Prediction of respiratory motion with a multi-frequency based Extended Kalman Filter L. Ramrath a , A. Schlaefer a , F. Ernst a , S. Dieterich2 b , A. Schweikard a a Institute for Robotics and Cognitive Systems, University of Luebeck b Sonja Dieterich, Department of Radiation Medicine, Georgetown University Hospital … Abstract. In this work, an Extended Kalman Filter formulation for respiration motion tracking is introduced. Based on the assumption of multiple sinusoidal components contributing to respiratory motion, a state-space model is developed. Performance of the filter is tested on data sets of patients subject to radiotherapy. Comparison to an nLMS predictor shows that the Kalman filter is less sensitive to systematic errors during target prediction. Keywords: respiration motion compensation, Extended Kalman filter, prediction 1. Introduction Recent technological developments have enabled highly precise image guided radiosurgical treatment to targets outside the skull. Using high resolution stereoscopic X-ray imaging the tumour region can be localized either directly or by means of artificial landmarks, e.g. implanted gold fiducials [1]. However, tumours in the thorax and abdomen are often subject to movements, primarily due to respiratory motion. New systems to move the treatment beams accordingly have been proposed [1, 2] and currently the robotic CyberKnife is used for motion compensated treatment in clinical practice at numerous sites. Although respiratory motion is cyclic, the motion pattern varies over time. Hence it is necessary to constantly monitor the motion and to generate control sequences to move the beam synchronously. The signal processing step and the mechanical inertia of the robotic system cause a small but noticeable system delay. In order to precisely compensate for target motion it is thus important to predict its position. Different approaches to respiratory motion prediction exist. Two major types can be distinguished: model-based and non-model-based predictors. Approaches not based on an explicit motion model include linear prediction, normalized Least-Mean-Squares (nLMS) prediction, and prediction with artificial neural networks [3, 4]. Model-based predictors incorporate certain assumptions on the dynamics of the respiratory motion in order to improve the prediction. For organ motion, models based on trigonometric functions can be used. A more general model-based prediction method is provided by the framework of the Kalman filter providing predicition capability based on the system dynamic behaviour. Existing approaches to Kalman filter prediction do not incorporate an exact model of the respiratory motion. This work therefore presents a Kalman filter based on an augmented sinusoidal motion model incorporating multiple frequencies. As the assumed model is nonlinear, the Extended Kalman filter formulation is applied. The predictor has been tested on a set of motion data from actual patients, and its performance is compared to that of an nLMS predictor with optimal parameter settings. Experimental results indicate that the EK filter is a reliable alternative for respiratory motion prediction.