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Intra-fractional motion is a concern during prostate radiation therapy, as it may cause deviations between planned and delivered radiation doses. Because accurate motion information during treatment delivery is critical to address dose deviation, we developed the Projection Marker Matching Method (PM3), a novel method for prostate motion reconstruction in volumetric modulated arc therapy. The purpose of this method is to reconstruct in-treatment prostate motion trajectory using projected positions of implanted fiducial markers measured in kV x-ray projection images acquired during treatment delivery. We formulated this task as a quadratic optimization problem. The objective function penalized the distance from the reconstructed 3D position of each fiducial marker to the corresponding straight line, defined by the x-ray projection of the marker. Rigid translational motion of the prostate and motion smoothness along the temporal dimension were assumed and incorporated into the optimization model. We tested the motion reconstruction method in both simulation and phantom experimental studies. We quantified the accuracy using 3D normalized root-mean-square (RMS) error defined as the norm of a vector containing ratios between the absolute RMS errors and corresponding motion ranges in three dimensions. In the simulation study with realistic prostate motion trajectories, the 3D normalized RMS error was on average 0.164 (range from 0.097 to 0.333). In an experimental study, a prostate phantom was driven to move along a realistic prostate motion trajectory. The 3D normalized RMS error was 0.172. We also examined the impact of the model parameters on reconstruction accuracy, and found that a single set of parameters can be used for all the tested cases to accurately reconstruct the motion trajectories. The motion trajectory derived by PM3 may be incorporated into novel strategies, including 4D dose reconstruction and adaptive treatment replanning to address motion-induced dose deviation.

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