Motion-Compensated Mega-Voltage Cone Beam CT Using the Deformation Derived Directly From 2D Projection Images

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1 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 32, NO. 8, AUGUST Motion-Compensated Mega-Voltage Cone Beam CT Using the Deformation Derived Directly From 2D Projection Images Mingqing Chen*, Kunlin Cao, Yefeng Zheng, and R. Alfredo C. Siochi Abstract This paper presents a novel method for respiratory motion compensated reconstruction for cone beam computed tomography (CBCT). The reconstruction is based on a time sequence of motion vector fields, which is generated by a dynamic geometrical object shape model. The dynamic model is extracted from the 2D projection images of the CBCT. The process of the motion extraction is converted into an optimal 3D multiple interrelated surface detection problem, which can be solved by computing a maximum flow in a 4D directed graph. The method was tested on 12 mega-voltage (MV) CBCT scans from three patients. Two sets of motion-artifact-free 3D volumes, full exhale (FE) and full inhale (FI) phases, were reconstructed for each daily scan. The reconstruction was compared with three other motion-compensated approaches based on quantification accuracy of motion and size. Contrast-to-noise ratio (CNR) was also quantified for image quality. The proposed approach has the best overall performance, with a relative tumor volume quantification error of % and % for FE and FI phases, respectively. The CNR near the tumor area is (FE) and (FI). These results show the clinical feasibility to use the proposed method to reconstruct motion-artifact-free MVCBCT volumes. Index Terms Image motion analysis, image reconstruction, motion compensation, motion estimation. I. INTRODUCTION I N CLINICAL practice, radiation therapy to nonsmall cell lung cancer (NSCLC) patients generally involves three stages: treatment planning, daily localization, and treatment delivery. Usually the treatment planning is done several days before the first treatment day. A 4D serial computed tomography (CT) [1] is used to scan the patient, which creates 3D volumes in multiple respiratory phases. These phase-correlated 3D volumes are generated by retrospectively sorting the trans- Manuscript received October 13, 2012; accepted November 20, Date of publication December 10, 2012; date of current version July 27, Asterisk indicates corresponding author. *M. Chen was with the Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA USA. He is now with Imaging and Computer Vision, Siemens Corporate Research, Princeton, NJ USA ( mingqingchen@gmail.com). Y. Zheng is with Imaging and Computer Vision, Siemens Corporate Research, Princeton, NJ USA. K. Cao is with the Biomedical Imaging Analysis Lab, GE Global Research Center, Niskayuna, NY USA. R. A. C. Siochi is with the Department of Radiation Oncology, University of Iowa, Iowa City, IA USA. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TMI Fig. 1. Typical workflow of radiotherapy to nonsmall cell lung cancer patients. verse slices according to the respiratory phase of the patient, which is indicated by a strain gauge placed on the patient s abdomen. The clinicians are then able to determine a plan for treatment based on those volumes, such as the gross tumor volume (GTV), dose distribution, respiratory gating threshold, etc. The course of treatment generally involves daily delivery in about 5 8 weeks. Prior to each daily treatment, a mega-voltage cone beam CT (MVCBCT) [2] [4] is used to create a 3D volume, which is reconstructed from 200 2D projection images acquired from different rotational angles. The 3D volume is then registered with 4D planning CT data to determine the tumor position. The treatment is delivered immediately after the localization procedure. The clinical workflow is illustrated in Fig. 1. The MVCBCT differs from the traditional 2D localization approaches. The 3D imaging capability improves the localization accuracy and reduces the possibility of target misalignment [5] [7]. Moreover, the MVCBCT uses the linear accelerator (linac), which is used for treatment, as X-ray source for the imaging. Thus, the localization and treatment procedure can be takenonthe same table. However, one of the disadvantages of the current MVCBCT technique is the motion artifacts. Since the projection images are acquired during the rotation of the gantry and the electronic portal imaging device (EPID), each projection image corresponds to a different time/phase point of the respiration (one rotation takes about 60 s, containing several respiratory cycles). The 3D volume is thus averaged through the image acquisition time, which introduces blur in the motion area. The blur degrades the accuracy of target localization and dose distribution [8]. Thus it is highly desirable to remove the blurring artifacts. Fig. 2 compares the reconstructed /$ IEEE

2 1366 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 32, NO. 8, AUGUST 2013 Fig. 2. An example showing that the motion artifact is reduced by using the proposed MC reconstruction approach: a coronal (a) and sagittal plane (c) of the reconstructed volume without MC, compared with the volume using MC [(b) and (d)]. Note that the blurring of the tumor is reduced in the MC reconstructed volume. MVCBCT volumes with and without using motion compensation technique. Previous tomographic reconstruction methods for reducing motion artifacts can be generally divided into respiratory correlation (RC) and motion compensation (MC) methods. The first one involves sorting the projection images into several subsets [9] [11]. It is limited by view-aliasing artifacts, which are caused by using an insufficient number of projection images. Experiments based on using multiple rotations or slowing the gantry rotation speed shows reduced artifacts and improved image quality [10], [12], but these methods are limited by increased image acquisition