Evolutionary Algorithms 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. An evolutionary algorithm is proposed for the joint solution of these two problems; namely: Transgenetic Algorithm. 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. Computational experiments are carried out to ascertain the algorithm and the proposed functions's effectiveness in optimizing the objective functions of each instance of the problem. Real cases of liver cancer are used in the experiments. The results obtained show the effectiveness in optimizing the objective functions, although the doses in the tumor are far from satisfactory. Further reformulations and experiments are needed to correct this problem.