Fung, Y. Elasticity of soft tissues in simple elongation. Gent, A. A new constitutive relation for rubber. Rubber Chem. Ogden, R. Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. A Math. Danso, E. Structure-function relationships of human meniscus.
Biomechanical properties of the canine knee articular cartilage as related to matrix proteoglycans and collagen. Arokoski, J. Normal and pathological adaptations of articular cartilage to joint loading.
Sports Rev. Article 10 , — Li, L. Strain-rate dependence of cartilage stiffness in unconfined compression: the role of fibril reinforcement versus tissue volume change in fluid pressurization.
Strain-rate dependent stiffness of articular cartilage in unconfined compression. Burgin, L. The mechanical and material properties of elderly human articular cartilage subject to impact and slow loading. Julkunen, P. Biomechanical, biochemical and structural correlations in immature and mature rabbit articular cartilage.
Shirazi, R. Role of cartilage collagen fibrils networks in knee joint biomechanics under compression. Lin, D. Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models. Khajehsaeid, H. Progressive deformation-induced degradation of knee articular cartilage and osteoarthritis.
Rashid, B. Mechanical characterization of brain tissue in compression at dynamic strain rates. Mow, V. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments.
Huang, C. The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage. Wilson, W. A fibril-reinforced poroviscoelastic swelling model for articular cartilage.
Download references. You can also search for this author in PubMed Google Scholar. Correspondence to Wei Zhang. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.
If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Reprints and Permissions. Li, H. The mechanical properties of tibiofemoral and patellofemoral articular cartilage in compression depend on anatomical regions. Sci Rep 11, Download citation. Received : 19 November Accepted : 04 March Published : 17 March Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative.
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Advanced search. Skip to main content Thank you for visiting nature. Download PDF. Subjects Biological physics Materials science. Abstract Articular cartilage in knee joint can be anatomically divided into different regions: medial and lateral condyles of femur; patellar groove of femur; medial and lateral plateaus of tibia covered or uncovered by meniscus.
Introduction Cartilage is an essential part of the tibiofemoral and patellofemoral joints and provides a shock-resistant, cushioning, and friction-reducing surface for the two joints 1.
Materials and methods Specimen preparation Beagle dogs were used as experimental animals provided by Dalian Medical University age: 3 years old, weight: 8—10 kg, raised in Experimental Animal Center of Dalian Medical University. Figure 1. Full size image. Figure 2. Figure 3.
Figure 4. Full size table. Figure 5. Figure 6. Figure 7. Table 2 Material parameters for cartilage obtained by fitting the models to experimental data. Discussion Cartilage is a biphasic material composed of a mass of interstitial fluid and the solid matrix, it usually exhibits a typical viscoelastic behavior when subjected to mechanical loading.
Conclusion In this study, the mechanical and biological properties of tibiofemoral and patellofemoral articular cartilages are investigated using unconfined compression test and histological sections. References 1.
Article Google Scholar 7. Article Google Scholar Google Scholar View author publications. Ethics declarations Competing interests The authors declare no competing interests. Additional information Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Supplementary Information.
Supplementary Information 1. Supplementary Information 2. About this article. Cite this article Li, H. This layer has high metabolic activity and supports compression forces. The cells are rounded and have the same characteristics as layer 2 but adopt a columnar arrangement.
They present a high protein synthesis. The collagen fibers are thick and they are distributed parallel to each other and perpendicular to the articular surface to provide resistance to compressive forces. The water content is less than in the previous layers and proteoglycans are most abundant. This is adjacent to the bone and separated from the previous layer by a basophilic line called tidal or "tidemark", which is a bar wavy tangential arrangement of its fibers and can withstand shear forces.
The cells are small and scarce. The matrix is rich in hydroxyapatite crystals. Cartilage anchoring to the sub-chondral bone occurs in this layer See Fig 3. The most common tests used for explaining the behavior of articular cartilage under load, expressed in computer models, that include the behavior of swelling or anisotropic properties of the collagen structure for determining the mechanical quality of articular cartilage are: confined compression, the unconfined compression, indentation and swelling Wilson, This can be reviewed extensively in the literature.
