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

A Convex Optimization Approach to Radiation Treatment Planning with Dose Constraints