PB-MDRS: A Unified Four-Compartment ODE Framework for Precision Bioactive Microenvironment Detoxification and Restoration in ICH, Solid Tumors, SAH, TBI, and Neuroimmune Disorders --- Analytical Derivations, In Silico Validation, Monte Carlo Uncertainty Quantification, and Global Sensitivity Analysis

Poor clinical outcomes in intracerebral hemorrhage (ICH), solid tumors (particularly glioblastomas), subarachnoid hemorrhage (SAH), traumatic brain injury (TBI), neuroinflammatory disorders, and autoimmune neuroimmune conditions are driven primarily by a persistent bioactive extracellular milieu of toxins that impairs neural repair, immune surveillance, and clearance mechanisms. Conventional interventions frequently exacerbate toxin exposure via iatrogenic spikes.Precision Bioactive Microenvironment Detoxification and Restoration Surgery (PB-MDRS) is a minimally invasive, image-guided, biosensor-driven, multi-lumen catheter platform designed for selective neutralization and clearance of neurotoxic, onco-toxic, and autoimmune mediators while preserving tissue integrity.We derive a unified four-compartment ordinary differential equation (ODE) model from first principles using mass-action kinetics. The system is solved analytically in the linear regime, cross-validated numerically to machine precision (max |T_num - T_anal| < 10^{-12}), and implemented in fully reproducible Python code (numpy + scipy only). Deterministic simulations demonstrate a precise 80.7% reduction in toxin area-under-curve (AUC) under PB-MDRS versus standard-of-care (225.23 → 43.38). Latin Hypercube Monte Carlo simulations (N=5,000, extensible to 12,000) with ±15% uniform parameter uncertainty confirm a mean 80.7% toxin-AUC reduction (95% CI 77.7--83.2%). Global sensitivity analysis identifies b_boost and c_detox^PB as dominant drivers. All figures, tables, and statistics are generated directly from the embedded code.The framework generalizes across SAH, TBI, neuroinflammation, and autoimmune disorders via domain-specific recalibration. Strict model assumptions, Popperian falsifiability criteria, limitations, and a 10-year translational roadmap are explicitly stated. All derivations and code are fully embedded for independent reproducibility.