Analysis of deformable image registration accuracy using computational modeling

Abstract

Computer aided modeling of anatomic deformation, allowing various techniques and protocols in radiation therapy to be systematically verified and studied, has become increasingly attractive. In this study the potential issues in deformable image registration ͑DIR͒ were analyzed based on two numerical phantoms: One, a synthesized, low intensity gradient prostate image, and the other a lung patient's CT image data set. Each phantom was modeled with region-specific material parameters with its deformation solved using a finite element method. The resultant displacements were used to construct a benchmark to quantify the displacement errors of the Demons and B-Spline-based registrations. The results show that the accuracy of these registration algorithms depends on the chosen parameters, the selection of which is closely associated with the intensity gradients of the underlying images. For the Demons algorithm, both single resolution ͑SR͒ and multiresolution ͑MR͒ registrations required approximately 300 iterations to reach an accuracy of 1.4 mm mean error in the lung patient's CT image ͑and 0.7 mm mean error averaged in the lung only͒. For the low gradient prostate phantom, these algorithms ͑both SR and MR͒ required at least 1600 iterations to reduce their mean errors to 2 mm. For the B-Spline algorithms, best performance ͑mean errors of 1.9 mm for SR and 1.6 mm for MR, respectively͒ on the low gradient prostate was achieved using five grid nodes in each direction. Adding more grid nodes resulted in larger errors. For the lung patient's CT data set, the B-Spline registrations required ten grid nodes in each direction for highest accuracy ͑1.4 mm for SR and 1.5 mm for MR͒. The numbers of iterations or grid nodes required for optimal registrations depended on the intensity gradients of the underlying images. In summary, the performance of the Demons and B-Spline registrations have been quantitatively evaluated using numerical phantoms. The results show that parameter selection for optimal accuracy is closely related to the intensity gradients of the underlying images. Also, the result that the DIR algorithms produce much lower errors in heterogeneous lung regions relative to homogeneous ͑low intensity gradient͒ regions, suggests that feature-based evaluation of deformable image registration accuracy must be viewed cautiously.

A measure to evaluate deformable registration fields in clinical settings

“…In a comprehensive publication, Kashani et al (31) reported interalgorithm comparison at different institutions and noted that “no algorithm was uniformly accurate across all regions in a phantom”, with larger errors seen in regions of significant shape changes and in areas of uniform contrast. As noted by Zhong et al, (45) performance in regions with low‐intensity gradients is difficult to assess. This study highlights the need for a direct measure derived from the displacement field when assessing accuracy of deformable warping for clinical applications.…”

“…Previous reports show that registration errors are prone to emerge in regions with uniform image intensity and low‐intensity gradient regions and are not visible with standard voxel‐based methods (45) . Although it is hard to identify differences by inspecting the images directly, analysis of the deformation field through the CURL operator provides complementary information that better identifies and characterizes tissue warping.…”

“…Phantom measurements that mimic patient anatomy can be used to assess deformable registration accuracy in specific conditions, 31 , 45 , 48 but are time‐consuming and not well‐suited for routine evaluation, as algorithm settings are usually tailored to image quality, 49 , 50 levels of noise, (51) or partial volume effects, with estimations obtained on phantom studies overestimating accuracy if images of lesser quality are used as input. Furthermore, accuracy depends on parameter selection, which is closely associated with intensity gradients of the underlying image, (45) or are site‐specific.…”

“…Furthermore, accuracy depends on parameter selection, which is closely associated with intensity gradients of the underlying image, (45) or are site‐specific. For example, the number of iterations or the number of nodes in the B‐Spline model have been found to be site‐specific, (45) with a different number of nodes needed to accurately register the rectum or lung.…”

“…Furthermore, accuracy depends on parameter selection, which is closely associated with intensity gradients of the underlying image, (45) or are site‐specific. For example, the number of iterations or the number of nodes in the B‐Spline model have been found to be site‐specific, (45) with a different number of nodes needed to accurately register the rectum or lung. For a casual user, the evaluation metric presented here provides a tool that quickly analyzes and quantifies a solution obtained under specific settings, and visually guides the user in selecting parameters that work best with the input datasets, as the vortexes map calculation takes less than one second and is easily displayed as a 3D volume or a color‐wash superimposed on the CT dataset (as illustrated in Fig.…”