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- Copyright © 2021 J.-G. Tseng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- 10.1155/2021/5512762
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Abstract
Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 5512762, 11 pages https://doi.org/10.1155/2021/5512762 Research Article 1 2 2 3 4 J.-G. Tseng , B.-W. Huang , Y.-T. Chen , S.-J. Kuo , and G.-W. Tseng Department of Leisure and Sports Management, Cheng Shiu University, Kaohsiung, Taiwan Department of Mechanical Engineering, Cheng Shiu University, Kaohsiung, Taiwan School of Medicine, China Medical University; Department of Orthopedic Surgery, China Medical University Hospital, Taichung, Taiwan School of Medicine, Medical College, China Medical University, Taichung, Taiwan Correspondence should be addressed to B.-W. Huang; huangbw@gcloud.csu.edu.tw Received 12 January 2021; Revised 13 April 2021; Accepted 21 April 2021; Published 11 May 2021 Academic Editor: Nicola Francesco Lopomo Copyright © 2021 J.-G. Tseng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The meniscus, composed of fibrocartilage, is a very important part of the human knee joint that behaves like a buffer. Located in the middle of the femoral condyles and the tibial plateau, it is a necessary structure to maintain normal biomechanical properties of the knee. Whether walking or exercising, the meniscus plays a vital role to protect the articular surface of both the femoral condyles and the tibial plateau by absorbing the conveying shock from body weight. However, modern people often suffer from irreversible degeneration of joint tissue due to exercise-induced harm or aging. Therefore, understanding its dynamic characteristics will help to learn more about the actual state of motion and to avoid unnecessary injury. This study uses reverse engineering equipment, a 3D optical scanner, and a plastic teaching human body model to build the geometry of knee joint meniscus. Then, the finite element method (FEM) is employed to obtain the dynamic characteristics of the meniscus. The results show the natural frequencies, mode shapes, and fatigue life analysis of meniscus, with real human material parameters. The achieved results can be applied to do subsequent knee dynamic simulation analysis, to reduce the knee joint and lower external impacts, and to manufacture artificial meniscus through tissue engineering. 1. Introduction combines cells, materials methods, engineering, and bio- chemical factors to restore, maintain, improve, or replace meniscus tissues with similar mechanical properties to the The meniscus is an important tissue in the human knee joint because of its load distribution, shock absorption, joint lubri- original one [3–5]. Given the increasing need of joint replace- ment, a rising interest in academia has driven researchers to cation, and joint stability functions. Meniscal damage, which may appear as tear, maceration, degeneration, or destruction, take a deep insight into the development of the leg joints is frequently found from a common sports injury or the oste- includes bones and cartilages. For a long time, biomechanical scientists have been com- oarthritis (OA) knee. Approximately, 23% of all adults or more than 54 million people in the U.S. suffer from some mitted to establishing an accurate geometric module either form of wear and tear arthritis. The annual direct medical with or without magnetic resonance imaging (MRI). FEM costs are at least $140 billion [1]. With the developments is employed for the knee or meniscus model later on for the and changes in time, the joint injury should no longer be con- dynamical analysis [6–9]. Meakin et al. [10] developed a finite element model of the knee meniscus to obtain the stress sidered as a problem that only occurs in the elderly, as many of whom are young people the age of 20 to 30 years old. The distribution of various geometrical and material properties usual treatments to repair the meniscus are using sutures or on the behavior of the meniscus under compressive load. staples to restore the integrity of the tissue, partial meniscect- Freutel et al. [11] reviewed many papers about finite element omy, or biodegradable tissue adhesives [2]. The new strategy modeling of soft tissues: material models, tissue interaction, and challenges. Musculoskeletal soft tissues, such as articular of meniscus reconstruction employs tissue engineering that 2 Applied Bionics and Biomechanics cartilage, ligaments, knee meniscus, and