A method to reconstruct intra-fractional liver motion in rotational radiotherapy using linear fiducial markers

Complex intra-fractional motion and deformation of the liver significantly impacts the accuracy of delivered dose in radiotherapy. It limits margin reduction, dose escalation and normal tissue sparing. A critical component of motion management is to accurately reconstruct tumor motion. In this study, we developed a six degrees of freedom projection marker matching method (6-DoF PM³) to reconstruct translational and rotational liver tumor motion in a rotational treatment delivery, such as volumetric modulated arc therapy (VMAT). Specifically, we modeled the use of two gold markers implanted in a linear form. The four endpoints of the two gold linear markers were used as tracking surrogates. During delivery, kV x-ray projection images were acquired. A method was developed to automatically identify the 2D marker-endpoints on the projection images. 3D marker positions were determined by solving an optimization problem with the objective function penalizing the distance from the reconstructed 3D position of each fiducial marker endpoint to the corresponding straight line defined by the kV x-ray projection of the endpoints. We performed a series of tests to evaluate different components of the method. For 2D marker endpoints identification, 99.9% of the marker endpoints were identified with an error (1 pixel) along both u and v directions. For 3D reconstruction of motion in simulation studies, error of rotational angle was without considering the 2D marker identification error. The rotational angle error was relatively sensitive to the accuracy of 2D marker identification. When the 2D error raised from 0.22 mm to 0.776 mm, the error of 3D rotational angle increased from 0.5° to 2.5°. In the experimental end-to-end tests, the mean root-mean square error of the 3D reconstructed marker positions was 0.75 mm and the mean error of rotational angle was within 1.7°. Our method can accurately determine intra-fractional liver tumor motion in rotational radiotherapy using kV projections of only two linear fiducial markers.