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Life sciences · Journal article
Journal of Numerical Simulations in Physics and Mathematics · October 16, 2026
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This study formulates a mathematical and computational model of tumor-cell-density regression in pancreatic cancer treated with carbon-ion hadron therapy. A reaction-diffusion equation with logistic proliferation and a local radiation-induced loss term is derived term by term, discretized with a two-dimensional finite-difference scheme and forward Euler time stepping, and implemented in Python. The treatment input follows a published carbon-ion schedule of 48~Gy(RBE) in 12 fractions of 4~Gy(RBE). The simulation produces sequential two- and three-dimensional maps of the modeled tumor-cell density as a function of accumulated dose; in the three-dimensional reconstruction the relative tumorvolume falls from 0.662 after the first fraction to 0.001 after the twelfth, while the two-dimensional density maps reach a thresholded value of zero from fraction six onward. The diffusion coefficient is held constant (homogeneous-medium approximation) and the dose response is linear; both are stated as simplifications, not as complete radiobiological descriptions. Possible translational uses, namely patient-specific parameter estimation, CT-derived geometry, dose optimization and treatment adaptation, are discussed together with the calibration and validation that would be required before any clinical decision-support application.