Microdosimetry Study of Proton Quality Factor Using Analytic Model Calculations

The quality factor (Q) is formally linked to the stochastic (e.g., carcinogenic) risk of diverse ionizing radiations at low doses and/or low dose rates. Q can be a function of the non-stochastic physical quantity Linear Energy Transfer (LET) or the microdosimetric parameter lineal energy (y). These two physical quantities can be calculated either by Monte Carlo (MC) track-structure simulations or by analytic models. In this work, various generalized analytical models were utilized and combined to determine the proton lineal energy spectra in liquid water spheres of various sizes (i.e., 10–3000 nm diameter) over the proton energy range of 1–250 MeV. The calculated spectra were subsequently used within the Theory of Dual Radiation Action (TDRA) and the ICRU Report 40 microdosimetric methodologies to determine the variation of Q¯ with proton energy. The results revealed that the LET-based Q values underestimated the microdosimetric-based Q¯ values for protons with energy below ~100 MeV. At energies relevant to the Bragg peak region (<20–30 MeV), the differences were larger than 20–50%, while reaching 200–500% at ~5 MeV. It was further shown that the microdosimetric-based Q¯ values for protons below ~100 MeV were sensitive to the sphere size. Finally, condensed-phase effects had a very small (<5%) influence on the calculated microdosimetric-based Q¯ over the proton energy range considered here.