  Conventional planning objectives in optimization of intensity-modulated
radiotherapy treatment (IMRT) plans are designed to minimize the violation of
dose-volume histogram (DVH) thresholds using penalty functions. Although
successful in guiding the DVH curve towards these thresholds, conventional
planning objectives offer limited control of the individual points on the DVH
curve (doses-at-volume) used to evaluate plan quality. In this study, we
abandon the usual penalty-function framework and propose planning objectives
that more explicitly relate to DVH statistics. The proposed planning objectives
are based on mean-tail-dose, resulting in convex optimization. We also
demonstrate how to adapt a standard optimization method to the proposed
formulation in order to obtain a substantial reduction in computational cost.
  We investigate the potential of the proposed planning objectives as tools for
optimizing DVH statistics through juxtaposition with the conventional planning
objectives on two patient cases. Sets of treatment plans with differently
balanced planning objectives are generated using either the proposed or the
conventional approach. Dominance in the sense of better distributed
doses-at-volume is observed in plans optimized within the proposed framework,
indicating that the DVH statistics are better optimized and more efficiently
balanced using the proposed planning objectives.