Architectural layout of the articular cartilage according to its various layers. Note the anisotropic distribution of the tissue in relation to the depth thereof. Mechanical properties of articular cartilage are attributed to their complex structure and composition of the extracellular matrix that is comprised of a fluid phase water containing dissolved ions and a solid matrix that consists mainly of a fibrous network of collagen type II and aggregates of proteoglycans as well as other type of proteins, lipids, and cells Wilson et al.
With the mechanical load, the interstitial fluid is redistributed through the pores of the permeable solid matrix, resulting in predominantly viscoelastic behavior See Fig 4. This highly viscoelastic behavior of articular cartilage is mainly due to two mechanisms: a the frictional drag force of interstitial fluid flow through the porous solid matrix i. Different forms of lubrication in articular cartilage given by the load applied to the tissue. This lubrication and nutrition takes various forms but mainly by the displacement of the fluid.
Terada et al. From the mechanical standpoint, the most important components of articular cartilage are strong and highly organized as a network of collagen together with the load of proteoglycans. Due to the fixed charges of proteoglycans, the cation concentration within the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling tissue.
The fibrillar collagen network resists pressure and swelling. This combination makes cartilage a unique, highly hydrated and pressurized tissue, reinforced by the tension of the collagen network Wilson, Articular cartilage can be described by the mixtures theory as a mixture of four elements: a fibrous network collagen fibres and proteoglycans , a fluid and a positively and negatively charged particle.
Hubertus, ; defines a component as a group of particles with the same properties and a phase as a set of miscible components. Thus in theory the four components can be separated into only two phases: a solid and a fluid phase. In this case the fluid is comprised of three components: the liquid, the cations and anions. This has allowed its analysis as a material with a porous-viscoelastic behavior, in an attempt to better understand its response to loads, forces and overload.
Continued use of simulation in medicine has allowed important data to be obtained about the biological, mechanical and chemical behavior of the organs and tissues using mathematical formalization and subsequent numerical simulation of complex biological processes.
Computer mechano-biology determines the quantitative rules governing actions for cellular expression, differentiation and maintenance of biological and mechanical stimuli, which can be simulated by numerical methods. The computational tests are simulated usually from problems in the contour value by which the mechanical loads on the boundary are transferred to local mechanical variables stress and strain.
On the biological side, these local mechanical or biophysical variables stimulate cell expression to regulate, for example, the composition of the matrix and the expression of molecular substances.
Both biological and mechanical parts are combined in a computational model, which considers the application of forces, mechano-transduction, cellular expression, genetics and the transformation of the characteristics of the extracellular matrix. Finite element computational analysis has been used as an approach to diverse biological processes including the biomechanical behavior of articular cartilage Wilson et al.
With the mechanical load, the interstitial fluid is redistributed through the pores of the permeable solid matrix, resulting in predominantly poro-elastic conduct. This behavior of the AC is mainly due to two mechanisms: a the frictional force due to drag flow of interstitial fluid through the porous solid matrix flow-dependent mechanism , and b the deformability of the matrix strong function of time flow-independent mechanism Wilson, This allowed analysis of the same material as a poro-elastic behavior capable of supporting loads.
The mathematical model of the AC as a biphasic material, analyzes the displacement u t, x of the solid matrix and pressure p x of the fluid displaced by the load, thanks to its characteristic of poro-elasticity. This model is described by the equations 1 and 2 :. Equation 1 is derived from the law of conservation of momentum and corresponds to the linear elasticity equation term 1a coupled with a term that represents fluid pressure term 1b.
In this equation, k is a constant representing the permeability of solid module. The mathematical expression of these conditions is :. This method allows implementing the numerical model presented in equations 1 and 2 simply and with low computation cost. The method consists of using a vectorial function W or weighting function and a scalar function of q , which minimizes the terms of the equations 1 and 2.