time and imaging dose. Methods based on algebraic reconstruction techniques and compressed sensing theory [13], [14] enable artifact-free reconstruction using a limited number of projection images, but extensive computation makes it impossible to implement clinically without a GPU platform. In the MC reconstruction approach, a prior motion model is incorporated into the de-convolution process during the backprojection. Usually, the motion model is represented by a time sequence of motion vector fields (MVF) [15], [16]. To derive the MVF, one can perform deformable registration among different phases of the 4D planning CT [10], [17], [18] or register the different phases of correlated CBCT images [19]. However, the first approach is limited by the variation in anatomy and motion between the treatment planning and treatment stage. The aliasing artifacts in correlated CBCT images bring inaccuracies to the MC reconstruction. A promising solution to derive accurate MVF just prior to the treatment delivery is to utilize the cone beam projection images, since they provide high temporal resolution (about 0.3 s for MVCBCT). Previous methods that make use of the projection images include monitoring tumor change by projecting a volume of interest [20], extracting the projected implanted marker [21] or diaphragm edge [22]. MVF derived by registration between the volume space and the projection space achieves improved image quality for MC reconstruction [17], [19], but the iterative scheme of forward-projection and optimization is extremely slow, making it difficult for an immediate application in the treatment room. In this work, a novel method is presented to compute a (3D ) multi-phase triangulated mesh of the lung from 2D projection space. The resulting dynamic lung model is further used to generate MVFs for MC reconstruction of the thoracic region, where a 3D volume in the full exhale (FE) and full inhale (FI) phase is created, respectively. The proposed method has the following advantages. 1) The method utilizes the projection images and maintains a clinically acceptable time frame. Instead of performing registration between volume and projection space, the MVFs are computed by interpolating from the motion vectors of the lung model, which has a much lighter computational load. 2) Different from previous 2D to 3D shape recovery methods [23] [27], an optimal multi-surface segmentation framework based on graph search algorithms [19], [28] is adapted in the process of multi-phase surface mesh detection. It detects the lung surface meshes in all sampled respiratory phases simultaneously, since the framework incorporates the motion constraint between adjacent phases into the graph formulation, which makes it robust in the presence of confounding organs in the projection image. The rest of the paper is organized as follows. Section II introduces the details of the proposed approach. Section III describes how the proposed method is compared and validated with three other MC reconstruction approaches and the evaluation result is also presented. Section IV concludes with a discussion of the experimental results. A. General Framework II. MATERIALS AND METHODS Fig. 3 shows the general framework for deriving MVFs from MVCBCT projection images. The method includes the following steps. 1) The lung with the tumor is segmented in the FE phase of the 4D planning CT. 2) A B-spline deformable registration method is used to derive the MVF from the FE phase to the FI phase of the planning CT [29]. 3) The MVF is then used to deform the lung mesh created from the FE image to generate a mesh for the FI phase. 4) On the treatment day, the lung model generated in the FE and FI phases of the planning CT is aligned to the 3D cone beam volume.

3 CHEN et al.: MOTION-COMPENSATED MEGA-VOLTAGE CONE BEAM CT USING THE DEFORMATION 1367 Fig. 3. General framework for deriving MVF from MVCBCT projection images. 5) The averaged mesh between the FE and the FI phases is computed and used as the initial mesh model, which is further projected onto each 2D projection image. 6) The cone beam projections are sorted according to 3D anatomical positions of the ipsi-lateral hemi-diaphragm apex (IHDA) into several respiratory bins [30]. 7) The multi-surface segmentation graph search framework [31] is adapted to compute the locations of mesh points in each respiratory phase after the deformation. For each phase, a subset of mesh points, which correspond to the strong boundary of the projected lung, are used to pull the mesh towards the desired new locations based on the gradient information of the projection images. These points are called candidate points. 8) Based on the detected lung surface mesh, a thin-platespline interpolation technique is implemented to estimate the MVFs from each respiratory phase bin to FE and FI phases respectively. 9) MC reconstruction based on the FDK algorithm is applied to create motion corrected 3D volumes in FE and FI phases. Generally, MC reconstruction compensates the motion of every voxel in the volume. To reconstruct the 3D volume at phase, the MVF should be derived for each phase to, which is denoted as. For voxel at phase, specifies the 3D motion vector at phase to the location of that voxel at phase.the MVF is applied during the back-projection step of the FDK algorithm, which is represented by the following theoretical equation: where represents the attenuation coefficients at phase at voxel. It is the summation over rotation angle from minimal angle to maximal angle of the gantry. is the distance between source and iso-center of the cone beam system. The divisor is used for distance weighting, where. The parameter represents the phase index that the projection image belongs to. (1) Fig. 4. An exemplary respiratory signal sorted into 20 respiratory bins ranging from 0 to 19. The denotation represents the attenuation coefficient after proper pre-weighting and extrapolation, which is