Medical Radiology and Radiation Safety. 2019. Vol. 64. No. 3. P. 5–10

DOI: 10.12737/article_5cf23053d04654.51745769

A.V. Belousov1,2, R.B. Bahtiosin2, M.A. Kolyvanova1, G.A. Krusanov1,3, L.I. Shulepova4, V.N. Morozov1

Calculation of the Depth Dependence of Relative Biological Effectiveness for Clinical Proton Beams

1. A.I. Burnasyan Federal Medical Biophysical Center, Moscow, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. ;
2. Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia;
3. D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia;
4. Federal High-Tech Center for Medical Radiology of Federal Medical Biological Agency, Dimitrovgrad, Russia

A.V. Belousov – Assoc. Prof., PhD Phys.-Math.;
R.B. Bahtiosin – Student;
M.A. Kolyvanova – Head of Lab.;
G.A. Krusanov – Research Fellow;
L.I. Shulepova – Director General; V.N. Morozov – Research Fellow


Purpose: Accurate establishing the value of relative biological effectiveness (RBE) for high energy protons is one of the main challenges of modern radiotherapy. The purpose of the study is to calculate the depth dependence of RBE for proton beams forming a spread-out Bragg peak.

Material and methods: Spatial distributions of absorbed dose and dose-average linear energy transfer (LET) for 50-100 MeV (0.5 MeV energy step) monochromatic proton beams were obtained by Monte-Carlo computer simulation using Geant4 software. A linear dependence of RBE on the dose-average LET was used. Absorbed dose distributions were obtained in a water phantom for monochromatic pencil proton beams of 2.5 mm radius. The absorbed dose and the dose-average LET values were calculated in voxels with dimensions of 2×2×0.2 mm.

Results: Calculations of depth dependencies of absorbed dose and dose-average LET for 50–100 MeV monochromatic proton beams were performed. Depth dependencies of RBE for these beams were established. The weighing coefficients values allowing to generate uniformspread-out Bragg peak (SOBP) were determined. Depth distribution of RBE-weighted dose and RBE values for SOBP were found.

Conclusion: The impact of the initial beam energy step on the degree of homogeneity of the modified Bragg curve was investigated. It was shown that a step up to 1.5 MeV is acceptable for generate a smooth Bragg curve. The depth dependence of the average RBE value is a complex function, which rapidly changes especially at the far end of the SOBP. RBE may vary up to 10–30 % compared to current clinical value. The linear model of RBE–LET dependence shown in the study can be easily used in dosimetric planning systems, that may will significantly improve the quality of proton radiotherapy.

Key words: proton radiotherapy, relative biological effectiveness, linear energy transfer, spread-out Bragg peak, Monte-Carlo method, Geant4


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For citation: Belousov AV, Bahtiosin RB, Kolyvanova MA, Krusanov GA, Shulepova LI, Morozov VN. Calculation of the Depth Dependence of Relative Biological Effectiveness for Clinical Proton Beams. Medical Radiology and Radiation Safety. 2019;64(3):5-10. (Russian).

DOI: 10.12737/article_5cf23053d04654.51745769

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