A comparison of the influence of global functional loads vs. local contact anatomy on articular cartilage thickness at the knee
A review of the techniques previously employed in the indentation and measurement of the thickness of articular cartilage has led to new and improved techniques for performing both measurements. By utilizing high-speed, microcomputer-controlled data logging techniques, simultaneous monitoring of signals from a dynamic load cell and a displacement transducer could be made throughout an indentation test. The position of the indenter as it touched the articular surface could thus be determined automatically by identifying the moment at which a positive change in the load signal occurred. Less accurate and more time consuming techniques previously required for determining the position of the cartilage surface were hence avoided. The apparatus also included a critically damped dashpot which prevented any transient loads being applied to the cartilage. Depths of indentation could be measured to an accuracy of 0.005 mm with a measurement repeatability of 2.14 per cent. By replacing the indenter with a sharp needle, the apparatus was also capable of measuring the undeformed thickness of cartilage. An accuracy of +/- 0.012 mm could be achieved with a measurement repeatability of 1.2 per cent. The apparatus is particularly suited to survey work where large numbers of indentation tests are to be performed.
Improved techniques for measuring the indentation and thickness of articular cartilage
Proceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine
Comparison of optical, needle probe and ultrasonic techniques for the measurement of articular cartilage thickness
Summary Neutral buffered 4% formaldehyde fixation for 48h preserved well the proteoglycan content of bovine articular cartilage. Neither subsequent demineralization in 10% EDTA, nor light microscopic tissue processing, reduced the hexosamine or uronic acid content of the tissue. Fixation in alcoholic solutions increased Safranin O binding as well as periodic acid Schiff reaction of the cartilage matrix as measured by microspectrophotometry. It is suggested that the enhanced staining of cartilage was due to better preservation of the glycoprotein oligosaccharides. Quaternary ammonium salts in the fixative suppressed the staining of cartilage matrix with Safranin O.
Fixation, decalcification, and tissue processing effects on articular cartilage proteoglycans
This paper describes the flow patterns and related viscoelastic behaviors of articular cartilage under four different loading configurations: 1) confined compression, 2) unconfined compression, 3) translating parabolic surface traction of constant loading span over a cartilage layer, and 4) spreading parabolic surface traction of periodically varying span on a cartilage layer. Brief summaries of formulations and solutions of these problems are given and discussed. For the first two cases, emphasis is given to the differences in the flow mechanisms giving rise to the observed compressive viscoelastic behavior of the tissue. These two fundamental solutions can provide a basis for interpreting the results of the deformation and flow patterns obtained from more complicated loading configurations. The last two cases simulate two main geometric features of joint articulations. Fluid efflux patterns at the articulating surface depend on the kinematics of loading as well as the intrinsic material properties of the tissue: the moduli and permeability of the solid matrix. The predominant mechanism controlling the viscoelastic behavior of the tissue in compression is determined by the relative magnitude of the fluid drag and the intrinsic stiffness of the organic solid matrix.
Fundamentals of fluid transport through cartilage in compression
Loss of or damage to the meniscus alters the pattern of loading in the knee joint and frequently leads to cartilage degeneration and osteoarthritis. The mechanical properties of articular cartilage have been shown to reflect the extent of cartilage degeneration in human osteoarthritis and in experimental models of joint disease, but there is little experimental data documenting changes in cartilage mechanics following meniscectomy. We hypothesized that the tensile properties of the surface zone of articular cartilage are altered following total medial meniscectomy. Twelve mongrel dogs underwent complete resection of the medial meniscus in the right knee, and the femoral cartilage was studied 12 weeks after the operation. We performed uniaxial, tensile stress-relaxation tests to determine the equilibrium tensile modulus of surface-zone cartilage. Water and glycosaminoglycan content were also measured at site-matched locations. The tensile moduli of the cartilage decreased significantly following meniscectomy. The linear region modulus decreased by 40%, from 25.5 +/- 7.7 to 15.3 +/- 7.2 MPa. There was a weak (r = -0.45), but significant, correlation between the linear region modulus and the gross morphological grade for cartilage damage. Water and glycosaminoglycan content did not change following meniscectomy. Composition was not correlated with mechanical properties or morphological grade, suggesting that cartilage structure may play a more important role than composition in determining the mechanical properties. The observed decrease in cartilage material properties provides a quantitative measure of the loss of cartilage function following meniscectomy and reflects a pattern of change that is consistent with damage to the collagen-proteoglycan solid network.
