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

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, which makes it possible to compute WI in large-scale datasets. Experimental results, on 314 subjects (140 Aβ + AD and 174 Aβ- normal controls) from the Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset, provide preliminary evidence that the proposed WI is correlated with a clinical cognitive measure (the Mini-Mental State Examination (MMSE) score), and it is able to identify group difference and achieve a good classification accuracy, outperforming two other popular univariate indices including hippocampal volume and entorhinal cortex thickness. The current pilot work suggests the application of WI as a potential univariate neurodegenerative biomarker.