Deformable Registration of Planning CT and Daily Cone beam CT for Image Guided Adaptive Radiation Therapy System

Deformable Regtration of Planning CT and Daily Cone beam CT for Image Guided Adaptive Radiation Therapy System Dengwang Li*, Xiuying Wang**, Hongjun Wang*, Yong Yin***, David Dagan Feng** * School of Information Science and Engineering, Shandong University, China (e-mail: lidengwang@mail.sdu.edu.cn) ** Biomedical & Multimedia Information Technology Research Group, University of Sydney, Australia (e-mail: xiuying@it.usyd.edu.au) *** Department of Radiation Oncology, Shandong Cancer Hospital, China, (e-mail: yinyongsd@yahoo.com.cn) Abstract: Adequate medical image data analys could provide improved dease understanding, diagnos, staging, and measurement of the response to the treatment, especially for radiation therapy system modeling. In image guided radiation therapy systems, it of great importance to regter the planning images with the daily images for adaptive radiation therapy. Because there are various local and global deformations between the image pairs to regter, we estimate the deformation in a coarse-to-fine manner using orthogonal wavelet bas. The wavelet coefficients are estimated by minimizing the energy function, where the internal forces are derived from the Navier partial differential equations (PDE) and the external forces are derived from the similarity measure between the regtration pairs using normalized mutual information. The experimental results on head-neck and chest cancer studies with both intra- and inter-fraction regtration are presented. And we validated the regtration method quantitatively using synthetic, pre-defined deformations, and qualitatively using clinical images. The applications of proposed algorithm for image guided adaptive radiation therapy, including automatic deformable re-contouring and automatic deformable re-dosing throughout the course of radiotherapy were also studied. Keywords: biomedical control system; image guided radiation therapy; deformable regtration; wavelet; multi-resolution; cone beam CT; Planning CT; adaptive radiation therapy I. INTRODUCTION Medical imaging data analys plays an important role in improving the clinical treatment, especially for radiation therapy system modeling. Radiation therapy has been proven as an effective treatment for many localized cancer types. Approximately 60% of cancer patients are treated with external beam radiotherapy during dease management (Khan and Stathak, 010). During the past 15 years, accuracy of delivered treatment doses has been greatly improved by the use of intensity modulated radiotherapy (IMRT). Although the dose can be accurately delivered to the planned location, intra and inter-fraction changes in patient geometry have required the use of motion-related margins in treatment plans (Stanton et al., 010). Recently, the advancement of volumetric imaging in the treatment room by using kilo-voltage cone beam computer tomography (CBCT), has provided the imaging data needed to perform image guided radiation therapy (IGRT) and adaptive radiation therapy (ART) (Sonke et al., 009). The goals of both IGRT and ART are to increase the radiation dose to the tumor, while minimizing the amount of healthy tsue exposed to radiation (Paquin et al., 009). Numerous clinical studies and simulations have demonstrated that such treatments can decrease both spreading of cancer in the patient and reducing healthy tsue complications (Lu et al., 006). In the adaptive radiation therapy treatment, to maximize radiation dose to the tumor and in the mean time to minimize radiation to healthy tsues, the patient alignment and the information on radiation beam angles are required to be updated continuously in the treatment room (Noel and et al., 010). The image guided adaptive radiation therapy provides method to monitor and adjust the treatment plans to accommodate the changes introduced by patients or organs. The concepts require advanced image processing tools in order to be successful in clinical practice. Deformable regtration algorithms play an essential role in optimizing radiation dose delivery in both of ART and IGRT systems. For instance, regtration of planning CT images with daily CBCT images can adjust the radiation planning. In addition, deformable regtration also important for treatment re-planning via re-contouring and re-dosing the daily CBCT when implementing radiation therapy planning (Lu et al., 006). Research has been done on deformable regtration for planning CT and CBCT. For instance, B-spline based regtration algorithms were used to estimate the deformation (Paquin et al., 009), and in their work multi-scale deformable strategy was used to improve the regtration efficiency. In the work by (Brock et al., 006), finite element model (FEM) was used for the regtration of planning CT and CBCT, which was aiming for obtaining a more accurate assessment of tumor response. In the head and neck cancer diagnos, demons deformable regtration algorithm was used for the CBCT Copyright by the International Federation of Automatic Control (IFAC) 601