intervertebral disk, were discussed in the reviewed papers. In that, quite a few PCL researchers adopted the isotropic, linear elasticity material model to limit computational cost and numerical difficulties. MM LM Bendjaballah et al. [12] developed a three-dimensional finite element model of the human knee joint. This model consists of hard-bone structures, their articular cartilage layers, ACL menisci, and principal ligaments. They obtained the principal-compressive stress distribution in the centroid of tibial cartilage elements for the meniscus joint with free axial rotation at 1000 N external load. In this study, we focused on Figure 1: Meniscus schematic diagram [24]. finding the fundamental normal modes, i.e., natural (reso- nant) frequencies and mode shapes of the human meniscus, to understand the dynamic characteristics of the knee joint. Natural frequencies are the existing in or initiated by nature, not produced or affected artificially, in the mechanical and biological structure when in motion. The motion pattern of a system oscillating at its natural frequency is called the nor- mal mode, i.e., all parts of the system move sinusoidally with that same frequency [13]. If the external excitation frequency near the natural frequency, the amplitude of the vibrating structure will increase with time until fracture occurred finally. That is why the natural frequency is crucial to be avoided from the normally encountered excitation frequency when designing and building biostructure via the tissue engi- neering process. To enable the geometric module more comparable to the complex motions of the natural knee, Pereira et al. [14] car- ried out dynamic mechanical analysis (DMA) with anterior, middle, and posterior segments of fresh menisci to regenerate Figure 2: Breuckmann SmartSCAN 3D scanner. meniscus lesions using tissue engineering strategies. Lots of related tissue engineering papers can also be found in the analysis to the knee model, the highest compression stress review articles [15, 16]. Tissue engineering using natural or occurred in the area of soft tissue—meniscus [25, 26]. It will synthetic matrices as a scaffold to guide tissue repair or be the main factor affecting the fatigue life of the meniscus. regeneration in three dimensions shows promising prospects for meniscus regeneration [17]. With a scaffold being the basis That helps to correlate the modal parameters and fatigue behavior [27]. Also, it applied cyclic stress loads and fatigue of new tissue structure [18, 19], multiple ingredients are used analysis to build simpler models with a fewer degree of in building a scaffold of the meniscus, including polyglycolic freedom. acid (PGA) and poly-L-lactic acid (PLA), and natural biologi- cal products, such as silk, collagen type I, and proteoglycans [20–22]. Our research results acquired the mechanical features 2. Materials and Methods of the human meniscus from the finite element modeling that can be compared and evaluated with those obtained from the 2.1. Geometry. Many researchers use a 3D scanning tech- regenerating meniscus by tissue engineering. nique to obtain the precise geometric model for the FEM As the tribological phenomenon played a significant role analysis. Fernandez et al. [28] developed a FEM model from in mechanical and clinical scenarios, Villa et al. [23] the 3D optical scanning results to investigate the failure pro- addressed the long-term structural integrity of metal tibial cess and the variation of the mechanical properties in cor- components in terms of fatigue life utilizing experimental roded steel reinforcement. tests and FEM simulations. To apprehend and avoid lower This research used a straightforward way by adopting a normal modes are the basic requirement to design the artifi- typical accurate teaching synthesis human knee joint model cial joint, this article also shows the fatigue behavior under manufactured by 3B Incorporation, made in plastic material the 1000 N cyclic load on the menisci via daily movement. (polypropylene). The meniscus, a physical component of the This research studies how the numerical modal analysis, knee-joint model, is reconstructed by the reverse engineering a nondestructive tool, characterizes and quantifies the fatigue method. Based on the triangular optical detection principle, a behavior of human menisci [24] (Figure 1) by employing 3D white light scanner, Breuckmann SmartSCAN 3D reverse engineering and FEM analysis. The response of (Figure 2), is employed to access the