Implementation of an improved dose-per-MU model for double-scattered proton beams to address interbeamline modulation width variability

Because treatment planning systems (TPSs) generally do not provide monitor units (MUs) for double-scattered proton plans, models to predict MUs as a function of the range and the nominal modulation width requested of the beam delivery system, such as the one developed by the MGH group, have been proposed. For a given nominal modulation width, however, the measured modulation width depends on the accuracy of the vendor's calibration process and may differ from this nominal value, and also from one beamline to the next. Although such a difference can be replicated in our TPS, the output dependence on range and modulation width for each beam option or suboption has to be modeled separately for each beamline in order to achieve maximal 3% inaccuracy. As a consequence, the MGH output model may not be directly transferable. This work, therefore, serves to extend the model to more general clinic situations. In this paper, a parameterized linear-quadratic transformation is introduced to convert the nominal modulation width to the measured modulation width for each beam option or suboption on a per-beamline basis. Fit parameters are derived for each beamline from measurements of 60 reference beams spanning the minimum and maximum ranges, and modulation widths from 2 cm to full range per option or suboption. Using the modeled modulation width, we extract the MGH parameters for the output dependence on range and modulation width. Our method has been tested with 1784 patient-specific fields delivered across three different beamlines at our facility. For these fields, all measured outputs fall within 3%, and 64.4% fall within 1%, of our model. Using a parameterized linear-quadratic modulation width, MU calculation models can be established on a per-beamline basis for each double scattering beam option or suboption.