guided procedures (Nithiananthan et al., 009). Optical flow based regtration was used for CBCT based IGRT (Østergaard Noe et al., 008) and the acceleration via graphics processing units (GPU) improved the regtration efficiency for an online CBCT system. In th work, for estimating deformation more efficiently, we use a multi-resolution wavelet representation to express the deformation field. Clinical applications in IGRT system demonstrate the efficiency of our proposed algorithm. II. MATERIAL Datasets were collected from 10 patients treated under the on-board imager (OBI cone beam CT, Varian Medical System) which has been in daily clinical use at Shandong Cancer Hospital. Before treatment planning, each patient underwent a series of imaging studies including an intravenous contrast planning CT imaging (Philips Brilliance Big Bore 16). Then the GTV (gross tumor volume) and PTV (planning target volume) were delineated on every section of the planning CT scans by the radiation oncologts. Radiation Physiatrt contoured the organs such as liver, external surface, spinal cord, kidneys, spleen, and stomach on the planning CT. These contours were reviewed and edited by radiation oncologts. Finally treatment planning made with four components including radiotherapy structure (RTstruct), radiotherapy planning (RTplan), radiotherapy dosing (RTdose) and Dose Volume Htograms (DVH) analys. At the time of each delivered treatment fraction, a KV CBCT was obtained during normal breathing. Of the 10 patients investigated, 5 cases had head-neck cancer and another 5 cases had chest cancer, where planning CT image size 51x51x96 and CBCT image size 384x384x64. The methods used for radiotherapy are IMRT for head-neck (H&N) and conformal radiation therapy (CRT) for chest. III. DEFORMABLE REGISTRATION ALGORITHM Firstly, we express deformable process using Navier partial differential equations (PDE), and then the deformation field represented using the wavelet bas. The deformation energy function includes two components. The first one internal force which derived from the Navier PDE, and the second one the external forces which are the normalized mutual information of image pairs to be regtered. A. Deformable regtraion problem The equilibrium state for an otropic homogeneous body can be described by Navier partial differential equation (PDE) (Holden, 008). In contrast to classic thin-plate or B-spline based regtration method, Navier PDE a physical model based method for deformable regtration. Navier PDE models movement of the organ tsues as an elastic object because that organs can be considered as elastic media that are exposed to external forces and are smoothly deformed. As in the multcale matching method by (Bajcsy and Kovacic, 1989), during the deformation process it assumes that the external forces are applied to deform the organs and tsues until an equilibrium state between the external forces and internal forces. Th process can be formulated as (Broit, 1981). μ u λ μ θ i xi + ( + ) + F = 0 i (i=1,,3), (1) In (1), θ cubical dilation and has following expression, θ 1 3 = + + x1 x x3 In (1)-(), X=(x 1, x, x 3 ) T represents the coordinate system before deformation process and F=(F 1, F, F 3 ) T the vector of external forces which are dtributed across organ and tsues. As in (Bajcsy and Kovacic, 1989), elastic constants µ and λ define the elastic properties of the body and u=(u 1, u, u 3 ) T the dplacement fields to find. Thus, the matching process through elastic deformation turns into the problem of deriving forces and selecting elastic properties, and then leading to constent dplacements. Thereby we model the deformable regtration process using Navier PDE that consted of external forces, internal forces and dplacement fields. B. Wavelet based regtration method Firstly, the internal force, Internal(c), in our energy function can be modeled by the first part in (1) while θ substituted by equation (): p u + 3 3 x q Internal ( c) = μ dx (3) p= 1 q= 1 1 3 ( λ+ μ) + + x1 x x3 As mentioned before, λ and µ are Lame s coefficients which reflect the elastic properties of the organs or tsues. These parameters values depend on the properties of the structures involved in the regtration. For example, Lame s coefficients for bone tsues and soft tsues are different from each other. In our work, we chose λ=0 and µ=1 for computational simplicity. The use of warp complexity by a coarse-to-fine strategy to express the deformation field effective to recover the deformation in the regtration process. The wavelet bas, which multi-resolution approximation of deformation field, suitable for such a coarse-to-fine optimization process starting from the low resolution approximation of global deformation, through the details in its different orientations, and ending with finest details of local deformation. Furthermore, wavelet bas has the advantage over Navier- Cauchy eigen functions because they allow deformations with local support to be modeled from a finite set of bas functions (Holden, 008). So we can do deformable regtration by expressing the deformation field using wavelet representation. Here, we expand the elastic deformation field u with wavelet transform and then estimate the wavelet parameter vector c, for 3D that yields: () 60

