BRIDGE: Learning Brain-Gut Metabolic Evidence for Alzheimer's Disease Diagnosis

Alzheimer's disease (AD) diagnosis may benefit from gut metabolic information associated with brain-gut interactions, yet existing models largely analyze cerebral glucose metabolism alone. Although whole-body fluorodeoxyglucose positron emission tomography (FDG-PET) can provide paired brain-gut observations, routine brain examinations rarely include gut imaging, limiting direct use of this information for diagnosis. In this paper, we present BRIDGE (Brain and Gut Representation Integration via Distribution-Guided Enhancement), a two-stage framework for transferring brain-gut metabolic knowledge to brain-only diagnosis. Specifically, BRIDGE integrates a conditional brain-to-gut latent transport module and a disease-evidence-guided cerebral pathway to capture subject-specific cross-organ correspondence and disease-relevant cerebral representations. For the cerebral pathway, a large language model (LLM) helps organize literature-derived descriptors into human-approved semantic anchors that guide feature learning. Additionally, we introduce a counterfactual-guided residual fusion mechanism, which uses matched and non-matched virtual-gut evidence to supervise a confidence gate and dynamically regulate the contribution of transported cross-organ information. At inference, BRIDGE exploits complementary gut-related context using brain PET alone, without measured gut PET. Extensive experiments across public and private cohorts demonstrate that BRIDGE outperforms brain-only and cross-organ baselines, achieving AUC gains of 6.0% and 5.2% over its brain-only counterpart for CN/MCI and CN/AD diagnosis, respectively. Notably, its ability to transfer complementary brain-gut metabolic context while preserving brain PET as the sole inference input highlights its potential for clinically practical diagnosis. Our code is available at https://github.com/CUHK-AIM-Group/BRIDGE.