later convoluted with a filter. The 3D to 2D projection geometry of the MVCBCT system is specified by a 4 3projectionmatrix.The expression takes the form of a change of coordinate system (2D to 3D) and represents the backprojection task handled by the projection matrices. The details of the MC framework can be found in Schafer et al. [15] or Ritchie et al. [16]. Since steps 1 3 are based on the 4D planning CT, they can be performed immediately after the 4D CT scan. The other steps are taken after the 2D projection images of the MVCBCT are acquired. All the steps are performed offline, thus no modification to the imaging protocol or dose level is needed. B. Respiratory Signals and Phase Sorting During the localization scan, the CB projections are correlated with the respiratory signal. The standard of care for this procedure is motion monitoring using the AZ-733V respiratory gating system (Anzai Medical, Tokyo, Japan). However, several studies have suggested that more accurate tumor motion may be determined when using internal anatomical surrogates, such as the apex of the diaphragm [8], [32]. The respiratory signal used in this study is based on this approach, which detects the apex of the diaphragm using our previously developed algorithm [22], [30]. For the proposed method, the respiratory sorting is based on both the motion amplitude of the diaphragm and the inhale/exhale session. This involves three steps. First, the local maxima and minima of the signal are detected. Second, based on those maxima/minima positions, each projection image is labeled with a binary respiratory state exhale or inhale. Finally, the projection images are sorted into multiple bins based on both the amplitude and the label. Fig. 4 illustrates an example of the respiratory sorting. C. The Initial Lung Model Segmentation of the lung takes two steps. First, an automatic algorithm is implemented to generate a binary image of the whole thoracic cavity based on gray level threshold and connected component labeling. The binary image contains both lungs, including the trachea and the bronchi. Second, manual adjustment is used to keep the cancerous lung while removing everything else. A triangulated mesh of the lung is generated from the binary image using the marching cubes algorithm [33]

4 1368 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 32, NO. 8, AUGUST 2013 Fig. 5. The major process of generating initial lung shape model in the MVCBCT coordinate. (a) Bony structures (red) segmented from 4D planning CT. (b) The alignment of the bony structures onto the fully reconstructed MVCBCT. (c) Triangulated lung mesh segmented from the FE phase of 4D planning CT. (d) The lung mesh transformed to the MVCBCT coordinate. [Fig. 5(c)]. Using an accurate B-spline deformable registration algorithm, we preserved both the parenchymal tissue volume and vesselness measure [29]. The optimization metric is based on the sum of the squared tissue volume difference and the sum of the squared vesselness measure difference, respectively [29]. The mesh created in the FI phase is derived from the FE phase based on the MVF computed during inter-phase registration. Using our in-house software platform, the MVCBCT image without MC is rigidly aligned to the coordinates of the 4DCT using bony anatomic structures [see Fig. 5(a) and (b)]. The lung meshes in the FE and FI phases are then transformed to the cone beam geometry [Fig. 5(d)], which provides the initial lung shape and motion model. The initial model is the average of the meshes of the FE and FI phases. For each mesh point, a range of motion is determined using the equation and,where and is the corresponding positions in FE and FI phases, respectively, and is the mean position. is used to control the allowed range, which is typically set between 1.5 and 2. In this study, it is assumed that each mesh point moves along the direction defined by and, providing a close approximation to the real motion trajectory. The generation of the initial mesh is performed offline during the planning stage and can be completed within 2 min. D. Candidate Edge Selection The gradient amplitude and the direction of the lung boundary are the most salient features of the projection images. In order to deform the initial mesh towards these desired locations, the mesh points that correspond to the strong boundary in the projection images should be selected as anchor points to guide the deformation of the other points. In our previous work on the extraction of left ventricle motion from cone beam projections, the strong boundary of the left ventricle in the projection images corresponds to the silhouette contour of the mesh [26]. Unlike the left ventricle, however, the lung mesh is a concave, not a convex shape. During inspiration the lung walls bulge outward while the diaphragm hollows inward. Due to this concave characteristic, the silhouette contour of the projected lung mesh may not correspond to an equally strong boundary in the projection image. This is indicated by the red arrow in Fig. 6(b). Instead of using the silhouette contour to deform the mesh according to the gradient of the projection image, we define a Fig. 6. (a) Original MVCBCT projection image. (b) The projection of the initial lung mesh (green) and the silhouette contour (red). Note that the part of the contour at the bottom does not have a corresponding strong gradient. (c) Projected initial lung mesh (green), detected candidate edge (red contour), projected motion direction (yellow line), and projected normal direction (blue line). Note that the candidate edges locate near the strong boundary, while some silhouette edges locate near the weak boundary in (b), that is why the deformation of the mesh is based on candidate edges instead of silhouette edges; (d) original candidate edge (red), projected motion direction (yellow line), and deformed candidate edge after optimal graph search (blue). subset of mesh edges as