Fiducial-based targeting accuracy for external-beam radiotherapy.

The accuracy of fiducial-based alignment of external radiotherapy beams is analyzed. The study considers three basic computational methods to determine the target position--the exact closed-form solution for three fiducials, the solution via singular value decomposition for four or more fiducials, and the iterative solution for any number of fiducials--and assesses their accuracy, robustness, and efficiency. Particular attention is paid to inaccuracies arising from the variability of fiducial positions in soft tissue. In nearly every test case it is found that all three solution methods, when properly implemented, yield the same result for the target position, but that the method of singular value decomposition must be modified to distinguish rotations from reflections. When an accurate measure of the rotation of the target site is needed, four fiducials give much better results than three, while more than five fiducials gain little further improvement.