An international journal published by K. N. Toosi University of Technology

Document Type : Research Article

Author

Department of Physics‎, ‎K.N‎. ‎Toosi University of Technology‎, ‎P.O‎. ‎Box 15875-4416‎, ‎Tehran‎, ‎Iran

Abstract

‎As one of the most clinically relevant parameters in proton radiotherapy‎, ‎the range of incident particles can be measured either by counting the number of protons or through depth-dose evaluation in the target‎. ‎In the latter‎, ‎the range is defined as the depth in the target at the distal 80% point of the Bragg peak‎. ‎In this work‎, ‎a highly accurate analytical model was employed to predict depth-dose distribution‎, ‎and hence the range‎, ‎in a desired target‎. ‎Aiming to study the effect of energy spread on the range‎, ‎proton beams with initial Gaussian distributions have been considered‎. ‎For our arbitrary tested energies‎, ‎the results show that the more the width of energy distribution increases‎, ‎the more the Bragg peaks shift in depth‎, ‎by about‎ -‎0.25% to‎ -25%, ‎compared with those of monoenergetic beams‎. ‎Furthermore‎, ‎it was found that for different widths of initial energy spectrum‎, ‎keeping the mean energy the same‎, ‎the range remains unchanged‎. ‎It was also shown that the results corresponding to utilizing analytical range determination for proton beams of different incident energies in stack of materials deviate from those of Monte Carlo simulations by less than 1.7%‎. ‎The results are encouraging‎, ‎although accurate modeling of analytical proton dose distribution in the presence of tissue inhomogeneities is still an unsolved problem‎.

Highlights

  • Range straggling, defined as spread in the stopping point of protons, is studied.
  • An analytical method for range determination through studying the depth-dose curves is proposed.
  • Effect of initial energy distribution on the values of the range is investigated.
  • The validity of range-energy approximation for stack of different materials is tested.
  • The results are encouraging for accurate dose modeling in tissue inhomogeneities.

Keywords

Bethe, H. (1997). Theory of the passage of fast corpuscular rays through matter. In Selected Works Of Hans A Bethe: (With Commentary), pages 77–154. World Scientific.

Bethe, H. A. and Ashkin, J. (1953). Passage of radiations through matter, Experimental Nuclear Physics E. Segre, 166-357.

Bortfeld, T. (1997). An analytical approximation of the bragg curve for therapeutic proton beams. Medical Physics, 24(12):2024–2033.

Charlwood, F. C., Aitkenhead, A. H., and Mackay, R. I. (2016). A Monte Carlo study on the collimation of pencil beam scanning proton therapy beams. Medical Physics, 43(3):1462–1472.

Goitein, M. (1978). A technique for calculating the influence of thin inhomogeneities on charged particle beams. Medical Physics, 5(4):258–264.

Goitein, M. and Sisterson, J. M. (1978). The influence of thick inhomogeneities on charged particle beams. Radiation Research, 74(2):217–230.

Gottschalk, B. (2010). On the scattering power of radiotherapy protons. Medical Physics, 37(1):352–367.

Gottschalk, B. (2012). Physics of proton interactions in matter, in: Proton Therapy Physics, Edited by Paganetti, H., CRC Press, Taylor Francis Group, BocaRaton.

ICRU (2007). Report No. 78, Prescribing, Recording, and Reporting Proton-Beam Therapy.

Janni, J. F. (1982). Energy loss, range, path length, time-of flight, straggling, multiple scattering, and nuclear interaction probability: In two parts. Part 1. For 63 compounds Part 2. For elements 1_ Z_ 92. Atomic Data and Nuclear Data Tables, 27(4-5):341–529.

Jette, D., Lanzl, L. H., Pagnamenta, A., et al. (1989). Electron dose calculation using multiple-scattering theory: Thin planar inhomogeneities. Medical Physics, 16(5):712–725.

Jette, D. and Walker, S. (1992). Electron dose calculation using multiple-scattering theory: Evaluation of a new model for inhomogeneities. Medical Physics, 19(5):1241–1254.

Jette, D., Yuan, J., and Chen, W. (2010). Oblique incidence for broad monoenergetic proton beams. Medical Physics, 37(11):5683–5690.

Lu, H. and Flanz, J. (2012). Characteristics of clinical proton beams, in: Proton Therapy Physics, Edited by Paganetti, H., CRC Press, Taylor Francis Group, BocaRaton.

Rasouli, F. S., Masoudi, S. F., and Jette, D. (2015). On the proton range and nuclear interactions in compounds and mixtures. Medical Physics, 42(5):2364–2367.

Rasouli, F. S., Masoudi, S. F., and Jette, D. (2016). On the analytical proton dose evaluation in compounds and mixtures. Medical Physics, 43(1):303–307.

Sawakuchi, G. O., Mirkovic, D., Perles, L. A., et al. (2010). An mcnpx monte carlo model of a discrete spot scanning proton beam therapy nozzle. Medical Physics, 37(9):4960–4970. Thomas, E. (1994). Stopping powers and ranges for protons and alpha particles. HEALTH PHYSICS, 66:352–352.