Glioblastoma (GBM) is a highly infiltrative primary brain tumor, and reaction-diffusion models are widely used to describe how its cells spread and proliferate. We derive the classical Fisher-KPP equation from mass conservation, Fickian diffusion, and logistic growth, and extend it to fractionated radiotherapy through a linear-quadratic survival update applied to the tumor-density field at each fraction. The Fisher-KPP equation is solved by finite differences on a three-dimensional voxel grid with 0.5-mm spacing; Geant4 is used only for Monte Carlo photon transport and dose calculation. The schedule of 60~Gy in 30 fractions from the clinical case reported by Roda et al. is reproduced, and th... More >

Mechanistic tumor-response models that are transparent and updatable with patient data are important for model-informed precision radiotherapy. This study presents a reproducible computational framework integrating an explicit mathematical derivation, numerical solver, clinical protocol-derived parameters, and three-dimensional visualization to simulate simplified lung tumor regression during radiotherapy for non-small cell lung cancer (NSCLC). A first-order Taylor approximation, equivalent to the forward Euler method, is derived from Taylor's formula with integral remainder, with local truncation error of order $h^2$. The resulting update rule is applied to a first-order regression model wi... More >