Predicting respiratory motion for four-dimensional radiotherapy

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Abstract
Adapting radiation delivery to respiratory motion is made possible through corrective action based on real-time feedback of target position during respiration. The advantage of this approach lies with its ability to allow tighter margins around the target while simultaneously following its motion. A significant hurdle to the successful implementation of real-time target-tracking-based radiation delivery is the existence of a finite time delay between the acquisition of target position and the mechanical response of the system to the change in position. Target motion during the time delay leads to a resultant lag in the system's response to a change in tumor position. Predicting target position in advance is one approach to ensure accurate delivery. The aim of this manuscript is to estimate the predictive ability of sinusoidal and adaptive filter-based prediction algorithms on multiple sessions of patient respiratory patterns. Respiratory motion information was obtained from recordings of diaphragm motion for five patients over 60 sessions. A prediction algorithm that employed both prediction models-the sinusoidal model and the adaptive filter model-was developed to estimate prediction accuracy over all the sessions. For each session, prediction error was computed for several time instants (response time) in the future (0-1.8 seconds at 0.2-second intervals), based on position data collected over several signal-history lengths (1-7 seconds at 1-second intervals). Based on patient data included in this study, the following observations are made. Qualitative comparison of predicted and actual position indicated a progressive increase in prediction error with an increase in response time. A signal-history length of 5 seconds was found to be the optimal signal history length for prediction using the sinusoidal model for all breathing training modalities. In terms of overall error in predicting respiratory motion, the adaptive filter model performed better than the sinusoidal model. With the adaptive filter, average prediction errors of less than 0.2 cm (1sigma) are possible for response times less than 0.4 seconds. In comparing prediction error with system latency error (no prediction), the adaptive filter model exhibited lesser prediction errors as compared to the sinusoidal model, especially for longer response time values (>0.4 seconds). At smaller response time values (<0.4 seconds), improvements in prediction error reduction are required for both predictive models in order to maximize gains in position accuracy due to prediction. Respiratory motion patterns are inherently complex in nature. While linear prediction-based prediction models perform satisfactorily for shorter response times, their prediction accuracy significantly deteriorates for longer response times. Successful implementation of real-time target-tracking-based radiotherapy requires response times less than 0.4 seconds or improved prediction algorithms.