Abstract
We present an analytical model to evaluate in a fast, simple and effective manner the energy delivered by proton beams moving through a cell model made of nucleus and cytoplasm, taking into account the energy carried by the secondary electrons generated along the proton tracks. The electronic excitation spectra of these subcellular compartments have been modelled by means of an empirical parameterization of their dielectric properties. The energy loss rate and target ionization probability induced by swift protons are evaluated by means of the dielectric formalism. With the present model we have quantified the energy delivered, the specific energy, and the number of ionizations produced per incoming ion in a typical human cell by a typical hadrontherapy proton beam having energies usually reached around the Bragg peak (below 20 MeV). We find that the specific energy per incoming ion delivered in the nucleus and in the cytoplasm are rather similar for all the proton energy range analyzed.
Similar content being viewed by others
References
J.S. Loeffler, M. Durante, Nat. Rev. Clin. Oncol. 10, 411 (2013)
F.A. Cucinotta, J.W. Wilson, R. Katz, W. Atwell, G.D. Badhwart, M.R. Shave, Adv. Space Res. 18, 183 (1996)
A.V. Solov’yov, E. Surdutovich, E. Scifoni, I. Mishustin, W. Greiner, Phys. Rev. E 79, 011909 (2009)
E. Surdutovich, A.V. Solov’yov, Eur. Phys. J. D, submitted (2013), arXiv:1312.0897v1 [physics.bio-ph]
L. Sanche, Eur. Phys. J. D 35, 367 (2005)
S. Incerti, H. Seznec, M. Simon, Ph. Barberet, C. Habchi, Ph. Moretto, Radiat. Prot. Dosim. 133, 2 (2009)
Ph. Barberet, F. Vianna, M. Karamitros, T. Brun, N. Gordillo, Ph. Moretto, S. Incerti, H. Seznec, Phys. Med. Biol. 57, 2189 (2012)
T.A. Carrillo-Cázares, E. Torres-García, Radiat. Prot. Dosim. 153, 411 (2013)
M. Douglass, E. Bezak, S. Penfold, Med. Phys. 39, 3509 (2012)
H.L. Byrne, A.L. McNamara, W. Domanova, S. Guatelli, Z. Kuncic, Phys. Med. Biol. 58, 1251 (2013)
R.M. Thomson, Å. Carlsson Tedgren, J.F. Williamson, Phys. Med. Biol. 58, 1123 (2013)
K.M. Prise, G. Schettino, M. Folkard, K. Held, Lancet Oncol. 6, 520 (2005)
M. Bleicher, L. Burigo, M. Durante, M. Herrlitz, M. Krämer, I. Mishustin, I. Müller, F. Natale, I. Pshenichnov, S. Schramm, G. Taucher-Scholz, C. Wälzlein, Beilstein J. Nanotechnol. 3, 556 (2012)
S.Q. Sun, S.-L. Shi, J.A. Hunt, R.D. Leapman, J. Microsc. 177, 18 (1995)
ICRU, Photon, Electron, Proton and Neutron Interaction Data for Body Tissues, International Commission on Radiation Units and Measurements, Report 46 (Bethesda, MD, 1992)
Z. Tan, Y. Xia, M. Zhao, X. Liu, F. Li, B. Huang, Y. Ji, Nucl. Instrum. Methods Phys. Res. B 222, 27 (2004)
R. Garcia-Molina, I. Abril, C.D. Denton, S. Heredia-Avalos, I. Kyriakou, D. Emfietzoglou, Nucl. Instrum. Methods B 267, 2647 (2009)
H. Hayashi, N. Watanabe, Y. Udagawa, C.-C. Kao, Proc. Natl. Acad. Sci. USA 97, 6264 (2000)
M. Inokuti, Rev. Mod. Phys. 43, 297 (1971)
M.A. Nastasi, J.W. Mayer, J.K. Hirvonen, Ion-Solid Interactions: Fundamentals and Applications (Cambridge University Press, Cambridge, 1996)
R. Garcia-Molina, I. Abril, S. Heredia-Avalos, I. Kyriakou, D. Emfietzoglou, Phys. Med. Biol. 56, 6475 (2011)
R. Garcia-Molina, I. Abril, P. de Vera, I. Kyriakou, D. Emfietzoglou, in Fast Ion-Atom and Ion-Molecule Collisions, edited by Dž. Belkic (World Scientific Publishing Company, Singapore, 2012)
M.A. Xapsos, Radiat. Res. 132, 282 (1992)
ICRU, Linear Energy Transfer, International Commission on Radiation Units and Measurements, Report 16 (Bethesda, MD, 1970)
E. Scifoni, E. Surdutovich, A.V. Solov’yov, Eur. Phys. J. D 60, 115 (2010)
E. Surdutovich, A.V. Solov’yov, Eur. Phys. J. D 66, 245 (2012)
M.P.R. Waligórski, R.N. Hamm, R. Katz, Nucl. Tracks Radiat. Meas. 11, 309 (1986)
D. Emfietzoglou, K. Karava, G. Papamichael, M. Moscovitch, Radiat. Prot. Dosim. 110, 871 (2004)
J. Lindhard, K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 28, 1 (1954)
R.H. Ritchie, Phys. Rev. 114, 644 (1959)
G. Schiwietz, P.L. Grande, Nucl. Instrum. Methods Phys. Res. B 175–177, 125 (2001)
P. de Vera, R. Garcia-Molina, I. Abril, A.V. Solov’yov, Phys. Rev. Lett. 110, 148104 (2013)
P. de Vera, I. Abril, R. Garcia-Molina, A.V. Solov’yov, J. Phys.: Conf. Ser. 438, 012015 (2013)
N.D. Mermin, Phys. Rev. B 1, 2362 (1970)
S. Heredia-Avalos, R. Garcia-Molina, J.M. Fernández-Varea, I. Abril, Phys. Rev. A 72, 052902 (2005)
R. Garcia-Molina, I. Abril, I. Kyriakou, D. Emfietzoglou, in Radiation Damage in Biomolecular Systems, edited by G. García Gómez-Tejedor, M.C. Fuss (Springer, Dordrecht, 2012)
I. Abril, R. Garcia-Molina, P. de Vera, I. Kyriakou, D. Emfietzoglou, Adv. Quant. Chem. 65, 129 (2013)
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Nano-scale Insights into Ion-beam Cancer Therapy”, edited by Andrey V. Solov’yov, Nigel Mason, Paulo Limão-Vieira and Malgorzata Smialek-Telega.
Rights and permissions
About this article
Cite this article
de Vera, P., Surdutovich, E., Abril, I. et al. Analytical model of ionization and energy deposition by proton beams in subcellular compartments. Eur. Phys. J. D 68, 96 (2014). https://doi.org/10.1140/epjd/e2014-50041-7
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2014-50041-7