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

Abstract

Changes in cognitive performance due to neurodegenerative diseases such as Alzheimer's disease (AD) are closely correlated to the brain structure alteration. A univariate and personalized neurodegenerative biomarker with strong statistical power based on magnetic resonance imaging (MRI) will benefit clinical diagnosis and prognosis of neurodegenerative diseases. However, few biomarkers of this type have been developed, especially those that are robust to image noise and applicable to clinical analyses. In this paper, we introduce a variational framework to compute optimal transportation (OT) on brain structural MRI volumes and develop a univariate neuroimaging index based on OT to quantify neurodegenerative alterations. Specifically, we compute the OT from each image to a template and measure the Wasserstein distance between them. The obtained Wasserstein distance, Wasserstein Index (WI) for short to specify the distance to a template, is concise, informative and robust to random noise. Comparing to the popular linear programming-based OT computation method, our framework makes use of Newton's method, ǂ Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database

Characterizing visual cortical magnification with topological smoothing and optimal transportation

“…Furthermore, we applied optimal transportation to utilize the projection from visual cortex to the 2D planar disk. By generalizing our prior work 27 to relocate the coordinate of each voxel on the 2D planar disk, we tested the performance of the conventional pRF solution, 25 pRF with topological smoothing, 26 and pRF with optimal transportation. We managed to improve the accuracy and credibility when solve the visual coordinates of receptive center, by our proposed pipeline.…”

Developing Univariate Neurodegeneration Biomarkers with Low-Rank and Sparse Subspace Decomposition

“…In the past decade, a variety of univariate morphological MRI biomarker algorithms have been developed (e.g. Racine et al, 2018;Cardenas et al, 2011;Cortechs Labs, 2020;Vemuri et al, 2008;Tu et al, 2020). Meanwhile, a few multivariate analysis frameworks (Hua et al, 2011;Gutman et al, 2013) took statistical or machine learning approaches to optimize the minimum sample size estimation for clinical trials.…”