Enhancing Diffusion MRI Measures By Integrating Grey and White Matter Morphometry With Hyperbolic Wasserstein Distance

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.

Hyperbolic Wasserstein Distance for Shape Indexing

Shape space is an active research topic in computer vision and medical imaging fields. The distance defined in a shape space may provide a simple and refined index to represent a unique shape. This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating hyperbolic Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram algorithms. The resulting hyperbolic Wasserstein distance can intrinsically measure the similarity between general topological surfaces. Our proposed algorithms are theoretically rigorous and practically efficient. It has the potential to be a powerful tool for 3D shape indexing research. We tested our algorithm with human face classification and Alzheimer's disease (AD) progression tracking studies. Experimental results demonstrated that our work may provide a succinct and effective shape index.

White Matter Brain Network Research in Alzheimer's Disease Using Persistent Features

Despite the severe social burden caused by Alzheimer’s disease (AD), no drug than can change the disease progression has been identified yet. The structural brain network research provides an opportunity to understand physiological deterioration caused by AD and its precursor, mild cognitive impairment (MCI). Recently, persistent homology has been used to study brain network dynamics and characterize the global network organization. However, it is unclear how these parameters reflect changes in structural brain networks of patients with AD or MCI. In this study, our previously proposed persistent features and various traditional graph-theoretical measures are used to quantify the topological property of white matter (WM) network in 150 subjects with diffusion tensor imaging (DTI). We found significant differences in these measures among AD, MCI, and normal controls (NC) under different brain parcellation schemes. The decreased network integration and increased network segregation are presented in AD and MCI. Moreover, the persistent homology-based measures demonstrated stronger statistical capability and robustness than traditional graph-theoretic measures, suggesting that they represent a more sensitive approach to detect altered brain structures and to better understand AD symptomology at the network level. These findings contribute to an increased understanding of structural connectome in AD and provide a novel approach to potentially track the progression of AD.