Tensile properties of articular cartilage are altered by meniscectomy in a canine model of osteoarthritis
Journal of Orthopaedic Research: Official Publication of the Orthopaedic Research Society
Indentation testing provides a quantitative technique to evaluate mechanical characteristics of articular cartilage in situ and in vivo. Traditionally, analytical solutions proposed by Hayes et al. [Hayes WC, Keer LM, Herrmann G, Mockros LF. A mathematical analysis for indentation tests of articular cartilage. J Biomech 1972;5(5):541-51] have been applied for the analysis of indentation measurements, and due to their practicality, they have been used for clinical diagnostics. Using this approach, the elastic modulus is derived based on scaling factors which depend on cartilage thickness, indenter radius and Poisson's ratio, and the cartilage model is assumed isotropic and homogeneous, thereby greatly simplifying the true tissue characteristics. The aim was to investigate the validity of previous model assumptions for indentation testing. Fibril-reinforced poroviscoelastic cartilage (FRPVE) model including realistic tissue characteristics was used to simulate indentation tests. The effects of cartilage inhomogeneity, anisotropy, and indentation velocity on the indentation response were evaluated, and scaling factors from the FRPVE analysis were derived. Subsequently, the validity of scaling factors obtained using the traditional and the FRPVE analyses was studied by calculating indentation moduli for bovine cartilage samples, and comparing these values to those obtained experimentally in unconfined compression testing. Collagen architecture and compression velocity had significant effects on the indentation response. Isotropic elastic analysis gave significantly higher (30-107%) Young's moduli for indentation compared to unconfined compression testing. Modification of Hayes' scaling factors by accounting for cartilage inhomogeneity and anisotropy improved the agreement of Young's moduli obtained for the two test configurations by 14-28%. These results emphasize the importance of realistic cartilage structure and mechanical properties in the indentation analysis. Although it is not possible to fully describe tissue inhomogeneity and anisotropy with just the Young's modulus and Poisson's ratio, accounting for inhomogeneity and anisotropy in these two parameters may help to improve the in vivo characterization of tissue using arthroscopic indentation testing.
Uncertainties in indentation testing of articular cartilage: A fibril-reinforced poroviscoelastic study
Uncertainties in indentation testing of articular cartilage
Chapter 3 - Cartilage and Chondrocytes from Firestein: Kelley's Textbook of Rheumatology on MD Consult
We undertook an interdisciplinary biomechanical and biochemical study to explore the extent and manner in which the total pool of proteoglycans influences the kinetic and static behavior of bovine articular cartilage in tension. Two biomechanical tests were used: (a) the viscoelastic creep test and (b) a slow constant-rate uniaxial tension test; and two enzymatic proteoglycan extraction procedures were used: (a) chondroitinase ABC treatment and (b) a sequential enzymatic treatment with chondroitinase ABC, trypsin, and Streptomyces hyaluronidase. We found that the viscoelastic creep response of all cartilage specimens may be divided into two distinct phases: an initial phase (less than 15 s), characterized by a rapid increase in strain following load application, and a late phase (15 s less than or equal to t less than 25,000 s), characterized by a more gradual increase in strain. A major finding of this study is that the kinetics of the creep response is greatly influenced by the glycosaminoglycan content of the tissue. For untreated and control specimens, the initial response comprises about 50% of the total strain, while for chondroitinase ABC and sequentially extracted specimens, the initial response comprises up to 83% of the total strain. Furthermore, most untreated and control specimens did not reach equilibrium within the 25,000 s test period, while enzymatically digested specimens often reached equilibrium in less than 100 s. Thus, we conclude that through their physical restraints on collagen, the bulk of proteoglycan present in the tissue acts to retard fibrillar reorganization and alignment under tensile loading, thereby effectively preventing sudden extension of the collagen network. In contrast, the results of our slow constant-rate uniaxial tension experiment show that essentially complete extraction of proteoglycan glycosaminoglycans does not affect the intrinsic tensile stiffness and strength of cartilage specimens or the collagen network in a significant manner. Hence, an important function of the bulk proteoglycans (i.e., the large aggregating type) in cartilage is to retard the rate of stretch and alignment when a tensile load is suddenly applied. This mechanism may be useful in protecting the cartilage collagen network during physiological situations, where sudden impact forces are imposed on a joint.
