A Convex Optimization Approach to Radiation Treatment Planning with Dose Constraints

TL;DR

This paper introduces a convex optimization framework for radiation treatment planning that handles various dose constraints, including a novel two-pass algorithm and an open-source software tool, ConRad.

Contribution

It proposes a convex formulation for dose constraints, including a conservative approximation for dose-volume constraints, and introduces ConRad, an open-source planning software.

Findings

Effective handling of dose constraints within a convex framework

Two-pass algorithm improves dose-volume constraint accuracy

Open-source software ConRad facilitates practical implementation

Abstract

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface.