Analytic-Gradient-Driven Joint Optimization of Spot Geometry and Intensity In Proton Radiotherapy Planning
Abstract
Purpose
In intensity-modulated proton therapy (IMPT), spot positions are conventionally fixed on uniform grids, and optimization is limited to spot weights. This constraint can restrict achievable dose conformity and increase the number of spots required to meet clinical objectives. The purpose of this study is to develop a clinically practical IMPT framework that jointly optimizes spot positions and weights to improve plan quality and delivery efficiency.
Methods
We propose a joint optimization of IMPT (JO-IMPT) framework that alternates between spot weight optimization and spot position updates. An analytic gradient of the objective function with respect to spot position is rigorously derived from the dose model and incorporated into a gradient-based optimization scheme. This formulation enables efficient and stable updates of spot locations without increasing model complexity. The proposed method is evaluated against conventional IMPT with uniform spot placement using identical optimization objectives.
Results
Compared with standard IMPT using uniform spot placement and the same number of spots, JO-IMPT achieves improved target coverage and enhanced sparing of organs at risk (OARs). Importantly, JO-IMPT produces plan quality comparable to or better than a reference IMPT plan with uniform spot placement that requires approximately three times more spots. This reduction in spot count improves spatial efficiency while maintaining or improving clinically relevant dosimetric endpoints.
Conclusion
Analytic-gradient-driven joint optimization of spot positions and weights enables clinically meaningful improvements in IMPT plan quality while substantially reducing the number of required spots. The proposed framework relaxes limitations imposed by fixed spot grids and provides a more flexible planning strategy without increasing computational or delivery complexity.