Effects of proteoglycan extraction on the tensile behavior of articular cartilage
Articular cartilage is a biological weight-bearing tissue covering the bony ends of articulating joints. Subtle changes in tissue composition can lead to degeneration of articular cartilage. This study develops an improved inhomogeneous triphasic model with four parameters and extracts the uniaxial modulus (Ha) for both normal and degenerated articular cartilage, and then predicts the swelling pattern of the cartilage. The results indicated that the new inhomogeneous triphasic model can extract uniaxial modulus more accurately, and the predict results also appeared to well match the experimental strain data. This inhomogeneous triphasic model can describe the depth-dependent material attribute of normal and degenerated articular cartilage more exactly.
Computation of Uniaxial Modulus of the Normal and Degenerated Articular Cartilage Using Inhomogeneous Triphasic Model
The material behavior of ligament is determined by its constituents, their organization and their interaction with each other. To elucidate the origins of the multiaxial material behavior of ligaments, we investigated ligament response to shear loading under both quasi-static and rate-dependent loading conditions. Stress relaxation tests demonstrated that the tissue was highly viscoelastic in shear, with peak loads dropping over 40% during 30 min of stress relaxation. The stress relaxation response was unaffected by three decades of change in shear strain rate (1.3, 13 and 130%/s). A novel parameter estimation technique was developed to determine material coefficients that best described the experimental response of each test specimen to shear. The experimentally measured clamp displacements and reaction forces from the simple shear tests were used with a nonlinear optimization strategy based around function evaluations from a finite element program. A transversely isotropic material with an exponential matrix strain energy provided an excellent fit to experimental load-displacement curves. The shear modulus of human MCL showed a significant increase with increasing shear strain (p<0.001), reaching a maximum of 1.72±0.4871 MPa. The results obtained from this study suggest that viscoelasticity in shear does not likely result from fluid flow. Gradual loading of transversely oriented microstructural features such as intermolecular collagen crosslinks or collagen-proteoglycan crosslinking may be responsible for the stiffening response under shear loading.
Ligament material behavior is nonlinear, viscoelastic and rate-independent under shear loading
OBJECTIVES: (a) To determine the topographical variations in cartilage thickness over the entire surfaces of cadaveric lower limb joints, and (b) to examine the correlations between: cartilage thickness and its site specific modulus; cartilage thickness and donor age, weight, height, and body mass index. METHODS: The cartilage thickness of 11 sets of cadaveric human joints each comprising an ankle, knee, and hip was measured using a needle probe technique. Statistical analysis was used to compare the cartilage thickness of the different lower limb joints and the differences in cartilage thickness over the surface of individual joints. It was further examined whether cartilage had a correlation with its stiffness, and any of the details of the specimen donors such as age, weight, height, and body mass index. RESULTS: The mean cartilage thickness of the knee was significantly greater than that of the ankle and hip (p < 0.001) in all 11 sets of joints, while the cartilage thickness of the hip was significantly greater than that of the ankle in 10 sets of joints (p < 0.001). The mass of specimen donors was found to correlate with the mean cartilage thickness of all three lower limb joints. A correlation was also found between the height of donors and the mean cartilage thickness of the knee and hip joints, while only in the ankle joint was a correlation found between the mean cartilage thickness and the body mass index of the specimen donors. A further correlation was found between cartilage thickness and its modulus; the thinner the cartilage, the higher the modulus. CONCLUSIONS: The thickness of articular cartilage seems to be related to the congruance of a joint; thin cartilage is found in congruent joints such as the ankle, whereas thick cartilage is found in incongruent joints such as the knee. The correlations in this study imply that the larger and heavier was a donor the thicker was the cartilage in the lower limb joints. The data further suggest the presence of an inverse relation between the mean cartilage thickness and mean compressive modulus in each of the joints examined.
