Optimization of brachytherapy dose distributions by simulated annealing

An algorithm based on the method of simulated annealing is presented for optimizing brachy-therapy dose distributions. The algorithm accommodates either static configurations of multiple sources or single stepping sources, hence in principle can be used to optimize both low- and high-dose rate treatments delivered with remote afterloading equipment. Required inputs include the specification of target dose rates and dose rate limits, expressed in absolute or relative terms, at operator selected points near the treatment site. The influence of the dose rate limits can be adjusted continuously through the use of one or more penalty factors. The algorithm generates a set of integer weights, one for each available source position, which are interpreted in terms of configuration occupancy numbers for static source arrangements and relative dwell times for stepping sources. Application is made to several variations of a hypothetical low-dose rate vaginal vault planning problem involving one rectal and six applicator calculation points. The algorithm's performance for different source strengths, annealing schedules, target dose rates, dose rate limits, and values of a single penalty factor lambda was examined. With a simple annealing schedule and value of lambda = 25, the algorithm found solutions of high quality for all problem variants. The CPU time required for optimization on a Vax 11/750 computer ranged from 2 min for a single configuration to 25 min for a solution consisting of four configurations. These results support the use of simulated annealing for clinical planning of low dose rate vaginal treatments, and encourage investigation of other applications in brachytherapy.