Research Papers

Importance of Material Properties and Porosity of Bone on Mechanical Response of Articular Cartilage in Human Knee Joint—A Two-Dimensional Finite Element Study

[+] Author and Article Information
Mikko S. Venäläinen

Department of Applied Physics,
University of Eastern Finland,
POB 1627,
Kuopio FI-70211, Finland
e-mail: mikko.s.venalainen@uef.fi

Mika E. Mononen, Jukka S. Jurvelin, Rami K. Korhonen

Department of Applied Physics,
University of Eastern Finland,
POB 1627,
Kuopio FI-70211, Finland

Juha Töyräs

Department of Applied Physics,
University of Eastern Finland,
POB 1627,
Kuopio FI-70211, Finland
Department of Clinical Neurophysiology,
Kuopio University Hospital,
POB 100,
Kuopio FI-70029, Finland

Tuomas Virén

Cancer Center,
Kuopio University Hospital,
POB 100,
Kuopio FI-70029, Finland

Manuscript received June 10, 2014; final manuscript received September 30, 2014; accepted manuscript posted October 15, 2014; published online October 28, 2014. Assoc. Editor: Sean S. Kohles.

J Biomech Eng 136(12), 121005 (Oct 28, 2014) (8 pages) Paper No: BIO-14-1255; doi: 10.1115/1.4028801 History: Received June 10, 2014; Revised September 30, 2014; Accepted October 15, 2014

Mechanical behavior of bone is determined by the structure and intrinsic, local material properties of the tissue. However, previously presented knee joint models for evaluation of stresses and strains in joints generally consider bones as rigid bodies or linearly elastic solid materials. The aim of this study was to estimate how different structural and mechanical properties of bone affect the mechanical response of articular cartilage within a knee joint. Based on a cadaver knee joint, a two-dimensional (2D) finite element (FE) model of a knee joint including bone, cartilage, and meniscus geometries was constructed. Six different computational models with varying properties for cortical, trabecular, and subchondral bone were created, while the biphasic fibril-reinforced properties of cartilage and menisci were kept unaltered. The simplest model included rigid bones, while the most complex model included specific mechanical properties for different bone structures and anatomically accurate trabecular structure. Models with different porosities of trabecular bone were also constructed. All models were exposed to axial loading of 1.9 times body weight within 0.2 s (mimicking typical maximum knee joint forces during gait) while free varus–valgus rotation was allowed and all other rotations and translations were fixed. As compared to results obtained with the rigid bone model, stresses, strains, and pore pressures observed in cartilage decreased depending on the implemented properties of trabecular bone. Greatest changes in these parameters (up to −51% in maximum principal stresses) were observed when the lowest modulus for trabecular bone (measured at the structural level) was used. By increasing the trabecular bone porosity, stresses and strains were reduced substantially in the lateral tibial cartilage, while they remained relatively constant in the medial tibial plateau. The present results highlight the importance of long bones, in particular, their mechanical properties and porosity, in altering and redistributing forces transmitted through the knee joint.

