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The Synchrony Respiratory Tracking System (RTS) is a treatment option of the CyberKnife robotic treatment device to irradiate extra-cranial tumors that move due to respiration. Advantages of RTS are that patients can breath normally and that there is no loss of linac duty cycle such as with gated therapy. Tracking is based on a measured correspondence model (linear or polynomial) between internal tumor motion and external (chest/abdominal) marker motion. The radiation beam follows the tumor movement via the continuously measured external marker motion. To establish the correspondence model at the start of treatment, the 3D internal tumor position is determined at 15 discrete time points by automatic detection of implanted gold fiducials in two orthogonal x-ray images; simultaneously, the positions of the external markers are measured. During the treatment, the relationship between internal and external marker positions is continuously accounted for and is regularly checked and updated. Here we use computer simulations based on continuously and simultaneously recorded internal and external marker positions to investigate the effectiveness of tumor tracking by the RTS. The Cyberknife does not allow continuous acquisition of x-ray images to follow the moving internal markers (typical imaging frequency is once per minute). Therefore, for the simulations, we have used data for eight lung cancer patients treated with respiratory gating. All of these patients had simultaneous and continuous recordings of both internal tumor motion and external abdominal motion. The available continuous relationship between internal and external markers for these patients allowed investigation of the consequences of the lower acquisition frequency of the RTS. With the use of the RTS, simulated treatment errors due to breathing motion were reduced largely and consistently over treatment time for all studied patients. A considerable part of the maximum reduction in treatment error could already be reached with a simple linear model. In case of hysteresis, a polynomial model added some extra reduction. More frequent updating of the correspondence model resulted in slightly smaller errors only for the few recordings with a time trend that was fast, relative to the current x-ray update frequency. In general, the simulations suggest that the applied combined use of internal and external markers allow the robot to accurately follow tumor motion even in the case of irregularities in breathing patterns.