outer profile of the modal parameters (damping ratio, natural (resonance) fre- components of the teaching synthesis plastic meniscus. The quency, and mode shapes) is obtained to assess the variations accuracy, volumetric accuracy, and measurement resolution in the meniscus. From the author’s previous study of impact of the SmartSCAN 3D are 0.05 mm, 0.05 mm, and 0.1 mm, Applied Bionics and Biomechanics 3 0.00 30.00 60.00 (mm) 15.00 45.00 Figure 3: FEM mesh of the meniscus. Figure 4: FEM mesh of the complete knee model (CKM) [25]. respectively. Despite its high resolution, there still exist holes, Table 1: Real human material parameters [29–34]. bumps, and crinkles on the surface of the model after each scanning. The rough surface geometry of the scanned menis- Young’s Poisson’s Density Components cus model is filled and smoothed, respectively, by the Geoma- modulus MPa ratio kg/m gic Studio software. This smoothed geometry of the meniscus Bone 17,000 0.3 2,132.6 model is ready to be imported into the finite element software Meniscus 59.0 0.49 1,024.0 package. Anterior cruciate 366.0 0.45 1,100.0 ligament (ACL) 2.2. Dynamic Analysis. This study utilized the FEM software Posterior cruciate ANSYS of various modules to analyze dynamic characteristics 131.5 0.45 1,100.0 ligament (PCL) of the 3D meniscal model includes natural vibration frequen- Patellar tendon 116.0 0.45 1,100.0 cies, mode shapes, and fatigue life limitation. There is an infi- nite number of natural frequencies and accompany mode Lateral ligament 366.0 0.45 1,100.0 shapes that existed in a continuous multidegree of freedom structure. Only the first couple of fundamental natural fre- Table 2: First four flexible vibration natural frequencies of meniscus quencies/modes is usually encountered by the external driving model. force and are important for the analysis. Dynamic analysis for simple structures can be carried out manually, but for complex Mode Flexible natural frequencies (Hz) structures like menisci, finite element analysis is usually used 1 72.4 to calculate their mode shapes and frequencies. 2 91.8 The finite element analysis included importing the built 3 127.1 model, meshing, setting up meniscus parameters and bound- 4 184.1 ary conditions, and proceeding element convergence test. The scanned model of the meniscus is imported into the ANSYS finite element software and using the Solid186 ele- ment for soft tissues. It can adjust the coarseness of the mesh gent mesh Element-strengthen technology to ensure accu- through the size and shape of the element and will affect the racy. Figure 3 shows the meniscus FEM mesh used for correctness of the analysis. The authors used ANSYS intelli- modal analysis under free boundary conditions. 4 Applied Bionics and Biomechanics A: Mode, modal 2 Total deformation Type: Total deformation Frequency: 72.4 Hz Unit: m Time: 72.4 2012/10/5 06:41 1427.8 Max 1271.1 1114.4 957.63 800.89 644.15 487.41 330.67 173.93 17.193 Min 0.000 0.035 0.070 (m) 0.018 0.053 (a) A: Mode, modal 2 Total deformation Type: Total deformation Frequency: 72.4 Hz Unit: m Time: 72.4 2012/10/5 06:43 1427.8 Max 1271.1 1114.4 957.63 800.89 644.15 487.41 330.67 173.93 17.193 Min 0.000 0.035 0.070 (m) 0.018 0.053 (b) Figure 5: First mode shape of meniscus model at 72.4 Hz (bending vibration via thickness direction). (a) First mode shape. (b) Vector plot of first mode shape. limitation satisfies the real motion situation, the new scanned Fatigue is the weakening of a material caused by repeti- tive loadings. When applies cyclic loading to material, con- meniscus model is combined with the authors’ previous work tinuous and localized structural damage will occur. The [25], consisted of femur, tibia, knee cap, anterior ligament, nominal maximum stress which causes such damage may posterior ligament, and lateral ligament, to form a complete be much less than the ultimate tensile stress limit. If the loads knee model (CKM), as shown in Figure 4. The complete knee are higher than a certain threshold, microscopic cracks will model (CKM) has three purposes: (1) to determine the min- begin to form at places of stress concentration. Eventually, imum number of meshed element for the model by evaluat- the crack will propagate suddenly when it reaches a critical ing the convergence of the natural frequency of the CKM, size, and the structure will fracture [27]. To find fatigue life (2) to check the correctness of the analysis by comparing Applied Bionics and Biomechanics 5 A: Mode, modal 2 Total deformation 