SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints




To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning.


We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction, we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS.


We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints.


This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints.

This work was supported by the Stanford BioX Graduate Fellowship and NIH Grant 5R01CA176553.