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Constitutive modeling of menisci tissue: a critical review of analytical and numerical approaches. Biomech Model Mechanobiol 2020; 19:1979-1996. [PMID: 32572727 DOI: 10.1007/s10237-020-01352-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2020] [Accepted: 05/28/2020] [Indexed: 02/07/2023]
Abstract
Menisci are fibrocartilaginous disks consisting of soft tissue with a complex biomechanical structure. They are critical determinants of the kinematics as well as the stability of the knee joint. Several studies have been carried out to formulate tissue mechanical behavior, leading to the development of a wide spectrum of constitutive laws. In addition to developing analytical tools, extensive numerical studies have been conducted on menisci modeling. This study reviews the developments of the most widely used continuum models of the meniscus mechanical properties in conjunction with emerging analytical and numerical models used to study the meniscus. The review presents relevant approaches and assumptions used to develop the models and includes discussions regarding strengths, weaknesses, and discrepancies involved in the presented models. The study presents a comprehensive coverage of relevant publications included in Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, Springer, and Scopus databases. This review aims at opening novel avenues for improving menisci modeling within the framework of constitutive modeling through highlighting the needs for further research directed toward determining key factors in gaining insight into the biomechanics of menisci which is crucial for the elaborate design of meniscal replacements.
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2
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Peloquin JM, Santare MH, Elliott DM. Short cracks in knee meniscus tissue cause strain concentrations, but do not reduce ultimate stress, in single-cycle uniaxial tension. ROYAL SOCIETY OPEN SCIENCE 2018; 5:181166. [PMID: 30564409 PMCID: PMC6281910 DOI: 10.1098/rsos.181166] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Accepted: 10/19/2018] [Indexed: 05/15/2023]
Abstract
Tears are central to knee meniscus pathology and, from a mechanical perspective, are crack-like defects (cracks). In many materials, cracks create stress concentrations that cause progressive local rupture and reduce effective strength. It is currently unknown if cracks in meniscus have these consequences; if they do, this would have repercussions for management of meniscus pathology. The objective of this study was to determine if a short crack in meniscus tissue, which mimics a preclinical meniscus tear, (a) causes crack growth and reduces effective strength, (b) creates a near-tip strain concentration and (c) creates unloaded regions on either side of the crack. Specimens with and without cracks were tested in uniaxial tension and compared in terms of macroscopic stress-strain curves and digital image correlation strain fields. The strain fields were used as an indicator of stress concentrations and unloaded regions. Effective strength was found to be insensitive to the presence of a crack (potential effect < 0.86 s.d.; β = 0.2), but significant strain concentrations, which have the potential to lead to long-term accumulation of tissue or cell damage, were observed near the crack tip.
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Affiliation(s)
- John M. Peloquin
- Department of Biomedical Engineering, University of Delaware, Newark, DE, USA
| | - Michael H. Santare
- Department of Mechanical Engineering, University of Delaware, Newark, DE, USA
| | - Dawn M. Elliott
- Department of Biomedical Engineering, University of Delaware, Newark, DE, USA
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Development and Validation of a Numerical Model for the Mechanical Behavior of Knee Prosthesis Analyzed by the Finite Elements Method. JOURNAL OF BIOMIMETICS BIOMATERIALS AND BIOMEDICAL ENGINEERING 2018. [DOI: 10.4028/www.scientific.net/jbbbe.37.12] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The human knee is a complex joint (the largest joint of the human body). During the different daily activities, this joint is exposed to significant loads and movements, may in some cases exceed the limit of the mechanical capacities of its components, which shows that the pathologies are quite numerous at the level of the human knee and the treatment sometimes requires surgery to either repair or implant (implant total knee prosthesis). As we know very well, the success of a total knee implant is highly dependent on the initial stability of the femoral or tibial implant and the integration of femur and tibia bone tissue with these implants in the long term. Due to the optimal distribution of mechanical stresses in the surrounding bone. It is for this reason that the search for reasonable solutions to compensate the damaged knee prosthesis and reduce the stresses in the cortical bone and spongy has become a very important research axis. In this regard, we have proposed three models of prosthesis knee joint from available literature and study the distribution of Von-Mises stresses and strains in the differents composents of knee prosthesis, know the total displacement between the model intact and model artificial of knee, 3D modeling software Solidworks 2016 is used for 3D modeling of knee prosthesis and finite element analysis software ANSYS 16.2 is used for numerical estimation of von-Mises stresses and strains. We find in this study that the maximum stresses and strains of Von Mises at the level of the tibia and tibial bone decrease, that is to say that the cement and the elastomer play a very important role in the absorption of the stresses and their minimization. On the other hand, the four knee prostheses (Model I (Ti6Al4V), Model II (CoCrMo), Model III (316L SS), Model IV (ZrO2)) implanted by elastomer contribute significantly to the reduction of stresses in the patella bone compared to the Intact Model. In general, both models of the knee prosthesis and reinforced by a stress reduction system (cement, elastomer) gave a lower stress level in the tibia and tibial bone of a normal person compared to a healthy model. The results obtained provide a theoretical basis for choosing an appropriate surgical model.
