A Convex Optimization Approach to Radiation Treatment Planning with Dose Constraints
Optimization and Engineering, vol. 20 (1): 277-300, March 2019.
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. It is available on Github along with documentation and examples.