Quantitative evaluation of the performance of different deformable image registration algorithms in helical, axial, and cone‐beam CT images using a mobile phantom

Abstract The goal of this project is to investigate quantitatively the performance of different deformable image registration algorithms (DIR) with helical (HCT), axial (ACT), and cone‐beam CT (CBCT). The variations in the CT‐number values and lengths of well‐known targets moving with controlled motion were evaluated. Four DIR algorithms: Demons, Fast‐Demons, Horn‐Schunck and Lucas‐Kanade were used to register intramodality CT images of a mobile phantom scanned with different imaging techniques. The phantom had three water‐equivalent targets inserted in a low‐density foam with different lengths (10–40 mm) and moved with adjustable motion amplitudes (0–20 mm) and frequencies (0–0.5 Hz). The variations in the CT‐number level, volumes and shapes of these targets were measured from the spread‐out of the CT‐number distributions. In CBCT, most of the DIR algorithms were able to produce the actual lengths of the mobile targets; however, the CT‐number values obtained from the DIR algorithms deviated from the actual CT‐number of the targets. In HCT, the DIR algorithms were successful in deforming the images of the mobile targets to the images of the stationary targets producing the CT‐number values and lengths of the targets for motion amplitudes <20 mm. Similarly in ACT, all DIR algorithms produced the actual CT‐number values and lengths of the stationary targets for low‐motion amplitudes <15 mm. The optical flow‐based DIR algorithms such as the Horn‐Schunck and Lucas‐Kanade performed better than the Demons and Fast‐Demons that are based on attraction forces particularly at large motion amplitudes. In conclusion, most of the DIR algorithms did not reproduce well the CT‐number values and lengths of the targets in images that have artifacts induced by large motion amplitudes. The deviations in the CT‐number values and variations in the volume of the mobile targets in the deformed CT images produced by the different DIR algorithms need to be considered carefully in the treatment planning for accurate dose calculation dose coverage of the tumor, and sparing of critical structures.


| INTRODUCTION
Deformable image registration (DIR) provides useful tools in radiation therapy where images from different modalities can be deformed and registered to account for anatomical variations because of patient motion, organ filling, tumor growth with time or shrinkage because of response to treatment with radiation therapy. 1 DIR has potential applications in image registration, segmentation and dose mapping that can enable the performance of adaptive radiation therapy (ART) by considering anatomical variations in order to obtain conformal dose coverage of tumors and sparing of organs-at-risk. [2][3][4][5][6] ART provides the tools to use updated computed tomographic (CT) images such as kV-cone-beam CT (CBCT) obtained from daily patient setup and tumor localization with image-guided radiation therapy (IGRT) to perform more frequent updates on the planning-target-volume (PTV) and other critical structures considering anatomical variations due to tumor response to treatment. 7 These variations in patient anatomy can be accounted for in reasonable time by considering auto-segmentation techniques that can use voxel-by-voxel deformation of the patient CT images used in treatment planning to current CBCT images obtained from daily patient setup. 8 Patient motion leads to variations in patient anatomy inter-and intrafractions where ART will provide tools to manage the geometric and dosimetric discrepancies between patient CT simulation and treatment planning and dose delivery. 2 The dose variations due to changes in patient anatomy can be evaluated from the deformed initial dose maps on a voxel-by-voxel basis using DIR algorithms. Furthermore, new treatment plans using current CT images acquired daily can be generated and delivered as the treatment course progresses considering variations in patient anatomy to achieve ART.
Patient motion may induce significant artifacts in CT images obtained from the simulation CT, which can affect accuracy of the shape and volume of tumor targets outlined for treatment planning. 9,10 For example, motion causes the blurring of the edges of mobile targets affecting the accuracy for determination of the boundary of the targets in the CT images with strong motion artifacts. [11][12][13] In addition, motion artifacts cause variations in CT-number values invalidating the accuracy of the values of electron density of the mobile target and thus the accuracy of dose calculation. 14 Different techniques are used to manage patient motion both during simulation CT imaging and dose delivery. 15 In simulation CT imaging, patient motion is managed by breath holding technique during scanning or by acquiring projection images at different motion phases when the patient is scanned in synchrony with a breathing signal and the projections are sorted in different motion phases to obtain 4D-CT images. 16 At the stage of dose delivery, patient motion management includes breath hold technique during irradiation or beam gating when the beam is held on if the motion signal is synchronized with the selected breathing phase window; and is held off outside the gating window. 17 The goals of this project are to investigate quantitatively the performance of different DIR algorithms with helical CT (HCT), axial CT (ACT), and CBCT images by evaluating the variations in the CT-number values and lengths of mobile targets inserted in a thorax phantom moving with controlled motion patterns that simulates tumor motion in lung. Four DIR algorithms: Demons, 18,19 Fast-Demons, 20,21 Horn-Schunk, 22 and Lucas-Kanade 23,24 from the DIRART software were selected to register CT images of a phantom which moved with controlled motion patterns. The variations in the volumes and CTnumber values of the mobile targets obtained from deformed images were quantified.

