A systematic study of the contribution of counting statistics to the final lineal energy uncertainty in microdosimetry

Abstract

Objectives. Microdosimetry is proving to be a reliable and powerful tool to be applied in different fields such as radiobiology, radiation protection and hadron therapy. However, accepted standard protocols and codes of practice are still missing. With this regard, a systematic and methodical uncertainty analysis is fundamental to build an accredited uncertainty budget of practical use. This work studied the contribution of counting statistics (i.e. number of events collected) to the final frequency-mean and dose-mean lineal energy uncertainties, aiming at providing guidelines for good experimental and simulation practice. The practical limitation of current technologies and the non-negligible probability of nuclear reactions require careful considerations and nonlinear approaches. Approach. Microdosimetric data were obtained by means of the particle tracking Monte Carlo code Geant4. The uncertainty analysis was carried out relying on a Monte Carlo based numerical analysis, as suggested by the BIPM's 'Guide to the expression of uncertainty in measurement'. Final uncertainties were systematically investigated for proton, helium and carbon ions at an increasing number of detected events, for a range of different clinical-relevant beam energies. Main results. Rare events generated by nuclear interactions in the detector sensitive volume were found to massively degrade microdosimetric uncertainties unless a very high statistics is collected. The study showed an increasing impact of such events for increasing beam energy and lighter ions. For instance, in the entrance region of a 250 MeV proton beam, about 5 - 107 events need to be collected to obtain a dose-mean lineal energy uncertainty below 10%. Significance. The results of this study help define the necessary conditions to achieve appropriate statistics in computational microdosimetry, pointing out the importance of properly taking into account nuclear interaction events. Their impact on microdosimetric quantities and on their uncertainty is significant and cannot be overlooked, particularly when characterising clinical beams and radiobiological response. This work prepared the ground for deeper investigations involving dedicated experiments and for the development of a method to properly evaluate the counting statistics uncertainty contribution in the uncertainty budget, whose accuracy is fundamental for the clinical transition of microdosimetry.