On the implementation of dose-volume objectives in gradient algorithms for inverse treatment planning

A method that allows a straightforward implementation of dose-volume constraints in gradient algorithms for inverse treatment planning is presented. The method is consistent with the penalty function approach, which requires the formulation of an objective function with penalty terms proportional to the magnitudes of constraint violations. Dose constraints with respect to minimum and maximum target dose levels are incorporated in quadratic, dose-penalty terms. Analogously, quadratic volume-penalty terms in the objective function reflect the violation of dose-volume constraints imposing limits on the fractions of healthy organ volumes that can be irradiated above specified dose levels. It has been demonstrated that within the framework of this formulation neither modified objective functions nor finite difference gradient calculations are necessary for the incorporation of gradient minimization algorithms. As an example, a simple steepest descent algorithm is presented along with its application to illustrate prostate and lung cases.