Journal of Biomechanical Science and Engineering

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1 Bulletin of the JSME Vol.9, No.2, 2014 Journal of Biomechanical Science and Engineering Finite element analysis of hip joint cartilage reproduced from real bone surface geometry based on 3D-CT image Takako OSAWA*, Shigeaki MORIYAMA*, ** and Masao TANAKA*** * Institute of Materials Science and Technology, Fukuoka University , Nanakuma, Jonan-ku, Fukuoka city, Fukuoka , Japan osawa@fukuoka-u.ac.jp ** Department of Mechanical Engineering, Faculty of Engineering, Fukuoka University , Nanakuma, Jonan-ku, Fukuoka city, Fukuoka , Japan *** Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University 1-3 Machikaneyama, Toyonaka city, Osaka , Japan Received 31 July 2013 Abstract Articular cartilage is a cushioning material which reduces contact pressure on joint, and protects subchondral bone from direct load. In the recent studies on mechanical behavior of cartilage, detailed cartilage geometries were available by means of in vivo CT and/or MR imaging. The mechanical property on the cross-section of cartilage is inhomogeneous due to its laminar microstructure. However, the studies are limited for detailed stress distribution in cartilage taking the effect of internal microstructure of cartilage even when those have taken the real bone/cartilage shape into account for finite element analysis (FEA). In this study, the FEA of cartilage layer of hip joint extracted from the 3D-CT image was performed in order to obtain knowledge of the stress distribution in detail considering the inhomogeneity of articular cartilage. The real bone surface geometries of femoral heads and acetabular fossae were extracted from 3D-CT image. The geometry of cartilage is defined by referring to the bone surface so that the femoral joint surfaces are reproduced. This study modeled the bilateral hip joints of healthy subjects. The reproduced femurs were discretized into 8-node brick elements for bone and cartilage layers of the hip joint. The mechanical properties used for FEA were those estimated by considering the microstructure in the previous study. High stress was observed mainly on cartilage surface covered with the acetabular fossa. Especially stress concentration was located at proximal surface of femoral head, while the stress at the lower distal region was not significant. Key words : Articular cartilage, Depth-dependent mechanical property, Hip joint, 3D-CT, Finite element analysis 1. Introduction The hip joint has the femoral head and the acetabular fossa. Articular cartilage is a soft tissue layer which covers both surfaces of acetabular fossa and femoral head. Under normal physiological conditions, cartilage protects the subchondral bone by working as a medium to absorb shocks and to distribute mechanical loading. Loss of cartilage tissue function yields the inhibition of dynamic joint function and the reduction of quality of life (QOL). Osteoarthritis is a degenerative joint disease which accompanies the joint space narrowing, the deformation of bone shape such as osteophyte, and so on. This disease is progressed by mechanical factors primarily. Mechanical properties are most reliable indicator for cartilage degeneration, but are very seldom referred in the clinical practice. The recent studies for mechanical behavior of cartilage in vivo frequently utilize the visualization of tissue shape through CTand/or MR-imaging (Herzog and Federico, 2006). The image-based inverse analysis is useful to understand cartilage mechanics, and is beneficial to utilize mechanical properties for degeneration diagnosis in future clinical application. Real geometry of the hip joint components and the articular cartilage of individual is the key in analyzing the stress distribution usable for early stage diagnosis of osteoarthritis. For this kind of analysis, important is the influence of the Paper No

