An interdimensional correlation framework for real-time estimation of six degree of freedom target motion using a single x-ray imager during radiotherapy

Increasing evidence suggests that intrafraction tumour motion monitoring needs to include both 3D translations and 3D rotations. Presently, methods to estimate the rotation motion require the 3D translation of the target to be known first. However, ideally, translation and rotation should be estimated concurrently. We present the first method to directly estimate six-degree-of-freedom (6DoF) motion from the target's projection on a single rotating x-ray imager in real-time. This novel method is based on the linear correlations between the superior-inferior translations and the motion in the other five degrees-of-freedom. The accuracy of the method was evaluated in silico with 81 liver tumour motion traces from 19 patients with three implanted markers. The ground-truth motion was estimated using the current gold standard method where each marker's 3D position was first estimated using a Gaussian probability method, and the 6DoF motion was then estimated from the 3D positions using an iterative method. The 3D position of each marker was projected onto a gantry-mounted imager with an imaging rate of 11 Hz. After an initial 110° gantry rotation (200 images), a correlation model between the superior-inferior translations and the five other DoFs was built using a least square method. The correlation model was then updated after each subsequent frame to estimate 6DoF motion in real-time. The proposed algorithm had an accuracy (±precision) of −0.03 ± 0.32 mm, −0.01 ± 0.13 mm and 0.03 ± 0.52 mm for translations in the left-right (LR), superior-inferior (SI) and anterior-posterior (AP) directions respectively; and, 0.07 ± 1.18°, 0.07 ± 1.00° and 0.06 ± 1.32° for rotations around the LR, SI and AP axes respectively on the dataset. The first method to directly estimate real-time 6DoF target motion from segmented marker positions on a 2D imager was devised. The algorithm was evaluated using 81 motion traces from 19 liver patients and was found to have sub-mm and sub-degree accuracy.