candidate edges to assure that the selected edges have corresponding strong gradient in the image. A candidate edge is required to satisfy two conditions: 1) all the neighboring points should be on one side of the edge in the projection space; 2) the surface region near the edge should be smooth, i.e., no sudden jump in the spatial location among the adjacent mesh points. The first criterion guarantees that the ray integrals on two sides of the candidate edge are different. The second one ensures that the difference is large enough to produce a high contrast. The detected intensity of the projection images can be computed as a ray integral of the attenuation coefficients in a 3D volume:. Since the attenuation coefficient of the lung is distinct from the surrounding tissue, the gradient in the CB projection is caused by the difference in the length of the beam that passes through the lung. Fig. 7 compares three locations where an edge may exist. Due to large differences in the ray accumulation, the top two locations are likely to correspond to a strong gradient, while the bottom location may have a weak or even invisible gradient. By using candidate edges instead of silhouette edges, the proposed method is able to avoid the weak boundary in the image. E. Multiple Surface Detection via Optimal Graph Search The mesh deformation is formulated as a multiple interrelated surface detection problem, with smoothness constraints. The deformation is expressed with the optimal graph search method, which computes the maximum-flow of an s-t graph [31], [34], [35]. The details are as follows: Given an initial mesh with points, find the location of those points in respiratory phases following cost function:, which minimizes the (2)

5 CHEN et al.: MOTION-COMPENSATED MEGA-VOLTAGE CONE BEAM CT USING THE DEFORMATION 1369 Fig. 7. Illustration of the graph construction for two connected mesh points in two phases. Three types of arcs are shown. The intra-column arcs describe the topological relationship among the graph nodes. The inter-column arcs and inter-phase arcs represent the imposed smoothness constraint in spatial and temporal domain, respectively. Only one inter-phase arc is displayed for clarity. where and denote the index and the total number of projection images, respectively. Function when the th point in the th projection image is the candidate point, which otherwise equals zero. is the cost function of point at projection image.wedefine this cost function as the negative dot product between two 2D vectors: the image gradient of the projected point and its projected motion direction,where is the operation of the 3D to 2D projection of a point or a vector. This definition is required in order to identify that the projected motion direction of the candidate point is opposite to the image gradient at the projected location [Fig. 6(c)]. The function maps projection image to the respiratory phase. The cost function can be represented as (3) There are three constraints placed on the displacements of the mesh points. First, each point is only allowed to move in the direction defined by and. Second, the deformed mesh in each phase should be relatively smooth. For any neighboring point and, the displacement vector from the initial position should not vary too much where is the smoothness constraint. The third constraint is the temporal constraint, where the displacement vector between neighboring phases should be smaller than The objective is to find the deformed mesh points along the predefined motion direction in multiple phases, which minimize the cost function under smoothness constraints in both spatial and temporal dimensions. The problem can be visualized in 2D projection space in Fig. 6(c), where the point belonging to the candidate edge (red) is expected to move to the new boundary location along the projected motion direction. Studies performed by Garvin, Li, and Song [31], [34], [35] explain in detail the maximum flow computation and the graph construction methods. In our method, a column of the s-t graph (4) (5) Fig. 8. An illustration representing likely strong and weak boundaries. The top two locations produce distinctive differences, as marked by the red lines passing through the lung. The bottom boundary is very indistinctive with little difference visible around its intersections with the lung. is created for each point of the initial mesh. Each column has a node which is equally distributed in the direction of motion. The graph consists of sub-graphs, each representing one respiratory phase. Each sub-graph contains columns, corresponding to mesh points. Fig. 8 illustrates a simple example of this graph construction. The weight for node in phase is assigned as This equation reveals that there are three types of mesh points in any given phase: noncandidate points, candidate points belonging to one projection, and candidate points belonging to different projections. It is the weight of the candidate points that contribute to surface detection and pulls the noncandidate points by smoothness constraints. For candidate points belonging to several candidate edges in different projections, the weight is a combination of image gradients in multiple CB projections. F. TPS Interpolation Fig. 6(d) shows the deformed candidate edges. The deformed edges move toward locations with strong image gradients, such as the diaphragm and the lung wall. Fig. 10 shows another example of the projected mesh after deformation, along with its candidate edges and silhouette edges. To generate the MVF, the displacements for all the voxels in the 3D volume need to be interpolated. The thin plate spline (TPS) interpolation algorithm [36] is used to generate a 3D MVF using the displacement of a known point set called anchor points. The TPS interpolation aims to minimize the physical energy function as follows: (6) (7)

