Transgenetic Algorithm for the Geometry and Intensity Problems in IMRT
Radiotherapy. IMRT. Geometry Problem. Intensity Problem. Evolutionary algorithms. Trangenetic Algorithm. Epsilon-constraint. Dose-volume functions.
Intensity Modulated Radiotherapy (IMRT) is a form of treatment of cancerous diseases in which the patient is irradiated with radiation beams, aiming to eliminate tumor cells while sparing healthy organs and tissues as much as possible. In addition, each beam is divided into beamlets that emit a particular dose of radiation. A treatment plan is composed of: (a) a set of beam directions (angles); (b) the amount of radiation emitted by the beamlets of each beam; and (c), a radiation delivery sequence. The elaboration of a plan can be modeled by optimization problems, usually NP-hard, where steps (a), (b) and (c) are called problems of Geometry, Intensity (or Fluence Map) and Realization, respectively. This work addresses the first two. A transgenetic algorithm is proposed for the joint solution of these two problems. It uses an adaptation of the epsilon-constraint method present in the literature to compute the fluence map of a set of beams. In addition, linear and quadratic approximation functions are proposed for a particular type of (non-convex) function present in radiotherapy optimization: the dose-volume function. Two groups of experiments are carried out to ascertain the effectiveness of the algorithm: one with the dose in the tumor as a restriction, and another with it as an objective function. Real cases of liver cancer are used in the experiments. The results for the first group show the effectiveness in the optimization of objective functions and doses below those desired for the tumor. The results for the second group show that the tumor dose as an objective function of the problem is in fact the most appropriate option.