Non-rigid registration methods assessment of 3D CT images for head-neck radiotherapy

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1 Non-rigid registration methods assessment of 3D CT images for head-neck radiotherapy Adriane Parraga a,d, Johanna Pettersson b, Altamiro Susin a, Mathieu De Craene c and Benoît Macq d a Dept. of Electrical Engineering, Federal University of Rio Grande do Sul, Av. Osvaldo Aranha, Sala 206-B, Porto Alegre, Brazil b Dept. of Biom. Engineering, Linköpings Universitet, S Linköping, Linköping, Sweden c Dept. of Technology, Pompeu Fabra University, Pg Circumvallacio 8, Barcelona, Spain d Dept. of Electrical Engineering, Place du Levant 2,Université Catholique de Louvain, Belgium ABSTRACT Intensity Modulated Radiotherapy is a new technique enabling the sculpting of the 3D radiation dose. It enables to modulate the delivery of the dose inside the malignant areas and constrain the radiation plan for protecting important functional areas. It also raises the issues of adequacy and accuracy of the selection and delineation of the target volumes. The delineation in the patient image of the tumor volume is highly time-consuming and requires considerable expertise. In this paper we focus on atlas based automatic segmentation of head and neck patients and compare two non-rigid registration methods: B-Spline and Morphons. To assess the quality of each method, we took a set of four 3D CT patient s images previously segmented by a doctor with the organs at risk. After a preliminary affine registration, both non-rigid registration algorithms were applied to match the patient and atlas images. Each deformation field, resulted from the non-rigid deformation, was applied on the masks corresponding to segmented regions in the atlas. The atlas based segmentation masks were compared to manual segmentations performed by an expert. We conclude that Morphons has performed better for matching all structures being considered, improving in average 11% the segmentation. Keywords: non-rigid registration, validation, segmentation, atlas 1. INTRODUCTION Intensity Modulated Radiotherapy (IMRT) is a new technique enabling the sculpting of the 3D radiation dose. It allows to sculpt a radiation zone of almost any shape and to modulate the beam intensity inside the target. If IMRT enables to constrain the radiation plan in the beam delivery as well as in the protection of important functional areas (e.g. spinal cord), it also raises the issues of adequacy and accuracy of the selection and delineation of the target volumes. In this paper, we focus on the clinical application of head and neck tumors. The imaging modality mainly used in this application, because of its excellent anatomical resolution, is the Computed Topography (CT). The delineation in the patient CT image of the tumor volume and organs to be radio-protected is most of the time performed by a specialist who delineates slice by slice the contours of interest. This task is highly time-consuming and requires experts knowledge. Moreover, intra- and inter-observer variability of the delineation may induce a lack of reproducibility. For all these reasons, the development of automatic segmentation methods based on atlases is a promising paradigm for speeding up the delineation process and reducing its variability. For assisting the radiologist in this segmentation task, we bring an atlas (segmented image of a sane individual) into alignment with the CT image of the patient. An affine registration is followed by a dense non-rigid deformation step. This atlas registration problem is made particularly challenging by the presence of tumors in the patient image, which induces changes in the anatomy of the patient. Several registration methods have been applied and validated for atlas-based segmentation of the brain 1, 2, 3 (like for Further author information: (Send correspondence to Adriane Parraga) Adriane Parraga: parraga@tele.ucl.ac.be, Telephone:

