A dose–volume constraint (DVC) projection‐based algorithm for IMPT inverse planning optimization

Abstract

Purpose Provide a projection‐based algorithm to solve the class of optimization problems encountered in intensity modulated proton therapy (IMPT). The algorithm can handle percentage dose–volume constraints (DVCs) that are usually found in such problems. Methods To seek a feasible solution, the automatic relaxation method was used to project the spot weight vector onto the interval defined by lower and upper bound target dose constraints. The obtained solution was optimized separately based on the objective of each organ at risk (OAR) in addition to maximizing the minimum target dose using the bisection search method using a stopping criterion of 10 cGy. The combined weight was used in the CQ algorithm to solve the split feasibility problem but with a special projection technique due to the nonconvexity of DVCs. The algorithm was applied to four clinical IMPT cases (meningioma, prostate, tongue, and oropharynx) and compared to the corresponding treatment plans optimized in Eclipse. Results The treatment plans obtained, for the four cases, using the BCQ‐ARM algorithm have dosimetric endpoints that are similar to their counterparts generated from Eclipse. The algorithm worked equally well with all cases, including the complex head and neck ones. The stopping criterion of 10 cGy results in making the generated plans slightly less optimal (ε$\epsilon$–optimal) rather than optimal, but with the advantage of the possibility of generating a database of plans. Conclusions The application of the BCQ‐ARM algorithm to different cases of IMPT plans with DVCs was demonstrated. The algorithm is successful in generating plans that are dosimetrically equivalent to their corresponding Eclipse plans. Thus, it is suitable to generate optimized treatment plans in a clinically reasonable time frame.

Superiorization of projection algorithms for linearly constrained inverse radiotherapy treatment planning

“…Our current implementation is, however, specifically geared for linear constraints. Yet other works on feasibility-seeking have shown that other relevant constraints, like, e.g., DVH constraints, can be incorporated into the feasibility-seeking framework, since they can still be interpreted as linear inequalities on a subset (relative volume) of voxels ( 25 – 27 ) .…”

“…If no feasible solution is found, these algorithms find a proximal solution, similar to the piece-wise least-squares approach. Even though they have seen further development over the last decades ( 24 ) and, more recently, also extension to dose-volume constraints ( 25 – 27 ), numerical optimizers have been the preferred choice in the field due to their abilities to handle the nonlinear objective functions, e.g., (generalized) equivalent uniform dose (EUD), which are often desired when prescribing treatment goals.…”