2 mechanical property inside tissue on the mechanical behavior of the joint scale. The mechanical property of cartilage in the cross-section is inhomogeneous because of its laminar microstructure (Quinn and Morel, 2006; Wilson et al., 2006; Hosoda et al., 2008; Julkunen et al., 2009). Stress distribution of cartilage at joint scale has been examined intensively in many FE studies (e.g. Han et al., 2005; Ün and Spilker, 2006) using the real bone/cartilage shape, but little attention has been paid for effect of the internal microstructure of cartilage. The FE modeling of cartilage based on the real joint shape is the first step for the reproduction of the in vivo mechanical environment during the diarthrodial joint motion. Although the voxel FE modeling is a typical approach for the CT-image-based analysis, it is not suitable for the joint scale analysis with the smooth cartilage surface. The conventional multilayer FE modeling with real bone shape is necessary also to take the depth dependent property of cartilage into account. In this study, the FEA of cartilage of hip joint extracted from the 3D-CT image was performed in order to obtain knowledge of the stress distribution in detail considering the inhomogeneity of articular cartilage due to its microstructure. The real surface geometries of femoral heads and acetabular fossae were extracted by the image-based modeling from 3D-CT image, and created was the geometry model of cartilage. The stress/strain distributions of cartilage were calculated by 3D-FE analysis using the mechanical properties resulted from its microstructure. 2. Materials and Methods 2.1 Geometry model of articular cartilage of hip joint Hip joint was chosen as subjects of this study, because it is the largest load-bearing joint in the body and has a relatively simple contact state of cartilage versus cartilage. The shape of bone was extracted from 3D-CT image, and the geometry of articular cartilage was reproduced by referring to the bone surface so that cartilage tissue covers the bone end anatomically. This study modeled the bilateral hip joints of the same healthy subjects. The protocol for a creation of geometry model of cartilage is shown in Fig. 1. The segmentation and 3D visualization of bone and cartilage were performed using the 3D reconstructing software (ZedView ver.8.5, LEXI). The region of interest (ROI) surrounding hip joint was selected from 3D-CT image ( mm/pixel), and the contrast was adjustment so that the cartilage geometry becomes clear. The masked areas of the coxal bone, the femur and the cartilage were chosen from ROI images. These components were segmented by extracting only the masked areas maintaining continuity between CT slices. The articular cartilage mask extracted was modified so as to fill the gap space between femoral head and acetabular fossa. Figure 2 shows the multi-valued image combined the mask of each component, and the reconstituted 3D shape using ZedView. Fig.1 Image-based modeling protocol of the hip joint for 3D-FEA. 2

3 The surface pixels of each component ( P i ) were defined by scanning the inspection line radially in sphere coordinate from the center of approximate ellipse for femoral head ( P c ), as shown in Fig. 3. These surface coordinates were calculated P i R,, Pi xi, yi, zi P x Rcos i c cos, y c Rsin cos, z c Rsin (1) from the surface pixels of each component, where R is the distance from the center P x y, z c c, c c to the surface pixel P i, is the longitude and is the latitude in the sphere coordinate. These surfaces were smoothed by the spline curve interpolation and the moving average. The thickness of cartilage was defined as a half of the distance between surfaces of femoral head and acetabular fossa. For femoral cartilage surface not covered with the acetabular fossa and difficult to identify the thickness from the images, the thickness was set to a half of the image resolution 0.78mm/pixel. a) Horizontal view of masked components. b) Multi-valued image of each component. Fig. 2 Coxal bone, femur and the cartilage on 3D-CT image. c) 3D-shape of these components (frontal view). a) Voxel elements of the coxal bone (green) and the femur (aqua). Fig. 3 Extraction of the bone surface coordinates. b) Scan of radial inspection line on 2D-pixel image of arbitrary cross-section of the voxel elements. 23