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Freutel M, Galbusera F, Ignatius A, Dürselen L. Material properties of individual menisci and their attachments obtained through inverse FE-analysis. J Biomech 2015; 48:1343-9. [PMID: 25843259 DOI: 10.1016/j.jbiomech.2015.03.014] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Accepted: 03/10/2015] [Indexed: 10/23/2022]
Abstract
Meniscal properties for computational methods have already been proposed. However, it is well known that there is high intra subject variability in the material properties of soft tissues and that disruption of the fiber network alters the biomechanics of the meniscus. Therefore, the objective of this study was to establish a non invasive method to determine the material properties of the individual menisci and their attachments using inverse FE-analyses. In a previous study, the 3D displacements of the meniscus and its attachments under axial joint loads were determined for intact porcine knees. To simulate the experimental response in individual FE-analyses (n=5), an anisotropic, hyperelastic meniscus matrix was embedded in a poroelastic model. During a particle swarm optimization, the difference between the force applied to the meniscus during the experiment and the femoral surface reaction force of the FE model at equilibrium was minimized by varying four material parameters. Afterwards, a prediction error was determined to describe how well the material parameter fit to each of the three displacement directions. Additionally, the stresses occurring in the meniscus were evaluated. The error of the material parameter optimization was on average 6.5±4.4%. The best fitting material parameter combination revealed an error of 1.2%. The highest stresses occurred in the region between the pars intermedia and posterior horn of the meniscus. The individual material properties of the meniscus were successfully obtained with a combination of previously reported, noninvasively measured 3D displacements and inverse FE-analyses. The methodology presented in this study is a promising contribution to the detection of degeneration within the meniscus.
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Affiliation(s)
- Maren Freutel
- Institute of Orthopaedic Research and Biomechanics, Centre of Musculoskeletal Research Ulm, University of Ulm, Ulm, Germany.
| | - Fabio Galbusera
- Laboratory of Biological Structures Mechanics, IRCCS Galeazzi Orthopedic Institute, Milan, Italy
| | - Anita Ignatius
- Institute of Orthopaedic Research and Biomechanics, Centre of Musculoskeletal Research Ulm, University of Ulm, Ulm, Germany
| | - Lutz Dürselen
- Institute of Orthopaedic Research and Biomechanics, Centre of Musculoskeletal Research Ulm, University of Ulm, Ulm, Germany
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Wang L, Wu Y, Tan Y, Fei X, Deng Y, Cao H, Chen B, Wang H, Magdalou J, Chen L. Cytotoxic effects of the quinolone levofloxacin on rabbit meniscus cells. J Appl Toxicol 2013; 34:870-7. [PMID: 23813946 DOI: 10.1002/jat.2903] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2013] [Revised: 05/11/2013] [Accepted: 05/11/2013] [Indexed: 12/31/2022]
Affiliation(s)
- Linlong Wang
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
| | - Yunpeng Wu
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
| | - Yang Tan
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
| | - Xi Fei
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
| | - Yu Deng
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
| | - Hong Cao
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
| | - Biao Chen
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
| | - Hui Wang
- Department of Pharmacology; Basic Medical School of Wuhan University; Wuhan 430071 China
| | - Jacques Magdalou
- UMR 7365 CNRS-Nancy Université; Faculté de Médicine; Vandoeuvre-lès-Nancy France
| | - Liaobin Chen
- Department of Orthopedic Surgery; Zhongnan Hospital of Wuhan University; Wuhan 430071 China
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Recent advances in computational mechanics of the human knee joint. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2013; 2013:718423. [PMID: 23509602 PMCID: PMC3590578 DOI: 10.1155/2013/718423] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2012] [Revised: 11/21/2012] [Accepted: 12/20/2012] [Indexed: 11/18/2022]
Abstract
Computational mechanics has been advanced in every area of orthopedic biomechanics. The objective of this paper is to provide a general review of the computational models used in the analysis of the mechanical function of the knee joint in different loading and pathological conditions. Major review articles published in related areas are summarized first. The constitutive models for soft tissues of the knee are briefly discussed to facilitate understanding the joint modeling. A detailed review of the tibiofemoral joint models is presented thereafter. The geometry reconstruction procedures as well as some critical issues in finite element modeling are also discussed. Computational modeling can be a reliable and effective method for the study of mechanical behavior of the knee joint, if the model is constructed correctly. Single-phase material models have been used to predict the instantaneous load response for the healthy knees and repaired joints, such as total and partial meniscectomies, ACL and PCL reconstructions, and joint replacements. Recently, poromechanical models accounting for fluid pressurization in soft tissues have been proposed to study the viscoelastic response of the healthy and impaired knee joints. While the constitutive modeling has been considerably advanced at the tissue level, many challenges still exist in applying a good material model to three-dimensional joint simulations. A complete model validation at the joint level seems impossible presently, because only simple data can be obtained experimentally. Therefore, model validation may be concentrated on the constitutive laws using multiple mechanical tests of the tissues. Extensive model verifications at the joint level are still crucial for the accuracy of the modeling.
