On a revised concept of an event that allows linking nanodosimetry and microdosimetry in nanometric sites with macroscopic dosimetry

Abstract

This work reviews the concepts of an event used in micro- and nanodosimetry and analyzes how single event distributions could theoretically be derived from probability distributions related to interactions of the primary particle which produce secondary electrons. It is shown that the corresponding mathematical expressions of conditional ionization cluster size distributions are alike those for the single event frequency distribution of energy imparted, particularly when all tracks are considered which intersect the volume in which interactions of the primary particle can result in energy deposits in the site. Track structure simulations of proton with energies between 1 MeV and 100 MeV are used to study how the occurrence of events depends on site size, beam radius, and proton energy. The range of impact parameters of particle tracks that contribute to energy imparted in a site appears not to depend on whether any energy deposits or only energy deposits by ionizations are considered. Since there is no longer a one-to-one correspondence between tracks passing a site and the occurrence of an event, it is proposed to use the fluence for which on average one event occurs as a substitute for single events. For protons, the product of this fluence and the site cross section or the average number of tracks necessary for an event shows an interesting dependence on site size and particle energy with asymptotic values close to unity for large sites and proton energies below 10 MeV. For a proton energy of 1 MeV, a minimum of the number of tracks is observed for sites between 5 nm and 10 nm diameter. The relative differences between the numbers of track per event on average obtained with different options of Geant4-DNA are in the order of 10 % and illustrate the need for further investigations into cross-section datasets and their uncertainties.