A Multi-Scale Stochastic Optimal Control Framework for Micro-Robotic Cerebrovascular Intervention NSAI: A Theoretical and Computational Framework, Not a Clinically Validated System

Background. Intracerebral hemorrhage (ICH) and acute ischemic stroke (AIS) remain leading causes of neurological death and disability worldwide. The Global Burden of Disease Study 2021 reports approximately 3.4 million incident ICH cases and 3.3 million ICH deaths globally, alongside a substantially larger absolute burden from AIS. Five landmark randomized controlled trials — STICH II, MISTIE III, MIND, DAWN, and DEFUSE 3 — establish that favorable functional outcomes plateau near 41–50%, with residual secondary-injury mechanisms (perihematomal edema, pressure-driven re-bleeding, excitotoxicity) largely unaddressed by any single intervention modality. No existing framework unifies continuum poroelastic tissue mechanics, stochastic micro-scale kinetics, and formal optimal-control theory into a single, mathematically rigorous, and computationally falsifiable structure.Methods. We develop the NSAI (NeuroSwarm AI-Guided) framework as a rigorously derived multi-scale stochastic control problem, not as a validated clinical technology. Macro-scale tissue mechanics follow the nonlinear Biot poroelasticity equations with constitutive parameters drawn from published indentation and permeability studies of brain parenchyma. Micro-scale kinetics are modeled as an Itô stochastic reaction–diffusion process derived via the Fokker–Planck–Kolmogorov forward equation. Optimal intervention is formulated through the exact stochastic Hamilton–Jacobi–Bellman (HJB) equation, with an explicit, provably convergent Linear-Quadratic-Gaussian (LQG) reduction whose algebraic Riccati equation is solved in closed form. We then construct a fully transparent, dimensionless, reduced-order computational testbed — distinct from and explicitly not a clinical predictor — to demonstrate, verify, and stress-test the mathematical control law. Every quantitative result in this manuscript, without exception, is generated by the single self-contained Python script reproduced verbatim in Appendix C; no result is asserted, assumed, or hand-set.Results. The closed-form algebraic Riccati solution yields feedback gain K∗ = −3.2127 and closed-loop eigenvalue λCL = −3.1627 < 0, proving exponential stability of the linearized control law. In the illustrative dimensionless testbed (10,000-run Monte Carlo, fixed seed for exact reproducibility), the closed-loop model drives the surrogate “residual volume” state below the 5% target in 100% of sampled parameter draws, with a genuine Saltelli–Sobol decomposition (1,024 base samples, 6,144 total model evaluations) attributing S1 = 0.606 (lysis-kinetics parameter) and S1 = 0.350 (control-input magnitude) of output variance, closing to ∑S1 = 0.948. Morris elementary-effects screening (100 trajectories) independently confirms this ranking. A Metropolis–Hastings demonstration on a synthetic Beta-Binomial problem converges to within 0.13% of the exact analytic posterior mean at a tuned acceptance rate of 41.3%, verifying correct MCMC implementation. These are properties of the mathematical control law and the illustrative testbed; they are explicitly not estimates of real-world clinical efficacy, for which no data of any kind currently exist.Conclusions. NSAI contributes a mathematically rigorous, fully reproducible, and formally falsifiable theoretical scaffold linking poroelastic neuromechanics, stochastic control, and Bayesian sensitivity analysis. Its scientific value at this stage is conceptual and methodological: it specifies precisely which physical quantities, which control law, and which falsification thresholds a future preclinical program must measure. It makes no claim of clinical efficacy, readiness, or validation, and none should be inferred. No external funding was received.