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Fowlie JG, Arnoczky SP, Lavagnino M, Stick JA. Stifle extension results in differential tensile forces developing between abaxial and axial components of the cranial meniscotibial ligament of the equine medial meniscus: a mechanistic explanation for meniscal tear patterns. Equine Vet J 2011; 44:554-8. [PMID: 22168479 DOI: 10.1111/j.2042-3306.2011.00532.x] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
REASON FOR PERFORMING THE STUDY To identify potential functional-anatomical characteristics of the cranial horn attachment of the medial meniscus (MM) that may help explain the pathogenesis of the common tear patterns that have been reported. HYPOTHESIS Full extension of the stifle generates a significant increase in tensile forces within the cranial meniscotibial ligament (CrMTL) of the MM, which may predispose this structure to injury. METHODS The effect of femorotibial angle (160°, 150°, 140° and 130°) on tensile forces in the axial and abaxial components of the CrMTL was examined in 6 mature cadaver stifles using an implantable force probe. Three additional specimens were used to examine the histological structure of the CrMTL and its connection to the cranial horn of the MM. RESULTS Full extension of the stifle (160°) resulted in a significantly greater tensile force in the abaxial component of the CrMTL when compared with the axial component (P = 0.001). The tensile force in the abaxial component of the CrMTL increased significantly between 150° and 160° of stifle extension (P = 0.011). The CrMTL appears to be comprised of 2 functional components, which become more visually distinct as the stifle is extended. Histologically, these components are separated by a cleft of highly vascularised, less organised connective tissue, which becomes less prominent at the junction of the ligament and the cranial horn of the MM. CONCLUSION A 4-fold difference in the tensile forces in the 2 functional components of the CrMTL of the MM was observed with full extension of the stifle. POTENTIAL RELEVANCE The functional anatomy of the CrMTL may place this region at greater risk of injury during hyperextension of the stifle and, therefore, may provide a mechanistic rationale for the commonly reported meniscal tear patterns in the horse.
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Affiliation(s)
- J G Fowlie
- Department of Large Animal Clinical Sciences, College of Veterinary Medicine, Michigan State University, MI, USA
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Fowlie J, Arnoczky S, Lavagnino M, Maerz T, Stick J. Resection of Grade III cranial horn tears of the equine medial meniscus alter the contact forces on medial tibial condyle at full extension: an in-vitro cadaveric study. Vet Surg 2011; 40:957-65. [PMID: 22091489 DOI: 10.1111/j.1532-950x.2011.00899.x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
OBJECTIVE To evaluate the magnitude and distribution of joint contact pressure on the medial tibial condyle after grade III cranial horn tears of the medial meniscus. STUDY DESIGN Experimental study. ANIMALS Cadaveric equine stifles (n = 6). METHODS Cadaveric stifles were mounted in a materials testing system and electronic pressure sensors were placed between the medial tibial condyle and medial meniscus. Specimens were loaded parallel to the longitudinal axis of the tibia to 1800 N at 130°, 140°, 150°, and 160° stifle angle. Peak pressure and contact area were recorded from the contact maps. Testing was repeated after surgical creation of a grade III cranial horn tear of the medial meniscus, and after resection of the simulated tear. RESULTS In the intact specimens, a significantly smaller contact area was observed at 160° compared with the other angles (P < .05). Creation of a grade III cranial horn tear in the medial meniscus did not significantly alter the pressure or contact area measurements at any stifle angle compared with intact specimens (P > .05). Resection of the tear resulted in significantly higher peak pressures in the central region of the medial tibial condyle at a stifle angle of 160° relative to the intact (P = .026) and torn (P = .012) specimens. CONCLUSIONS Resection of grade III cranial horn tears in the medial meniscus resulted in a central focal region of increased pressure on the medial tibial condyle at 160° stifle angle.
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Affiliation(s)
- Jennifer Fowlie
- Department of Large Animal Clinical Studies, College of Veterinary Medicine, Michigan State University, East Lansing, MI 48824-1314, USA.