4 2.2 Multilayer model of hip joint cartilage for finite element analysis The geometry model of hip joint cartilage reproduced from 3D-CT image was discretized into 8-node brick finite elements for analysis, as shown in Fig. 4. The cartilage was divided into multiple layers expressing its laminar structure. Single layer of bone elements with 1mm thickness was provided for the subchondral bone layer of acetabular fossa or femur, respectively. The cartilage layers on acetabular fossa and femur were discretized into 5 layers of equal thickness, for representing the inhomogeneous material properties in each layer due to its microstructure. Material properties of cartilage and bone are described in the next section. As the boundary conditions, the displacements at the inferior surface of subchondral bone of femoral side were fixed completely in all directions; and the compress load of 150 N was given in the direction shown in Fig.4 at the bone surface of coxal bone side assuming the one leg stance condition. The articular surfaces of femoral side and coxal bone side were set to the contact condition with the friction coefficient of This compression analysis of hip joints was performed using the general-commercial FE software (Abaqus ver. 6.13, SIMULIA). Fig. 4 Multilayer model of the hip joint cartilage and boundary condition for finite element analysis. 2.3 Material properties of articular cartilage by the microstructural model The solid phase of cartilage consists of collagen fiber, cartilage cell and proteoglycan. These form the depth-dependent laminar microstructure, and have a significant influence on the mechanical behavior such as stress distribution inside cartilage. Collagen fibril orientation is observed to be parallel to the articular surface in the superficial layer, no preferential orientation in the middle layer, and orthogonal to the bone interface in the deep layer. Then, it contributes to the mechanical properties distribution inside tissue. Because of the arrangement of cells and fibers, cartilage can be modelled as the transversely isotropic composite, the transverse plane being parallel to the articular surface and the bone-cartilage interface. The mechanical model considering its microstructure was provided in the previous report, for the evaluation of the mechanical properties distribution in the depth direction (axial direction) on the cross-section of cartilage (Osawa et al., 2012). This mechanical model takes into account of anisotropy and inhomogeneity of its microstructure, and it was able to evaluate the depth-dependent distribution of mechanical properties that was not available from a conventional method assuming isotropy and homogeneity of tissue. The distribution of elastic modulus in tissue was predicted by fitting the 3D-FE analytical results using the microstructural model, and the time-history of reaction force measured for fresh normal bovine femoral heads (n=7). The axial elastic modulus estimated by the microstructural model was higher in the deep layer than the surface layer (Osawa et al., 2012). To evaluate the influence of histological characteristics with the cartilage depth, the material properties of cartilage used for FEA were considered two patterns of homogeneous and inhomogeneous distribution of elastic properties on the cross-section of cartilage. For the inhomogeneous case, the cartilage was assumed as the transversely isotropic elastic body, the transverse plane being parallel to the articular surface. The inhomogeneous material properties of cartilage layer were given by the mechanical properties with reference to the value (Osawa et al., 2012) changing with 24

5 depth, shown in Table 1. For the homogeneous case, the material property of the middle layer was assumed throughout the whole depth. The cartilage for the homogeneity was defined the isotropic elastic body with the elastic modulus 0.45MPa and the Poison s ratio The elastic modulus of the bone had a value sufficiently high compared to the cartilage. The elastic modulus and Poisson s ratio of bone were set to 2000MPa and 0.3. The bone was isotropic elastic body. Table 1 Material properties of cartilage for the inhomogeneous case. E r is elastic modulus, r is Poisson s ratio, G r is shear modulus of component r (a: axial direction, p: in-plane direction). E a [MPa] E p [MPa] ap pa p G p [MPa] G a [MPa] Cartilage Layer Layer Layer Layer Layer Results Figure 5 shows the finite element models of bilateral hip joints reproduced from 3D-CT. Figure 6 shows the distribution of Mises equivalent stress on articular cartilage surface of femoral heads viewed from proximal femoral head. The red grid in the Fig. 6a and 6d is the surface covered by acetabular fossae. In both of left and right joints, relatively large stress was observed mainly on cartilage surface covered with the acetabular fossae. Especially stress concentration was located at proximal surface of femoral heads, while the stress at the lower distal region was not significant. The stress distributions of the articular surface over the femurs did not exhibit any significant difference regardless the assumption of inhomogeneous of material properties. The distributions and directions of minimum principal strain in the sagittal cross-section of the cartilage on the femoral heads were shown in Fig. 7. The strain distribution of cartilage in depth was very different between the homogeneous and inhomogeneous material properties patterns. Large strain was observed in the surface layer in the model for which the inhomogeneous material properties. The principal strain directions of a large strain were observed to be orthogonal to the articular surface. The direction of the arrow is inside, so this shows the compression. Fig. 5 Finite element model of the bilateral hip joints. 25