2 Type: Total deformation Frequency: 91.8 Hz Unit: m Time: 91.8 2012/10/5 06:45 1123.8 Max 999.84 875.86 751.87 627.89 503.9 379.92 255.93 131.94 7.9582 Min 0.000 0.035 0.070 (m) 0.018 0.053 (a) A: Mode, modal 2 Total deformation 2 Type: Total deformation Frequency: 91.8 Hz Unit: m Time: 91.8 06:44 2012/10/5 1123.8 Max 999.84 875.86 751.87 627.89 503.9 379.92 255.93 131.94 7.9582 Min 0.000 0.035 0.070 (m) 0.018 0.053 (b) Figure 6: Second mode shape of meniscus model at 91.8 Hz (shrinkage–expansion vibration in the surface perpendicular to thickness direction). (a) Second mode shape. (b) Vector plot of second mode shape. the FEM calculated natural frequency with the experimental modulus (E) of 59 MPa and a Poisson’s ratio (ν) of 0.45. result provided by Wakeling, and (3) to analyze the fatigue of The articular cartilage is the smooth, white tissue that covers the meniscus within the CKM which can better simulate the the ends of bones, for instance, the femur and tibia, where real situation of leg movement. they come together to form joints. To simplify the problem in this study, they are neglected in the model and are seg- 2.3. Material Properties. Real human bone and different soft mented as unique parts with their relative femur and tibia tissue (meniscus, fibrochondrocytes, etc.) material parame- structures. Hence, they are not segmented as separated parts. ters [29–34] (Table 1), such as Young’s modulus, Poisson’s 2.4. Boundary Conditions. The boundary conditions are set ratio, and density, are set in the FEM models. Soft tissues usually exhibit significant damping. The damping ratio is “free” around the boundary of the meniscus model in FEM set 0.1 in this case. The meniscus is modelled as isotropic modal analysis for obtaining natural frequencies and mode single-phase linear elastic material with an elastic (Young’s) shapes. The free boundary condition means no loads or 6 Applied Bionics and Biomechanics A: Mode, modal 2 Total deformation 3 Type: Total deformation Frequency: 127.1 Hz Unit: m Time: 127.1 06:45 2012/10/5 1270.6 Max 1130.3 989.87 849.49 709.11 568.72 428.34 287.96 147.58 7.1967 Min 0.000 0.035 0.070 (m) 0.018 0.053 (a) A: Mode, modal 2 Total deformation 3 Type: Total deformation Frequency: 127.1 Hz Unit: m Time: 127.1 2012/10/5 06:46 1270.6 Max 1130.3 989.87 849.49 709.11 568.72 428.34 287.96 147.58 7.1967 Min 0.000 0.035 0.070 (m) 0.018 0.053 (b) Figure 7: Third mode shape of meniscus model at 127.1 Hz (bending vibration via thickness direction). (a) Third mode shape. (b) Vector plot of third mode shape. constraints applied on the surface of the 3D meniscus model. wise. For fatigue analysis, the cyclic loads of 1,000 N were Hence, along with many flexible body modes, there are six applied on the distal tibia to represent the repeated ground rigid body modes found by FEM: three translation modes reaction force to the leg during movement. and three rotation modes along with x, y, and z-axis, respec- tively. These rigid body modes do not have a relative dis- 2.5. Convergence Criterion. In finite element analysis, solu- placement between each molecule of the meniscus. So they tion accuracy is judged in terms of convergence as the ele- possess zero natural frequency theoretically. ment “mesh” is refined. Mesh refinement is one of the To simulate the real situation of leg movement, the essential issues in computational mechanics to assure accu- fatigue life analysis of meniscus is carried out by combining racy. It is related to how small the elements need to be, while the current meniscus model and other parts of the knee the results are not affected by changing the size of the mesh. model, which was built by the authors’ previous work, to Usually, the procedure repeats the analysis with progressively form a CKM. The boundary conditions of this CKM are reduced mesh size until the variation of the analyzed param- assigned fixed at the femur head-hip position and free other- eter value, natural frequency for this case, becomes less than a Applied Bionics and Biomechanics 7 A: Mode, modal 2 Total deformation 4 Type: Total deformation Frequency: 184.1 Hz Unit: m Time: 184.1 01:31 2012/10/11 41.417 Max 36.887 32.358 27.828 23.299 18.769 14.24 9.7105 5.181 0.65157 Min 0.000 0.045 0.090 (m) 0.022 0.068 (a) A: Mode, modal 2 Total deformation 4 Type: Total deformation Frequency: 184.1 Hz Unit: m Time: 184.1 2012/10/11 01:39 41.417 Max 36.887 32.358 27.828 23.299 18.769 14.24 9.7105 5.181 0.65157 Min 0.000 0.045 0.090 (m) 0.022 0.068 (b) Figure 8: Fourth