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Turner, C. H., and Burr, D. B., 1993, “Basic Biomechanical Measurements of Bone: A Tutorial,” Bone, 14(4), pp. 595–608. [CrossRef] [PubMed]
Wolff, J., 1892, Das Gesetz Der Transformation Der Knochen, Verlag von August Hirschel, Berlin, Germany.
Frost, H. M., 1987, “Bone “Mass” and the “Mechanostat”: A Proposal,” Anat. Rec., 219(1), pp. 1–9. [CrossRef] [PubMed]
Poelert, S., Valstar, E., Weinans, H., and Zadpoor, A. A., 2013, “Patient-Specific Finite Element Modeling of Bones,” Proc. Inst. Mech. Eng. H, 227(4), pp. 464–478. [CrossRef] [PubMed]
Trabelsi, N., Milgrom, C., and Yosibash, Z., 2014, “Patient-Specific FE Analyses of Metatarsal Bones With Inhomogeneous Isotropic Material Properties,” J. Mech. Behav. Biomed. Mater., 29, pp. 177–189. [CrossRef] [PubMed]
Koivumaki, J. E., Thevenot, J., Pulkkinen, P., Kuhn, V., Link, T. M., Eckstein, F., and Jamsa, T., 2012, “CT-Based Finite Element Models Can Be Used to Estimate Experimentally Measured Failure Loads in the Proximal Femur,” Bone, 50(4), pp. 824–829. [CrossRef] [PubMed]
Austman, R. L., Milner, J. S., Holdsworth, D. W., and Dunning, C. E., 2008, “The Effect of the Density-Modulus Relationship Selected to Apply Material Properties in a Finite Element Model of Long Bone,” J. Biomech., 41(15), pp. 3171–3176. [CrossRef] [PubMed]
Hambli, R., 2013, “Micro-CT Finite Element Model and Experimental Validation of Trabecular Bone Damage and Fracture,” Bone, 56(2), pp. 363–374. [CrossRef] [PubMed]
Kadir, M. R., Syahrom, A., and Ochsner, A., 2010, “Finite Element Analysis of Idealised Unit Cell Cancellous Structure Based on Morphological Indices of Cancellous Bone,” Med. Biol. Eng. Comput., 48(5), pp. 497–505. [CrossRef] [PubMed]
Parr, W. C., Chamoli, U., Jones, A., Walsh, W. R., and Wroe, S., 2013, “Finite Element Micro-Modelling of a Human Ankle Bone Reveals the Importance of the Trabecular Network to Mechanical Performance: New Methods for the Generation and Comparison of 3D Models,” J. Biomech., 46(1), pp. 200–205. [CrossRef] [PubMed]
Hambli, R., 2010, “Application of Neural Networks and Finite Element Computation for Multiscale Simulation of Bone Remodeling,” ASME J. Biomech. Eng., 132(11), p. 114502. [CrossRef]
Hambli, R., 2011, “Apparent Damage Accumulation in Cancellous Bone Using Neural Networks,” J. Mech. Behav. Biomed. Mater., 4(6), pp. 868–878. [CrossRef] [PubMed]
Fields, A. J., Eswaran, S. K., Jekir, M. G., and Keaveny, T. M., 2009, “Role of Trabecular Microarchitecture in Whole-Vertebral Body Biomechanical Behavior,” J. Bone Miner. Res., 24(9), pp. 1523–1530. [CrossRef] [PubMed]
Donahue, T. L., Hull, M. L., Rashid, M. M., and Jacobs, C. R., 2002, “A Finite Element Model of the Human Knee Joint for the Study of Tibio-Femoral Contact,” ASME J. Biomech. Eng., 124(3), pp. 273–280. [CrossRef]
Bao, H. R., Zhu, D., Gong, H., and Gu, G. S., 2013, “The Effect of Complete Radial Lateral Meniscus Posterior Root Tear on the Knee Contact Mechanics: A Finite Element Analysis,” J. Orthop. Sci., 18(2), pp. 256–263. [CrossRef] [PubMed]
Shirazi, R., and Shirazi-Adl, A., 2009, “Computational Biomechanics of Articular Cartilage of Human Knee Joint: Effect of Osteochondral Defects,” J. Biomech., 42(15), pp. 2458–2465. [CrossRef] [PubMed]
Pena, E., Calvo, B., Martinez, M. A., and Doblare, M., 2006, “A Three-Dimensional Finite Element Analysis of the Combined Behavior of Ligaments and Menisci in the Healthy Human Knee Joint,” J. Biomech., 39(9), pp. 1686–1701. [CrossRef] [PubMed]
Adouni, M., Shirazi-Adl, A., and Shirazi, R., 2012, “Computational Biodynamics of Human Knee Joint in Gait: From Muscle Forces to Cartilage Stresses,” J. Biomech., 45(12), pp. 2149–2156. [CrossRef] [PubMed]
Guess, T. M., Thiagarajan, G., Kia, M., and Mishra, M., 2010, “A Subject Specific Multibody Model of the Knee With Menisci,” Med. Eng. Phys., 32(5), pp. 505–515. [CrossRef] [PubMed]
