https://doi.org/10.1140/epjp/s13360-024-05886-6
Regular Article
Analytical calculation of proton beam Bragg curve inside heterogeneous media
Physics Department, Hakim Sabzevari University, P.O. 9617976487, Daneshgah Blvd, Sabzevar, Iran
a h.baghani@hsu.ac.ir, hamidreza.baghani@gmail.com
Received:
24
September
2024
Accepted:
29
November
2024
Published online:
14
December
2024
Determination of Bragg curve in proton therapy is of main importance. Bortfeld derived an impressive analytical equation for calculation of proton dose inside water as a homogeneous medium. However, during penetrating through the body, proton may traverse different tissues. The current study aims to derive an analytical expression for proton dosimetry inside heterogeneous media. Some heterogeneous media consisting of different consecutive layers of bone, muscle, and PMMA with various thicknesses (ranging from 10.5 cm to 23 cm) were considered, and an analytical expression was derived for proton Bragg curve quantification according to introduced structures by Bortfeld and Zhang et al. studies. Geant4 Monte Carlo Toolkit was also applied for Bragg curve calculation inside the investigated heterogeneous media at different proton energies of 120 MeV, 135 MeV, 140 MeV, 150 MeV, and 200 MeV. Finally, the simulated and analytically calculated Bragg curves were quantitatively compared through gamma analysis (1%/1mm criteria) to examine the validity of the introduced analytical equation. In this regard, a very close agreement was found between the analytical and Monte Carlo results, where the gamma index values were always lower than unity in all investigated scenarios. The mean gamma index values for all calculations were less than 0.37. This finding confirms the validity of the derived equation for analytical Bragg curve calculation inside heterogeneous media. From the results, it can be concluded that the derived analytical equation can be reliably used for proton dose calculation along central axis and inside any arbitrary heterogeneous media, provided that the required analytical parameters for contributing media would be available.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
