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: R_multi(t) = Σ w_i Var[λ_i(t)] ρ₁[λ_i](t) A_i(t) + Σ w_ij Corr(λ_i, λ_j) where the first term captures within-modality instability and the second captures cross-structural decoupling. A control formulation is introduced: V_control(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 ∫ R_multi(t) dt subject to |A(ω)| ≤ A_max 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.