### A survey of algorithms for respiratory motion prediction in robotic radiosurgery

*Floris Ernst*

*and Achim Schweikard*

#### Abstract

In robotic radiosurgery, a standard six-jointed industrial robot carries a linear accelerator. The accelerator can be moved such as to compensate for respiratory motion. Unfortunately, this motion cannot be compensated perfectly since the motion of the robot lags behind the motion of the target organ by - in systems currently employed clinically - approximately 150 ms. This delay is compensated by prediction algorithms, i.e., the time series stemming from human respiration is forecast. We have compared the performance of seven algorithms implemented in a common prediction tool kit. They are: multi-frequency tracking with Extended Kalman Filtering (EKF), normalised and regular Least Mean Squares filters (LMS and nLMS), wavelet-based multiscale autoregression (wLMS), a recursive least squares filter (RLS), multi-step linear methods (MULIN) and prediction based on support vector regression (SVR- pred). All algorithms were tested on two signals: a simulated signal, corrupted by Gaussian noise, and a real breathing motion signal from a treatment session with the CyberKnife R at Georgetown University Hospital. The results are clear: the SVRpred algorithm outperforms the best other algorithm (wLMS for the real signal and MULIN for the simulated signal) by 15 and 9 percentage points, respectively.

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