Computational Modeling of PancreaSolve-HNX: A Falsifiable, Uncertainty-Quantified Framework for Multi-Modal Hybrid-Nanoparticle Therapy Dynamics in Pancreatic Ductal Adenocarcinoma

Pancreatic ductal adenocarcinoma (PDAC) remains among the most lethal solid malignancies, with a five-year relative survival near 13%, driven substantially by a desmoplastic, immunosuppressive tumor microenvironment (TME) that occupies 80 to 90% of tumor volume and restricts drug penetration. We present PancreaSolve-HNX, a conceptual hybrid organic-inorganic nanoparticle: a gold core with sonosensitizing character, a mesoporous silica interlayer, and a Zr4+-based metal-organic framework (MOF) shell, designed to co-deliver high-payload gemcitabine monophosphate (GMP), enable focused-ultrasound-triggered sonodynamic/photothermal ablation, degrade hyaluronan-rich stroma, and engage adaptive immunity via bispecific anti-CD47/PD-L1 nanobodies. We formalize its prospective mechanism using a seven-compartment nonlinear ODE model of tumor, stroma, immune, nanoparticle, drug, effector, and toxicity dynamics, and analyze it computationally rather than empirically: all reported figures are theoretical model outputs, not experimental measurements. Dimensional analysis of the governing equations motivated three formulation choices central to the model's internal consistency: (i) the sonodynamic/photothermal cytotoxic term is a saturable Hill/Emax function rather than an unbounded bilinear rate law, avoiding a numerically stiff, biologically implausible near-instantaneous sterilization artifact; (ii) stromal fibrogenesis scales with the fraction of carrying capacity occupied by the tumor while nanoparticle-driven stromal degradation is a saturable function of nanoparticle concentration, so that the two competing terms operate on comparable scales rather than one trivially dominating the other; and (iii) an explicit toxicity-burden compartment, driven by systemic drug and photothermal exposure and offset by physiological repair, allows a therapeutic index to be computed rather than assumed. Under a three-infusion induction regimen synchronized with three focused-ultrasound sessions (days 0, 7, 14), baseline simulation predicts greater than 90% cytoreduction sustained through day 21, but the corrected stromal dynamics reveal a mechanistically important and clinically relevant consequence: because effective stromal depletion removes a substantial fraction of the tumor's intrinsic growth restraint, the tumor rebounds beyond its pre-treatment burden by day 28 to 40 once nanoparticle exposure ends, a model behavior consistent with independent experimental reports that stromal elements can restrain rather than support PDAC progression. We therefore formulate maintenance dosing as a constrained optimization problem and identify, via grid search over dosing interval subject to a minimum therapeutic-index safety constraint, a maintenance schedule (re-dosing every 4 days) that sustains greater than 97% cytoreduction through day 60 at a therapeutic index of 1.52, compared with induction alone, which loses control by day 28. Global Sobol sensitivity analysis (Saltelli sampling, Jansen total-order estimator, n equals 256 base samples, 2560 total model evaluations) identifies the photothermal maximal kill rate Emax,P (first-order index S1 equals 0.55) and the intrinsic tumor proliferation rate rT (total-order index ST equals 0.65, reflecting substantial interaction effects) as the dominant drivers of day-21 outcome variance, while stromal-degradation rate γN and fibrogenesis rate βT remain negligible even under the corrected, dimensionally consistent formulation, indicating that outcome sensitivity to these two parameters is intrinsically limited by their saturable functional form rather than by a scaling artifact. Monte Carlo uncertainty propagation (n equals 150, ±50% parameter draws) yields an 8.7% probability of reaching a molecular-residual-disease proxy threshold (≤10^6 viable cells) by day 21 under induction alone. We provide a complete, independently executable Python implementation (NumPy/SciPy/Matplotlib only) that reproduces every number and figure in this manuscript exactly, an explicit falsifiability and experimental roadmap, and a dedicated risk assessment of the framework's critical assumptions. We emphasize throughout that this is a hypothesis-generating, theoretical and computational exercise: no wet-lab, in vitro, or in vivo data were generated or used, and all quantitative outputs describe the behavior of the mathematical model under stated assumptions, not validated biological or clinical outcomes.