title: A numerical method to optimise the spatial dose distribution in carbon ion radiotherapy planning.
abstract: The authors describe a numerical algorithm to optimise the entrance spectra of a composition of pristine carbon ion beams which delivers a pre-assumed dose-depth profile over a given depth range within the spread-out Bragg peak. The physical beam transport model is based on tabularised data generated using the SHIELD-HIT10A Monte-Carlo code. Depth-dose profile optimisation is achieved by minimising the deviation from the pre-assumed profile evaluated on a regular grid of points over a given depth range. This multi-dimensional minimisation problem is solved using the L-BFGS-B algorithm, with parallel processing support. Another multi-dimensional interpolation algorithm is used to calculate at given beam depths the cumulative energy-fluence spectra for primary and secondary ions in the optimised beam composition. Knowledge of such energy-fluence spectra for each ion is required by the mixed-field calculation of Katz's cellular Track Structure Theory (TST) that predicts the resulting depth-survival profile. The optimisation algorithm and the TST mixed-field calculation are essential tools in the development of a one-dimensional kernel of a carbon ion therapy planning system. All codes used in the work are generally accessible within the libamtrack open source platform.
authors.affiliation: Institute of Nuclear Physics PAN, Krakow, Poland Leszek.Grzanka@ifj.edu.pl.
authors.forename: L
authors.initials: L
authors.lastname: Grzanka
authors.affiliation: Institute of Nuclear Physics PAN, Krakow, Poland.
authors.forename: M
authors.initials: M
authors.lastname: Korcyl
authors.affiliation: Institute of Nuclear Physics PAN, Krakow, Poland.
authors.forename: P
authors.initials: P
authors.lastname: Olko
authors.affiliation: Institute of Nuclear Physics PAN, Krakow, Poland The Marie Skłodowska-Curie Centre of Oncology, Krakow Division, Krakow, Poland.
authors.forename: M P R
authors.initials: MP
authors.lastname: Waligorski
mesh_terms: D000465:Algorithms; D000818:Animals; D016466:CHO Cells; D002470:Cell Survival / Q000528:radiation effects*; D003198:Computer Simulation; D006224:Cricetinae; D003412:Cricetulus; D063193:Heavy Ion Radiotherapy / Q000592:standards*; D018499:Linear Energy Transfer / Q000528:radiation effects*; D008962:Models, Theoretical; D009010:Monte Carlo Method; D011874:Radiometry / Q000379:methods; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods* / Q000592:standards*