Thickness of human articular cartilage in joints of the lower limb
In locomotive activities, areas of cartilage in both the hip, and especially the knee, experience periods of complete unloading between loading cycles as contact is lost between opposing articulating surfaces. During these periods these cartilage sites experience load-free recovery. Therefore, it was decided to model as closely as possible the physiological situation described, in order to study the deformation response of articular cartilage to physiological cyclic loading. For this it was necessary to design an apparatus in order to overcome some of the difficulties experienced with servo-hydraulic materials testing apparatus when specifying a lower load limit of zero. Cyclic loading in the frequency range 0-2.5 Hz was controlled by a cam and follower assembly driven by a stepper motor. The ratio of loading to recovery duration per cycle could be adjusted using a two-plate cam design enabling cartilage loading to occur for a duration as short as 20 ms within a 1 Hz cycle. Interchangeable impervious, porous, hemispherical or plane-ended indenters could be used. Load amplitude was controlled by compression of a spring giving a wide range of contact stresses (0.04-7.0 MPa). Load rise times were controlled by the spring in conjunction with a dashpot, enabling critically damped loads to reach their maximum value within an interval as short as 15 ms. The measurement technique and subsequent analysis relied on simultaneous recording of indenter load and vertical displacement at a sampling frequency of 5 kHz.
Articular cartilage deformation under physiological cyclic loading--Apparatus and measurement technique
Biomechanics and Modeling in Mechanobiology
Abstract Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.
Contribution of tissue composition and structure to mechanical response of articular cartilage under different loading geometries and strain rates
Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.
Experimental and theoretical methods were used to investigate the linearity of the stress response of articular cartilage to ramp and sinusoidal tests in confined compression, as well as the role of cartilage-porous platen and lateral confinement boundary conditions in determining material responses. With respect to linearity, we posed the question as to whether the elicited stress responses to ramp compression, ramp release and sinusoidal tests were similar. With respect to boundary conditions we inquired as to the necessity of specifying a detailed interdigitating contact with the porous filter and of specifying the level of confinement present at the lateral edge of the disk. We found that the stress responses to the three types of tests were dissimilar, with ramp compression the only test exhibiting linear behavior. Ramp release from a static compression offset was non-linear in a manner such that the cartilage maintained a compressive stress higher than expected by a linear theory. Sinusoidal compression also displayed a non-linear response consistent with the presence of a release phase in each cycle. The actual boundary conditions present at the cartilage/porous-filter interface were visualized histologically. Areas (tens of microns) of cartilage in contact with the metal of the filter were interspersed with areas expanded into the pores of the filter. Finite-element analysis incorporating this information suggested that precise specification of this interface and of the level of the extent of lateral confinement would be necessary for the estimation of material properties, such as the hydraulic permeability, from these tests. The trends of the linearity studies did not appear to be significantly affected by the problems posed by these difficult to quantitate boundary conditions. The non-linear cartilage response to release and sinusoidal displacements therefore appear to be physiologically interesting. The maintained, that is higher than would be linear, compressive stress observed during release may be a beneficial adaptation to repeated loading where temporal variations in tissue stresses would be minimized.
Confined compression of articular cartilage: linearity in ramp and sinusoidal tests and the importance of interdigitation and incomplete confinement
Confined compression of articular cartilage
The intrinsic tensile behavior of the matrix of bovine articular cartilage and its variation with age
The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage
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.
Viscoelastic shear properties of the equine medial meniscus
The intrinsic compressive and tensile properties of normal bovine medial menisci were measured, and the variations in these properties with respect to the structural organization of the tissue and test specimen location were examined. Using a confined compression experiment, the compressive aggregate modulus and permeability of the meniscus were determined. The permeability of the tissue was also compared with the permeability as measured experimentally using a direct permeation experiment. Deep posterior specimens are significantly stiffer in compression than deep anterior and central-anterior specimens, while deep anterior specimens are significantly less stiff than deep posterior and central-posterior specimens. Posterior specimens have a significantly higher average water content. In addition, the permeability of the bovine meniscus was found to be about one-tenth that of bovine articular cartilage. The tensile stiffness of meniscal tissue was determined from constant strain rate uniaxial tension tests. To asses the directional variations in the tensile properties, specimens were obtained from the circumferential and radial orientations. The results indicate that the femoral surface of the meniscus is isotropic in tension, while specimens from within the meniscus are anisotropic--the circumferential specimens are much stiffer than the radial specimens. Furthermore, circumferential posterior specimens from the interior of the meniscus are significantly stiffer than similar anterior specimens. Layer inhomogeneities in the tensile properties with respect to distance from the femoral surface are also present.
