Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Analytical approach to study the scattering of protons at the boundary of stack of inhomogeneous slabs in proton therapy

Document Type : Research Paper

Author

F.S. Rasouli

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

https://doi.org/10.24200/nst.2022.1379
Abstract
In proton therapy, as a prominent method for treating tumors, investigation of transport of the protons in the matter, which is a result of three main interactions of stopping, scattering, and nonelastic nuclear interactions, is highly important. In addition to the experimental method: Monte Carlo simulations and the analytical process. There are sufficiently accurate physical beam models in the analytical approach to approximate the depth-dose distribution. However, this study involves challenges in the presence of localized inhomogeneities, which are unavoidable in body tissues. Investigating the behavior of protons in such a medium is vital to investigate three factors, including scattering, energy distribution, and fluence reduction in the boundaries. The present study deals with the scattering of protons in the slabs of different lengths and materials using the Fermi-Eyges theory. The results showed that the material composition also has a key effect on the scattering of protons in addition to the depth of penetration. The studies on the arrangement of layers and the effect of energy on the scattering showed that the arrangement of materials in the beam path has no significant effect on the final result. The scattering decreases with increasing the energy of the incident beam. It was found that the results are confirmed with the expected physics of the solved problems. To validate the results, the maximum scattering angle of the analytical method was compared with those of to the simulation using the MCNPX Monte Carlo code.

Highlights

1. T. Bortfeld, An analytical approximation of the Bragg curve for therapeutic proton beams, Med. Phys, 24, 2024-2033 (1997).

 

2. M. Goitein, A technique for calculating the influence of thin inhomogeneities on charged particle beams, Med. Phys, 5, 258-264 (1978).

 

3. M. Urie, et al., Degradation of the Bragg peak due to inhomogeneities, Phys. Med. Biol, 31, 1-15 (1986).

 

4. Jette, Electron dose calculation using multiple-scattering theory: Localized inhomogeneities-A new theory, Med. Phys, 182, 123-132 (1991).

 

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

 

6. H.A. Bethe, Molière’s theory of multiple scattering, Phys. Rev, 89, 1256-1266 (1953).

 

7. B. Gottschalk, On the scattering power of radiotherapy protons, Med. Phys, 37, 352-367 (2010).

 

8. Eyges, Leonard, Multiple scattering with energy loss, Physical Review, 74 (10), 1534 (1948).

 

9. Jette, David, Electron dose calculation using multiple‐scattering theory: A new theory of multiple scattering, Med. Phys, 23 (4), 459-477 (1996).

 

10. D. Jette, Electron dose calculation using multiple-scattering theory: A. Gaussian multiple scattering theory, Med. Phys, 15, 123-137 (1988).

 

11. D. Newhauser, R. Zhang, The physics of proton therapy, Phys. Med. Biol, 60, R155-R209 (2015).

 

12. E. Pedroni, et al, Experimental characterization and physical modelling of the dose distribution of scanned proton pencil beams, Physics in Medicine & Biology, 50 (3), 541 (2005).

 

13. D. Jette, et al., Oblique incidence for broad monoenergetic proton beams, Med. Phys, 37, 5683-5690 (2010).

 

14. F.S. Rasouli, S.F. Masoudi, D. Jette, On the proton range and nuclear interactions in compounds and mixtures, Med. Phys, 42, 2364-2367 (2015).

 

15. B. Gottschalk, Physics of Proton Interactions in Matter, in Proton therapy physics, Edited by H. Paganetti, (2012), CRC Press.

Keywords

Bragg curve
Proton therapy
Analytical method
Fermi-Eyges theory
Scattering Power
1. T. Bortfeld, An analytical approximation of the Bragg curve for therapeutic proton beams, Med. Phys, 24, 2024-2033 (1997).
 
2. M. Goitein, A technique for calculating the influence of thin inhomogeneities on charged particle beams, Med. Phys, 5, 258-264 (1978).
 
3. M. Urie, et al., Degradation of the Bragg peak due to inhomogeneities, Phys. Med. Biol, 31, 1-15 (1986).
 
4. Jette, Electron dose calculation using multiple-scattering theory: Localized inhomogeneities-A new theory, Med. Phys, 182, 123-132 (1991).
 
5. Jette, S. Walker, Electron dose calculation using multiple scattering theory: Evaluation of a new model for inhomogeneities, Med. Phys, 19, 1241-1254 (1992).
 
6. H.A. Bethe, Molière’s theory of multiple scattering, Phys. Rev, 89, 1256-1266 (1953).
 
7. B. Gottschalk, On the scattering power of radiotherapy protons, Med. Phys, 37, 352-367 (2010).
 
8. Eyges, Leonard, Multiple scattering with energy loss, Physical Review, 74 (10), 1534 (1948).
 
9. Jette, David, Electron dose calculation using multiple‐scattering theory: A new theory of multiple scattering, Med. Phys, 23 (4), 459-477 (1996).
 
10. D. Jette, Electron dose calculation using multiple-scattering theory: A. Gaussian multiple scattering theory, Med. Phys, 15, 123-137 (1988).
 
11. D. Newhauser, R. Zhang, The physics of proton therapy, Phys. Med. Biol, 60, R155-R209 (2015).
 
12. E. Pedroni, et al, Experimental characterization and physical modelling of the dose distribution of scanned proton pencil beams, Physics in Medicine & Biology, 50 (3), 541 (2005).
 
13. D. Jette, et al., Oblique incidence for broad monoenergetic proton beams, Med. Phys, 37, 5683-5690 (2010).
 
14. F.S. Rasouli, S.F. Masoudi, D. Jette, On the proton range and nuclear interactions in compounds and mixtures, Med. Phys, 42, 2364-2367 (2015).
 
15. B. Gottschalk, Physics of Proton Interactions in Matter, in Proton therapy physics, Edited by H. Paganetti, (2012), CRC Press.

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