TY  - JOUR
AU  - Farias, Matheus dos Santos
PY  - 2026
DA  - 2026/10/16
TI  - Carbon Ion Hadron Therapy: Analytical Formulation of Tumor Regression in Pancreatic Cancer by Computed Tomography
JO  - Journal of Numerical Simulations in Physics and Mathematics
T2  - Journal of Numerical Simulations in Physics and Mathematics
JF  - Journal of Numerical Simulations in Physics and Mathematics
VL  - 3
IS  - 1
SP  - 38
EP  - 50
DO  - 10.62762/JNSPM.2026.765432
UR  - https://www.icck.org/article/abs/JNSPM.2026.765432
KW  - pancreatic cancer
KW  - carbon-ion therapy
KW  - reaction-diffusion model
KW  - finite-difference method
KW  - Euler method
KW  - computational simulation
AB  - 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 tumor volume 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.
SN  - 3068-9082
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Farias2026Carbon,
  author = {Matheus dos Santos Farias},
  title = {Carbon Ion Hadron Therapy: Analytical Formulation of Tumor Regression in Pancreatic Cancer by Computed Tomography},
  journal = {Journal of Numerical Simulations in Physics and Mathematics},
  year = {2026},
  volume = {3},
  number = {1},
  pages = {38-50},
  doi = {10.62762/JNSPM.2026.765432},
  url = {https://www.icck.org/article/abs/JNSPM.2026.765432},
  abstract = {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 tumor volume 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.},
  keywords = {pancreatic cancer, carbon-ion therapy, reaction-diffusion model, finite-difference method, Euler method, computational simulation},
  issn = {3068-9082},
  publisher = {Institute of Central Computation and Knowledge}
}