Proton energy optimization and reduction for intensity-modulated proton therapy

Intensity-modulated proton therapy (IMPT) is commonly delivered via the spotscanning technique. To 'scan' the target volume, the proton beam is controlled by varying its energy to penetrate the patient's body at different depths. Although scanning the proton beamlets or spots with the same energy can be as fast as 10-20 m s^-1, changing from one proton energy to another requires approximately two additional seconds. The total IMPT delivery time thus depends mainly on the number of proton energies used in a treatment. Current treatment planning systems typically use all proton energies that are required for the proton beam to penetrate in a range from the distal edge to the proximal edge of the target. The optimal selection of proton energies has not been well studied. In this study, we sought to determine the feasibility of optimizing and reducing the number of proton energies in IMPT planning. We proposed an iterative mixed-integer programming optimization method to select a subset of all available proton energies while satisfying dosimetric criteria. We applied our proposed method to six patient datasets: four cases of prostate cancer, one case of lung cancer, and one case of mesothelioma. The numbers of energies were reduced by 14.3%-18.9% for the prostate cancer cases, 11.0% for the lung cancer cases and 26.5% for the mesothelioma case. The results indicate that the number of proton energies used in conventionally designed IMPT plans can be reduced without degrading dosimetric performance. The IMPT delivery efficiency could be improved by energy layer optimization leading to increased throughput for a busy proton center in which a delivery system with slow energy switch is employed.