The practical radius of a pencil beam in proton therapy

The central Gaussian shaped high dose region of a pencil beam (PB) in light ion beam therapy (LIBT) is enveloped by a low dose region causing non-negligible field size effects and impairs the dose calculation accuracy considerably if the low dose envelope is not well modeled. The purpose of this study was to calculate the practical radius, R${}_c$, at which a PB does not influence a field more than a certain accuracy level. Lateral dose profiles of proton beams in water were simulated using GATE/Geant4. Those lateral dose profiles were integrated numerically and used to calculate field size factors (FSFs). The R${}_c$ was then determined such, that the lateral dose at radii exceeding R${}_c$ can be neglected without compromising the FSF of a 20 cm × 20 cm field more than a desired accuracy level c. The practical radius R${}_c$ yielding c = 0.5% was compared to the frequently applied concept of full width at a ratio x of the maximum (FWxM). The sensitivity to variations of the beam width was tested by increasing the initial beam width σ${}_C$ of the clinical beam model by 0.5 and 1 mm, respectively. Neglecting the dose at radii exceeding R${}_c$ resulted in the desired FSF accuracy, whereas using the FW0.01%M cut resulted in varying accuracy. In order to yield a constant FSF accuracy, the ratio x in FWxM ranged from 0.003% to 0.065% of the maximum. In contrast to R${}_c$, FWxM was sensitive to variations of the initial beam width. The maximum R${}_c$ over all depths was less than 7 cm for the low(62.4 MeV) and medium(148.2 MeV) proton energy beam, which suggests that a plane parallel ionization chamber exceeding that radius is sufficient to acquire laterally integrated depth dose distributions for those energies. However, this holds not true for the highest energy (252.7 MeV) or when including a range shifter (RaShi). The values of R${}_c$ are specific to our beam line configuration as the maximum R${}_c$ was depending on both, the scattering material in the Nozzle as well as the distance of the air-gap between Nozzle and phantom.