Dynamic adaptive correlation over synchronous streaming time series

Paired streaming time series data are acquired frequently in medical treatment. Discovering the correlation between the synchronously acquired streaming time series has great usage in health care. This study investigates the correlation between the 1D motion signal of the external skin surface marker and the 3D motion of the internally implanted fiducial marker, acquired simultaneously in image guided cancer radiation treatment (IGRT). Four correlation approaches have been studied: The linear correlation calculates internal position using a min max normalization. The static correlation accounts for any non-linear behavior by using a polynomial correlation based on pretreatment motion data. The dynamic correlation deals with changes in the breathing pattern over time and updates the correlation in an online fashion. The piecewise dynamic correlation disseminate the motion signal with breathing phases and correlates the internal/external signal based on phase specific motion characteristics. The resulting average RMS errors and standard deviations showed that, in general, internal/external correlation based on polynomial functions results in smaller RMS errors. The dynamic correlation approaches, especially with the piecewise dynamic correlation, outperformed the static correlation. Additionally, the correlation algorithm can generate satisfactory correlation results even when the internal imaging rate is reduced from 30 Hz to 2 Hz which would significantly reduce the patients' radiation dose.