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Yasura K, Mizuno Y, Nakagawa Y, Mori K, Takenaka M, Ohashi T, Yamada K, Kobayashi M, Ando K, Kuroki H, Suzuki T, Ikeuchi K, Tsutsumi S, Nakamura T. Estimation of the mechanical property of meniscus using ultrasound: examinations of native meniscus and effects of enzymatic digestion. J Orthop Res 2007; 25:884-93. [PMID: 17343280 DOI: 10.1002/jor.20256] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We previously developed a novel ultrasound assessment system featuring wavelet transform to evaluate the material properties of articular cartilage. We aimed in this study to demonstrate the feasibility of quantitative evaluation of meniscus using ultrasound and to elucidate the relationships between its acoustic, mechanical, and biochemical properties. Meniscal disc specimens from mature pigs were assessed by ultrasound and compression testing, and their correlation was analyzed. A positive correlation was found between the ultrasound signal intensity and apparent Young's modulus (r=0.61). Subsequently, the porcine meniscal discs were treated with various enzymes and then characterized by ultrasound, by compression tests, by biochemical analyses, and by histology and immunohistochemistry. The signal intensity was decreased not by hyaluronidase but by collagenase treatment. Hyaluronidase-treated menisci showed a discrepancy between acoustic and mechanical properties, suggesting that the ultrasound reflection could not detect a reduction in proteoglycan content. Also, ultrasound signal intensity could only reflect superficial layers of the material. Several limitations exist at present, and further studies and improvements of the device are required. However, given the noninvasive nature and the requirement of only small equipment, this ultrasound assessment system will be an instrumental diagnostic tool for meniscal function in both research and clinical fields.
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Affiliation(s)
- Ko Yasura
- Department of Orthopaedic Surgery, Graduate School of Medicine, Kyoto University, Kyoto, Japan
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Yao J, Funkenbusch PD, Snibbe J, Maloney M, Lerner AL. Sensitivities of medial meniscal motion and deformation to material properties of articular cartilage, meniscus and meniscal attachments using design of experiments methods. J Biomech Eng 2006; 128:399-408. [PMID: 16706589 DOI: 10.1115/1.2191077] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
This study investigated the role of the material properties assumed for articular cartilage, meniscus and meniscal attachments on the fit of a finite element model (FEM) to experimental data for meniscal motion and deformation due to an anterior tibial loading of 45 N in the anterior cruciate ligament-deficient knee. Taguchi style L18 orthogonal arrays were used to identify the most significant factors for further examination. A central composite design was then employed to develop a mathematical model for predicting the fit of the FEM to the experimental data as a function of the material properties and to identify the material property selections that optimize the fit. The cartilage was modeled as isotropic elastic material, the meniscus was modeled as transversely isotropic elastic material, and meniscal horn and the peripheral attachments were modeled as noncompressive and nonlinear in tension spring elements. The ability of the FEM to reproduce the experimentally measured meniscal motion and deformation was most strongly dependent on the initial strain of the meniscal horn attachments (epsilon(1H)), the linear modulus of the meniscal peripheral attachments (E(P)) and the ratio of meniscal moduli in the circumferential and transverse directions (E(theta)E(R)). Our study also successfully identified values for these critical material properties (epsilon(1H) = -5%, E(P) = 5.6 MPa, E(theta)E(R) = 20) to minimize the error in the FEM analysis of experimental results. This study illustrates the most important material properties for future experimental studies, and suggests that modeling work of meniscus, while retaining transverse isotropy, should also focus on the potential influence of nonlinear properties and inhomogeneity.
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Affiliation(s)
- Jiang Yao
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
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11
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Zielinska B, Donahue TLH. 3D finite element model of meniscectomy: changes in joint contact behavior. J Biomech Eng 2006; 128:115-23. [PMID: 16532624 DOI: 10.1115/1.2132370] [Citation(s) in RCA: 106] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
The goal of this study is to quantify changes in knee joint contact behavior following varying degrees of the medial partial meniscectomy. A previously validated 3D finite element model was used to simulate 11 different meniscectomies. The accompanying changes in the contact pressure on the superior surface of the menisci and tibial plateau were quantified as was the axial strain in the menisci and articular cartilage. The percentage of medial meniscus removed was linearly correlated with maximum contact pressure, mean contact pressure, and contact area. The lateral hemi-joint was minimally affected by the simulated medial meniscectomies. The location of maximum strain and location of maximum contact pressure did not change with varying degrees of partial medial meniscectomy. When 60% of the medial meniscus was removed, contact pressures increased 65% on the remaining medial meniscus and 55% on the medial tibial plateau. These data will be helpful for assessing potential complications with the surgical treatment of meniscal tears. Additionally, these data provide insight into the role of mechanical loading in the etiology of post-meniscectomy osteoarthritis.
