Use of proximal operator graph solver for radiation therapy inverse treatment planning

Most radiation therapy optimization problems can be formulated as an unconstrained problem and solved efficiently by quasi-Newton methods such as the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. However, several next generation planning techniques such as total variation regularization- based optimization and MV+kV optimization, involve constrained or mixed-norm optimization, and cannot be solved by quasi-Newton methods. Using standard optimization algorithms on such problems often leads to prohibitively long optimization times and large memory requirements. This work investigates the use of a recently developed proximal operator graph solver (POGS) in solving such radiation therapy optimization problems.

Radiation therapy inverse treatment planning was formulated as a graph form problem, and the proximal operators of POGS for quadratic optimization were derived. POGS was exploited for the first time to impose hard dose constraints along with soft constraints in the objective function. The solver was applied to several clinical treatment sites (TG119, liver, prostate, and head&neck), and the results were compared to the solutions obtained by other commercial and non-commercial optimizers.

For inverse planning optimization with nonnegativity box constraints on beamlet intensity, the speed of POGS can compete with that of LBFGSB in some situations. For constrained and mixed-norm optimization, POGS is about one or two orders of magnitude faster than the other solvers while requiring less computer memory.

POGS was used for solving inverse treatment planning problems involving constrained or mixed-norm formulation on several example sites. This approach was found to improve upon standard solvers in terms of computation speed and memory usage, and is capable of solving traditionally difficult problems, such as total variation regularization-based optimization and combined MV+kV optimization.