6 1370 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 32, NO. 8, AUGUST 2013 III. EXPERIMENTS AND RESULTS Fig. 9. MVF from the FE to FI phase with the mesh in the FE phase. A. Imaging Data Our data were collected on Siemens Oncor MVCBCT (Siemens Medical Systems, Oncology Care Systems, Concord, CA, USA), which uses an amorphous silicon flat panel, electronic portal imaging device (EPID) to acquire 2D projection images. The dimensions of the pixel grid are with a pixel spacing of 0. mm. The source to axis distance (SAD) and the source to imager distance (SID) are 100 and 145 cm, respectively. Using the standard protocol [3], 200 EPID projection images are acquired as the gantry rotates clockwise from to 110 in 1 min. These EPID projections are used to reconstruct a 3D volume, with a field of view (FOV) of cm. Since the frame rate for 2D projections is about 3 frames per second (fps), the anatomical change due to respiratory motion is well preserved in the projection images. Our method is tested on 12 MVCBCT localization scans taken from three patients who have large NSCLC tumors cm in the bottom lobes of their lungs. A total of four sets of 4D planning CTs were used to generate the initial lung mesh model (Section II-C) and provide a reference for evaluation. For the first two patients, one planning CT scan was taken several days prior to the treatment session. Two scans were captured for the third patient, since the tumor changed during the course of treatment and replanning was required. For each 4D CT set, a 3D time sequence of volumes was acquired, representing ten different respiratory phases evenly distributed in a respiratory cycle. All the algorithms introduced in this study were implemented using our in-house software. Fig. 10. An illustration of the detection. (a) An original projection image. (b) The projection of the deformed mesh (blue). (c) The candidate edge and silhouette edge of the deformed mesh (blue). (d) The candidate and silhouette edge of the static mesh (red), the deformed mesh (blue), and the motion vector foreachmeshpoint(yellow). The first term of the algorithm represents the interpolation error of the anchor points while the second term represents the bending energy of the transformation of a thin plate. The parameter is tuned appropriately to control the balance between the exact mapping of the anchor points and the rigidity of the deformation. For our purposes the candidate points are used as anchor points. Fig. 9 shows the MVF from the FE to FI phase. To reconstruct a motion-free volume in the FE phase, the MVF is generated from the FE phase to every phase ( MVFs in total). Each MVF is used to compensate the motion for the corresponding projection images during the backprojection process. The same procedure is applied to reconstruct the FI phase. B. Other Methods for Comparison Three different methods are used in comparison to the proposed approach: 1) respiratory correlated reconstruction based on conventional FDK; 2) MC using the MVFs computed from the correlated MVCBCT; 3) MC using the MVFs computed from the 4D CT. For the first approach, the projection images are sorted into two subsets (FE/FI) to reconstruct 3D volumetric images. The limited number of projection images (200 using the default setting) restricts image production in other respiratory phases, since fewer projections occur during the middle of inhalation or exhalation. The sorting of the projection images is based on the superior inferior direction of the IHDA signal only, since the motion pattern differs in the middle of the inhale/exhale phases. Compared to phase-based sorting schemes, amplitude-based methods are able to control the residual motion by adjusting the gating window. The size of the gating window is a tradeoff between view-aliasing artifact and motion artifact. Based on our experience, at least 30 projection images are needed in each phase to produce a clinically meaningful image set. To include sufficient images, the width of the gating window ranges from 10% to 25% for the FE phase, and 20% 40% for the FI phase (We scale the maximum and minimum of the amplitude to 100% and 0%, respectively). The correlated MVCBCT in the FE and FI phase is used to generate two setsof3dmvfs(fetofi,fitofe)forthemc approach. Similar to the correlated FDK method, two phases

7 CHEN et al.: MOTION-COMPENSATED MEGA-VOLTAGE CONE BEAM CT USING THE DEFORMATION 1371 TABLE I MAIN PROCEDURE OF THE FOUR EXPERIMENTED METHODS AND THE ESTIMATED RUNNING TIME (one at FE and one at FI) of images are produced. MVF from FE to FI are used to deform the backprojection from the 2D projection images during the FE phase, while MVF from FI to FE are used to deform the images in the inhale phase. During the reconstruction, the MVFs are interpolated for CB projections that belong to intermediate phases. For the third approach, since there are more than 10 phases of images in one 4D CT set, the 4D MVFs are generated by registering the 3D volumes in every intermediate phase to FE and FI phase, respectively. The MVFs are then converted into cone beam coordinates using the transformation information derived during the alignment of the two images [see Fig. 5(a) and (b)]. It should be noted that all the tested methods are based on currently available image datasets. Since they are performed without changing the image acquisition of the CT systems, no modification is made to the current clinical workflow, the imaging dose or the scanning time. For imaging dose, each daily localization MVCBCT scan uses a beam of 6 mega-electron-volt (MeV) with a dose of 10 monitor unit (MU), which is equivalent to about 70 mgy in areas near iso-center. It takes about one minute to acquire all the 200 projection images. To maintain standard diagnostic image quality, 4D planning CT generally requires more imaging dose than a conventional single scan. The typical dose amount would be mgy, with a scan time about 1 min. Table I illustrates the main procedures of all the four experimented methods and the