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Affiliation(s)
- Barbara Zielinska
- Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Dr., Houghton, MI 49931, USA
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Yao J, Snibbe J, Maloney M, Lerner AL. Stresses and Strains in the Medial Meniscus of an ACL Deficient Knee under Anterior Loading: A Finite Element Analysis with Image-Based Experimental Validation. J Biomech Eng 2005; 128:135-41. [PMID: 16532627 DOI: 10.1115/1.2132373] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
The menisci are believed to play a stabilizing role in the ACL-deficient knee, and are known to be at risk for degradation in the chronically unstable knee. Much of our understanding of this behavior is based on ex vivo experiments or clinical studies in which we must infer the function of the menisci from external measures of knee motion. More recently, studies using magnetic resonance (MR) imaging have provided more clear visualization of the motion and deformation of the menisci within the tibio-femoral articulation. In this study, we used such images to generate a finite element model of the medial compartment of an ACL-deficient knee to reproduce the meniscal position under anterior loads of 45, 76, and 107N. Comparisons of the model predictions to boundaries digitized from images acquired in the loaded states demonstrated general agreement, with errors localized to the anterior and posterior regions of the meniscus, areas in which large shear stresses were present. Our model results suggest that further attention is needed to characterize material properties of the peripheral and horn attachments. Although overall translation of the meniscus was predicted well, the changes in curvature and distortion of the meniscus in the posterior region were not captured by the model, suggesting the need for refinement of meniscal tissue properties.
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Affiliation(s)
- Jiang Yao
- Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA
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Meakin JR, Shrive NG, Frank CB, Hart DA. Finite element analysis of the meniscus: the influence of geometry and material properties on its behaviour. Knee 2003; 10:33-41. [PMID: 12649024 DOI: 10.1016/s0968-0160(02)00106-0] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
A finite element model of the knee meniscus was developed to investigate the effects of various geometrical and material properties on the behaviour of the meniscus under compressive load. Factorial methods were used to determine the relative effect of varying the properties by +/-10% of their initial value. It was found that the stresses in the meniscus were more sensitive to geometry (meniscus width and radius of curvature of the femoral surface of the meniscus) than material properties. The model was also used to investigate the effect of incongruency between the radius of curvature of the femur and the femoral surface of the meniscus. It was shown that mismatch between the curvatures of the femur and meniscus has a large effect on the stresses both in the meniscus and in the underlying cartilage. The results from the study have implications for the design and development of meniscal repair devices and replacements.
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Affiliation(s)
- Judith R Meakin
- Joint Injury and Arthritis Research Group, University of Calgary, Calgary, Alta, Canada.
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LeRoux MA, Setton LA. Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension. J Biomech Eng 2002; 124:315-21. [PMID: 12071267 DOI: 10.1115/1.1468868] [Citation(s) in RCA: 99] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young's moduli (E1=67.8 MPa, E2=11.1 MPa) and Poisson's ratios (v12=2.13, v21 =1.50, v23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1 =0.09x10(-16) m4/Ns, k2=0.10x10(-16) m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.
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Affiliation(s)
- Michelle A LeRoux
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
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15
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Donahue TLH, Hull ML, Rashid MM, Jacobs CR. A finite element model of the human knee joint for the study of tibio-femoral contact. J Biomech Eng 2002; 124:273-80. [PMID: 12071261 DOI: 10.1115/1.1470171] [Citation(s) in RCA: 358] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior, and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (ie., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 mm by 5 mm to 1 mm by 1 mm. The solution was considered converged for an average element size of 2 mm by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.
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Affiliation(s)
- Tammy L Haut Donahue
- Department of Mechanical Engineering, Michigan Technological University, Houghton 49931, USA
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16
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Ikeuchi K, Sakoda H, Sakaue R, Tsuji K, Tomita N. A new method for accurate measurement of displacement of the knee menisci. Proc Inst Mech Eng H 1998; 212:183-8. [PMID: 9695637 DOI: 10.1243/0954411981533962] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
It is difficult to measure the displacement of the menisci under external forces by the radiographic method using markers because the movement may be smaller than the detecting limit. A device with a flexible needle attached to a journal of a miniature linear bearing is developed to investigate the meniscal functions which depend on the mobility. The needle tip is fixed to the target point in the meniscus and the axial displacement is measured with a laser sensor. According to the test, the lower limit for detection was 10 microns, the error due to non-linearity was less than 5 per cent and the reactive force was less than 0.15 N in the operating range of +/- 3 mm. Displacement vectors were determined at four points in a pair of menisci in a porcine knee subjected to external forces. This accurate method will lead to further investigation into the mechanical function of the menisci.
