Optimization of intensity modulated beams with volume constraints using two methods: Cost function minimization and projections onto convex sets

For accurate prediction of normal tissue tolerance, it is important that the volumetric information of dose distribution be considered. However, in dosimetric optimization of intensity modulated beams, the dose-volume factor is usually neglected. In this paper we describe two methods of volume-dependent optimization for intensity modulated beams such as those generated by computer-controlled multileaf collimators, The first method uses a volume sensitive penalty function in which fast simulated annealing is used for cost function minimization (CFM). The second technique is based on the theory of projections onto convex sets (POCS) in which the dose-volume constraint is replaced by a limit on integral dose. The ability of the methods to respect the dose-volume relationship was demonstrated by using a prostate example involving partial volume constraints to the bladder and the rectum. The volume sensitive penalty function used in the CFM method can be easily adopted by existing optimization programs. The convex projection method can find solutions in much shorter time with minimal user interaction. (C) 1998 American Association of Physicists in Medicine. [S0094-2405(98)01004-9].