Conformal radiotherapy computation by the method of alternating projections onto convex sets

Synthesis of beam profiles for a given dose prescription is a central problem in radiotherapy. Care must be taken in the beam design to expose the tumour volume at a high level, to avoid significant irradiation of critical organs, and to minimize exposure of all other tissue. Use of the synthesis procedure known as alternating projections onto convex sets (POCS) is shown to be a viable approach to beam design. POCS is a powerful tool for signal and image restoration and synthesis. Convex sets of signals obeying desired constraint sets are first specified. Then, by repeated projections onto these sets, convergence is to a signal obeying all desired constraints if the constraint sets have a finite intersection. In this paper we apply the method of POCS to conformal radiotherapy dose computation. The performance of the method is shown through three representative examples.