/ 1 x = x+ / y = y+ / 3 z = z+ where (x, y, z) are coordinates in the floating image and (x /, y /, z / ) are corresponding coordinates in the reference image. The regtration algorithm estimates the wavelet coefficient c by minimizing the energy function in following sections. The 3D separable wavelet decomposition of deformation field, u(x), everywhere within a cubical support N=(N x,n y,n z ) can be presented : N -1 u K= 0 N K = ( kx, ky, kz), X = ( xyz,, ), i = 1,, 3 J i J i1 1 J ( X) cj ΚΦ ( X K) = + J 8 N j -1 j s j c jkφ j= R s= K = 0 j j j N = ( Nx, Ny, Nz) ( X K ) In (5), as in normal wavelet transformation, i an index denoting the three directions x, y and z of the vector function u(x), s an index denoting the subband, j an index denoting the resolution levels, and k=(k x, k y, k z ) the translational index j j within N N = ( N, N, N ) support. Each wavelet j x y z coefficient c indexed by the directions i, the orientation s, the resolution j, and the spatial location k it stands for. The bas functions are 3D functions that are translated across a cubical grid with intervals of j and within a support of N=(N x,n y,n z ). Each bas function weighted by the corresponding wavelet coefficient c (4) (5). The bas functions are a tensor product of one-dimensional scaling and wavelet functions. Substituting the deformation field, u, in (3) as represented in (5) results in a linear combination of the integral (Gefen et al., 003). It can be concluded that the result linearly proportional to the Wavelet-Galerkin dcretization matrix of the homogenous static Navier PDE (Gefen et al., 004). Th implies that minimizing the elastic energy equivalent to solving Navier PDE. C. Similarity measure as the Constraint Once the internal force and expression of the deformation field are obtained, the most important part of the elastic matching model where and how the external forces are applied in order to obtain constent deformation. The solution to th problem depends on the forces and with the appropriate force modeling with which we can estimate the deformation locally as well as globally. There are many different ways to formulated the external forces, such as using information from the input data, from external knowledge (i.e., interactively or from a knowledge base) or from some other processes. In the regtration process the task of external forces to bring similar regions in patient images into correspondence. So the external force which we need then the global and local similarity measure between the region at some particular position x = (x 1, x, x 3 ) T in one object and corresponding regions in another object at position x + u, u = (u l, u, u 3 ) T. The similarity function at some particular position x denoted as S(u). The best possible match expected for the dplacement vector u which maximizes S. Provided that the similarity function has a maximum, a force proportional to the gradient vector of the similarity function S(u) can be applied to increase the similarity measure. The external forces are determined in such a way that an image-based similarity metric maximized. Using image intensity as the similarity measure, for instance, normalized mutual information (NMI), has the advantage of directly exploiting the raw data without requiring segmentation or extensive user interaction. The external force defined as a proportion to the NMI. Because the energy function should be minimized for estimating the wavelet coefficients, here we define external forces as the inverse of NMI: external c ( ) 1/ NMI( X, X ( u)) = (6) The energy function E(c) composed of external forces, external(c), and internal forces, internal(c): E ( c ) = internal ( c ) +external(c) (7) The deformation determined by the regtration parameters that are represented as the wavelet coefficients c. Firstly wavelet coefficients in the highest scales corresponding to the lowest resolution signal component are estimated and then the wavelet coefficients corresponding to higher resolution signal components are estimated. Normally, the number of parameters c identical to the number of grid points in the represented transformation cubical support, and the optimization algorithm needs to handle a large number of parameters. However, since the deformation of interest (the elastic deformation) by its nature smooth, it can be