Toward Genetic Fingerprint Informed Precision Oncology: A Quantitative Modeling and Uncertainty Quantification Framework for Solid Tumor Drug Transport and Response

Solid tumors remain difficult to treat pharmacologically because dense extracellular matrix, elevated interstitial fluid pressure, and chaotic vasculature limit the penetration of systemically delivered agents, while intratumoral genetic heterogeneity undermines the durability of any single molecular target. This paper develops and numerically validates a quantitative, mechanistic modeling framework intended to support future genetic fingerprint informed treatment design. The framework couples a reaction diffusion advection model of drug transport through tumor interstitium, solved with an unconditionally stable Crank Nicolson scheme; a mass action ligand receptor binding model; a Hill type pharmacodynamic dose response relationship; and a Gompertzian tumor growth model calibrated by a self contained Bayesian Markov chain Monte Carlo sampler, using four independent chains with Gelman Rubin statistics below 1.02 for every parameter. Global parameter sensitivity is quantified with a Saltelli sampled, Jansen estimated Sobol variance decomposition, implemented from first principles and validated against the closed form Ishigami benchmark, with estimated and analytical indices agreeing to within 0.003. We report the resulting posterior parameter distributions, penetration and binding kinetics profiles, and first and total order sensitivity indices, all reproduced exactly by the accompanying code. We explicitly do not claim clinical or experimental validation. No genomic sequencing, molecular synthesis, animal, or human data were used, and the calibration data are synthetic and clearly labeled as such. The paper's contribution is the mathematical and computational scaffold, together with an explicit falsifiability and experimental validation roadmap and a risk and limitations assessment, required before any genetic fingerprint informed synthesis pipeline could be responsibly pursued.