Discovering Spreading Pathways of Neuropathological Events in Alzheimer’s Disease Using Harmonic Wavelets Jiazhou Chen 1 , Defu Yang 2 , Hongmin Cai 1(B ) , Martin Styner 2 , and Guorong Wu 2 1 School of Computer Science and Engineering, South China University of Technology, Guangzhou, China hmcai@scut.edu.cn 2 Department of Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, USA Abstract. A plethora of neuroscience studies show that neurodegenerative dis- eases such as Alzheimer’s disease (AD) manifest network dysfunction much ear- lier before the onset of clinical symptoms, where neuropathological burdens often propagate across brain networks in a prion-like manner. In this context, char- acterizing the in-vivo spreading pathway of neuropathological events provides a new window to understand the pathophysiological mechanism of AD progression. However, little attention has been paid to the intrinsic geometry associated with the spreading pathway of neuropathological events, which indeed requires a network- specific algebra to quantify the associated propagation profile across individuals. To address this challenge, we propose a novel manifold harmonic approach to construct a set of region-adaptive harmonic wavelets, which allow us to capture diverse local network geometry in the aging population using the “swiss army knife” of the network topology. The learned common harmonic wavelets consti- tute the most representative spreading pathways that can be used to characterize the local propagation patterns of neuropathology on an individual basis. We have evaluated the power of our novel harmonic wavelets in identifying AD-related spreading pathways that lead to cognitive decline. Compared with other popular empirical biomarkers, the harmonic-based propagation patterns show much high sensitivity and specificity in stratifying cognitive normal (CN), early-stage mild cognitive impairment (MCI), and late-stage MCI, which indicates the great poten- tial of being a putative biomarker in predicting the risk of developing AD at the pre-clinical stage. Keywords: Biomarkers · Brain network · Harmonic wavelets · Manifold optimization · Alzheimer’s disease 1 Introduction Modern neuroimaging technology allows us to investigate the connection of two brain regions in vivo, where we used to study each region separately. For example, we can measure the diffusion of water molecules at each voxel using the diffusion-weighted © Springer Nature Switzerland AG 2021 A. Feragen et al. (Eds.): IPMI 2021, LNCS 12729, pp. 228–240, 2021. https://doi.org/10.1007/978-3-030-78191-0_18