Propagation of calibration errors in prospective motion correction using external tracking.

PURPOSE: Prospective motion correction of MRI scans using an external tracking device (such as a camera) is becoming increasingly popular, especially for imaging of the head. In order for external tracking data to be transformed into the MR scanner reference frame, the pose (i.e., position and orientation) of the camera relative to the scanner--or cross-calibration--must be accurate. In this study, we investigated how errors in cross-calibration affect the accuracy of motion correction feedback in MRI. THEORY AND METHODS: An operator equation is derived describing how calibration errors relate to errors in applied motion compensation. By taking advantage of spherical symmetry and performing a Taylor approximation for small rotation angles, a closed form expression and upper limit for the residual tracking error is provided.
RESULTS: Experiments confirmed theoretical predictions of a bilinear dependence of the residual rotational component on the calibration error and the motion performed, modulated by a sinusoidal dependence on the angle between the calibration error axis and motion axis. The residual translation error is bounded by the sum of the rotation angle multiplied by the translational calibration error plus the linear head displacement multiplied by the calibration error angle.
CONCLUSION: The results make it possible to calculate the required cross-calibration accuracy for external tracking devices for a range of motions. Scans with smaller expected movements require less accuracy in cross-calibration than scans involving larger movements. Typical clinical applications require that the calibration accuracy is substantially below 1 mm and 1°.