Monitor unit calculations for range-modulated spread-out Bragg peak fields

We derive, from first principles, a model to predict the output factors for spread-out Bragg peak proton fields (SOBP). The model is based on the simple observation that the output factor is the ratio of SOBP plateau dose to the dose measured in the ionization reference chamber. The latter, in turn, equates to the entrance dose of the SOBP corrected for inverse square. We use a theoretical derivation of this ratio to establish the relationship between the output factor and the distal range and modulation width of the SOBP. In addition, the theoretical derivation reduces the dependence on the distal range and modulation width into a single factor r = (R - M)/M. We compare the theoretical derivation against measurements obtained at the Northeast Proton Therapy Facility for output factors for clinical fields. The agreement between measurements and prediction is 2.9%.