Purpose: The purpose of this study was to evaluate a novel technique for dynamically predicting respiration motion and uncertainty using time-delay kernel regression (TDKR). The primary objective of this study was to evaluate the TDKR model using a large database of measured respiration cycles.
Methods: Respiration motion was measured using an RPM system and was used to develop a model to predict respiration amplitude using TDKR. Amplitude inputs from the gating system were concatenated to form the time-delay matrix. The distance of the current amplitude observation from each of the historical amplitude exemplars was calculated. For this application, the Euclidean distance was used. The distances were supplied as inputs to a kernel function, which converted the distances to weights (similarities) using a Gaussian kernel function. The weights from the Gaussian kernel were used to predict the amplitudes as a weighted average of the amplitude exemplars.
Results: Respiration cycles were measured for 388 patients with the RPM system. These respiration cycles were used to generate motion predictions 0.5 and 1.0 seconds into the future. The root mean square (RMS) error between the predicted and actual positions were calculated for each patient. The mean phase error was 1.0±0.8 mm for the 0.5 second predictions and 1.9±1.4 mm for the 1.0 second predictions. Patients with a respiration period of 2 to 3 seconds had the lowest RMS, while patients with a respiration cycle of 7 to 8 seconds had the highest RMS.
Conclusion: The TDKR model has the capability to learn respiration patterns and make predictions 0.5 to 1.0 sec into the future. One significant advantage of TDKR is that it uses a memory matrix and the model is automatically updated as more data is acquired. This allows the model to adapt to changes in respiration motion and make predictions for irregular breathing.