A viscous fluid model for large-scale motion estimation in image-guided radiotherapy.

backgroundImage-guided radiotherapy (IGRT) is often hampered by geometric inaccuracies introduced by anatomical and physiological motion. Although a wide array of deformable image registration (DIR) solutions have been proposed toward motion estimation and compensation during IGRT, their accuracy and precision generally deteriorates within areas showcasing particularly large displacements such as the thorax, abdomen and pelvis. PURPOSE: In this work, we propose a physics-derived DIR algorithm for motion estimation during IGRT, designed to be specifically suitable for highly deforming anatomical areas. The proposed solution also has a single configuration parameter controlling the volumetric deformations of the anatomy and a high computational performance, lending it particularly compatible with online adaptive workflows.

methodsWe hereby address the DIR problem by modeling anatomical motion as the flow of a viscous fluid. In this context, we solve a simplified form of the Navier-Stokes equations where the dissimilarity between the registered images plays the role of actuating force. The high degree-of-freedom of the solutions resulting from viscous fluid dynamics thereby allows for the estimation of large-scale deformations. For computational purposes, a highly parallelizable FFT-based numerical solver was used, allowing for its seamless implementation on graphical processing units. The Jacobian determinant was used to analyze tissue compression and expansion at a voxel-wise level and to identify implausible deformations. The accuracy and precision of the proposed algorithm was analyzed for thoracic CT and pelvic MR images showcasing particularly large deformations. A gold standard consisting of annotated landmarks was available for the CT images, while for the MR data manually-approved contours were generated using a semi-automatic procedure.

resultsThe proposed DIR solution showcased an overall accuracy of 1 - 2 mm for the thoracic CT data and a Dice similarity coefficient of 0.8 - 0.9 for the contours defined on the MR images. Moreover, the model estimates motion with a smooth distribution of the Jacobian determinant. The average computational latency ranged between 20 s to 3.5 min, dependent on the size of the registered images.

conclusionsIn this work, we have formulated the DIR problem under the shape of a system of equations describing the dynamics of a viscous fluid. The algorithm demonstrated capabilities for estimating large deformations in the thorax and pelvis for both CT and MR images, with an accuracy and precision in line with recommendations for clinical acceptability. Together with its computational performance, this could make it an attractive solution for motion management during online IGRT.