Material properties of the normal medial bovine meniscus
This paper describes the development and use of a direct compression stimulator for culturing explants from the meniscus of the knee and articular cartilage. Following design and fabrication of the instrument along with its data acquisition system, the function of the machine was verified by both mechanical means and tissue effect. The loading chamber can hold up to 45 5 mm diameter samples. While designed to stimulate samples up to 4 mm thick, axial displacements as little as 0.127 microm are within the theoretical capacity of the stimulator. In gene expression studies, collagen II and aggrecan expression were examined in explants from articular cartilage as well as medial and lateral menisci subjected to dynamic stimulation and static compression. These results were then compared to free swelling samples. It was found that static compression to cut thickness down-regulated aggrecan and collagen II expression in articular cartilage explants compared to free swelling controls by 94% and 90%, respectively. The application of a dynamic, intermittent, 2% oscillation around the cut thickness returned expression levels to those of free swelling controls at 4 h but not at 76 h. In medial meniscus samples, dynamic compression up-regulated aggrecan expression by 108%, but not collagen II expression, at 4 and 76 h compared to static controls. No difference in gene expression was observed for lateral meniscal explants. Thus, effects of direct compression seen in articular cartilage may not necessarily translate to the knee meniscus. The design of this stimulator will allow a variety of tissues and loading regimens to be examined. It is hoped that regimens can be found that not only return samples to the production levels of free swelling controls, but also surpass them in terms of gene expression, protein synthesis, and functional properties.
A direct compression stimulator for articular cartilage and meniscal explants
This review details current efforts to tissue engineer the knee meniscus successfully. The meniscus is a fibrocartilaginous tissue found within the knee joint that is responsible for shock absorption, load transmission, and stability within the knee joint. If this tissue is damaged, either through tears or degenerative processes, then deterioration of the articular cartilage can occur. Unfortunately, there is a dearth in the amount of work done to tissue engineer the meniscus when compared to other musculoskeletal tissues, such as bone. This review gives a brief overview of meniscal anatomy, biochemical properties, biomechanical properties, and wound repair techniques. The discussion centers primarily on the different components of attempting to tissue engineer the meniscus, such as scaffold materials, growth factors, animal models, and culturing conditions. Our approach for tissue engineering the meniscus is also discussed.
Toward tissue engineering of the knee meniscus
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.
Finite element analysis of the meniscus: the influence of geometry and material properties on its behaviour
The menisci appear at approximately the 8th to 10th week of fetal development. They are discernible in the adult knee joint as crescent-shaped fibrocartilagenous wedges between the femoral and tibial condyles. Their unique design, structure, composition, and anatomic attachments allow the menisci to play an integral role in normal knee joint function. The primary biomechanical function of the meniscus is load transmission. Other functions include shock absorption, joint stability and congruity, and joint lubrication and nutrition.
Anatomy and biomechanics of the meniscus
Volumetric changes of articular cartilage during stress relaxation in unconfined compression
The function of articular cartilage is to support and distribute loads and to provide lubrication in the diarthrodial joints. Cartilage function is described by proper mechanical and rheological properties, strain and depth-dependent, which are not completely assessed. Unconfined and confined compression are commonly used to evaluate the Young's modulus (E) and the aggregate modulus (H(A)), respectively. The Poisson's ratio (nu) can be calculated indirectly from the equilibrium compression data, or using the biphasic indentation technique; it has recently been optically evaluated by using video microscopy during unconfined compression. The transient response of articular cartilage during confined compression depends on its permeability k; a constant value of k can be easily identified by a simple analytical model of confined compression tests, whereas more complex models or direct measurements (permeation tests) are needed to study the permeability dependence on deformation. A poroelastic finite element model of articular cartilage was developed for this purpose. The elastic parameters (E,nu) of the model were evaluated performing unconfined compression creep tests on human articular cartilage disks, whereas k was identified from the confined test response. Our combined experimental and computational method can be used to identify the parameters that define the permeability dependence on deformation, as a function of depth from articular surface.