mode shape of meniscus model at 184.1 Hz (bending vibration via thickness direction). (a) Fourth mode shape. (b) Vector plot of fourth mode shape. certain percentage, under 5% for instance [35–37]. Then, the is greater than 3,500, the first natural frequency of meniscus converges to 72.4 Hz. Therefore, this study adopts 3,500 FE mesh size is evaluated to be optimal, and the analysis result is determined to be accurate. This research performs the mesh elements for the modal analysis of the meniscus. elements convergence test to find the optimal element size On the other hand, the first natural frequency of CKM before the analysis. If the convergence analysis diagram pre- converged to 17.25 Hz at 40,000 elements. It is convinced to sents a divergence phenomenon, one must return to the pre- use those elements for fatigue life analysis. Also, since the process section; adjust the settings of material parameters, CKM is not a sturdy structure, with mere ligaments and contact conditions, or boundary conditions; and begin to meniscal soft tissues supporting the knee, its first natural fre- re-analyze again. Fundamental natural frequency is used to quency is relatively low (17.25 Hz). exam the convergence of the model. The convergence crite- rion is specified to be less than 5% of the variation of the fre- 3. Results and Discussion quencies when increasing the mesh elements. This article investigates the convergence test of the mesh elements for 3.1. Comparison of the First Natural Frequency of the CKM the first natural frequency of meniscus referring to the Model with Other Papers. Wakeling et al. [38] used a hydrau- authors’ previous work [25]. When the number of elements lic shaker to stimulate the human leg at the foot end and 8 Applied Bionics and Biomechanics 3.0E+06 2.5E+06 2.0E+06 1.5E+06 1.0E+06 5.0E+05 0.0E+00 Cycle Figure 9: Meniscus S-N curve used for meniscus fatigue analysis. conducted the modal test of the lower extremity via acceler- guish the nodal area and vibration part, as shown in ometers. The average measured experimental data of the first Figures 6–9. natural frequency of the lower extremity is 15.25 Hz. This On the right-hand side of Figures 5(b)–8(b), the defor- data is very close to our FEM calculated first natural fre- mation vector plots of the first to fourth mode are shown, quency, 17.25 Hz, of the CKM model (refer to the conver- respectively. The vector plot is another way to view the defor- gence criterion section). The difference between the two mation of the vibrating body. data is around 11.6%. This promising result proves that both The system design engineers are trained to examine the the CKM and meniscus models are acceptable for the natural frequencies and mode shapes of the structure. They dynamic analysis. will like to or even change the design to avoid the natural fre- quencies, resonance, when the structure is in the motion cir- 3.2. Modal Analysis Results of Meniscus Model. The modal cumstance. When the structure is in a resonance situation, analysis of the meniscus alone model is achieved under a free the vibration displacement will grow with time until fracture boundary condition. There is an infinite number of natural happened. frequencies in a continuous structure. Only the first few A lot of papers discussing cell-based tissue engineering from a micro point of view instead of a macro point of view lower modes are significant and will be discussed in the anal- ysis. The first six zero-frequency modes are rigid body modes as this study. Therefore, hardly could we find similar studies and will not be discussed here. Table 2 shows the first four about modal and fatigue analysis with similar conditions in flexible vibration natural frequencies of the meniscal model. the literature to compare with. It is suggested that the synthe- Because it is a thin and small structure, the natural fre- sis human meniscus model manufactured by 3B Incorpora- tion, made in plastic material (polypropylene), can be used quencies of the meniscus are as high as 72.4 Hz and above. Figure 5(a) shows the first mode shape of the meniscus model to execute the experimental modal analysis. The measured at 72.4 Hz, bending vibration mode through-thickness direc- fundamental natural frequency can be compared with the tion. The maximum displacement occurs at the front-end tip one by finite element analysis in this study. The estimated of the meniscus. Figure 6(a) shows the second mode shape of difference between them should be under 15%, according to