The set of finite elements forms a partition of the domain called discretization which together are described by equations 14 and 15 :. In 16 , the shape functions correspond to the case of one-dimensional element with three nodes See Fig.
For two-dimensional case four node elements are used, whose standard shape functions are shown in matrix form 17 and in Figure 5 b. Representation of the shape functions standard. Solution of these equations for both u and p are implemented using a routine programmed in Fortran and a desktop PC with 2.
Conditions for the simulation were based on experiments by Frijns, and Wu et al. Simulations were performed for 1D and 2D looking tissue response to the application of: a compression, b tensile and c oscillating or cyclical loads. The simulation time is 45 seconds of load in all cases. The loads applied in 1D and 2D simulations were performed with the parameters shown in Table 1.
The tests considered the AC as a continuous and homogeneous material with the chondrocytes being part of the continuum. Parameters for the homogeneous material characteristics Wu et al.
For the 1D simulation a mesh was performed that represents a fragment of 0. From this mesh nodes and elements of 3 nodes were obtained.
In the 2D simulation a mesh was performed that represents a fragment of articular cartilage 0. In this case 10, nodes were obtained, equivalent to 10, elements of 4 nodes. Simulation was performed so as not to allow displacement at the bottom.
Load was applied on the upper edge, allowing the fluid outlet only at the bottom of the tissue fragment, as shown in Figure 6 a. For 2D, a condition of tissue confinement was simulated, as shown the Figure 6b, so as to present only flow at the bottom. The burden was placed at the top and lateral and bottom movement were restricted, similar conditions to those reported in several experimental studies, including that of Ateshian et al, ; Frijns, and Wu et al, AC scheme for the confinement conditions in a 1D and b 2D.
Calculations to simulate the applied load were performed from the data for the AC reported by Wu et al. For the 1D simulations, a load was applied of In 2D simulations a load was applied on the upper face of cartilage fragment corresponding to the value For cyclic loading, it was applied at a frequency equivalent to 0.
Responses from the evidence to compressive loads can be seen in Figure 7. Figure 7a shows the negative shift of the solid component that increases its value negatively with increasing loading time. As the liquid flows, the behavior is similar to a linear elastic behavior, because the only component that supports the load is solid.
Figure 7b shows the decrease in pressure due to the fluid outlet presented by the compression of the tissue. Response of tissue to compression forces. Displacement of solid matrix.
Changes in the fluid pressure in the tissue in presence of the displacement of the same. Figure 8 summarizes the results obtained for tensile strength. Figure 8a shows the positive displacement of the solid component in response to tensile load imposed on tissue. The figure shows how the displacements are positive in presence of tension maintained over time. Response of tissue to tensile forces. Displacement of solid component tissue upward.
Correct answer 1. Hyaline cartilage is highly resistant to compression. It does NOT always have a perichondrium as in articular cartilage. Its matrix consists of type II collagen and hyaluronan, and it is NOT found in the pinna of the ear and epiglottis elastic cartilage is found there.
Correct answer 5. All of the statements are TRUE. Note that statement 3 is TRUE. The matrix of fibrocartilage does contain type II collagen and some hyaluronan of course, there's also a lot of type I collagen just because type 1 collagen wasn't mentioned does NOT make the statement incorrect.
Correct answer 2. A chondroblast in hyaline cartilage. Osteogenic progenitors are located in the connective tissue perichondrium. Jump to: Suggested Reading. Learning Objectives. Hyaline cartilage. Elastic cartilage. Electron Micrographs.
Review Questions. Practice Questions. Suggested Reading. Ch 10 Cartilage. Be able to recognize the three major cartilage types hyaline, elastic and fibrocartilage in light microscopic sections and know where each type is found in the body. Be able to identify cells and structures in a sections of cartilage e.
Know the contents of cartilage matrix and understand the molecular basis for cartilage resilience. Are there identifiable stem cells in cartilage? Be able to describe the process of chondrogenesis and know how cartilage grows. What is the regenerative potential of cartilage?
0コメント