Motion-compensating intensity maps in intensity-modulated radiation therapy

Managing the effects of tumor motion during radiation therapy is critical to ensuring that a robust treatment is delivered to a cancer patient. Tumor motion due to patient breathing may result in the tumor moving in and out of the beam of radiation, causing the edge of the tumor to be underdosed. One approach to managing the effects of motion is to increase the intensity of the radiation delivered at the edge of the tumor—an edge-enhanced intensity map—which decreases the likelihood of underdosing that area. A second approach is to use a margin, which increases the volume of irradiation surrounding the tumor, also with the aim of reducing the risk of underdosage. In this paper, we characterize the structure of optimal solutions within these two classes of intensity maps. We prove that the ratio of the tumor size to the standard deviation of motion characterizes the structure of an optimal edge-enhanced intensity map. Similar results are derived for a three-dimensional margin case. Furthermore, we extend our analysis by considering a robust version of the problem where the parameters of the underlying motion distribution are not known with certainty, but lie in pre-specified intervals. We show that the robust counterpart of the uncertain 3D margin problem has a very similar structure to the nominal (no uncertainty) problem.