Analytical calculation of the dose to a spherical target by an ion at almost all impact parameters, and calculation of the energy deposition spectra

Abstract

Microdosimetry can be used to estimate or evaluate quality factors for risk assessment in radiation protection and to quantify relative biological effectiveness for treatment planning of hadron radiation therapy. Radiation physics has shown that energetic ions deposit energy at the sub-cellular level in a complex manner: the track structure. Amorphous track models such as the Local Effect Model (LEM) and the Kiefer-Chatterjee Model are often used as an approximation of the complex ion track structure. We have previously calculated an analytical expression for the dose to a spherical target fully located in the penumbra of an ion track using the LEM. In this work, the analytical calculation has been extended to include almost all impact parameters. Furthermore, using the dose as a function of the impact parameter, it was possible to obtain the theoretical energy deposition spectra to a sphere irradiated uniformly. The analytical calculations were compared with simulations performed using the radiation track structure code RITRACKS (Relativistic Ion Tracks) using six ions of interest (¹H⁺, 1,000 MeV; ⁴He²⁺, 250 MeV/n; ¹²C⁶⁺, 290 MeV/n; ¹⁶O⁸⁺, 325 MeV/n; ²⁸Si¹⁴⁺, 300 MeV/n; ⁵⁶Fe²⁶⁺, 1,000 MeV/n). The results show an excellent agreement of the dose as a function of impact parameter. The dose deposition spectra show better agreement with RITRACKS at high Linear Energy Transfer (LET) than at low LET. This model could be useful in situations where microdosimetry calculations are needed without requiring the use of Monte-Carlo track structure codes.