A NOVEL BAYESIAN FRAMEWORK UNCOVERING BRAIN CONNECTIVITY-TO-SHAPE RELATIONSHIP IN PRECLINICAL ALZHEIMER'S DISEASE.

Alzheimer's disease (AD) is a progressive neurodegenerative disorder characterized by amyloid-beta plaques and tau tangles, with significant pathological changes occurring in subcortical brain regions. While previous research has focused primarily on volumetric reductions in areas such as the hippocampus, thalamus, and caudate, emerging evidence suggests that their fine-grained shape deformations may offer greater sensitivity to early disease pathology. Moreover, understanding how these shape alterations influence brain functional connectivity (FC) networks could provide critical insights into the neurobiological mechanisms underlying the progression of AD. In this context, we propose a novel statistical approach, the Connectivity-on-Shape Regression (COSR) model, designed to investigate the spatially varying impact of brain subcortical shape on FC, accounting for the intrinsic modularity of functional networks. Under a Bayesian framework, COSR employs a relaxed-thresholded Gaussian process prior model to promote feature selection and integrates a stochastic block model to capture the unknown modular organization of FC. To facilitate the practical application of COSR with vertex-level shape measurements, we develop a computationally efficient variational inference approach to achieve posterior inference. Extensive simulations demonstrate the superiority of COSR over existing alternatives in accurately uncovering connectivity-to-shape associations and identifying neurobiological signals. Applying COSR to data from the Anti-Amyloid Treatment in Asymptomatic Alzheimer's study, we discover meaningful neural structural-functional relationships in amyloid-positive individuals, highlighting the potentially complex interplay between structural and functional brain alterations during this crucial preclinical stage of AD.