Mathematical modeling and scientific computing are very important in improving the quality of radiotherapy. I my talk, I will go through some of the steps of the entire process of radiotherapy where mathematical modeling is important. In particular, I will talk about the following two topics in detail.
The first topic is on accurate radiation dose delivery in volumetric modulated arc therapy (VMAT) in cancer radiotherapy. It can be described as an optimization problem, where beam parameters, such as directions, shapes, and intensities, can be adjusted in simulations to yield desired dose distributions. Treatment plan optimization in this setting, however, can be quite complicated due to constraints arising from the equipment involved. We introduce a variational model in the VMAT setup for the optimization of beam shapes and intensities under these constraints. Our numerical tests on real data reveal that our algorithm shows great promise in the generation of desired dose distributions for treatment plans in cancer radiotherapy.
The second topic is on optimal marker selection for tumor motion estimation in lung cancer radiotherapy. We propose a novel mathematical model and an efficient algorithm to automatically determine the optimal number and locations of fiducial markers on patient’s surface (typically on the chest) for predicting lung tumor motion. Experiments on the 4DCT data of 4 lung cancer patients have shown that usually 6-7 markers are selected on patient’s external surface. Using these markers, the lung tumor positions can be predicted with an average 3D error of approximately 1mm. Both the number of markers and the prediction accuracy are clinically acceptable, indicating that our method can be used in clinical practice.