Shannon Entropy of Gray Matter Eigenmodes: A Novel Biomarker for Alzheimer's Disease and Heterogeneous MCI Trajectories

Abstract Current Alzheimer's disease (AD) diagnostics rely on late‐stage cognitive assessments or invasive biomarkers. Neuroimaging offers non‐invasive alternatives, but single‐modality approaches (structural atrophy or functional connectivity) face limitations in sensitivity and specificity for early detection. Entropy and temperature, novel structure‐function coupling (SFC) biomarkers based on gray matter eigenmodes, are introduced to quantify cortical disorganization in early AD. Using multimodal MRI and amyloid‐PET data from two cohorts (BABRI: N = 135; ADNI: N = 275), including cognitively normal (CN), mild cognitive impairment (MCI), and AD individuals, entropy is computed by projecting fMRI onto structural eigenmodes and temperature via eigenmode‐based functional connectivity reconstruction. These indices are tested for diagnostic classification, Aβ prediction, and MCI subtype stratification (reversed/stable/progressed). Entropy is significantly higher in AD than CN and MCI (Δ = 8–21%, p < 0.001) in both cohorts. Left‐hemisphere entropy yielded optimal diagnostic accuracy (AUC = 0.901 for CN vs MCI), while right/global entropy predicted Aβ burden (error reduction: 38.7–42.1%, p < 0.01). Entropy also distinguished MCI subtypes and captured biphasic changes in progressors. Temperature indices showed no significant group differences. Entropy from gray matter eigenmodes is a sensitive, non‐invasive biomarker for AD diagnosis and pathology prediction, revealing hemispheric asymmetries and nonlinear progression in MCI.