2 instance B-splines 4 ). We would like to investigate which registration method is the most suitable for head and neck images, also taking into account the pathological and anatomical variations. In this paper we compare two non-rigid registration methods, B-splines and Morphons. While the former has already been explored in the literature for some time, the later is an emerging feature based registration method. To assess the quality of each method, we took a set of four CT 3D patient s images, which were previously segmented by a doctor with the organs to be protected for radiotherapy planning, called organs at risk (OAR). Each deformation field, resulting from the non-rigid deformation, was applied on the masks corresponding to the segmented regions in the atlas. The performance of each method was measured by a similarity metric between manual delineation on the patient and automatic atlas mask propagation. The results show that the Morphons method has performed better for matching structures with high contrast (such as bones). The resulting image was also validated qualitatively by a doctor, who confirmed that the bones are better aligned with the Morphons method, and consequently the spinal cord, as we can see in Figure 2. Most previously presented methods concerned 2D dataset 5 or they are not totally automatic since they are based on landmarks. The specificity of this paper is to perform a measure of the clinical impact of different registration methods by introducing a validation based on organs at risk. This paper also introduces head and neck atlas registration as a new application of the Morphons method. This task is particularly hard to accomplish when we try to register two 3D volumes with a very different anatomy, as in the case of atlas-patient registration. The results indicate that both methods seem promising for this task. Yet, Morphons has performed better that B-splines for all the OAR investigated. The best performance was obtained in the spinal cord, which means that the vertebras were very well aligned. In the next section we briefly describe the theory of the registration methods under investigation. In the methodology section we describe some details of the implementation and the similarity metric used. In the following section, we compare both qualitatively and quantitatively the segmentation results obtained after applying the two atlas registration techniques. In the last section, we discuss the results obtained so far and we plan for further studies and algorithmic improvements. 2. REGISTRATION METHODS Registration is the process of finding a transformation T that best matches two images according to a criterion of similarity. One image is the reference, which remains fixed during the registration process, while the other is deformed in the geometric space of the reference. The reference image is also called fixed or target image and the transformed image is called the moving image B-spline B-spline is a non-rigid registration algorithm that has been widely used in the past few years. The transformation model is a free-form deformation (FFD) that is described by a cubic B-spline 6, 7. T(x, y, z) = 3 3 l=0 m=0 n=0 3 β l (u)β m (v)β n (w)φ i+l,j+m,k+n (1) The parameter φ i,j,k is the set of the deformation coefficients which is defined on a sparse, regular grid of control points placed over the moving image. The spacing between the control points are denoted by δ x, δ y and δ z. For any point x,y and z of the moving image, the B-spline transformation is computed from the positions of the surrounding 4x4x4 control points. The i, j and k are the indices of the control points i = x δ x 1, j = y δ y 1 and k = z δ z 1 and u, v and w are the relative positions of (x,y,z) inside that cell in the 3D space: u = x δ x x δ x, v = y δ y y δ y, w = z δ z z δ z (2) The functions β 0 through β 3 are the third-order spline polynomials: β 0 (t) = ( t 3 + 3t 2 3t + 1)/6 (3) β 1 (t) = (3t 3 6t 2 + 4)/6 (4)

3 More details related to B-spline based registration can also be found in Morphons β 2 (t) = ( 3t 3 + 3t 2 + 3t + 1)/6 (5) β 3 (t) = t 3 /6 (6) The morphons algorithm has previously been presented in e.g. 9,10 It is a non-rigid registration method in which a template image/volume is iteratively deformed to match a target image/volume using phase information. A dense deformation field is accumulated in each iteration under the influence of certainty measures. These certainty measures are associated with the displacement estimates found in each iteration and assure that the accumulated field is built from the most reliable estimates. The displacement estimates are derived using local image phase, which makes the method invariant to intensity variations between the template and target. This implies that no pre-processing of the data is needed in the morphon method. The updated accumulated deformation field, d n+1, is found in each iteration by adding the displacement estimates from the current iteration, d, to the accumulated deformation field from the previous iteration, d n. This sum is weighted with certainty measures associated with the accumulated field, c n, and certainty measures associated with the displacement field form this iteration, c. d n+1 = d n + c d c n + c (7) The displacement estimates are found from local phase difference. The local image phase can be derived using so called quadrature filters. 11 Quadrature filters are onedimensional and must be associated to a specific direction when used for multidimensional data. Therefore a set of quadrature filters, each one sensitive to structures in a certain direction, is applied to the target and template respectively. The output of one quadrature filter is: q = (q s)( x) = A(x)e iφ(x) (8) The phase difference between two signals can be found from the complex valued product between the filter output from the first signal, the target, and the complex conjugate (denoted by ) of the output from the second signal, the template: q 1 q 2 = A 1A 2 e i φ(x) (9) The local displacement estimate d i in a certain filter direction i is proportional to the local phase difference in that direction, which is found as the argument of this product, φ( x) = φ 1 ( x) φ 2 ( x). A displacement estimate is found for each pixel and for each filter in the filter set. Thus, a displacement field d i is obtained for each filter direction ˆn i. These fields are combined into one displacement field, covering all directions, by solving the following least square problem: min d [c i ( ˆn T i d d i )] 2 (10) i where d is the sought displacement field, ˆn is the direction of filter i, and c i is the certainty measure (equal to the magnitude of the product in equation 9) Dataset 3. METHODOLOGY A set of four 3D CT patients previously segmented by a doctor has been used to asses the registration methods for atlas-based segmentation. The size of the CT volumes is of 256x256x128 pixels with a voxel size of x x mm 3. In radiotherapy planning, the following structures are segmented during the treatment planning phase: external body contours, organs at risk (parotid glands and spinal cord), and nodal clinical target volume (CTV-N) defined as an extension of the macroscopic tumor volume for taking into account tumoral infiltration in permeable tissues (e.g. fat). 12 The delineation of CTV-N is performed because of the risk of microscopic extension of the tumors and/or nodes in the fatty tissues.

