Structural Medicine v1.9: Data-Driven Reconstruction of Structural Potential in Neurodegenerative Dynamics

This work presents Structural Medicine v1. 9, a data-driven framework for reconstructing the effective structural potential governing neurodegenerative progression from longitudinal cognitive data. Conventional models describe disease progression as a monotonic decline. In contrast, we demonstrate that neurodegeneration follows a two-stage dynamical process: (1) Variance instability — an early-stage increase in structural fluctuations (2) Directional collapse bias — a late-stage irreversible drift toward degradation Using ADNI longitudinal data, we define structural persistence F (t) from normalized MMSE and compute the local structural decay rate λ (t). From these trajectories, we reconstruct: - empirical drift fields - effective structural force F_λ (λ) - reconstructed structural potential V (λ) The results reveal a consistent deformation of the underlying potential landscape across disease stages: balanced basin → flattening → directional deformation → collapse-biased dynamics This provides a unified structural interpretation linking statistical fluctuation, asymmetry emergence, and dynamical instability within a single potential-based framework. All figures are reproducible using the included Python scripts. Synthetic data generation is provided for demonstration purposes when ADNI data is unavailable. This work bridges clinical longitudinal analysis and dynamical systems theory, offering a new perspective on neurodegenerative processes as structural transitions rather than simple decline.