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Affiliation(s)
- K Ikeuchi
- Research Center for Biomedical Engineering, Kyoto University, Japan
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17
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Prendergast PJ. Finite element models in tissue mechanics and orthopaedic implant design. Clin Biomech (Bristol, Avon) 1997; 12:343-366. [PMID: 11415744 DOI: 10.1016/s0268-0033(97)00018-1] [Citation(s) in RCA: 123] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/10/1996] [Accepted: 03/06/1997] [Indexed: 02/07/2023]
Abstract
This article attempts to review the literature on finite element modelling in three areas of biomechanics: (i) analysis of the skeleton, (ii) analysis and design of orthopaedic devices and (iii) analysis of tissue growth, remodelling and degeneration. It is shown that the method applied to bone and soft tissue has allowed researchers to predict the deformations of musculoskeletal structures and to explore biophysical stimuli within tissues at the cellular level. Next, the contribution of finite element modelling to the scientific understanding of joint replacement is reviewed. Finally, it is shown that, by incorporating finite element models into iterative computer procedures, adaptive biological processes can be simulated opening an exciting field of research by allowing scientists to test proposed 'rules' or 'algorithms' for tissue growth, adaptation and degeneration. These algorithms have been used to explore the mechanical basis of processes such as bone remodelling, fracture healing and osteoporosis. RELEVANCE: With faster computers and more reliable software, computer simulation is becoming an important tool of orthopaedic research. Future research programmes will use computer simulation to reduce the reliance on animal experimentation, and to complement clinical trials.
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Affiliation(s)
- P J Prendergast
- Department of Mechanical Engineering, Trinity College, Dublin, Ireland
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18
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Collier S, Ghosh P. Effects of transforming growth factor beta on proteoglycan synthesis by cell and explant cultures derived from the knee joint meniscus. Osteoarthritis Cartilage 1995; 3:127-38. [PMID: 7584318 DOI: 10.1016/s1063-4584(05)80045-7] [Citation(s) in RCA: 105] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Repair of meniscal tears depends in part upon the ability of the resident fibrochondrocytes to produce new extracellular matrix molecules including proteoglycans. Three culture systems have been used to investigate proteoglycan production by meniscal fibrochondrocytes from the inner, middle and outer zones of medial and lateral menisci of the sheep stifle joint. Cultures of meniscal explants, monolayered cells, and cells encapsulated in alginate beads were labeled with 35SO4H2 for 48 h in the absence and presence of transforming growth factor beta (TGF beta) and the proteoglycans were analysed by Sephacryl S-1000 chromatography. In general, the lateral meniscus produced more proteoglycan than the medial. Explants from the inner and middle zones produced predominantly aggrecan-like proteoglycan, together with a smaller proteoglycan population eluting with an average distribution coefficient of around 0.65. The outer meniscal zones synthesized less proteoglycan overall, the majority of which consisted of the smaller proteoglycans. These characteristic proteoglycan size profiles obtained with explant cultures also were preserved when cells isolated from the respective zones were cultured in alginate beads. Monolayer cell cultures, however, produced almost entirely small proteoglycans, regardless of their zone of origin. Chromatography of chondroitinase AC and ABC digested samples indicated that the small proteoglycan population comprised mostly dermatan sulphate-containing proteoglycans. In all meniscal zones and in all culture systems, TGF beta stimulated proteoglycan production by up to 100% and the proteoglycans were slightly larger. TGF beta also stimulated cell division in fibrochondrocyte monolayer cultures. Long term intermittent stimulation of alginate bead cultures with TGF beta resulted in large increases in proteoglycan synthesis, increased aggregation of large proteoglycan monomers, and an increase in the production of the larger of two small proteoglycans, putatively, biglycan.
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Affiliation(s)
- S Collier
- Raymond Purves Bone and Joint Research Laboratories (University of Sydney), Royal North Shore Hospital of Sydney, St Leonards, NSW, Australia
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19
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Abstract
The nonlinear stress-strain characteristics of the human menisci were determined by uniaxial elongation tests performed on circumferential and radial specimens prepared from different regions, layers, and locations. The properties of the collagen fibers and the matrix were calculated using the test results along with the values of the volume fractions of the meniscal components. Regression analysis showed that only three parameters, the elastic modulus, the maximum strain, and the strain intersect, are sufficient to define the nonlinear stress-strain relation up to failure. For radial specimens, the layer had a significant effect (p < 0.01) on the elastic modulus and the maximum strain, but had no effect on the strain intersect and the maximum stress. For the same specimens, the region had a significant effect (p < 0.01) only on the strain intersect and the maximum stress. For circumferential specimens, analysis indicated no significant effect of either the region, the layer, or the location of the specimens on the material parameters defining the stress-strain relation.