6 Fig. 6 Mises stress distributions on the articular surface of cartilage over femoral head (Bird eye view). a) Cartilage shape of left joint. The red grid is the surface covered by acetabular fossa. b) Distribution for homogeneous material properties of left joint. c) Distribution for inhomogeneous material properties of left joint. d) Cartilage shape of left joint. e) Distribution for homogeneous material properties of left joint. f) Distribution for inhomogeneous material properties of left joint. Fig. 7 Minimum principal strain distributions and directions in sagittal section of cartilage layer over femoral heads. a) Distribution for homogeneous material properties of left joint. b) Distribution for inhomogeneous material properties of left joint. c) Distribution for homogeneous material properties of left joint. d) Distribution for inhomogeneous material properties of left joint. 26

7 4. Discussion Smooth surface shape of the bilateral joints was reproduced for stress analysis of cartilage. To confirm the reproducibility of the bone surface shape by means of the present method, verification was performed by comparison with the voxel FE model that uses image pixels as finite elements and is the typical in the image-based modeling using the medical image. Figure 8(a) shows the process of bone surface extraction in an arbitrary sagittal section. Black line represents a surface extracted from the coordinates of the surface pixels, and the red line indicates a smoothed surface employed in this study. The bone surface reproduced by the present method was matched well with the characteristic shape obtained from voxel element discretization. Therefore, this present method enables a precise reproduction of the bone surface geometry of hip joint from 3D-CT image. Because it was possible to reproduce clear shapes of both the right and left joints, this modeling method may be able to accommodate to the individual shape. Fig. 8 Comparison FE model shape and the voxel element shape. a) 2D-pixel image of arbitrary cross-section of the voxel elements. Black solid line represents a surface extracted from the coordinates of the surface pixels; the red solid line indicates smoothed it. b) 3D-FE model shape of bone of the femoral bead. c) Voxel element shape of bone of femur. In this FE analysis, relatively large stress was observed at the articular surface covered with acetabular fossa. Brown and coworker investigated the contact stress distribution over femoral head by the in situ compression test using 24 transducers on the head bone (Brown and Shaw, 1983). As the results, they have ascertained that the maximum stress on the femoral head was observed in the region covered with the fossa. The stress distribution calculated by this study was consistent with this experimental knowledge. The strain distribution of the sagittal cross-section of femoral head cartilage was examined to evaluate the influence of depth-dependent inhomogeneity of cartilage material properties on the mechanical cartilage behavior. The strain distribution in the case of homogeneous material properties was the almost uniform distribution in the cross-section of cartilage, while that in the case of inhomogeneous properties exhibited larger strain in the surface layer than in deeper layers. The strain distribution in cartilage tissue has been reported in experiments measuring the local strain of cartilage plugs determined by referring to the fluorescently-stained cell-to-cell distances before and after compression (Murakami et al., 2004; Schinagl et al., 1997). Reported was that the strain in the surface layer was larger than that in deep layer. In addition, the normal strain of surface layer was larger than deep layer in the study measuring the three-dimensional strain field in the cartilage specimen under the unconfined compression (Neu et al., 2005). This pattern of depth-dependent strain distribution was considered to be coming from histological anisotropy by collagen fibril orientation in these reports. Strain distribution in this study was consistent with that in the tissue which has been confirmed by in vitro compressive test of the specimen level. Therefore, the laminar inhomogeneous material properties are the key to analyze mechanical behavior of cartilage in real joints. Articular cartilage is a connective soft tissue, consisting of two phases of the fluid phase (interstitial water 27

