An iterative sequential mixed-integer approach to automated prostate brachytherapy treatment plan optimization

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Abstract
Conventional treatment planning for interstitial prostate brachytherapy is generally a 'trial and error' process in which improved treatment plans are generated by iteratively changing, via expert judgement, the configuration of sources within the target volume in order to achieve a satisfactory dose distribution. We have utilized linear mixed-integer programming (MIP) and the branch-and-bound method, a deterministic search algorithm, to generate treatment plans. The rapidity of dose falloff from an interstitial radioactive source requires fine sampling of the space in which dose is calculated. This leads to a large and complex model that is difficult to solve as a single 3D problem. We have therefore implemented an iterative sequential approach that optimizes pseudo-independent 2D slices to achieve a fine-grid 3D solution. Using our approach, treatment plans can be generated in 20-45 min on a 200 MHz processor. A comparison of our approach with the manual 'trial and error' approach shows that the optimized plans are generally superior. The dose to the urethra and rectum is usually maintained below harmful levels without sacrificing target coverage. In the event that the dose to the urethra is undesirably high, we present a refined optimization approach that lowers urethra dose without significant loss in target coverage. An analysis of the sensitivity of the optimized plans to seed misplacement during the implantation process is also presented that indicates remarkable stability of the dose distribution in comparison with manual treatment plans.