Mean position tracking of respiratory motion.

Modeling and predicting tumor motion caused by respiration is challenging due to temporal variations in breathing patterns. Treatment approaches such as gating or adaptive bed adjustment/ alignment may not require full knowledge of instantaneous position, but might benefit from tracking the general trend of the motion. One simple method for tracking mean tumor position is to apply moving average filters with window sizes corresponding to the breathing periods. Yet respiratory motion is only semiperiodic, so such methods require reliable phase estimation, which is difficult in the presence of noise. This article describes a robust method to track the mean position of respiratory motion without explicitly estimating instantaneous phase. We form a state vector from the respiration signal values at the current instant and at a previous time, and fit an ellipse model to training data. Ellipse eccentricity and orientation potentially capture hysteresis in respiratory motion. Furthermore, we provide two recursive online algorithms for real time mean position tracking: a windowed version with an adaptive window size and another one with temporal discounting. We test the proposed method with simulated breathing traces, as well as with real time-displacement (RPM, Varian) signals. Estimation traces are compared with retrospectively generated moving average results to illustrate the performance of the proposed approach.