Wilson, W., Van Donkelaar, C. C., Van Rietbergen, B., Ito, K., and Huiskes, R., 2004, “Stresses in the Local Collagen Network of Articular Cartilage: A Poroviscoelastic Fibril-Reinforced Finite Element Study,” J. Biomech., 37(3), pp. 357–366. [CrossRef] [PubMed]
Julkunen, P., Korhonen, R. K., Herzog, W., and Jurvelin, J. S., 2008, “Uncertainties in Indentation Testing of Articular Cartilage: A Fibril-Reinforced Poroviscoelastic Study,” Med. Eng. Phys., 30(4), pp. 506–515. [CrossRef] [PubMed]
Mononen, M. E., Julkunen, P., Toyras, J., Jurvelin, J. S., Kiviranta, I., and Korhonen, R. K., 2011, “Alterations in Structure and Properties of Collagen Network of Osteoarthritic and Repaired Cartilage Modify Knee Joint Stresses,” Biomech. Model. Mechanobiol., 10(3), pp. 357–369. [CrossRef] [PubMed]
Li, L. P., Soulhat, J., Buschmann, M. D., and Shirazi-Adl, A., 1999, “Nonlinear Analysis of Cartilage in Unconfined Ramp Compression Using a Fibril Reinforced Poroelastic Model,” Clin. Biomech., 14(9), pp. 673–682. [CrossRef]
Vaziri, A., Nayeb-Hashemi, H., Singh, A., and Tafti, B. A., 2008, “Influence of Meniscectomy and Meniscus Replacement on the Stress Distribution in Human Knee Joint,” Ann. Biomed. Eng., 36(8), pp. 1335–1344. [CrossRef] [PubMed]
Mow, V. C., Fithian, D. C., and Kelly, M. A., 1990, “Fundamentals of Articular Cartilage and Meniscus Biomechanics,” Articular Cartilage and Knee Joint Function: Basic Science and Arthroscopy, J. W.Ewing, ed., Raven Press Ltd., New York, pp. 1–18.
Danso, E. K., Honkanen, J. T., Saarakkala, S., and Korhonen, R. K., 2014, “Comparison of Nonlinear Mechanical Properties of Bovine Articular Cartilage and Meniscus,” J. Biomech., 47(1), pp. 200–206. [CrossRef] [PubMed]
Hengsberger, S., Kulik, A., and Zysset, P., 2002, “Nanoindentation Discriminates the Elastic Properties of Individual Human Bone Lamellae Under Dry and Physiological Conditions,” Bone, 30(1), pp. 178–184. [CrossRef] [PubMed]
Zysset, P. K., Guo, X. E., Hoffler, C. E., Moore, K. E., and Goldstein, S. A., 1999, “Elastic Modulus and Hardness of Cortical and Trabecular Bone Lamellae Measured by Nanoindentation in the Human Femur,” J. Biomech., 32(10), pp. 1005–1012. [CrossRef] [PubMed]
Rho, J. Y., Roy, M. E., 2nd, Tsui, T. Y., and Pharr, G. M., 1999, “Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation,” J. Biomed. Mater. Res., 45(1), pp. 48–54. [CrossRef] [PubMed]
Hakulinen, M. A., Day, J. S., Toyras, J., Timonen, M., Kroger, H., Weinans, H., Kiviranta, I., and Jurvelin, J. S., 2005, “Prediction of Density and Mechanical Properties of Human Trabecular Bone in Vitro by Using Ultrasound Transmission and Backscattering Measurements at 0.2-6.7 MHz Frequency Range,” Phys. Med. Biol., 50(8), pp. 1629–1642. [CrossRef] [PubMed]
Van Rietbergen, B., Weinans, H., Huiskes, R., and Odgaard, A., 1995, “A New Method to Determine Trabecular Bone Elastic Properties and Loading Using Micromechanical Finite-Element Models,” J. Biomech., 28(1), pp. 69–81. [CrossRef] [PubMed]
Ferguson, V. L., Bushby, A. J., and Boyde, A., 2003, “Nanomechanical Properties and Mineral Concentration in Articular Calcified Cartilage and Subchondral Bone,” J. Anat., 203(2), pp. 191–202. [CrossRef] [PubMed]
Schneider, C. A., Rasband, W. S., and Eliceiri, K. W., 2012, “NIH Image to ImageJ: 25 Years of Image Analysis,” Nat. Methods, 9(7), pp. 671–675. [CrossRef] [PubMed]
Malo, M. K., Rohrbach, D., Isaksson, H., Toyras, J., Jurvelin, J. S., Tamminen, I. S., Kroger, H., and Raum, K., 2013, “Longitudinal Elastic Properties and Porosity of Cortical Bone Tissue Vary With Age in Human Proximal Femur,” Bone, 53(2), pp. 451–458. [CrossRef] [PubMed]
Julkunen, P., Wilson, W., Jurvelin, J. S., Rieppo, J., Qu, C. J., Lammi, M. J., and Korhonen, R. K., 2008, “Stress-Relaxation of Human Patellar Articular Cartilage in Unconfined Compression: Prediction of Mechanical Response by Tissue Composition and Structure,” J. Biomech., 41(9), pp. 1978–1986. [CrossRef] [PubMed]
