A new mathematical model for intensity matrix decomposition using multileaf collimator

Cancer is one of the major causes of death all over the globe and radiotherapy is considered as one of its most effective treatment methods. Designing a radiotherapy treatment plan was done entirely manually in the past. Recently, Intensity Modulated Radiation Therapy (IMRT) was introduced as a new technology with advanced medical equipment in the recent years. IMRT provides the opportunity to deliver complex dose distributions to cancer cells while sparing the vital tissues and cells from the harmful effects of radiations. Designing an IMRT treatment plan is a very complex matter due to the numerous calculations and parameters which must be decided for. Such treatment plan is designed in three separate phases: 1) selecting the number and the angle of the beams, 2) extracting the intensity matrix or the corresponding dose map of each beam, and 3) realizing each intensity matrix. The third phase has been studied in this research and a nonlinear mathematical model has been proposed for multileaf collimators. The proposed model has been linearized through two methods and an algorithm has been developed on its basis in order to solve the model with cardinality objective function. Obtained results are then compared with similar studies in the literature which reveals the capability of proposed method.