Using cone-beam CT projection images to estimate the average and complete trajectory of a fiducial marker moving with respiration

Stereotactic body radiotherapy of lung cancer often makes use of a static cone-beam CT (CBCT) image to localize a tumor that moves during the respiratory cycle. In this work, we developed an algorithm to estimate the average and complete trajectory of an implanted fiducial marker from the raw CBCT projection data. After labeling the CBCT projection images based on the breathing phase of the fiducial marker, the average trajectory was determined by backprojecting the fiducial position from images of similar phase. To approximate the complete trajectory, a 3D fiducial position is estimated from its position in each CBCT project image as the point on the source-image ray closest to the average position at the same phase. The algorithm was tested with computer simulations as well as phantom experiments using a gold seed implanted in a programmable phantom capable of variable motion. Simulation testing was done on 120 realistic breathing patterns, half of which contained hysteresis. The average trajectory was reconstructed with an average root mean square (rms) error of less than 0.1 mm in all three directions, and a maximum error of 0.5 mm. The complete trajectory reconstruction had a mean rms error of less than 0.2 mm, with a maximum error of 4.07 mm. The phantom study was conducted using five different respiratory patterns with the amplitudes of 1.3 and 2.6 cm programmed into the motion phantom. These complete trajectories were reconstructed with an average rms error of 0.4 mm. There is motion information present in the raw CBCT dataset that can be exploited with the use of an implanted fiducial marker to sub-millimeter accuracy. This algorithm could ultimately supply the internal motion of a lung tumor at the treatment unit from the same dataset currently used for patient setup.