Variation method for inverse treatment planning

A new inverse planning method based on the theory of variation is developed for the computation of beam intensities that produce highly conformal dose distributions to the target volume that have an arbitrary complex geometry. It is shown that the objective function defined for the optimization of external beam intensities has a unique minimum. A corresponding algorithm is then designed to generate a sequence of intensity functions that converge to the minimum. The algorithm is applied to a test geometry where the target volume has concavity and then are adjacent critical organs. The cumulative dose-area histogram, the two-dimensional version of the cumulative dose-volume histogram, is used to evaluate the outcomes of this new inverse planning method. The results show that this method creates a group of intensity-modulated external beams that produce a dose distribution consistent with the given dose prescription. (C) 1999 American Association of Physicists in Medicine. [S0094-2405(99)01503-5].