Abstract
The spatial distribution of energy deposition events is an essential aspect in the determination of the radiobiological effects of ionizing radiation at the cellular level. Microdosimetry provides a theoretical framework for the description of these events, and has been used in several studies to address problems such as the characterization of Linear Energy Transfer (LET) and Relative Biological Effectiveness (RBE) of ion beams for proton therapy applications. Microdosimetry quantities and their distributions can be obtained by means of Monte Carlo simulations. In this work, we present a track structure Monte Carlo (MC) application, based on Geant4-DNA, for the computation of microdosimetric distributions of protons in liquid water. This application provides two sampling methods uniform and weighted, for the scoring of the quantities of interest in spherical sites, with diameters ranging from 1 to 10 μm. As an element of novelty, the work shows the approach followed to calculate, without resorting to dedicated simulations, the distribution of energy imparted to the site per electronic collision of the proton, which can be used to obtain the macroscopic dose-averaged LET as proposed by Kellerer. Furthermore, in this work the concept of effective mean chord length is proposed to take into account δ-ray influx and escape in the calculation of macroscopic dose-averaged LET for proton track segments and retrieve the agreement predicted by Kellerer’s formula. Finally, the results obtained demonstrate that our MC application is reliable and computational-efficient to perform calculations of microdosimetric distributions and dose-averaged LET of proton track segments in liquid water.
Highlights
The radiobiological effects of ionizing radiation can be traced back to the microscopic patterns of energy deposition in irradiated media, which can be described quantitatively with the formalism of microdosimetry [1,2,3]
We present the main features of a Monte Carlo (MC) code developed with Geant4 [19,20,21] for the computation of microdosimetric distributions generated by proton track segments in liquid water via track-structure simulations done with the package Geant4-DNA [22,23,24,25]
Regarding the weighted-averaged energy deposited per individual proton collision, δ2, an intermediate step is necessary to extract its value from the simulations. This quantity is an independent random factor from Linear Energy Transfer (LET) and chord length, their variances should not be included in the computation of δ2 when calculating LD with Eq 12
Summary
The radiobiological effects of ionizing radiation can be traced back to the microscopic patterns of energy deposition in irradiated media, which can be described quantitatively with the formalism of microdosimetry [1,2,3]. In view of the growing awareness of the variations of proton Relative Biological Effectiveness (RBE) with increasing Linear Energy Transfer (LET) [4,5,6], several studies have turned to the framework of microdosimetry to approach problems such as the characterization of LET. Microdosimetry, on one hand, permits the calculation of RBE from a microscopic approach by means of the Microdosimetric-Kinetic Model (MKM) [11,12,13] for cell killing endpoint and, on the other hand, provides physical concepts and computational tools to calculate macroscopic dose-averaged LET (LD) distributions. The difference between LD and yD is given by energy straggling, which can be accounted for by considering the weighted average δ2 of the energy imparted to the site per individual collision εc of the incident particle. The mathematical description of this relation was given by Kellerer, and can be used to extract the macroscopic dose-averaged LET of a beam from its microdosimetric distributions [16,17,18]
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