Computing Univariate Neurodegenerative Biomarkers with Volumetric Optimal Transportation: A Pilot Study

Cortical Surface Shape Analysis Based on Alexandrov Polyhedra

Shape analysis has been playing an important role in early diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's diseases (AD). However, obtaining effective shape representations remains challenging. This paper proposes to use the Alexandrov polyhedra as surface-based shape signatures for cortical morphometry analysis. Given a closed genus-0 surface, its Alexandrov polyhedron is a convex representation that encodes its intrinsic geometry information. We propose to compute the polyhedra via a novel spherical optimal transport (OT) computation. In our experiments, we observe that the Alexandrov polyhedra of cortical surfaces between pathology-confirmed AD and cognitively unimpaired individuals are significantly different. Moreover, we propose a visualization method by comparing local geometry differences across cortical surfaces. We show that the proposed method is effective in pinpointing regional cortical structural changes impacted by AD.

Developing univariate neurodegeneration biomarkers with low-rank and sparse subspace decomposition

Cognitive decline due to Alzheimer's disease (AD) is closely associated with brain structure alterations captured by structural magnetic resonance imaging (sMRI). It supports the validity to develop sMRI-based univariate neurodegeneration biomarkers (UNB). However, existing UNB work either fails to model large group variances or does not capture AD dementia (ADD) induced changes. We propose a novel low-rank and sparse subspace decomposition method capable of stably quantifying the morphological changes induced by ADD. Specifically, we propose a numerically efficient rank minimization mechanism to extract group common structure and impose regularization constraints to encode the original 3D morphometry connectivity. Further, we generate regions-of-interest (ROI) with group difference study between common subspaces of Aβ+AD and Aβ-cognitively unimpaired (CU) groups. A univariate morphometry index (UMI) is constructed from these ROIs by summarizing individual morphological characteristics weighted by normalized difference between Aβ+AD and Aβ-CU groups. We use hippocampal surface radial distance feature to compute the UMIs and validate our work in the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort. With hippocampal UMIs, the estimated minimum sample sizes needed to detect a 25% reduction in the mean annual change with 80% power and two-tailed P=0.05are 116, 279 and 387 for the longitudinal Aβ+AD, Aβ+mild cognitive impairment (MCI) and Aβ+CU groups, respectively. Additionally, for MCI patients, UMIs well correlate with hazard ratio of conversion to AD (4.3, 95% CI = 2.3-8.2) within 18 months. Our experimental results outperform traditional hippocampal volume measures and suggest the application of UMI as a potential UNB.