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Affiliation(s)
- M Tissakht
- Department of Mechanical Engineering, McGill University, Montreal, PQ, Canada
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20
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Hope N, Ghosh P, Taylor TK, Sun D, Read R. Effects of intraarticular hyaluronan on matrix changes induced in the lateral meniscus by total medial meniscectomy and exercise. Semin Arthritis Rheum 1993; 22:43-51. [PMID: 8342052 DOI: 10.1016/s0049-0172(10)80018-6] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Total medial meniscectomy was performed in 12 adult merino sheep. Immediately after surgery, 8 animals received high-molecular-weight hyaluronan (HA) (1 mL, 10 mg/mL) and 4 were given sterile saline (1 mL) intraarticularly. Injections were given for 5 more weeks. In week 3 an exercise program, consisting of walking 24 km/wk, was initiated. This program was continued until the animals were killed at week 26 postmeniscectomy. At necropsy the lateral menisci were removed and divided into three concentric zones--inner, middle, and outer. Powdered aliquots of tissues from each zone were analyzed for collagen and hexuronate contents using colormetric methods. The glycosaminoglycans (GAGs)--chondroitin-O-sulfate (C-O-S), chondroitin-4-sulfate (C-4-S), chondroitin-6-sulfate (C-6-S), and dermatan sulfate (DS)--were determined using a high-performance liquid chromatography method. The lateral menisci from the joints of animals injected with HA showed higher hexuronate and GAG levels than those of controls. This increase was mainly due to C-6-S, which had highest levels in the inner and middle meniscal zones. In addition, dermatan sulfate levels increased significantly in the middle and outer zones of the lateral menisci compared with the same zones of the meniscus from the saline-treated group. Collagen and C-O-S levels were not statistically different from those of controls. These data suggest that intraarticular administration of high-molecular-weight HA immediately after open total medial meniscectomy may help preserve the proteoglycans in the lateral meniscus remaining in the joint.
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Affiliation(s)
- N Hope
- Raymond Purves Bone and Joint Research Laboratories (University of Sydney), Royal North Shore Hospital of Sydney, St Leonards, New South Wales, Australia
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21
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Abstract
This article provides a review of the basic science and clinical information available to the orthopedist on which a systematic approach to meniscal surgery can be based. Attitudes toward the meniscus have changed dramatically in the last 50 years. Laboratory investigations show that the menisci participate in many important functions, including tibiofemoral load transmission, shock absorption, lubrication, and passive stabilization of the knee joint. Histologic/structural analyses reveal the menisci to be annular structures, with the ability to transmit and properly distribute load over the tibial plateau, primarily facilitated by the circumferential collagen fibers in the peripheral third of the meniscus, in conjunction with their strong bony attachments at the anterior and posterior horns. Biologic studies demonstrate that meniscal healing can occur through two pathways: an intrinsic ability of the meniscal fibrochondrocyte to migrate, proliferate, and synthesize matrix (provided they are given the proper environment), and extrinsic stimulation through neovascularization (when the meniscal injury occurs in the vascular periphery). This review makes it clear that the menisci are essential components of the normal knee, and that techniques intended to preserve the menisci are both possible and mandatory. As evidence has accumulated from both animal and clinical studies of the frequent development of degenerative changes following meniscectomy, surgeons have become increasingly aggressive in their efforts to conserve as much meniscal tissue as possible. Current approaches to treatment of meniscal tears are based on a thorough understanding of meniscal structure, biology, and function, as well as familiarity with the basic principles of meniscal repair and resection. To synthesize these principles, the article concludes with an algorithm intended to guide surgeons in decision making when faced with a variety of meniscal lesions in different clinical situations.
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Affiliation(s)
- A P Newman
- Division of Orthopedic Surgery, University of Utah School Of Medicine, Salt Lake City 94132
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22
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Anderson DR, Newman AP, Daniels AU. In vitro load transmission in the canine knee: the effect of medial meniscectomy and varus rotation. Knee Surg Sports Traumatol Arthrosc 1993; 1:44-50. [PMID: 8535997 DOI: 10.1007/bf01552158] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
The purpose of this study was to determine the in vitro load-transmission characteristics of the canine knee, paying particular attention to the positioning effect of the meniscus in the coronal plane. The intact joint was first loaded and then tested under two different loading conditions after a complete medial meniscectomy. The first set of test conditions attempted to simulate those used by previous investigators, by ignoring the spacer effect of the meniscus. The second set of tests were carried out following varus rotation of the joint (to account for the loss of the meniscal spacer) to assure initial contact in both tibiofemoral compartments at the start of test cycle. It is presumed that this varus realignment occurs during weight bearing following meniscectomy in vivo. As in previous studies, the joints experienced slightly larger displacements (although not statistically significant) and had lower stiffness values following medial meniscectomy than when intact. However, following varus realignment of the joint after meniscectomy, the displacement was markedly smaller (-35% to -49%; P < 0.01) and the structural stiffness was much greater (47-123%; P < 0.05) over the range of forces analyzed, compared with the intact joint. The ratio of dissipated to input energy was 42% for the intact joint, and increased following meniscectomy to 54% (P < 0.05) with realignment and 55% (P < 0.05) without realignment. Measured contact area decreased by 17% (P < 0.05) following meniscectomy alone, and by 12% (P < 0.05) following meniscectomy with realignment.(ABSTRACT TRUNCATED AT 250 WORDS)
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Affiliation(s)
- D R Anderson
- Department of Orthopaedics, University of Tennessee, Chattanooga, USA
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23
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Abstract
A finite element model of the meniscus is presented, based on an axisymmetric geometric approximation of the menisci and a biphasic description of the tissue as a mixture of solid and fluid components. The highly fibrous nature of the meniscal tissue is accounted for by using a fiber-reinforced, transversely isotropic description of the solid phase. This model is used to study the response of a meniscus resting on a perfectly lubricated tibial surface and subjected to distributed loads applied to the femoral surface, and to examine the effects of changes in loading conditions at the femoral and tibial interfaces. Quantities of interest include the stress, pressure and strain distributions at discrete times early in the meniscal response, and the flow of the fluid phase relative to the solid phase. Of particular interest are regions of large tensile strains which could lead to meniscal failures such as the bucket-handle tear. We show that all components of strain are positive in regions of the outer third of the meniscus, and that the maximum tensile strain perpendicular to the circumferentially arranged fibers (largest principal strain in the axisymmetric cross section) is positive throughout most of the cross section. Changing the partition of the load on the femoral surface and the permeability at the tibial surface changes the time-dependent response, but has little effect on the strain distributions at times of the order of 5 s considered in this study. The inclusion of a transversely isotropic, fibrous representation of the solid phases is shown to be essential to proper meniscal simulation. The results demonstrate the importance of the biphasic representation since the fluid phase is shown to carry a significant part of the applied load.
