Vertex Position Optimization for LATTICE Therapy

Abstract

LATTICE radiation therapy (RT) aims to deliver 3D heterogenous dose of high peak-to-valley dose ratio (PVDR) to the tumor target, with peak dose at lattice vertices inside the target and valley dose for the rest of the target. In current clinical practice the lattice vertex positions are constant during treatment planning. This work proposes a new LATTICE plan optimization method that can optimize lattice vertex positions as plan variables, which is the first lattice vertex position optimization study to the best of our knowledge. The new LATTICE treatment planning method optimizes lattice vertex positions as well as other plan variables (e.g., photon fluences or proton spot weights), with optimization objectives for target PVDR and organs-at-risk (OAR) sparing. To satisfy mathematical differentiability, the lattice vertices are approximated in sigmoid functions. For geometric feasibility, proper geometry constraints are enforced onto the lattice vertex positions. The lattice vertex position optimization problem is solved by iterative convex relaxation method, where lattice vertex positions and photon/proton plan variables are jointly updated via the Quasi-Newton method. Both photon and proton LATTICE RT were considered, and the optimal lattice vertex positions in terms of plan objectives were found by solving all possible combinations on given discrete positions via heuristic searching based on standard IMRT/IMPT, which served as the ground truth for validating the new LATTICE method ("NEW"). That is, the plan with the smallest optimization objective ("BEST"), the plan with the median optimization objective ("MID"), and the plan with the largest optimization objective ("WORST") were selected as the reference plans to be compared with NEW. The table was for an abdomen case with the large bowel as the OAR, where the parameters are total optimization objective f, the mean valley dose of target Dvalley, the mean peak dose of target Dpeak, PVDR = Dpeak/Dvalley, and the mean dose of large bowel Dbowel. The unit of doses is Gy. The results in the table show that the new method indeed provided the optimal lattice vertex positions with the smallest optimization objective, the largest target PVDR, and the best OAR sparing. A new LATTICE treatment planning method is proposed and validated that can optimize lattice vertex positions as well as other photon or proton plan variables for improving target PVDR and OAR sparing.