4 3.2. Implementation First, the patient volumes and the atlas have been segmented, resulting in a contour of the regions previously described, such as body contour, left and right parotid, spinal cord and left and right CTV. Each contour has been converted to a binary mask by a rasterisation filter. An affine transformation of the atlas has been applied, bringing the atlas into a geometric alignment with the patient. Then, both non-rigid registration methods have been performed, resulting in dense deformation fields, which have been then applied to the masks of the atlas. The atlas masks registered to the patient are the segmented regions sought. To evaluate the segmentation, we compared the atlas propagated masks with the manual delineation performed by an expert of the head and neck anatomy (radiotherapist). The metric used to measure spatial intersection of two binary images (masks) is the similarity index (SI). 13 SI = 2. M P M A M P + M A (11) where is the number of non-zero pixels of the masks and SI [0, 1]. The perfect match between the masks gives SI = 1 and the worst case, i.e. totally mismatch, SI = 0. SI was calculated between the masks of the patient, M P, and the masks of the atlas being registered to the patient, M A, as in eq. 11. The similarity index defined in eq. 11 has been introduced in the area of image segmentation to measure the agreement between different classifications. 14 The bloc diagram in Figure 1 describes the methodology applied for each registration method. Figure 1. The pipeline starts with the patient and the atlas and its correspondent masks with the following regions: body contour, left and right parotid, spinal cord and left and right CTV. The letter F means fixed M moving in the registration process. Firstly, an affine registration is performed and so its correspondents masks, followed by a dense non-rigid deformation. The deformation field is then applied to the masks, which is compared quantitatively with the segmented regions of the patient performed by a doctor. The registration process was implemented in the ITK 15 registration framework for the B-spline algorithm and in Matlab for the Morphons. In this particular application we have set a grid size of 8 for the B-Spline method,

5 Table 1. Similarity index for Patient 04 and atlas: Similarity metric between pre-segmented regions at the patients and at the atlas non-rigidly registered. The results are presented for both algorithms investigated: B-splines and Morphons. B-spline Morphons Body contour Clinical Target Volume N Left Clinical Target Volume N Right Left parotid gland Right parotid gland Spinal Cord (sc) Table 2. Similarity index for Patient 09 and atlas: Similarity metric between pre-segmented regions at the patients and at the atlas non-rigidly registered. The results are presented for both algorithms investigated : B-splines and Morphons. B-spline Morphons Body Contour Clinical Target Volume N Left Clinical Target Volume N Right Left parotid gland Right parotid gland Spinal Cord (sc) Table 3. Similarity index for Patient 10 and atlas: Similarity metric between pre-segmented regions at the patients and at the atlas non-rigidly registered. The results are presented for both algorithms investigated : B-splines and Morphons. B-spline Morphons Body contour Clinical Target Volume N Left Clinical Target Volume N Right Left parotid Right parotid gland Spinal Cord the transformation parameters have been optimized using a conjugate gradient descent algorithm (LBFGS optimizer) 15 and the cost function to be optimized have been the Mutual Information similarity of the fixed and the moving images. Mutual information is an entropy-based measure of image alignment derived from probabilistic measures of image intensity values, RESULTS This section presents the results we have obtained as described in Figure 1. Tables 1, 2 and 3 show the SI between the patients and atlas masks. Table 4 is the average of the patients for both methods. Figure 2 shows one slice of the volumes with a sagittal view of the patient, atlas and the results. Figure 2(a) is the patient and also the fixed image in the registration process. Figure 2(b) is the atlas being registered to the patient. Figure 2(c) and Figure 2(d) are the results using B-spline and Morphons, respectively. Figure 3 has also one slice of the volumes of the patient, atlas and the results, but with the axial view. To better compare the images, we have traced a blue contour over the patient image and superimposed it over the other ones. The SI values show that the Morphons method has performed better when comparing it with B-splines. The resulting images have been qualitatively validated by a doctor, who has confirmed that the bones are better aligned with the Morphons, and consequently the spinal cord. This is because of the high contrast of the bones. The segmentation has improved with Morphons in average 11% in relation to B-spline.

