...Using a novel mathematical framework called "Director Field Analysis" (DFA), we investigated the geometric microstructural properties (i.e., splay, bend, twist, and total distortion) in the orientation of white matter fibers in AD, amnestic mild cognitive impairment (aMCI), and cognitively normal (CN) individuals from the Alzheimer's Disease Neuroimaging Initiative 2 database. Results revealed that AD patients had extensive orientational changes in the bilateral anterior thalamic radiation, corticospinal tract, inferior and superior longitudinal fasciculus, inferior fronto-occipital fasciculus, and uncinate fasciculus in comparison with CN. We postulate that these orientational changes of white matter fibers may be partially caused by the expansion of lateral ventricle, white matter atrophy, and gray matter atrophy in AD. In contrast, aMCI individuals showed subtle orientational changes in the left inferior longitudinal fasciculus and right uncinate fasciculus, which showed a significant association with the cognitive performance, suggesting that these regions may be preferential vulnerable to breakdown by neurodegenerative brain disorders, thereby resulting in the patients' cognitive impairment. To our knowledge, this article is the first to examine geometric microstructural changes in the orientation of white matter fibers in AD and aMCI. Our findings demonstrate that the orientational information of white matter fibers could provide novel insight into the underlying biological and pathological changes in AD and aMCI.