Wakeling’s result mentioned above. the meniscus model at 91.8 Hz, in-plane shrinkage–expan- sion vibration mode in the surface perpendicular to the thick- ness direction. The maximum displacement occurs at the 3.3. Fatigue Analysis Results of Meniscus Model. It is hard to front-end tip of the meniscus. Figure 7(a) shows the third find the fatigue analysis of human meniscus in reference. mode shape of the meniscus model at 127.1 Hz, bending The material properties include the ultimate strength of 6.23 MPa, the tensile strength of 5.8 MPa [39], and the com- vibration mode through-thickness direction. Two parallel nodal lines are tilt in the southeastern direction. The maxi- pressive strength of 3.27 MPa [12] of knee joint cartilage, mum displacement occurs at two sides and the front-end which is employed to simulate the real motion of the human tip of the meniscus. Figure 8(a) shows the fourth mode shape meniscus in the knee joint [40, 41]. The maximum stress of of the meniscus model at 184.1 Hz, bending vibration mode 3.0 MPa, corresponding to a cyclic load of 1000 N, is used to obtain the meniscus fatigue S-N (stress vs. number of through-thickness direction. Two parallel nodal lines are tilt in the northeastern direction. The maximum displacement cycles) curve, as shown in Figure 9. The finite element occurs at the lower-left open end of the meniscus. One ANSYS fatigue solver utilizes this meniscus S-N curve to cal- should remember that each natural (resonance) frequency culate the meniscus fatigue analysis. has a corresponding mode. The displacement scale of each Figure 10(a) shows the stress distribution diagram of meniscus life analysis. The blue color regions represent long vibration mode is magnified thousands of times to distin- Stress (N/m ) 1.0E+02 2.0E+02 5.0E+02 1.0E+03 2.0E+03 5.0E+03 1.0E+04 2.0E+04 5.0E+04 1.0E+05 2.0E+05 5.0E+05 1.0E+06 Applied Bionics and Biomechanics 9 B: Model, transient 3 Life Type: Life Time: 0 2012/10/7 09:03 1e6 Max 1e5 0.1 0.01 0.001 0.0001 1e-5 1e-6 1e-7 0 Min 0.00 30.00 60.00 (m) 15.00 45.00 (a) B: Model, transient 3 Safety factor Type: Safety factor Time: 0 2012/10/7 09:01 15 Max 9.2857 8.5714 7.8571 7.1429 6.4286 5.7143 0.038151 Min 0.00 30.00 60.00 (m) 15.00 45.00 (b) Figure 10: Stress distribution of meniscus under fatigue life analysis. (a) Available cycle. (b) Safety factor. life, i.e. sustain tens of millions of cycles loading of the menis- applied to do subsequent knee dynamic simulation analysis, cus. A few red color spots are stress concentration due to to reduce the knee joint and lower external impacts, and to scanned model roughness and should be eliminated from manufacture artificial meniscus through tissue engineering. the FEM. Figure 10(b) presents the safety factor fatigue sim- Nevertheless, these results should be interpreted with caution ulation. The most orange color region indicates that life anal- because of several limitations in this study. First, we only ysis can reach the safety factor of 1.5 as acceptable by normal considered one size of the “meniscus sample” here. Second, practice. The abovementioned stress concentration issue also the scanned surface are the ones of a model of the menisci causes fewer red spots of lower safety factors. and not of the menisci themselves. Third, the authors charac- terize the mechanical characteristics of the meniscus as the 3.4. Limitations. This is the first study using natural fre- isotropic single-phase linear elastic material. It is prospected quency, mode shape, and fatigue analysis for the human to consider the viscoelasticity of the tissue in the future work meniscus in the literature. The results of this study can be [42–44]. Hence, future studies with an improved design and 10 Applied Bionics and Biomechanics better control of confounding factors are required to enable a [2] A. I. Bochynska, T. G. Van Tienen, G. Hannink, P. Buma, and D. W. Grijpma, “Development of biodegradable hyper- more thorough understanding. branched tissue adhesives for the repair of meniscus tears,” Acta Biomaterialia, vol. 32, pp. 1–9, 2016. 4. Conclusions [3] B. Bilgen, C. T. Jayasuriya, and B. D. Owens, “Current con- cepts in meniscus tissue engineering and repair,” Advanced The normal mode and fatigue life analysis of the meniscus is Healthcare Materials, vol. 7, no. 11, article e1701407, 2018. obtained by FEM ANSYS simulation. 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Applied Bionics and Biomechanics – Hindawi Publishing Corporation
Published: May 11, 2021