6 (a) Patient - as fixed image (b) Atlas - as moving image (c) result with B-spline (d) result with Morphons Figure 2. Non-rigid registration results showing a sagittal view of one slice from 3D dataset of head and neck region (a) patient as fixed image and also as the reference with the blue contour over other slices (b) atlas as a moving image (c) registered atlas using B-splines algorithm (d) registered atlas using Morphons algorithm Table 4. Average Similarity index for the previously patients B-spline Morphons Body contour Clinical Target Volume N Left Clinical Target Volume N Right Left parotid Right parotid gland Spinal Cord

7 (a) Patient - as fixed image (b) Atlas - as moving image (c) result with B-spline (d) result with Morphons Figure 3. Non-rigid registration results showing an axial view of one slice from the 3D dataset of head and neck region (a) patient as fixed image and also as the reference with the blue contour over other slices (b) atlas as a moving image (c) registered atlas using B-splines algorithm (d) registered atlas using Morphons algorithm. 5. DISCUSSIONS AND CONCLUSIONS In this paper we have investigated two multi-modality registration algorithms for addressing the problem of inter-subject registration of CT head and neck images. This task is particularly hard to accomplish when we try to register 3D patient volumes with a very different anatomy, as in the case of atlas to patient registration. To choose the most suitable algorithm for atlas-based segmentation in the context of head and neck radiotherapy, we compared quantitatively two non-rigid multi-modality registration algorithms: Morphons and B-splines. After an affine registration, the remaining transformation to be recovered is the one due to anatomical variabil-

8 ity of the population, as we can see in Figures 2(a) and 2(b). Morphons has performed better for matching all structures being considered, improving the segmentation 11% (in average), as we can see in table 4. The quality of the registration can also be observed in Figures 3(d) and 2(d), where the results with Morphons method exhibits better alignment. The registration has also been validated by an expert. Because of their high contrast, bones can drive the registration of adjacent structures like spinal cord, since Morphons method is based in the alignment of edges and lines in the multi-resolution way. The B-spline approach seems to require more parameters adjustments. We have also increased the grid resolution trying to improve the alignment between the fixed and moving images, but the resulting image was too warped, in a way that the bones were deformed unrealistically. On the other hand, B-Spline provides a very compact way to represent the transformation. The main novelty of morphons compared to classical intensity based registration methods is to introduce a directional feature selection by mean of quadratic filters. The experiments presented in this paper show that this feature selection step seems to bring a significant improvement in terms of atlas based segmentation for the Head and Neck application. Experiments on a larger database are needed to assess the over-performing of Morphons for head and neck image matching. Although the results seem promising, we still have improvements to do for clinical application. Extension of these results to more cases will be considered as future work, as well as the use of B-Spline in multi-resolution way. Another extension of this work will consist of replacing our deterministic atlas by a probabilistic atlas such as described in 18 for the brain Acknowledgments We gratefully acknowledge the support from the SIMILAR Network of Excellence and the Brazilian Education Ministry (MEC-CAPES) for financial support. The authors wish to thank Vincent Nicolas for developing efficient visualization tools ( The authors are grateful to Dr. V. Grégoire and his team for providing the images and their manual delineations. REFERENCES 1. M. Ferrant, O. Cuisenaire, and B. Macq, Multi-object segmentation of brain structures in 3d mri using a computerized atlas, in SPIE Medical Imaging, B. M. Dawant, S. L. Hartmann, J.-P. Thirion, F. Maes, D. Vandermeulen, and P. Demaerel, Automatic 3d segmentation of internal structures on the head in mr images using a combination of similarity and free form transormations: Part i, metholody and validation on normal subjects., IEEE Trans. Med. Imaging 18(10), pp , M. B. Cuadra, C. Pollo, A. Bardera, O. Cuisenaire, J. Villemure, and J.-P. Thiran, Atlas-based segmentation of pathological mr brain images using a model of lesion growth., IEEE Trans. Med. Imaging 23(10), pp , D. Rueckert, A. F. Frangi, and J. A. Schnabel, Automatic construction of 3d statistical deformation models of the brain using non-rigid registration., IEEE Trans. Med. Imaging 22(8), pp , N. Houhou, V. Duay, A. Allal, and J. Thiran, Medical images registration with a hierarchical atlas, in 13th European Signal Processing Conference, September D. Mattes, D. R. Haynor, H. Vesselle, T. K. Lewellen, and W. Eubank, Pet-ct image registration in the chest using free-form deformations., IEEE Trans. Med. Imaging 22(1), pp , D. Rueckert, L. I. Sonoda, C. Hayes, D. L. G. Hill, M. O. Leach, and D. J. Hawkes, Non-rigid registration using free-form deformations: Application to breast mr images, IEEE Trans. Med. Imaging 18(8), pp , T. Rohlfing, R. Brandt, C. R. Maurer, Jr., and R. Menzel, Bee brains, B-splines and computational democracy: Generating an average shape atlas, in IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, H. Knutsson and M. Andersson, Morphons: Segmentation using elastic canvas and paint on priors, in IEEE International Conference on Image Processing (Proceedings of the IEEE International Conference on Image Processing 05), (Genova, Italy), September 2005.

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