An Anatomical Atlas to Support the Virtual Planning of Hip Operations

Transcription

1 An Anatomical Atlas to Support the Virtual Planning of Hip Operations J. Ehrhardt a, H. Handels a, T. Malina a, B. Strathmann b, W. Plötz b, S. J. Pöppl a a Institute for Medical Informatics and b Department of Orthopedic Surgery Medical University of Lübeck, Ratzeburger Allee 160, 3538 Lübeck, Germany. ehrhardt@medinf.mu-luebeck.de Abstract. Two three-dimensional digitized atlases of a female and a male pelvis were generated to support the virtual 3D-planning of hip operations. Beside the anatomical labeling of bone structures the determination of orthopedic measures, like angles, distances or sizes of contact areas, is important for the planning of hip operations. Thus, each atlas consists of labeled reference CT data sets, a set of landmarks as well as definitions of orthopedic measures and methods for their automatic computation. Furthermore, methods for the automatic transfer of anatomical labels from the atlas to an individual data set are presented resulting in three-dimensional models of the patient s bone structures. The anatomical atlases are designed to replace the interactive, time-consuming pre-processing steps for the virtual 3D operation planning. 1. Introduction In orthopedic surgery computer assisted systems are getting more and more important. Due to the complex geometry of the pelvis t he exact planning of the hip operation is essential for the operation result. The application of virtual planning procedures opens up new possibilities with regards to effort of time and costs and to an improved quality. During the computer assisted planning anatomical knowledge is required in the virtual environment. This is usually achieved by an interactive time-consuming segmentation step. The main idea of the presented approach is to represent the needed knowledge in an digital anatomical atlas and to use automatic algorithms to transfer this knowledge to the patient data. In the past digital atlases have been used for several purposes [1-4]. Especially atlases of the brain have been designed for teaching purposes, automatic segmentation and neurosurgical planning. In the considered application, a three-dimensional atlas of the human pelvis based on the CT data of the Visible Human Data Set [5] has been built up to facilitate virtual planning procedures in hip surgery. The atlases consists of labeled CT data sets, anatomical point landmarks and computation instructions for orthopedic measures.. Motivation The segmentation of different bone structures is necessary to address or analyze these structures in a virtual planning environment. Furthermore, the localization of landmarks is needed

2 to derive orthopedic measures, like distances or angles. For instance the virtual planning of an endoprosthetic reconstruction in bone tumor surgery requires at least the segmentation of the left and right hip bone, sacrum, left and right femur as well as a series of landmarks, e.g. the center of the femoral head or points on the border of the acetabulum [6]. The segmentation of the mentioned structures requires several hours using semi-automatic volume growing algorithms and interactive post-processing tools. If further measures are needed the number of labeled structures and landmarks increases. For example measuring of the contact area between acetabulum and femoral head requires the segmentation of both structures, the computation of the antetorsion requires the localization of the centers of the femoral head and the femoral leg as well as the condyles. This may increase the needed pre-processing time essentially. The goal of the presented approach is to avoid these time-consuming steps and to enable an automatic recognition of hip structures by using a digital atlas of the hip. 3. Digital anatomical atlas of the hip The virtual planning of hip operations is based on bone structures extracted from CT data. Starting point to built up the two atlases are high resolution CT image sequences of a woman and a man taken from the Visible Human Data Set. In a first step, threshold based volume growing algorithms are used for a rough segmentation of the bones. In the next interactive step the different bone structures are separated and insignificant structures, like vessels or sinews, are removed. Incomplete bone contours are closed with an semi-automatic "live-wire" [7] algorithm in a post-processing step. Finally, the segmentation result was reviewed and corrected by an expert. The separated structures are hip bones, acetabuli, sacrum, os coccygis and femuri composed by femoral head and shaft. A set of landmarks and measures for hip interventions are gathered by the surgeons. During the implementation two main problems arise: the verbal definitions of landmarks and measures are unprecise and most of them are based on x-rays. So the verbal descriptions are transformed to exact definitions of localization and computation instructions and the two-dimensional x-ray based measures are transferred into the three-dimensional space. Anatomical landmarks, e.g. promotorium or spina iliaca anterior superior, are selected interactively on the bone surface and methods for the computation of orthopedic measures, e.g. the center of femoral head, the antetorsion or the center-edge-angle, are implemented (fig. 1). Fig. 1: The centers of the femoral head (left) and the acetabulum (right) can be determined by an approximation with a sphere. In the right figure the center of femoral head (blue) and acetabulum (red) are visualized.