Benninghoff, A., 1925, “Form Und Bau Der Gelenkknorpel in Ihren Beziehungen Zur Funktion,” Z. Zellforsch. Mikrosk. Anat., 2(5), pp. 783–862. [CrossRef]
Julkunen, P., Kiviranta, P., Wilson, W., Jurvelin, J. S., and Korhonen, R. K., 2007, “Characterization of Articular Cartilage by Combining Microscopic Analysis With a Fibril-Reinforced Finite-Element Model,” J. Biomech., 40(8), pp. 1862–1870. [CrossRef] [PubMed]
Petersen, W., and Tillmann, B., 1998, “Collagenous Fibril Texture of the Human Knee Joint Menisci,” Anat. Embryol., 197(4), pp. 317–324. [CrossRef] [PubMed]
Bullough, P. G., Munuera, L., Murphy, J., and Weinstein, A. M., 1970, “The Strength of the Menisci of the Knee As It Relates to Their Fine Structure,” J. Bone Jt. Surg. Br., 52(3), pp. 564–567.
Wilson, W., Van Donkelaar, C. C., Van Rietbergen, B., and Huiskes, R., 2005, “A Fibril-Reinforced Poroviscoelastic Swelling Model for Articular Cartilage,” J. Biomech., 38(6), pp. 1195–1204. [CrossRef] [PubMed]
Tissakht, M., and Ahmed, A. M., 1995, “Tensile Stress–Strain Characteristics of the Human Meniscal Material,” J. Biomech., 28(4), pp. 411–422. [CrossRef] [PubMed]
Komistek, R. D., Stiehl, J. B., Dennis, D. A., Paxson, R. D., and Soutas-Little, R. W., 1998, “Mathematical Model of the Lower Extremity Joint Reaction Forces Using Kane's Method of Dynamics,” J. Biomech., 31(2), pp. 185–189. [CrossRef] [PubMed]
Plochocki, J. H., Ward, C. V., and Smith, D. E., 2009, “Evaluation of the Chondral Modeling Theory Using Fe-Simulation and Numeric Shape Optimization,” J. Anat., 214(5), pp. 768–777. [CrossRef] [PubMed]
Soltz, M. A., and Ateshian, G. A., 1998, “Experimental Verification and Theoretical Prediction of Cartilage Interstitial Fluid Pressurization at an Impermeable Contact Interface in Confined Compression,” J. Biomech., 31(10), pp. 927–934. [CrossRef] [PubMed]
Most, E., Axe, J., Rubash, H., and Li, G., 2004, “Sensitivity of the Knee Joint Kinematics Calculation to Selection of Flexion Axes,” J. Biomech., 37(11), pp. 1743–1748. [CrossRef] [PubMed]
Mononen, M. E., Jurvelin, J. S., and Korhonen, R. K., 2013, “Implementation of a Gait Cycle Loading into Healthy and Meniscectomised Knee Joint Models With Fibril-Reinforced Articular Cartilage,” Comput. Methods. Biomech. Biomed. Eng., 18(2), pp. 141–152. [CrossRef]
Thambyah, A., Goh, J. C., and De, S. D., 2005, “Contact Stresses in the Knee Joint in Deep Flexion,” Med. Eng. Phys., 27(4), pp. 329–335. [CrossRef] [PubMed]
Poh, S. Y., Yew, K. S., Wong, P. L., Koh, S. B., Chia, S. L., Fook-Chong, S., and Howe, T. S., 2012, “Role of the Anterior Intermeniscal Ligament in Tibiofemoral Contact Mechanics During Axial Joint Loading,” Knee, 19(2), pp. 135–139. [CrossRef] [PubMed]
Bai, B., Kummer, F. J., Sala, D. A., Koval, K. J., and Wolinsky, P. R., 2001, “Effect of Articular Step-Off and Meniscectomy on Joint Alignment and Contact Pressures for Fractures of the Lateral Tibial Plateau,” J. Orthop. Trauma, 15(2), pp. 101–106. [CrossRef] [PubMed]
Mcerlain, D. D., Milner, J. S., Ivanov, T. G., Jencikova-Celerin, L., Pollmann, S. I., and Holdsworth, D. W., 2011, “Subchondral Cysts Create Increased Intra-Osseous Stress in Early Knee OA: A Finite Element Analysis Using Simulated Lesions,” Bone, 48(3), pp. 639–646. [CrossRef] [PubMed]
Papaioannou, G., Demetropoulos, C. K., and King, Y. H., 2010, “Predicting the Effects of Knee Focal Articular Surface Injury With a Patient-Specific Finite Element Model,” Knee, 17(1), pp. 61–68. [CrossRef] [PubMed]
Isaksson, H., Toyras, J., Hakulinen, M., Aula, A. S., Tamminen, I., Julkunen, P., Kroger, H., and Jurvelin, J. S., 2011, “Structural Parameters of Normal and Osteoporotic Human Trabecular Bone Are Affected Differently by microCT Image Resolution,” Osteoporosis Int., 22(1), pp. 167–177. [CrossRef]
Kersh, M. E., Zysset, P. K., Pahr, D. H., Wolfram, U., Larsson, D., and Pandy, M. G., 2013, “Measurement of Structural Anisotropy in Femoral Trabecular Bone Using Clinical-Resolution CT Images,” J. Biomech., 46(15), pp. 2659–2666. [CrossRef] [PubMed]