estimated running time for each procedure. The running time is separated into planning stage and treatment stage respectively. It is measured on a desktop computer with an Intel Core i7-2620m 2.70GHz CPU and 8GB RAM. There is no clinical time requirement for the offline procedures after planning stage. But for localization and treatment delivery, deriving the FE and FI images within one minute after the acquisition of MVCBCT projection images would be desirable. Though the given time for treatment stage exceeds this limit, it should be noted that all the algorithms are currently implemented as a single-threaded program. We believe that all the methods can fulfill the clinical time requirement based on multiple cores or the GPU platform, since computation of the deformable registration, the MVF, maximum flow and MC reconstruction could be parallelized. C. Reconstructed Images Fig. 11 shows the results of MVCBCT at the FE phase using the various approaches discussed in this paper. It is evident that Fig. 11. Reconstructed MVCBCT at the FE phase for PATIENT1 using different approaches. From left to right are the images of sagittal, coronal and axial views, respectively. (a) Conventional FDK using all the projection images; (b) RC; (c) MC using 4D CT; (d) MC using RC MVCBCT; (e) The proposed approach. for the FDK without MC (row a), strong motion artifacts in both tumor and diaphragm are visible. For correlated reconstruction (row b), the motion artifact is greatly reduced, however there are still strong view-aliasing artifacts (the streaking

8 1372 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 32, NO. 8, AUGUST 2013 Fig. 12. Profile of reconstructed MVCBCT (blue) and 4D CT (red) along superior-inferior direction (x-axis is superior inferior direction in physical coordinate, y-axis is the CT number). (a) Conventional FDK. (b) Correlated reconstruction. (c) Proposed approach. The difference in edge location is due to the change in motion pattern between planning CT and CBCT. and banding). For the MC methods [rows (c) (e)], the motion is reduced without introducing aliasing artifacts. Fig. 12 shows a single profile aligned in a superior-inferior direction passing through the tumor. It is evident that the edge of the tumor and the diaphragm is blurred in Fig. 9(a), showing obvious motion artifacts. For both the correlated reconstruction and the proposed approach, the edge becomes much sharper. Some features generated using the 4D CT approach [Fig. 12(b)] are preserved in the image reconstructed using the proposed approach [Fig. 12(c)]: the two small peaks located between the tumor and the lung wall are particularly noteworthy. The difference in the location of the edges between the reconstructed MVCBCT and the 4D CT is due to the different respiratory sorting techniques applied for the reconstruction. Further differences were introduced due to the change of motion that occurred between the time the patients were planned for treatment and the time they were treated. D. Evaluation Several metrics are used to evaluate the target localization and image quality of the reconstructed image. First, the accuracy of tumor volumetric measurement is tested on data derived from 12 MVCBCT scans. For images with poor quality, such as correlated FDK, there would be a very large variance of manually annotated contours of the tumor by different physicians. The edge of the tumor is sometimes difficult to define on these images. To minimize inter-observer variability, a semi-automatic approach is implemented to segment the tumor and quantify the tumor size. The algorithm starts with a user-definedregionof interest (ROI) in the 3D volume. The Otsu threshold [37] and connected region labeling is used to segment the tumor within theroi.sincethedataprovidedbythectscansofthetumor and the surrounding soft tissue inside the lung differs greatly, the Otsu threshold tries to find the optimal threshold that minimizes the intra-variance of the two different classes. The tumor volume calculated from the planning 4D CT is used as ground truth and the relative error is computed as follows: Fig. 13 shows the relative error of tumor quantification of 12 MVCBCT daily localization scans. To reduce errors that may occur due to any change in tumor volume between the planning CT and the treatment/localization CBCT, we also analyze four MVCBCT scans taken closest to the planning day for each patient. The time period between the planning CT and MVCBCT (8) Fig. 13. Relative error of tumor volume quantification in 12 MVCBCT images. The bars with an asterisk represent the first MVCBCT scan after the 4D planning CTwhichisusedasgroundtruth. TABLE II OVERALL RELATIVE VOLUME ERROR TABLE III OVERALL RELATIVE VOLUME ERROR FOR THE FOUR MVCBCT CLOSEST TO PLANNING CT scan is less than six days and there is no radiation therapy during this intermission. These images are marked with asterisks in Fig. 13. According to a study on tumor growth conducted by Arai et al., a large cell carcinoma has a doubling time of 67.5 days, which is the most aggressive type of NSCLC [38]. Based on the linear growth and exponential growth models, the growth rate for a six-day time period can be estimated to be 8.9% and 6%, respectively, which can be considered as an upper bound. Tables II and III show that MC reconstruction based on 4D CT scans and the proposed method have better tumor quantification accuracy than the other two approaches (correlated MVCBCT, MC reconstruction using MVF computed from 4D CT, and MC reconstruction using MVF computed from correlated MVCBCT are abbreviated for correlated, MC-4DCT, MC-CBCT, respectively). Motion measurement accuracy is another important clinical parameter in radiotherapy. In this study the motion of IHDA positions from FE to FI is manually identified, which has a very small inter-observer variability. The displacement of the IHDA in the superior inferior (SI) direction is compared to the average peak-to-valley IHDA motion in the SI direction, which is detected from the 2D projection images and back-projected to 3D spatial location. This is considered as ground truth. The SI direction of motion of the IHDA is automatically determined from the 2D projection images using our previous method [22], [30]. Similar to volume measurement, a relative error is used (9)

