Structural Medicine v3.1: Optimal Control and Resonant Stabilization of Neurodegenerative Dynamics

This repository accompanies the preprint: "Structural Medicine v3. 1: Optimal Control and Resonant Stabilization of Neurodegenerative Dynamics" Structural Medicine v3. 1 extends a predictive framework for neurodegenerative progression (v2. 0–v3. 0) into a control-oriented formulation based on dynamical systems and optimal control theory. Rather than modeling neurodegeneration as a purely monotonic decline, the framework interprets disease progression as a transition from structural persistence to structural instability, followed by a controllable stabilization phase. The model is built on three core quantities: - Structural persistence F (t) - Local structural decay rate λ (t) - Directional asymmetry A Empirical analysis based on longitudinal ADNI-derived cognitive trajectories shows: - Increased directional asymmetry is associated with shorter time to conversion- Structural asymmetry predicts elevated hazard risk (HR ≈ 2. 75) - Variance and lag-1 autocorrelation increase prior to conversion (critical slowing down) These results are consistent with early warning signals observed in complex systems approaching critical transitions. Structural Medicine v3. 1 introduces a multidimensional instability score: Rₘulti (t) = Σ wᵢ Varλᵢ (t) ρ₁λᵢ (t) Aᵢ (t) + Σ wᵢj Corr (λᵢ, λⱼ) where the first term captures within-modality instability and the second captures cross-structural decoupling. A control formulation is introduced: Vcontrol (λ) = V (λ) + U (λ, t) with resonant intervention defined as: U (λ, t, ω) = A (ω) sin (ωt + φ) where ω is matched to intrinsic system dynamics. The optimal intervention is defined by: min ∫ Rₘulti (t) dt subject to |A (ω) | ≤ Aₘax Simulation results demonstrate that resonant control suppresses structural instability, providing a conceptual bridge from passive prediction to active stabilization. Figures included in this repository are synthetic demonstration visualizations for reproducibility, while reported summary statistics (hazard ratios, log-rank tests, and AUC values) are derived from empirical ADNI-based analysis. This repository includes: - Full preprint (PDF) - Python figure generation script- Complete figure set (Fig1–Fig12) Data source: Alzheimer’s Disease Neuroimaging Initiative (ADNI) https: //adni. loni. usc. edu This work provides a unified framework connecting early warning signals, structural dynamics, and optimal control, forming a basis for predictive and interventional structural medicine.