estimated with only lower resolution levels and still can provide reasonable accuracy. In our work, we use the sixth resolution level. In order to simplify expression for the elastic energy and to reduce computational complexity, it assumed that the scaling and wavelet functions used satfy a principle which called threefold orthogonality. The consequence of satfying th property of threefold orthogonality that minimizing the elastic energy of the deformation equivalent to minimizing separately the elastic energy of the different deformation components (Gefen et al., 003). In our work, we only approximate threefold orthogonality using semi-orthogonal spline wavelet of order 3. The outputs of regtration are deformation maps that are the voxel-to-voxel dplacements between reference image and floating images. 603

IV. EXPERIMENT AND DISCUSSION CBCT-CBCT, PCT-PCT and PCT-CBCT are regtered respectively for both mono-modality and multi-modality experiments. We compare proposed method with traditional B- spline based free from deformation method. Both artificially deformed images and real clinical images are performed in our experiment for validation. A. Validation of the algorithm with known deformation Experiments on a set of reference and floating image pairs with known deformations were carried out to establh the ground truth for validating regtration accuracy. In our experiment, floating images were obtained by deforming the reference images using known B-spline vector, and therefore the deformation between reference image and floating image was available as ground truth. The difference between known deformations and deformation vectors calculated by proposed algorithm can be served as a criterion for accuracy evaluation. Ground truth data should be obtained for evaluating the efficiency of algorithm qualitatively. We applied three levels of known deformation fields on reference images. Both monomodality and multi-modality image regtrations were tested in the experiments. We repeated th procedure for all different PCT-CBCT image pairs, and PCT-CBCT image pairs were regtered by oncologts using commercial software manually in Shandong cancer hospital before our experiment. PCT-PCT, CBCT-CBCT and PCT-CBCT were regtered respectively. For each experiment, the floating images were deformed used known spline vectors as mentioned before, and then regtered with the reference image. We computed the deformation difference (DD) with the pixel-we sum of mean absolute difference between the vector deformation worked out by proposed method and the known vector deformation for each pair of images. Table 1 the DD comparon for the H&N patients between the proposed wavelet based method (WR) and the traditional B- spline based free form deformation method (FFD) (Mattes et al., 003), while Table for the chest cases. Each value in Table 1 and Table the mean value of all experiments using clinical data. Table 1. H&N-Deformation difference between the WR and FFD PCT-PCT CBCT-CBCT PCT-CBCT FFD(D1) 0.347 0.418 0.537 WR(D1) 0.309 0.377 0.508 FFD(D) 0.365 0.503 0.595 WR(D) 0.357 0.475 0.51 FFD(D3) 0.53 0.588 0.693 WR(D3) 0.468 0.504 0.584 Table. Chest-Deformation difference between the WR and FFD PCT-PCT CBCT-CBCT PCT-CBCT FFD(D1) 0.471 0.501 0.613 WR(D1) 0.46 0.483 0.589 FFD(D) 0.537 0.613 0.670 WR(D) 0.478 0.575 0.645 FFD(D3) 0.607 0.674 0.701 WR(D3) 0.545 0.617 0.657 From Table 1 and Table, DDs gained by WR are always smaller than the FFD, indicating that the WR more accurate than the FFD for three level of deformation. The CBCT images contain noe and artifact which would reduce the regtration accuracy and robustness. Furthermore, the regtration accuracy affected by the deformation between the reference image and the floating image. Larger deformation can decrease the accuracy. However, from the tables, WR more robust than FFD method with more stable lower DD for three kinds of regtration and three levels of deformation. Chest deformation larger than H&N deformation, from tables (1) and () deformation in chest more difficult to resume than the deformation in H&N. Accuracy of the WR regtration was also demonstrated by better vualization of the checkboard images after regtration from figure 1. Fig. 1. Checkboard after planning CT and CBCT deformable regtration, the first row using WR, the second row using FFD (Chest patient) V. CLINICAL APPLICATION FOR ADAPTIVE RADIATION THERAPY Deformable automatic re-contouring and re-dosing for improving the treatment processing are ART applications of deformable regtration. We performed qualitative evaluation of the automatically generated contours for all cases by vual inspection of the contour matches with the underlying structures in CBCT images. The deformable regtration technique provides the voxelto-voxel mapping between reference image and floating image. The vertices of the reference surface were dplaced in accordance with