Three-dimensional spatial modelling of the correlation between abdominal motion and lung tumour motion with breathing

The aim of this research was to investigate whether a spatial correlation could be found between an external 3-D respiratory signal and the tumour trajectory. The respiratory signal was obtained by tracking the abdominal movement and the tumour trajectory was obtained by automatically determining the tumour position in a series of portal images. Three different models, based on Systems Identification, are presented to model the correlation using a 1-D respiratory signal, a 3-D respiratory signal and a 3-D respiratory signal together with previously determined tumour positions. Adequate correlation was found for all models in the direction of the tumour movement with standard deviations of 0.89 mm, 0.72 mm and 0.75 mm, respectively, and model fit of Rt2 = 0.19, 0.63 and 0.82, respectively. Increasing the frame rate for the acquisition of portal images from 3 to 15 frames per second improved the standard deviation and model fit. In summary, it is possible to spatially correlate a 3-D respiratory signal with the tumour trajectory using this approach. The models presented provide a framework that can be extended to include more information if required. A 3-D respiratory signal is preferable to a 1-D signal in modelling the tumour motion that is not along the main axis of tumour movement.