9 CHEN et al.: MOTION-COMPENSATED MEGA-VOLTAGE CONE BEAM CT USING THE DEFORMATION 1373 Fig. 14. Relative error of IHDA motion quantificationin12mvcbctimages. TABLE IV OVERALL RELATIVE ERROR FOR IHDA MOTION TABLE V CNR IN DIFFERENT REGIONS USING DIFFERENT RECONSTRUCTION APPROACHES Fig. 14 shows the relative error for 12 patients. The overall accuracy for the four methods is shown in Table IV, where the correlated reconstruction method and the proposed method have greater accuracy than both the MC-4DCT and the MC-CBCT. Motion correction based on 4D CT reveals the largest error which is mainly due to the inconsistency of the motion pattern between the planning session and the localization session. Contrast-to-noise ratio (CNR) is a simple and objective measure of the detectability of certain structures with uniform intensity. In this study it is used to assess the image quality in the tumor and diaphragm region based on the following formula: (10) where and are the mean and standard deviation within the object (tumor or diaphragm) or background. The segmentation of the tumor and the diaphragm is based on the same approach that is used for tumor volume measurement. The results of CNR are shown in Table V, where it is evident that 4D CT has significantly better CNR than MVCBCT, and correlated CBCT has smallest CNR value. CNR of the proposed method is slightly better than the other three approaches. IV. DISCUSSION AND CONCLUSION In the previous section, the four reconstruction approaches are compared on different evaluation metrics. Each evaluation metric is focused on one aspect of the reconstructed image. Generally, the tumor volume measurement indicates how accurate the clinicians are able to delineate the boundary. The IHDA displacement shows how accurately one can determine the absolute position and how much motion is compensated on the image. The CNR, on the other hand, measures the general image quality and detectability of organs of interest. Based on those evaluations, the proposed approach has the best overall performance on all three metrics. For tumor volume measurement, the error of the proposed method is slightly larger than MC based on 4D CT. But MC based on 4D CT has the worst result in diaphragm motion measurement. In IHDA motion measurement, the proposed approach is comparable to respiratory correlated reconstruction. The RC reconstruction is assumed to be able to sufficiently compensate the motion artifact within the gating window size. However, its performance is poor in tumor volume and CNR measurement. It can be concluded that the proposed approach sufficiently compensates the motion artifacts in our experiment. It should be noted that there is some limitation of using the 4D CT data to provide the ground truth for tumor volume quantification. As discussed in Section III-D, there is a time interval up to six days between the 4D CT scan and the first treatment day. If the tumor is assumed to continue growing during this interval, the tumor volume in the 4D CT data only provides an upper bound (based on growth rate estimation) for the first MVCBCT scan. Since it is impractical to acquire a 4D CT scan on the first treatment day, the ground truth for the tumor volume on that day is unavailable. The reference of 4D CT data is the best approximation based on the current state-of-the-art. The improved reconstruction accuracy of the proposed method contributes to several factors. First, generating an MVF based on 2D CB projection images is more accurate than using the 4D CT and correlated CBCT. This comparison formed the basis of the previous study by Li et al. [19]. Correlated CBCT contains severe aliasing artifacts, which cause inaccuracies in the 4D MVF during registration. This is well illustrated by our results of the motion measurement error; correlated FDK has the best accuracy among the four, but MC using those correlated CBCT images is more error-prone. On the other hand, the deformation fields acquired during the 4D planning CT is not reliable for use with the MVCBCT scan, as seen in the motion quantification result. The MC reconstruction using MVF from 4D CT has up to 47% relative error in motion quantification. The IHDA motion between 0% and 100% exhale of the 4D CT is also quantified, which is much smaller than the average peak to valley IHDA motion extracted from CB projections. In one case the IHDA motion in 4D CT was 8 mm, while the average IHDA motion in one MVCBCT scan was up to 22 mm. Apart from the change in motion amplitude, another possible reason to account for this inconsistency is that the respiratory signal used during 4D CT acquisition is based on relative phase. The proposed method, on the other hand, avoids the inter-fractional change, such as motion amplitude and tumor volume, between the planning stage and the treatment day by generating MVFs solely from the daily MVCBCT scan. On the other hand, it utilizes the absolute 3D IHDA position as the respiratory signal. The deformation of the projected mesh points in 2D space can

