Controlling the dose distribution with gEUD-type constraints within the convex radiotherapy optimization framework.

Radiation therapy is an important modality in treating various cancers. Various treatment planning and delivery technologies have emerged to support intensity modulated radiation therapy (IMRT), creating significant opportunities to advance this type of treatment. However, one of the fundamental questions in treatment planning and optimization, 'can we produce better treatment plans relying on the existing delivery technology?' still remains unanswered, in large part due to the underlying computational complexity of the problem, which, in turn, often stems from the optimization model being non-convex. We investigate the possibility of including the dose prescription, specified by the dose-volume histogram (DVH), within the convex optimization framework for inverse radiotherapy treatment planning. Specifically, we study the quality of approximating a given DVH with a superset of generalized equivalent uniform dose (gEUD)-based constraints, the so-called generalized moment constraints (GMCs). As a bi-product, we establish an analytic relationship between a DVH and a sequence of gEUD values. The newly proposed approach is promising as demonstrated by the computational study where the rectum DVH is considered. Unlike the precise partial-volume constraints formulation, which is commonly based on the mixed-integer model and necessitates the use of expensive computing resources to be solved to global optimality, our convex optimization approach is expected to be feasible for implementation on a conventional treatment planning station.