Integrated beam orientation and scanning‐spot optimization in intensity‐modulated proton therapy for brain and unilateral head and neck tumors
Authors: Gu Wenbo , O'Connor Daniel , Nguyen Dan , Yu Victoria Y. , Ruan Dan , Dong Lei , Sheng Ke 
Published: February 2018

Purpose

Intensity‐Modulated Proton Therapy (IMPT) is the state‐of‐the‐art method of delivering proton radiotherapy. Previous research has been mainly focused on optimization of scanning spots with manually selected beam angles. Due to the computational complexity, the potential benefit of simultaneously optimizing beam orientations and spot pattern could not be realized. In this study, we developed a novel integrated beam orientation optimization (BOO) and scanning‐spot optimization algorithm for intensity‐modulated proton therapy (IMPT).

Methods

A brain chordoma and three unilateral head‐and‐neck patients with a maximal target size of 112.49 cm3 were included in this study. A total number of 1162 noncoplanar candidate beams evenly distributed across 4 steradians were included in the optimization. For each candidate beam, the pencil‐beam doses of all scanning spots covering the PTV and a margin were calculated. The beam angle selection and spot intensity optimization problem was formulated to include three terms: a dose fidelity term to penalize the deviation of PTV and OAR doses from ideal dose distribution; an L1‐norm sparsity term to reduce the number of active spots and improve delivery efficiency; a group sparsity term to control the number of active beams between 2 and 4. For the group sparsity term, convex L2,1‐norm and nonconvex L2,1/2‐norm were tested. For the dose fidelity term, both quadratic function and linearized equivalent uniform dose (LEUD) cost function were implemented. The optimization problem was solved using the Fast Iterative Shrinkage‐Thresholding Algorithm (FISTA). The IMPT BOO method was tested on three head‐and‐neck patients and one skull base chordoma patient. The results were compared with IMPT plans created using column generation selected beams or manually selected beams.

Results

The L2,1‐norm plan selected spatially aggregated beams, indicating potential degeneracy using this norm. L2,1/2‐norm was able to select spatially separated beams and achieve smaller deviation from the ideal dose. In the L2,1/2‐norm plans, the [mean dose, maximum dose] of OAR were reduced by an average of [2.38%, 4.24%] and[2.32%, 3.76%] of the prescription dose for the quadratic and LEUD cost function, respectively, compared with the IMPT plan using manual beam selection while maintaining the same PTV coverage. The L2,1/2 group sparsity plans were dosimetrically superior to the column generation plans as well. Besides beam orientation selection, spot sparsification was observed. Generally, with the quadratic cost function, 30%~60% spots in the selected beams remained active. With the LEUD cost function, the percentages of active spots were in the range of 35%~85%.The BOO‐IMPT run time was approximately 20 min.

Conclusion

This work shows the first IMPT approach integrating noncoplanar BOO and scanning‐spot optimization in a single mathematical framework. This method is computationally efficient, dosimetrically superior and produces delivery‐friendly IMPT plans.