3 4. Matching of atlas and patient data For the transfer of the atlas information to the patient data set a registration of atlas and patient data is necessary. Due to the anatomical variations of the hip local transformations are needed in order to obtain correct results. A number of methods of varying complexity have been developed for the inter-patient 3D-3D registration of medical image volumes. Collins et al. has applied a multi-resolution approach with piecewise linear transformations [5]. Bajcsy et al. used an elastic model approach [6,7]. Algorithms based on viscous fluid models are developed by Christensen et al. [8] and Bro- Nielsen et al. [9]. Thirion presented an algorithm, which trades the strict physical modeling to simplify the implementation and speed up the execution of the registration [10]. In our application the applied registration method is divided into two parts: a global alignment of the two data sets and the local matching of corresponding structures. In the first step, an affine alignment of the two data sets is performed using the software tool AIR provided by Woods et al. [11]. Here, the affine Transformation T opt is determined, which minimizes the least squares distance T = arg min I ( T ( s )) I, opt T s where s are the coordinates of a point in the patient volume I P (s) and I A ( T ) is the intensity value of the atlas volume at the transformed coordinates T (s). Afterwards the atlas volume is resampled using the transformation T opt and trilinear interpolation. Due to the high resolution of the atlas data set the introduced interpolation errors are low. For the local matching of corresponding structures a totally freeform registration process based on Thirion s concept of demons is used. The basic idea of this algorithm is to consider the object contours in one static image as hemipermeable membrans and to consider the other image as a deformable model diffusing through these membranes. The demons are located onto the contours of the static image and push the deformable model in the normal direction of the object contour, but the orientation of the movement depends on the nature of the corresponding point in the model image. If the point is inside the model, the direction of the movement is inward, and if the point is outside, the direction is outward. In this way, the inside points of the model image are diffusing into the inside of the object contours of the static image, and vice versa for outside points. In an iterative process this strategy leads to a matching of static and model image. The iso-intensity contours in medical images are closely related to object contours. The demons are associated to each voxel s of the static image I 1, where the gradient norm I(s) is greater zero. The gradient I 1( s ) can be treated as the normal vector of the iso-intensity contour in s. The demon pushes the model image I according to I 1 if I 1 < I and according to I 1( s ) if I ( ) ( ) 1 s > I s. Precisely, the pushing force f of the demon is computed by ( I I1( s)) I1( s) f =. I1( s) + ( I I1( s)) The equation is derived from the optical flow formulation and has the desired behavior of a demon, for details see [11]. By the force vectors a displacement field is defined, i. e. each voxel could be moved by the computed vector. In order to achieve smooth deformations a regularization is necessary. Thirion proposed to apply a Gaussian filter to each of the three components of f. The standard deviation σ of the filter can be used to control the deformability of the model. The larger σ, the less deformable the image. A P 3

4 In our implementation the static image is the patient data set I P and the model image is the (global aligned) atlas data set I A. The matching is first computed on coarse downsampled images then successively on images with a finer spatial resolution. Each final solution at one scale serves to initialize the registration at the next finer scale. This strategy speeds up the computations and the convergence of the algorithm. By this technique macroscopic features are aligned first and afterwards microscopic features. Due to the strong anatomical variations in soft tissues a correct inter-patient matching of the whole pelvis region is nearly impossible. Hence, for the planning of orthopedic interventions the atlas-matching is limited to bones and surrounding voxel. For the coarse levels of the multiresolution strategy segmented atlas and patient data are used. Therefore, an automatic segmentation of the bone structures of the patient data is applied using conventional threshold based methods and morphological operators. The registration of the segmented atlas and patient data leads to a fast and robust matching of the bone surfaces. In order to enable a good adjustment of internal bone structures and to be tolerant in relation to errors of the threshold based segmentation, the original CT-volumes are used for the registration process on the finest resolution. The demons are placed in the static patient data volume. Due to the criterion I 0, for segmented images the demons are located on the object contours. For the registration of the gray value CT data the demons positions are determined by the result of the threshold based segmentation and a following dilatation. By this strategy, only bone structures are aligned and the matching of non-corresponding soft tissue is avoided. Figure shows a CT slice of a patient s data set overlaid with the contours of the atlas bone structures before and after the freeform registration. A good fit of atlas and patient data is obtained, but nevertheless small deviations can occur. 5. Recognition of anatomical structures and surface generation The atlas information is transferred by means of a nearest-neighbor approach to the patient data. Based on the threshold segmentation of the patient s bone structures the label of the nearest structure in the transformed atlas data set is assigned to each segmented voxel. Thus, bony patient voxels, which are not covered by an atlas label, are added to the nearest bone structure. For every labeled bone structure a surface model is constructed applying the marching cubes algorithm to the original CT data [9]. The chosen threshold must be the same as for the automatic segmentation. It can be determined by choosing standard hounsfield units for the corticalis ( ~ 100 HU ). Before the surface is generated, all voxels above the threshold, which are not belonging to the actual label, are set to values below the threshold. By using original CT data for the surface generation rather than segmented data, smooth surfaces with appropriate normals and gradients are generated. A triangle decimation algorithm [10] is used to reduce the number of the generated polygons significantly. The position of the anatomical point landmarks is determined by calculating the nearest point onto the patient s bone surface for every landmark in the transformed atlas data set. Figure 3 shows the surface models generated from the atlas data using the algorithm described above. The position of the anatomical landmarks is indicated by small blue points. The models consist of about triangles due to the high resolution of mm. 5. Automatic determination of orthopedic parameters 4

