Geometric optimization of dose distribution in spatially fractionated radiation therapy

Objective. Current planning methods for spatially fractionated radiation therapy (SFRT) use peak-dose spheres of equal size with uniform spacing and rely on inexact optimization methods for placement, which may lead to suboptimal coverage of target volumes of widely variable geometry. This work aimed to develop a flexible optimization model for SFRT planning that addresses the shortcomings of existing approaches in terms of sphere sizes and arrangements and offers exact solution algorithms. Approach. This objective was sought through a graph-theoretic approach. By discretizing the tumor volume, a graph was constructed, where the vertices represent candidate locations and sizes for the peak-dose spheres, and the edges represent conflicts among candidate vertices, primarily due to valley-dose requirements. The valley-dose calculations and estimation of the dose received by organs-at-risk were performed by modeling the dose fall-off for each peak-dose sphere size as a set of iso-dose contours and interpolating between them. The optimal configuration of the peak-dose spheres (spatial locations and sizes) was determined by solving the maximum weight independent set problem on this graph. Main results. The model was built and solved using retrospective imaging data from a patient with oral cavity cancer. The optimal solution involved three peak-dose spheres, characterized by their center coordinates and diameters. These spheres were introduced as planning target volumes in the treatment planning system. After review by a radiation oncologist and medical physicist, the plan was deemed clinically acceptable and aligned with the computational model in terms of the dose fall-off between the spheres and the valley dose. Significance. This work presents a systematic approach for identifying optimal configuration of peak-dose spheres (spatial locations and size) in SFRT, addressing the shortcomings of existing methods. Optimal solutions to the proposed model provide input for creating SFRT plans using conventional treatment planning systems.