Evaluation of the range shifter model for proton pencil-beam scanning for the Eclipse v.11 treatment planning system

Existing proton therapy pencil-beam scanning (PBS) systems have limitations on the minimum range to which a patient can be treated. This limitation arises from practical considerations, such as beam current intensity, layer spacing, and delivery time. The range shifter (RS) - a slab of stopping material inserted between the nozzle and the patient - is used to reduce the residual range of the incident beam so that the treatment ranges can be extended to shallow depths. Accurate modeling of the RS allows one to calculate the beam spot size entering the patient, given the proton energy, for arbitrary positions and thicknesses of the RS in the beam path. The Eclipse version 11 (v11) treatment planning system (TPS) models RS-induced beam widening by incorporating the scattering properties of the RS material into the V-parameter. Monte Carlo simulations with Geant4 code and analytical calculations using the Fermi-Eyges (FE) theory with Highland approximation of multiple Coulomb scattering (MCS) were employed to calculate proton beam widening due to scattering in the RS. We demonstrated that both methods achieved consistent results and could be used as a benchmark for evaluating the Eclipse V-parameter model. In most cases, the V-parameter model correctly predicted the beam spot size after traversing the RS. However, Eclipse did not enforce the constraint for a nonnegative covariance matrix when fitting the spot sizes to derive the phase space parameters, which resulted in incorrect calculations under specific conditions. In addition, Eclipse v11 incorrectly imposed limits on the individual values of the phase space parameters, which could lead to incorrect spot size values in the air calculated for beams with spot sigmas <3.8 mm. Notably, the TPS supplier (Varian) and hardware vendor (Ion Beam Applications) inconsistently refer to the RS position, which may result in improper spot size calculations.