5 Fig. : CT slice of a patient s data set overlaid with the edges of the atlas bone structures (white) before (left) and after the non-rigid registration (right). Fig. 3: Three dimensional surface model of the female atlas data. The separated structures are presented in different colours. 6. Results and Conclusion For a first evaluation of the presented registration method, we register the two atlas data sets of the woman and the man. The image volumes are resliced to a resolution of mm resulting in voxels. To obtain a good starting position an affine pre-registration is performed. For an automatic labeling of the female bone structures both atlas data sets are binarized using the manual segmentation results. These binary data sets are registered and the labels from the male data set are transferred to the female. In comparison to the manual segmentation results 99.5% of the bony voxels are labeled correctly. Hence, a nearly perfect automatic labeling of the regarded anatomical structures is possible. In practice, for the patient data set only a rough threshold based segmentation is available. Therefore, a matching is performed on gray value data to evaluate the recognition accuracy in the practical application. During the registration process the CT data set of the visible female is treated as a patient data set. The female bone structures are labeled automatically by the transformed male atlas information. For 98.5% of the bony voxels the correct labels are assigned. In figure 4 the distance from the female bone surface to the bone surface of the male after the registration is visualized. The light surface regions correspond to distances near to the voxel resolution. Inaccuracies are introduced by varying anatomical details and intensities (e.g. 5

6 different calcification of bones). Furthermore, the smoothness constrain of the deformation field establishes a compromise between intensity resemblance and uniform local deformations. The presented methods are a central step to provide the surgeon with all conditions needed for the virtual planning without interactive pre-processing steps. Beside the separated surface models orthopedic measures of the patient s hip are necessary for a successful planning. By defining point landmarks and measures in the atlas we have done the first step in this direction. Since an automatic measuring of the patient s hip needs a very precise landmark localization we are developing algorithms for an automatic correction of landmark positions in a post-processing step. Fig. 4: Visualization of the surface fit: For every point located on the surface of the visualized bone the distance to the registered atlas surface is represented by gray scale values. References [1] K. H. Höhne, M. Bomanns, M. Riemer, R. Schubert, U. Tiede, W. Lierse: A 3D Anatomical Atlas Based on a Volume Model. IEEE Comput. Graphics Appl., 1, 4 (199), pp [] R. Kikinis, M. E. Shenton, D. V. Iosifescu, R. W. McCarley, P. Saiviroonporn, H. H. Hokama, A. Robatino, D. Metcal, C. G. Wible, C. M. Portas, R. M. Donnino and F. A. Jolesz: A Digital Brain Atlas for Surgical Planning, Model-Driven Segmentation and Teaching, IEEE Trans. Visualiz. Comput. Graphics, 3 (1996), pp [3] D. L. Collins, T. M. Peters, W. Dai, A. C. Evans: Model Based Segmentation of Individual Brain Structures from MRI Data. In R. A. Robb (ed.), Visualization in Biomedical Computing II, Proc. SPIE 1808, Chapel Hill, 199, pp [4] S. Warfield, J. Dengler, J. Zaers, C. R. G. Guttmann, W. M. Wells, G. J. Ettinger, J. Hiller, R. Kikinis: Automatic Identification of Gray Matter Structures from MRI to Improve the Segmentation of White Matter Lesions. In Proc. of Medical Robotics and Computer Assisted Surgery, 1995, pp [5] M. J. Ackermann, The Visible Human Project: A Resource for Anatomical Visualization. In: B. Cesnik, A.T. McCray, J.-R. Scherrer (ed.), 9 th World Congress on Medical Informatics, MEDINFO 98. IOS Press, Seoul, Korea, 1998, pp [6] H. Handels, J. Ehrhardt, W. Plötz and S.J.Pöppl, Computer-Assisted Planning and Simulation of Hip Operations Using Virtual Three-Dimensional Models. In: P. Kokol, B. Zupan, J. Stare, M. Premik, R. Engelbrecht (ed.), Medical Informatics Europe, MIE 99, IOS Press, Amsterdam, 1999, pp [7] W. A. Barrett and N.E. Mortensen, An Interactive Live-Wire Boundary Extraction, Medical Image Analysis, 1, 1 (1996) [8] J. P. Thirion, Non-Rigid Matching Using Demons, Proc. Int. Conf. Computer Vision and Pattern Recognition (CVPR 96),

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