Nonlinear Set Membership time series prediction of breathing

In radiation therapy, tumor motion induced by patient´s respiration may lead to significant differences between the planned and delivered radiation dose. Compensating for tumor motion is therefore crucial for accurate and efficient treatment. The focus of the presented research is on real-time tumor tracking, due to its potential to overcome the limitations of other approaches, such as margin expansion, breath-holding, and gating. A real challenge in tumor tracking is the presence of delays in the treatment system. Prediction of tumor displacement is then necessary to overcome such delays. In this paper, we propose a method for the prediction of breathing signals based on a Nonlinear Set Membership (NSM) algorithm. The algorithm does not require the choice of a predefined functional form for the prediction model, and addresses the issue of measurement noise with minimal assumptions on its statistical properties. The NSM method was tested on nine clinical signals and its performance compared favorably with reported results as well as an optimized nonlinear neural network predictor.