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Affiliation(s)
- R L Spilker
- Department of Mechanical Engineering, Rensselaer Polytechnic Institute Troy, NY 12180-3590
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Aspden RM, Larsson T, Svensson R, Heinegård D. Computer-controlled mechanical testing machine for small samples of biological viscoelastic materials. JOURNAL OF BIOMEDICAL ENGINEERING 1991; 13:521-5. [PMID: 1770815 DOI: 10.1016/0141-5425(91)90102-d] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Time dependency in the mechanical properties of viscoelastic materials means that a variety of tests is often required to fully characterize their properties. Computer control is the best way of controlling loads and displacements and the rate at which they are applied, as well as recording and analysing the data produced. This paper describes apparatus for measuring the viscoelastic properties of articular cartilage in compression which is readily adaptable to any small sample in which accurate strain measurements require small, carefully controlled displacements. An IBM-type microcomputer is used to control a stepper motor driving a ball screw with a positional accuracy of about 1 micron.
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Affiliation(s)
- R M Aspden
- Department of Medical and Physiological Chemistry, University of Lund, Sweden
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25
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Abstract
Recent studies have shown that the meniscus is highly anisotropic in tension and that its compressive creep behavior can be modeled using biphasic theory. In this study, an alternative approach is used, where viscoelastic shear properties of the meniscal fibrocartilage are measured to determine the anisotropy and inhomogeneity of this tissue with respect to specimen location and fiber orientation. Medial menisci were obtained from eight skeletally-mature horses. Nine test specimens were taken from the circumferential midsubstance of each meniscus, at three circumferential and three axial positions. The magnitude of the complex shear modulus and the phase angle were determined for each specimen from 100-800 Hz, in 100 Hz increments. Data were gathered shearing parallel and perpendicular to the circumferentially-oriented fibers. The magnitude of the shear modulus and the phase angle were both found to be frequency dependent, anisotropic, and inhomogeneous. The magnitude of the shear modulus increased with frequency, and was greatest in specimens from the posterior superior region, shearing parallel to the fibers. The phase angle decreased slightly with frequency and was lowest in specimens from the midsubstance of the anterior region, shearing perpendicular to the fibers. Our data demonstrated that collagen fibers substantially stiffen the meniscus in the direction of its fibers and that the solid matrix of the meniscus, like articular cartilage, behaves largely as an elastic material.
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Affiliation(s)
- D R Anderson
- Division of Orthopaedics and Rehabilitation, University of California, San Diego
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26
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Schreppers GJ, Sauren AA, Huson A. A numerical model of the load transmission in the tibio-femoral contact area. Proc Inst Mech Eng H 1990; 204:53-9. [PMID: 2353993 DOI: 10.1243/pime_proc_1990_204_228_02] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
An axisymmetric finite element model is applied to the analysis of the force transmission between the tibia-meniscus-femur. The model assumes linear elastic material properties, static loading and sliding contact between the components. The study explores the effects of (a) tibial surface geometry (plane, convex, concave), (b) inclusion of soft layers on the bony components and (c) anisotropic properties of the meniscus. When soft layers are absent, tibial surface geometry is found to affect the total axial stiffness of the model, the radial displacement of the meniscal ring as well as the meniscal share in load transmission. Inclusion of soft layers yields qualitatively the same results for the different geometries, under the understanding that axial stiffness decreases while meniscal radial displacements increase. However, the effect of tibial geometry on the meniscal share in load transmission almost disappears as soon as soft layers are applied, while at the same time a significant increase of this share is observed. Increased circumferential stiffness of the meniscal ring raises this share even more.
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Affiliation(s)
- G J Schreppers
- Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands
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