Biomechanical properties of human articular cartilage under compressive loads
Comparison of the equilibrium response of articular cartilage in unconfined compression, confined compression and indentation
The equilibrium stiffness of articular cartilage is controlled by flow-independent elastie properties (Young's modulus, Es, and Poisson's ratio, vs) of the hydrated tissue matrix. In the current study, an optical (microscopic) method has been developed for the visualization of the boundaries of cylindrical bovine humeral head articular cartilage disks (n = 9), immersed in physiological solution, and compressed in unconfined geometry. This method allowed a direct, model-independent estimation of Poisson's ratio of the tissue at equilibrium, as well as characterization of the shape changes of the sample during the nonequilibrium dynamic phase. In addition to optical analyses, the equilibrium behavior of cartilage disks in unconfined and confined ramp-stress relaxation tests provided a direct estimation of the aggregate modulus, Ha, and Young's modulus and, indirectly. Poisson's ratio for the articular cartilage. The mean value for Poisson's ratio obtained from the optical analysis was 0.185 ± 0.065 (mean ± S.D., n = 9). Values of elastic parameters obtained from the mechanical tests were 0.754 ± 0.198 MPa, 0.677 ± 0.223 MPa, and 0.174 ± 0.106 for Ha, Es, and vs, respectively (mean ± S.D., n = 7). The similar vs-values obtained with optical and mechanical techniques imply that, at equilibrium, for these two tests, the isotropic model is acceptable for mechanical analysis. However, the microscopic techniques revealed that the lateral expansion, especially during the initial phase of relaxation, was inhomogeneous through the tissue depth. The superficial cartilage zone expanded less than the radial zone. The zonal differences in expansion were attributed to the known zonal differences in the fibrillar collagen architecture and proteoglycan concentration.
Optical and mechanical determination of poisson's ratio of adult bovine humeral articular cartilage
Unconfined Compression of Articular Cartilage: Nonlinear Behavior and Comparison With a Fibril-Reinforced Biphasic Model
Unconfined Compression of Articular Cartilage
Mapping the depth dependence of shear properties in articular cartilage
Mechanical behaviour of articular cartilage under tensile cyclic load
Zonal changes in the three-dimensional morphology of the chondron under compression: The relationship among cellular, pericellular, and extracellular deformation in articular cartilage
Zonal changes in the three-dimensional morphology of the chondron under compression
The role of viscoelasticity of collagen fibers in articular cartilage: axial tension versus compression
The role of viscoelasticity of collagen fibers in articular cartilage
Dynamic unconfined compression of articular cartilage under a cyclic compressive load
1. The orientation of collagen fibres of the menisci of the knee has been demonstrated by polarised light microscopy.2. As might be supposed from its fibre structure, the ultimate tensile strength of the meniscal tissue is dependent upon the axis of loading.3. The tensile strength of the meniscus is similar to that of articular cartilage.
THE STRENGTH OF THE MENISCI OF THE KNEE AS IT RELATES TO THEIR FINE STRUCTURE
The integrity of the knee joint depends upon the muscles and tendons about the knee, the articular capsule, the intrinsic ligaments of the joint, and the bone architecture of the tibia and femur.Lateral motion of the knee joint in extension is controlled by the capsule, collateral ligaments, and cruciate ligaments; in flexion, by the same structures minus the fibular collateral ligament.Rotary motion of the knee joint in extension is controlled by capsule, collateral ligaments, and cruciate ligaments; in flexion, by the same structures minus the fibular collateral ligament.Forward gliding of the tibia on the femur is controlled by the anterior cruciate ligament.Backward gliding of the tibia on the femur is controlled by the posterior cruciate ligament.Lateral gliding of the tibia on the femur is controlled by the tibial intercondyloid eminence and the femoral condyles with the aid of all the ligaments.Hyperextension is controlled by both collateral ligaments, both cruciate ligaments, both menisci, the posterior aspect of the articular capsule, the oblique popliteal ligament, and the architecture of the femoral condyles.Hyperflexion is controlled by both cruciate ligaments, both menisci, the femoral attachment of the posterior aspect of the capsule, the femoral attachment of both heads of the gastrocnemius muscle, and the bone structure of the condyles of the femur and the tibia.The menisci cushion hyperextension and hyperflexion.The tibial collateral ligament is closely related to the medial meniscus, but there is no strong fibrous-tissue attachment between them.The tibial collateral ligament glides forward and backward in extension and flexion.The drawings from which were made Figures 1 to 12 are the work of Ruth Bialek.