Boutroy, S., Bouxsein, M. L., Munoz, F., and Delmas, P. D., 2005, “In Vivo Assessment of Trabecular Bone Microarchitecture by High-Resolution Peripheral Quantitative Computed Tomography,” J. Clin. Endocrinol. Metab., 90(12), pp. 6508–6515. [CrossRef] [PubMed]
Link, T. M., Vieth, V., Langenberg, R., Meier, N., Lotter, A., Newitt, D., and Majumdar, S., 2003, “Structure Analysis of High Resolution Magnetic Resonance Imaging of the Proximal Femur: In Vitro Correlation With Biomechanical Strength and BMD,” Calcif. Tissue Int., 72(2), pp. 156–165. [CrossRef] [PubMed]
Donnelly, E., 2011, “Methods for Assessing Bone Quality: A Review,” Clin. Orthop., 469(8), pp. 2128–2138. [CrossRef]
Pahr, D. H., and Zysset, P. K., 2009, “A Comparison of Enhanced Continuum FE With Micro FE Models of Human Vertebral Bodies,” J. Biomech., 42(4), pp. 455–462. [CrossRef] [PubMed]
Kozanek, M., Hosseini, A., Liu, F., Van De Velde, S. K., Gill, T. J., Rubash, H. E., and Li, G., 2009, “Tibiofemoral Kinematics and Condylar Motion During the Stance Phase of Gait,” J. Biomech., 42(12), pp. 1877–1884. [CrossRef] [PubMed]
Mononen, M. E., Mikkola, M. T., Julkunen, P., Ojala, R., Nieminen, M. T., Jurvelin, J. S., and Korhonen, R. K., 2012, “Effect of Superficial Collagen Patterns and Fibrillation of Femoral Articular Cartilage on Knee Joint Mechanics—A 3D Finite Element Analysis,” J. Biomech., 45(3), pp. 579–587. [CrossRef] [PubMed]
Zhao, D., Banks, S. A., D'lima, D. D., Colwell, C. W.Jr., and Fregly, B. J., 2007, “In Vivo Medial and Lateral Tibial Loads During Dynamic and High Flexion Activities,” J. Orthop. Res., 25(5), pp. 593–602. [CrossRef] [PubMed]
Werner, F. W., Ayers, D. C., Maletsky, L. P., and Rullkoetter, P. J., 2005, “The Effect of Valgus/Varus Malalignment on Load Distribution in Total Knee Replacements,” J. Biomech., 38(2), pp. 349–355. [CrossRef] [PubMed]
Moisio, K., Chang, A., Eckstein, F., Chmiel, J. S., Wirth, W., Almagor, O., Prasad, P., Cahue, S., Kothari, A., and Sharma, L., 2011, “Varus-Valgus Alignment: Reduced Risk of Subsequent Cartilage Loss in the Less Loaded Compartment,” Arthritis Rheum., 63(4), pp. 1002–1009. [CrossRef] [PubMed]
Hakulinen, M. A., Day, J. S., Toyras, J., Weinans, H., and Jurvelin, J. S., 2006, “Ultrasonic Characterization of Human Trabecular Bone Microstructure,” Phys. Med. Biol., 51(6), pp. 1633–1648. [CrossRef] [PubMed]
Turner, C. H., Rho, J., Takano, Y., Tsui, T. Y., and Pharr, G. M., 1999, “The Elastic Properties of Trabecular and Cortical Bone Tissues are Similar: Results From Two Microscopic Measurement Techniques,” J. Biomech., 32(4), pp. 437–441. [CrossRef] [PubMed]
Baca, V., Horak, Z., Mikulenka, P., and Dzupa, V., 2008, “Comparison of an Inhomogeneous Orthotropic and Isotropic Material Models Used for FE Analyses,” Med. Eng. Phys., 30(7), pp. 924–930. [CrossRef] [PubMed]
Henak, C. R., Anderson, A. E., and Weiss, J. A., 2013, “Subject-Specific Analysis of Joint Contact Mechanics: Application to the Study of Osteoarthritis and Surgical Planning,” ASME J. Biomech. Eng., 135(2), p. 021003. [CrossRef]
Kujala, U. M., Kettunen, J., Paananen, H., Aalto, T., Battie, M. C., Impivaara, O., Videman, T., and Sarna, S., 1995, “Knee Osteoarthritis in Former Runners, Soccer Players, Weight Lifters, and Shooters,” Arthritis Rheum., 38(4), pp. 539–546. [CrossRef] [PubMed]
Miyazaki, T., Wada, M., Kawahara, H., Sato, M., Baba, H., and Shimada, S., 2002, “Dynamic Load at Baseline Can Predict Radiographic Disease Progression in Medial Compartment Knee Osteoarthritis,” Ann. Rheum. Dis., 61(7), pp. 617–622. [CrossRef] [PubMed]
Hart, D. J., Mootoosamy, I., Doyle, D. V., and Spector, T. D., 1994, “The Relationship Between Osteoarthritis and Osteoporosis in the General Population: The Chingford Study,” Ann. Rheum. Dis., 53(3), pp. 158–162. [CrossRef] [PubMed]


