Network Diffusion-Constrained Variational Generative Models for Investigating the Molecular Dynamics of Brain Connectomes Under Neurodegeneration.

Alzheimer's disease (AD) is a complex and progressive neurodegenerative condition with significant societal impact. Understanding the temporal dynamics of its pathology is essential for advancing therapeutic interventions. Empirical and anatomical evidence indicates that network decoupling occurs as a result of gray matter atrophy. However, the scarcity of longitudinal clinical data presents challenges for computer-based simulations. To address this, a first-principles-based, physics-constrained Bayesian framework is proposed to model time-dependent connectome dynamics during neurodegeneration. This temporal diffusion network framework segments pathological progression into discrete time windows and optimizes connectome distributions for biomarker Bayesian regression, conceptualized as a learning problem. The framework employs a variational autoencoder-like architecture with computational enhancements to stabilize and improve training efficiency. Experimental evaluations demonstrate that the proposed temporal meta-models outperform traditional static diffusion models. The models were evaluated using both synthetic and real-world MRI and PET clinical datasets that measure amyloid beta, tau, and glucose metabolism. The framework successfully distinguishes normative aging from AD pathology. Findings provide novel support for the "decoupling" hypothesis and reveal eigenvalue-based evidence of pathological destabilization in AD. Future optimization of the model, integrated with real-world clinical data, is expected to improve applications in personalized medicine for AD and other neurodegenerative diseases.