Learning pyramidal multi-scale harmonic wavelets for identifying the neuropathology propagation patterns of Alzheimer's disease.

Previous studies have established that neurodegenerative disease such as Alzheimer's disease (AD) is a disconnection syndrome, where the neuropathological burdens often propagate across the brain network to interfere with the structural and functional connections. In this context, identifying the propagation patterns of neuropathological burdens sheds new light on understanding the pathophysiological mechanism of AD progression. However, little attention has been paid to propagation pattern identification by fully considering the intrinsic properties of brain-network organization, which plays an important role in improving the interpretability of the identified propagation pathways. To this end, we propose a novel harmonic wavelet analysis approach to construct a set of region-specific pyramidal multi-scale harmonic wavelets, it allows us to characterize the propagation patterns of neuropathological burdens from multiple hierarchical modules across the brain network. Specifically, we first extract underlying hub nodes through a series of network centrality measurements on the common brain network reference generated from a population of minimum spanning tree (MST) brain networks. Then, we propose a manifold learning method to identify the region-specific pyramidal multi-scale harmonic wavelets corresponding to hub nodes by seamlessly integrating the hierarchically modular property of the brain network. We estimate the statistical power of our proposed harmonic wavelet analysis approach on synthetic data and large-scale neuroimaging data from ADNI. Compared with the other harmonic analysis techniques, our proposed method not only effectively predicts the early stage of AD but also provides a new window to capture the underlying hub nodes and the propagation pathways of neuropathological burdens in AD.