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Fig. 3

(a) Maximum principal stress, (b) pore pressure, (c) fibril strain, and (d) maximum principal strain distributions for the model with rigid bones (model I) and the differences between the model I and the other models

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Fig. 4

(a) Maximum principal stress distributions for models with different porosities. (b) Maximum principal stresses, (c) pore pressures, (d) fibril strains and (e) maximum principal strains averaged over the contact area on the lateral and medial tibial plateau as a function of trabecular bone porosity. All estimated parameters in the lateral tibial plateau decreased noticeably while in the medial tibial plateau they remained relatively unaltered for all implemented porosities.

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Fig. 2

(a) Close-up images of the FE meshes in the joint area (see Fig. 1(d)). Primary collagen fibril orientations in (b) articular cartilage and (c) menisci. Crosses in (c) indicate circumferentially oriented fibrils.

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Fig. 1

(a) Lining up femur and tibia prior to cutting. (b) Gray-scale image of the knee after cutting it in a coronal plane. (c) Bone structures segmented from the image (C = cortical, T = trabecular, S = subchondral). (d) Model geometry including trabecular structure accompanied with applied boundary conditions (distal nodes of tibia fixed), constraints (reference point, RP, coupled with the surface of proximal femur marked with red solid line) and loads (arrow) used in FE simulations. (e)–(f) Close-up images of the areas marked with green squares in (b) and (d). The FE mesh is seen in (f).



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