2.A | Phantom setup and imaging
Three tissue-equivalent targets were inserted in a thorax phantom that was mounted on a mobile platform (Standard Imaging, Inc., Middleton, WI, USA). The three targets small, medium, and large had well-known shapes and volumes with lengths of 10, 20, and 40 mm in the direction of motion were embedded in low-density foam simulating lung-tissue as shown in Fig. 1. The phantom moved along the | 63 Y-axis in the superior-inferior direction with adjustable motion amplitudes and frequencies. In this experiment, the phantom was imaged with different techniques, helical, axial, and cone-beam CT while it was stationary and moving. The phantom moved during imaging with different motion amplitudes in the range (0-20 mm) and frequencies  flow involves the displacements between two image sets during a temporal sequence that is represented in intensity variations. 18,19 The Demons algorithm follows similar theoretical physics principles as the Maxwell's demons in fluids. The diffusion model in image registration is based on the physics of thermodynamics of gases or fluids that is applied in the information theory for mutual entropy minimization techniques. The Demons algorithm uses two images that are considered to be bounded by semipermeable membranes.
Then, one image diffuses through the other as a deformable grid that is driven by 'demons' forces on the perimeter of the image. In a diffusing model, the demons force at each point is sampled at the image boundary. The forces collectively diffuse the moving image through the boundary of the static image and remain constantly decreasing in magnitude until the images are aligned in the same coordinate space. The Demons algorithm needs an additional constraint to solve the aperture problem. 22 The optical flow is calculated in two steps: (a) the instantaneous optical flow is computed for every point within the static image, and (b) the deformation field is regularized by smoothing with a Gaussian filter. 18 The Fast-Demons algorithm explicitly takes into account Newton's third law of motion in combination with the diffusing model used by the Demons algorithm. 20,21 In Fast-Demons, the demons forces allow additionally the moving object to diffuse through the static or reference image. 21 This active force in the Fast-Demons algorithm serves as an amplifying factor in the overall force applied in the Demons algorithm. 20,21 The Horn-Schunck algorithm represents optical flow as variations in the image intensity by an apparent distribution of velocities from the movement of different image voxels. 22 A global smoothness constraint is imposed to satisfy the aperture problem where the number of independent variables is larger than the number of independent linear equations. 22 The aperture problem is solved by considering an        In order to be able to use DIR algorithms in ART, it is crucial to produce the actual shapes, volumes, and the CT-number values of the mobile targets. This is important to determine accurate tumor volume that is used in treatment planning to define the PTV. However, this study demonstrated that the performance of the different DIR algorithms depends on the motion artifacts and the modality of imaging. For small motion amplitudes, most of the DIR algorithms used in this study were able to reproduce the lengths of the mobile targets along the direction of motion. However, at large motion amplitudes, nearly all four DIR algorithms were not able to produce the shapes and volumes of the mobile targets. Besides the volumes and shapes of the different tumor targets, motion artifacts affected the CT-number values which were not reproduced in the deformed images by the different DIR algorithms at large motion amplitudes in all CT-imaging modalities. At small motion amplitudes, the different DIR algorithms performed better in HCT compared to ACT and CBCT. Therefore, the use of the target volumes and CT-number values obtained from DIR algorithms has to be evaluated carefully F I G . 9. CT-number profiles for (a) the small and medium targets, and (b) the larger target along the direction of motion for motion in pixel (2.5 mm) amplitudes in the range 0-20 mm from ACT images. before use in treatment planning and dose calculation to correct heterogeneity in radiation therapy.

| CONCLUSIONS
This study used a mobile thorax phantom that has three waterequivalent targets with well-known shapes and sizes that are inserted in low-density material in order to evaluate quantitatively the performance of different DIR algorithms. The performance of the DIR algorithms depends strongly on the image artifacts in the different CT-imaging modalities induced by motion. In CBCT, DIR algorithms produced successfully the volumes and shapes of the stationary targets without producing accurate CT-numbers. In HCT, the DIR algorithms produced the CT-number values, lengths, and shapes of the stationary targets even at large motion amplitudes. The ACT images had large image artifacts at large motion amplitudes. The different DIR algorithms failed to produce the shapes, volumes, and CT-number values of the stationary targets. Thus, the use of deformed CT images from different algorithms and imaging modalities in treatment planning and dose calculation for cancer patients treated with radiation therapy should be evaluated carefully.

CONF LICT OF I NTEREST
There is no conflict of interest.