10 1374 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 32, NO. 8, AUGUST 2013 be accurately back-projected to 3D space using the projection matrix of the cone beam system. Second, the proposed approach can be used on-the-fly in cases where the estimation and compensation of the respiratory motion during the acquisition of CB projections is needed. Although manual editing of the initial lung model derived from the 4D CT is required, these procedures can be accomplished right after the acquisition of the planning CT. To further improve efficiency, the manual alignment correction may be replaced with available commercial registration software. For MC reconstruction using the proposed method, the deformation, MVF interpolation and MC reconstruction are fully automated (see Fig. 3). The proposed approach obviates the protracted need of forward projection registration required by the image-space to projection-space registration method [19]. Computation time for the deformed mesh computation via optimal graph search takes about a minute using an Intel Core i M CPU with 4GB RAM. Generating an MVF using the same processor takes about 5 min, although calculation times may be reduced through the use of a computationally light interpolation technique. Though free of reconstruction artifacts, 2D projection images contain a lot of noise due to MV photon scatter (Fig. 6). There are confounding edges that lead the mesh deformation towards the wrong locations in projection space. The proposed method consists of two components to avoid those edges. First, the use of the dot product between the vector of the projected motion direction and the gradient can eliminate the indistinct edges with the gradient which is not conforming to the desired direction. The second one is the use of the smoothness and inter-phase constraints in the optimal graph search method, where the motion of one mesh point in one respiratory phase is limited by the position of its neighboring point and its neighboring phase. Several issues should be considered in order to make the proposed method applicable to clinical situations. First, the method is based on the assumption that the surface shape of the lung is same for all the 2D projection views that are sorted to the same respiratory phase bin. In reality, the slight differences of the lung surface shape in the corresponding 2D views always exist, since the deformation pattern of the respiration varies cycle-by-cycle. Thus reducing this variance would make the approximation closer to the assumption. That is why we use the IHDA to provide the respiratory signal in this study, since it is more reliable to represent the phase of projection images than the external surrogate. The patients in our study have different respiratory frequencies during the scan, even for the same patient under different fractions. The number of respiratory cycles during each scan ranges from 5 to 15. The motion constraint in the graph search framework should be set properly in order to make the detection robust to different respiratory frequencies. Generally, a too loose constraint has no effect in limiting the motion. It also degrades the 4D graph search framework into multiple independent 3D cases. If the constraint is too restrictive, it induces errors for rapid respiratory cycles. For clinical applications, the clinicians prefer a predefined optimal motion constraint without online parameter tuning. In our implementation, the value of the allowed motion is set to be slightly larger than the maximal possible motion displacement. The same rule is applied to the smoothness constraint, where it is set to allow the maximal possible gradient of the shape surface. Based on our experiment, the influence of the value of the constraint to the running time of the graph search is negligible. It should be noted that for obese patients, the signal to noise ratio would be smaller and more overlap of other tissues or organs would occur. Generally, the performance of the algorithm is not influenced by obese patients. The fore-mentioned factors in motion-constraints are much more important in determining the accuracy of the algorithm. Another source of inaccuracy is the location of the lung in some of the CB projections. Among the image sets that we used, the whole lung is visible in only one CB projection set. A portion of the lung is located outside of the field of view on the two remaining image sets. In cases where the lower part of the diaphragm is located outside of the image, the algorithm has difficulty in detecting the candidate edges, which may explain why the motion error is greater for two of the patients. All three patients used in this study had large NSCLC tumors cm. Large tumors also form a part of the initial lung mesh so that the candidate edges that delineate the tumor in CB projections can guide the tumor deformation during MVF estimation Fig. 10 However, there might be no candidate edge for a small tumor in the projection space. The tumor deformation hastorelyontheinterpolationfromthedeformedlungmesh only, which may not represent the real tumor deformation and for this reason there may be no candidate edges for small tumors. Future studies will focus on patients with tumors of varying sizes in more locations. The accuracy of mesh deformation will also be evaluated in the projection space. Generally, the proposed method can be applied to any organ (e.g., the liver and kidney, etc.) that is under quasi-periodic motion imaged by the cone beam CT system. However, an organ well below the diaphragm (e.g., the prostate) is only slightly affected by the respiratory motion; therefore the potential gain by applying the proposed method is small. The lung has a large respiratory motion, which cannot be ignored in CT reconstruction. Another prominent example is the left ventricle (LV), which has a large and more rapid cardiac motion. The proposed method can be applied to generate MVFs for motion compensated (MC) reconstruction of the LV in a C-arm cone beam CT system. It is currently tested on estimating the MVF of the LV endocardium surface on about 10 rotational angiocardiogram datasets captured from a C-arm system. The preliminary results are promising. In all, we have developed a novel approach to reduce the motion artifacts of MVCBCT during the localization scan. Compared with three previous methods, the proposed method shows superior target localization and image quality. 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