Range-modulated pencil beam algorithm for proton dose calculations

The range-modulated pencil beam algorithm (RMPBA) has been developed for pr oton treatment planning on the basis of the pencil beam algorithm (PBA) to reduce the calculation time yet realize sufficient accuracy. It uses the de pth-dose distribution of the range-modulated beam as a central-axis term of pencil beams. The spread of the range-modulated pencil beam is derived by assuming that the protons pass through the average thickness of the ridge-f ilter. The accuracy of dose calculations by the RMPBA is verified by compar ison with dose measurements in water performed using a silicon semiconducto r detector. The results of the measured dose distributions agree well with those of the calculations using the RMPBA, Furthermore. the calculation tim e required by the RMPBA is one-sixth of that required by the PBA in the cas e of the six-step ridge-filter. Therefore, the dose-calculation method by t he RMPBA will be useful and applicable to actual treatment planning of prot on therapy.