In the US at least 700,000 patients yearly undergo radiation therapy in connection with cancer treatment. The hazard with radiotherapy is that it does not only destroy tumor cells, but likewise affects healthy tissue. Therefore, based on the images of computed tomography, for each patient a treatment plan has to be set up which has to form a compromise between the two conflicting goals: to deposit a sufficiently high dose into the the cancerous tissue and to simultaneously spare, as much as possible, the organs at risk and the other healthy tissue.

Conventionally treatment planning for radiotherapy is performed by a forward type approach where, by a trial-and-error procedure, the radiation effects of a few different dose distribution arrangements are assessed with respect to the anatomy of the patient. A better control of the radiation effects is reached by inverse dose planning in which the treatment goals are prescribed and approximately fulfilled in some optimal way. In particular an inverse approach combined with the new technique of intensity modulated radiation therapy (IMRT) enables the treatment of patients who, because of too high risks for their health, could not be treated by radiotherapy before.

To obtain a dose plan for IMRT, an optimization model for the beamlet intensities is needed that takes the individual treatment goals and the radiation effects into account. Following an introduction into the topic, various competing models are discussed in this talk and a new model based on biological criteria is suggested. Furthermore, a numerical method for the solution of the resulting large-scale optimization problems is proposed and results for a clinical case example are shown. The new model and the algorithm can also be applied to compute treatment plans for the quite recent technique of intensity modulated proton therapy (IMPT), which is explained and compared with IMRT by a case example.