A sector-integration method for dose/MU calculation in a uniform scanning proton beam

An accurate, simple and time-saving sector integration method for calculating the proton output (dose/monitor unit, MU) is presented based on the following treatment field parameters: aperture shape, aperture size, measuring position, beam range and beam modulation. The model is validated with dose/MU values for 431 fields previously measured at our center. The measurements were obtained in a uniform scanning proton beam with a parallel plate ionization chamber in a water phantom. For beam penetration depths of clinical interest (6-27 cm water), dose/MU values were measured as a function of spread-out Bragg peak (SOBP) extent and aperture diameter. First, 90 randomly selected fields were used to derive the model parameters, which were used to compute the dose/MU values for the remaining 341 fields. The min, max, average and the standard deviation of the difference between the calculated and the measured dose/MU values of the 341 fields were used to evaluate the accuracy and stability, for different energy ranges, aperture sizes, measurement positions and SOBP values. The experimental results of the five different functional sets showed that the calculation model is accurate with calculation errors ranging from -2.4% to 3.3%, and 99% of the errors are less than +/- 2%. The accuracy increases with higher energy, larger SOBP and bigger aperture size. The average error in the dose/MU calculation for small fields ( field size <25 cm(2)) is 0.31 +/- 0.96 (%).