title: Geodesic distance on a Grassmannian for monitoring the progression of Alzheimer's disease.
abstract: We propose a geodesic distance on a Grassmannian manifold that can be used to quantify the shape progression patterns of the bilateral hippocampi, amygdalas, and lateral ventricles in healthy control (HC), mild cognitive impairment (MCI), and Alzheimer's disease (AD). Longitudinal magnetic resonance imaging (MRI) scans of 754 subjects (3092 scans in total) were used in this study. Longitudinally, the geodesic distance was found to be proportional to the elapsed time separating the two scans in question. Cross-sectionally, utilizing a linear mixed-effects statistical model, we found that each structure's annualized rate of change in the geodesic distance followed the order of AD>MCI>HC, with statistical significance being reached in every case. In addition, for each of the six structures of interest, within the same time interval (e.g., from baseline to the 6th month), we observed significant correlations between the geodesic distance and the cognitive deterioration as quantified by the ADAS-cog increase and the MMSE decrease. Furthermore, as the disease progresses over time, this linkage between the inter-shape geodesic distance and the cognitive decline becomes considerably stronger and more significant.
authors.affiliation: Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA.
authors.forename: Liangyan
authors.initials: L
authors.lastname: Gui
authors.affiliation: Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA; Sun Yat-sen University-Carnegie Mellon University (SYSU-CMU) Joint Institute of Engineering, Sun Yat-sen University, Guangzhou, Guangdong, China; Sun Yat-sen University-Carnegie Mellon University (SYSU-CMU) Shunde International Joint Research Institute, Shunde, Guangdong, China; School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, Guangdong, China. Electronic address: tangxiaoy@mail.sysu.edu.cn.
authors.forename: Xiaoying
authors.initials: X
authors.lastname: Tang
authors.affiliation: Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA.
authors.forename: José M F
authors.initials: JMF
authors.lastname: Moura
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D000544:Alzheimer Disease / Q000000981:diagnostic imaging / Q000473:pathology*; D000679:Amygdala / Q000000981:diagnostic imaging / Q000473:pathology; D001921:Brain / Q000000981:diagnostic imaging / Q000473:pathology*; D001931:Brain Mapping / Q000379:methods*; D060825:Cognitive Dysfunction / Q000000981:diagnostic imaging / Q000473:pathology; D018450:Disease Progression; D005260:Female; D006624:Hippocampus / Q000000981:diagnostic imaging / Q000473:pathology; D006801:Humans; D020547:Lateral Ventricles / Q000000981:diagnostic imaging / Q000473:pathology; D016014:Linear Models; D008279:Magnetic Resonance Imaging; D008297:Male; D008875:Middle Aged
keywords: Alzheimer's disease; Amygdala; Geodesic distance; Grassmannian; Hippocampus; Shape