Large scale optimization of beam weights under dose-volume restrictions

The problem of choosing weights for beams in a multifield plan which maximizes tumor dose under conditions that recognize the volume dependence of organ tolerance to radiation is considered, and its solution described. Structures are modelled as collections of discrete points, and the weighting problem described as a combinatorial linear program (LP). The combinatorial LP is solved as a mixed 0/1 integer program with appropriate restrictions on normal tissue dose. The method is illustrated through the assignment of weights to a set of 10 beams incident on a pelvic target. Dose-volume restrictions are placed on surrounding bowel, bladder, and rectum, and a limit placed on tumor dose inhomogeneity. Different tolerance restrictions are examined, so that the sensitivity of the target dose to changes in the normal tissue constraints may be explored. It is shown that the distributions obtained satisfy the posed constraints. The technique permits formal solution of the optimization problem, in a time short enough to meet the needs of treatment planners.