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

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.