8 occupying 80% of the total tissue volume) and the solid phase (cartilage cells and its extracellular matrix). There are significant effects of fluid phase on the mechanics of connective tissue (Myers and Mow, 1983). The consideration of biphasic properties is important for accurate description of the mechanical behavior of cartilage as is reviewed by Wilson and coworkers (2005). That is, the depth-dependent inhomogeneity in this study is a must for mechanical analysis of cartilage in real joint, but it is expected to expand to take this aspect. 5. Conclusion Finite element analyses were conducted for hip joint cartilage with multilayer FE model. The model was reproduced by referring to the bone shape segmented from 3D-CT images. The inhomogeneity of mechanical properties of cartilage was taken into account by referring to the previous study. The strain distribution in cartilage was very dependent on the depth-dependent distribution of elastic modulus, and it was enabled to examine the detailed stress/strain distribution in real hip joints. References Brown, T. and Shaw, D. T., In vitro contact stress distributions in the natural human hip. Journal of Biomechanics, Vol. 16, No. 6 (1983), pp Han, S. K., Federico, S., Epstein, M. and Herzog, W., An articular cartilage contact model based on real surface geometry. Journal of Biomechanics, Vol. 38, No. 1 (2005), pp Herzog, W. and Federico, S., Considerations on joint and articular cartilage mechanics. Biomechanics and Modeling in Mechanobiology, Vol. 5, No. 2-3 (2006), pp Hosoda, N., Sakai, N., Sawae, Y. and Murakami, T., Depth-dependence and time-dependent in mechanical behaviors of articular cartilage in unconfined compression test under constant total deformation. Journal of Biomechanical Science and Engineering, Vol. 3, No. 2 (2008), pp Julkunen, P., Harjula, T., Marjanen, J., Helminen, H. J. and Jurvelin, J. S., Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage. Journal of Biomechanics, Vol. 42, No. 5 (2009), pp Murakami, T., Sakai, N., Sawae, Y., Tanaka, K. and Ihara, M., Influence of Proteoglycan on time-dependent mechanical behaviors of articular cartilage under constant total compressive deformation. JSME International Journal Series C, Vol. 47, No. 4 (2004) pp Myers, E. R. and Mow, V. C., Edit. Hall, B. K., Cartilage volume 1 Structure, Function and Biochemistry. Academic Press, (1983), pp Neu, C. P., Hull, M. L. and Walton, J. H., Heterogeneous three-dimensional strain fields during unconfined cyclic compression in bovine articular cartilage explants. Journal of Orthopaedic Research, Vol. 23, No. 6 (2005), pp Osawa, T., Matsumoto, T., Naito, H. and Tanaka, M., Evaluation of viscoelastic property of articular cartilage based on mechanical model considering tissue microstructure. Journal of Biomechanical Science and Engineering, Vol. 7, No. 1, (2012), pp Quinn, T. M. and Morel, V., Microstructural modeling of collagen network mechanics and interactions with the proteoglycan gel in articular cartilage. Biomechanics and Modeling in Mechanobiology, Vol. 10, No. 1-2 (2006), pp Schinagl, R. M., Gurskis, D., Chen, A. C. and Sah, R. L., Depth-dependent confined compression modulus of full-thickness bovine articular cartilage. Journal of Orthopaedic Research, Vol. 15, No. 4 (1997), pp Ün, K. and Spilker, R. L., A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: Finite element simulations. Journal of Biomechanical Engineering, Vol. 128, No. 6 (2006), pp Wilson, W., Donkelaar, C. C., Rietbergen, B., Ito, K. and Huiskes, R., The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage. Medical Engineering and Physics, Vol. 27, No. 10 (2005), pp Wilson, W., Driessen, N. J. B., Donkelaar, C. C. and Ito, K., Prediction of collagen orientation in articular cartilage by a collagen remodeling algorithm. Osteoarthritis and Cartilage, Vol. 14, No. 11 (2006), pp

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