCs, which challenges the conventional understanding that AD is consistently associated with reduced complexity. Moreover, widely reported abnormal brain regions in AD, such as the hippocampus and parahippocampal gyrus, exhibit significant differences only at specific frequency bands, indicating the necessity of frequency-resolved analysis. These findings uncover new characteristics of functional brain networks in AD patients and provide deeper insights into the disease's complex neural mechanisms.