Range and modulation dependencies for proton beam dose per monitor unit calculations

Calculations of dose per monitor unit (D/MU) are required in addition to measurements to increase patient safety in the clinical practice of proton radiotherapy. As in conventional photon and electron therapy, the D/MU depends on several factors. This study focused on obtaining range and modulation dependence factors used in D/MU calculations for the double scattered proton beam line at the Midwest Proton Radiotherapy Institute. Three dependencies on range and one dependency on modulation were found. A carefully selected set of measurements was performed to discern these individual dependencies. Dependencies on range were due to: (1) the stopping power of the protons passing through the monitor chamber; (2) the reduction of proton fluence due to nuclear interactions within the patient; and (3) the variation of proton fluence passing through the monitor chamber due to different source-to-axis distances (SADs) for different beam ranges. Different SADs are produced by reconfigurations of beamline elements to provide different field sizes and ranges. The SAD effect on the D/MU varies smoothly as the beam range is varied, except at the beam range for which the first scatterers are exchanged and relocated to accommodate low and high beam ranges. A geometry factor was devised to model the SAD variation effect on the D/MU. The measured D/MU variation as a function of range can be predicted within 1% using the three modeled dependencies on range. Investigation of modulated beams showed that an analytical formula can predict the D/MU dependency as a function of modulation to within 1.5%. Special attention must be applied when measuring the D/MU dependence on modulation to avoid interplay between range and SAD effects.