Cancer is the second largest mortal disease in Sweden, and high efforts are made to develop the treatment of cancer. One of the main treatment methods is radiotherapy, which uses ionizing radiation to damage the cancerous cells. This has the chance of stopping the cell reproduction, and the goal is to reduce the tumor and stop the tumor growth. The most common forms of radiotherapy uses external beams to irradiate the tumor. In intensity modulated radiotherapy, IMRT, the beam fluences are optimized to give a highly conformal dose, i.e. a dose distribution which is restricted to the tumor and has low dose values outside of the tumor. A conformal dose is necessary to spare healthy tissue and sensitive organs, and thus keep the side-effects of the treatment at an acceptable level. The optimized beam shapes are created using a multileaf collimator, MLC. Finding the leaf positions and dose levels is formulated as a problem in the framework of mathematical optimization. Currently, one of the limitations in delivering conformal dose is due to patient movement during the treatment. In IMRT, the beams are delivered by consecutive segments, and the exact pairing of the segments with the patient position will have an impact on the delivered dose. This is called the interplay effect, and can cause both underdosage of the tumor and overdosage of the surrounding tissue. There are methods of mitigating the interplay effect. For example, the beam could be restricted to a single phase of the motion by repeatedly turning it on and off. This is known as gating. However, gating and many other interplay mitigation techniques lead to prolonged treatment times, which decreases the clinical throughput, causes higher patient discomfort and gives higher uncertainties in the delivered dose. This makes it desirable to find methods which avoid prolonged treatment times, while still giving highly conformal doses. Ideally, the best method would be to have a beam which follows any target movement. This idea is known as target tracking. In this thesis, an optimization method is suggested which includes the interplay effect in the treatment optimization. Two main treatment strategies are proposed. The method which is simplest to implement clinically is to create plans which are robust against uncertainties in the times for the patient motion. The resulting doses are found to give acceptable target covering where similar, conventional plans give a significant target underdose. To further increase the conformality of the doses, a non-robust method paired with gating technology is suggested. This method can effectively be seen as a target tracking method, and has the possibility to give highly conformal doses under acceptable treatment times.

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