A fully flexible joint lattice position and dose optimization method for LATTICE therapy.

Background: Lattice radiotherapy (LATTICE) is a technique of spatially fractionated radiation therapy (SFRT) that delivers high radiation doses to specific regions (vertices) within a large tumor, forming a spatially modulated "lattice" pattern, while surrounding areas receive lower doses to minimize damage to healthy tissues. In LATTICE, vertices (regions of high dose) are typically placed at regular intervals within tumors, such as simple cubic or hexagonal arrangement, which limits the flexibility needed to adapt to irregular tumor shapes and the proximity of critical organs, potentially leading to unexpected hotspots or under-treatment of tumor regions. Optimizing the placement of vertices in LATTICE is beneficial for precisely targeting high-dose regions within the tumor while minimizing radiation exposure to adjacent healthy tissue, but there is still no optimization method available for solving the positions of fully flexible placed vertices. The great challenge in such optimization lies in handling the constraints on the relative positions between different vertices. Purpose: This work aims to develop a new treatment planning method for LATTICE with fully flexible placement of vertices and joint optimization of the position of each lattice vertex and dose, to improve overall plan quality compared with conventional LATTICE planning methods relying on manual regular placements of lattice vertices. Methods: The proposed method jointly optimizes each lattice vertex position and other plan optimization variables (proton spot weights or photon fluences) during the dose optimization process. This is formulated as a new constrained optimization problem by adding each lattice vertex position to optimization variables with appropriate constraints to meet the requirements of the LATTICE vertices placement guideline on the 1) center-to-center distance between lattice vertices and 2) distance of lattice vertices to the target boundaries. The optimization problem is solved by the alternating direction method of multipliers and iterative convex relaxation methods. Results: Plans of our proposed method (NEW) were compared with conventional LATTICE plans. We created 100 LATTICE plans for the abdomen and lung patients, respectively, with different vertices positions, respectively, from which three plans, termed BEST, MID and WORST, were selected for each anatomical location with the largest, median and smallest total optimization objective Conclusion: A new LATTICE treatment planning approach with fully flexible joint lattice position and dose optimization is introduced and demonstrated to improve target PVDR and OAR sparing, compared to conventional LATTICE method with regular placements of lattice vertices.