the deformation map, forming the deformed surface. The new contours were reconstructed by cutting the deformed surface slice by slice along transversal, sagittal and coronal directions (Lu et al., 006). The contours and dose in planning CT image can be transferred to CBCT image by deformation maps. Figure one example of the chest patient, where contours in CBCT are generated automatically by the deformation map. Similarly, figure 3 shows corresponding dose dtributing in CBCT generated automatically by same deformation map. After stattic analys with the radiation oncologt, the overlap between the automatically generated contours and the contours delineated by the oncologt using the planning system over 90%, while the dose dtributing overlap also over 90%. The WR deformable regtration algorithm provides deformation maps to quickly create, transform, quantitative 604

analys, aiding adaptive therapy, transferring contours and dose to radiation therapy treatment planning systems, and archiving contours and dose for patient follow-up and management. Fig.. Re-contouring in CBCT image using the deformation map for chest patient. The first row the planning CT which contoured by the oncologt manually. Contours in the second row are generated by the deformation map automatically using the wavelet based regtration. Fig. 3. Re-dosing in CBCT image using the deformation map for chest patient. The first row dose dtributing in the planning CT which generated by the oncologt using planning system. The second row automatically generated dose dtributing by the deformation map. VI. CONCLUSION In th paper, we presented a deformable regtration method for image guided adaptive radiation therapy based on multi-resolution wavelet. After obtaining the deformation maps with the regtration method, adaptive re-contouring and redosing can be achieved for the image guided adaptive radiation therapy application. ACKNOWLEDGMENT Th work supported by the Shandong Natural Science Foundation (ZR010HM010 and ZR010HM071) and NSFC (National Natural Science Foundation of China: 30870666). Th work also supported ARC and PolyU grants. REFERENCES Bajcsy, R., and Kovacic, S. (1989). Multiresolution elastic matching. Computer Vion, Graphics, and Image Processing 46, 1-1. Brock, K. K., Dawson, L. A., Sharpe, M. B., Moseley, D. J., and Jaffray, D. A. (006). Feasibility of a novel deformable image regtration technique to facilitate classification, targeting, and monitoring of tumor and normal tsue. International Journal of radiation oncology, biology, physics 64, 145-154. Broit, C. (1981). Optimal Regtration of Deformed Images. Ph.D.thes, Computer and Information Science Dept., University of Pennsylvania, Philadelphia, PA. Gefen, S., Tretiak, O., and Nsanov, J. (003). Elastic 3-D alignment of rat brain htological images. Medical Imaging, IEEE Transactions on, 1480-1489. Gefen, S., Tretiak, O., Bertrand, L., Rosen, G. D., and Nsanov, J. (004). Surface alignment of an elastic body using a multiresolution wavelet representation. Biomedical Engineering, IEEE Transactions on 51, 130-141. Holden, M. (008). A Review of Geometric Transformations for Nonrigid Body Regtration. Medical Imaging, IEEE Transactions on 7, 111-18. Sonke, J. J, Maddalena, R., Jochem, W., Marcel van, H., Eugene, D., and Jose, B. (009). Frameless Stereotactic Body Radiotherapy for Lung Cancer Using Four- Dimensional Cone Beam CT Guidance. International journal of radiation oncology, biology, physics 74, 567-574. Khan, F. M., and Stathak, S. (010). The Physics of Radiation Therapy. Medical Physics 37, 1374-1375. Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K., and Eubank, W. (003). PET-CT image regtration in the chest using free-form deformations. Medical Imaging, IEEE Transactions on, 10-18. Nithiananthan, S., Brock, K. K., Daly, M. J., Chan, H., Irh, J. C., and Siewerdsen, J. H. (009). Demons deformable regtration for CBCT-guided procedures in the head and neck: Convergence and accuracy. Medical Physics 36, 4755-4764. Noel, C. E., and et al. (010). An automated method for adaptive radiation therapy for prostate cancer patients using continuous fiducial-based tracking. Physics in Medicine and Biology 55, 65-7. Østergaard Noe, K., De Senneville, B. D., Elstrøm, U. V., Tanderup, K., and Sørensen, T. S. (008). Acceleration and validation of optical flow based deformable regtration for image-guided radiotherapy. Acta Oncologica 47, 186-193. Paquin, D., Levy, D., and Xing, L. (009). Multcale regtration of planning CT and daily cone beam CT images for adaptive radiation therapy. Medical Physics 36, 4-11. Stanton, R., Stinson, D., and Mihailid, D. (010). Applied Physics for Radiation Oncology, Reved Edition. Medical Physics 37, 301-301. Lu, W., and et al. (006). Deformable regtration of the planning image (kvct) and the daily images (MVCT) for adaptive radiation therapy. Physics in Medicine and Biology 51, 4357-4374. 605