A model for prostate brachytherapy planning with sources and needles position optimization

Low dose rate brachytherapy is one of the treatments for localized prostate cancer. In the prostate case, the radioactive sources are located through needles into the organ tissue. The sources are placed in a way that enough dose is delivered to treat the tumor while preserving the surrounding healthy tissue. Since there are several location possibilities for tens of sources in use and constraints among them, the problem where to locate the sources becomes difficult. To solve the problem, this work proposes a mathematical model based on the previous ones, by adding definitions related to needles, and formal definitions for constraints, quality indicators and implicated organs. This model enables the simultaneous optimization of both the sources to be placed in the needles and the positions where to place the needles. A genetic algorithm is developed to solve the problem based on the proposed mathematical model, optimizing an objective function that takes into account the dose coverage constraints on the prostate and its surroundings, the rectum and the urethra, while reducing the total number of needles used in the treatment. It uses an integer encoding for the chromosome of the solutions and controls its feasibility by construction. Experimental results obtained are compared with manual planning performed by specialists using standard indicators. The algorithm obtains results of acceptable quality by the considered criteria, with suitable computation times for preoperative planning. The quality of the obtained solutions is comparable with the manual planning achieving better control over the dose on the rectum and urethra.