Split Common Coincidence Point Problem: A Formulation Applicable to (Bio)Physically-Based Inverse Planning Optimization

Abstract

Inverse planning is a method of radiotherapy treatment planning where the care team begins with the desired dose distribution satisfying prescribed clinical objectives, and then determines the treatment parameters that will achieve it. The variety in symmetry, form, and characteristics of the objective functions describing clinical criteria requires a flexible optimization approach in order to obtain optimized treatment plans. Therefore, we introduce and discuss a nonlinear optimization formulation called the split common coincidence point problem (SCCPP). We show that the SCCPP is a suitable formulation for the inverse planning optimization problem with the flexibility of accommodating several biological and/or physical clinical objectives. Also, we propose an iterative algorithm for approximating the solution of the SCCPP, and using Bregman techniques, we establish that the proposed algorithm converges to a solution of the SCCPP and to an extremum of the inverse planning optimization problem. We end with a note on useful insights on implementing the algorithm in a clinical setting.