An Optimal Transportation Based Univariate Neuroimaging Index
The alterations of brain structures and functions have been considered closely correlated to the change of cognitive performance due to neurodegenerative diseases such as Alzheimer's disease. In this paper, we introduce a variational framework to compute the optimal transformation (OT) in 3D space and propose a univariate neuroimaging index based on OT to measure such alterations. We compute the OT from each image to a template and measure the Wasserstein distance between them. By comparing the distances from all the images to the common template, we obtain a concise and informative index for each image. Our framework makes use of the Newton's method, which reduces the computational cost and enables itself to be applicable to large-scale datasets. The proposed work is a generic approach and thus may be applicable to various volumetric brain images, including structural magnetic resonance (sMR) and fluorodeoxyglucose positron emission tomography (FDG-PET) images. In the classification between Alzheimer's disease patients and healthy controls, our method achieves an accuracy of 82.30% on the Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline sMRI dataset and outperforms several other indices. On FDG-PET dataset, we boost the accuracy to 88.37% by leveraging pairwise Wasserstein distances. In a longitudinal study, we obtain a 5% significance with p-value = 0.0000113 in a t-test on FDG-PET. The results demonstrate a great potential of the proposed index for neuroimage analysis and the precision medicine research.
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