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A numerical method to optimise the spatial dose distribution in carbon ion radiotherapy planning

L. GrzankaInstitute of Nuclear Physics PAN, Krakow, PolandM. KorcylInstitute of Nuclear Physics PAN, Krakow, PolandP. OlkoInstitute of Nuclear Physics PAN, Krakow, PolandM.P.R. WaligórskiInstitute of Nuclear Physics PAN, Krakow, Poland

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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.

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