THE MECHANICS OF THE LIGAMENTS AND MENISCI OF THE KNEE JOINT
Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments
Biphasic creep and stress relaxation of articular cartilage in compression?
Mechanical properties of the heel pad: current theory and review of the literature
The mechanical property of articular cartilage determines to a great extent the functionality of diarthrodial joints. Consequently, the early detection of mechanical and, thus, functional changes of cartilage is crucial for preventive measures to maintain the mobility and the quality of life of individuals. An alternative to conventional mechanical testing is the inverse finite element approach, enabling non-destructive testing of the tissue. We evaluated a method for the assessment of the equilibrium material properties of the patellar cartilage based on magnetic resonance imaging during patellofemoral compression. We performed ex vivo testing of two equine patellas with healthy cartilage, one with superficial defects, and one with synthetically degenerated cartilage to simulate a pre-osteoarthritic stage. Static compression with 400 N for 2 h resulted in morphological changes comparable to physiological in vivo deformations in humans. We observed a decrease of the equilibrium Young's modulus of the degenerated cartilage by -59%, which was in the range of the results from indentation (-74%) and confined compression tests (-58%). With the reported accuracy of magnetic resonance imaging and its reproducibility, the results indicate the potential to measure differences in Young's modulus with regard to cartilage degeneration and consequently to distinguish between healthy and pre-osteoarthritic cartilage.
MRI-based inverse finite element approach for the mechanical assessment of patellar articular cartilage from static compression test
Biomedizinische Technik. Biomedical Engineering
The menisci serve several important biomechanical functions in the knee. They distribute stresses over a broad area of articular cartilage, absorb shocks during dynamic loading, and probably assist in joint lubrication. These functions enhance the ability of articular cartilage to provide a smooth, near-frictionless articulation and to distribute loads evenly to the underlying bone of the femur and tibia. In addition, the menisci provide stability to the injured knee when the cruciate ligaments or other primary stabilizers are deficient. The ability to perform these mechanical functions is based on the intrinsic material properties of the menisci as well as their gross anatomic structure and attachments. The material properties of the menisci are determined by their biochemical composition and, perhaps more important, by the organization and interactions of the major tissue constituents: water, proteoglycan, and collagen. Interactions among the important constituents of the fibrocartilage matrix cause meniscal tissue to behave as a fiber-reinforced, porous, permeable composite material similar to articular cartilage, in which frictional drag caused by fluid flow governs its response to dynamic loading. The menisci are one-half as stiff in compression and dissipate more energy under dynamic loading than articular cartilage. Energy dissipation, or shock absorption, by the menisci is the result of high frictional drag caused by low permeability of the matrix, which is about one-sixth as permeable as articular cartilage. The dynamic shear modulus of meniscal tissue is only one-fourth to one-sixth as great as that of articular cartilage. The coarse, circumferential Type I collagen fiber bundles of the meniscus give the tissue great tensile stiffness (range, 100-300 megapascals) and strength. The highly oriented collagen ultrastructure of the menisci makes the tissue anisotropic in tension, compression, and shear and appears to dominate its behavior under all loading conditions.
Material properties and structure-function relationships in the menisci
Clinical Orthopaedics and Related Research
OBJECTIVE: Studies of cartilage mechanics seek to determine the fundamental relationships between mechanical behavior and the composition and structure of healthy cartilage and to determine mechanisms for changes associated with degeneration. METHOD: The mechanics of normal and osteoarthritic (OA) human articular cartilage are reviewed. Studies of the initiation and pathogenesis of cartilage degeneration in the anterior cruciate ligament transection (ACLT) model of joint instability are also presented. RESULTS: In human cartilage with OA, tensile, compressive and shear behaviors are dramatically altered. These changes present as decreases in the modulus or stiffness of OA cartilage in tension, compression and shear loading, and increases in the propensity to swell as compared to healthy cartilage. In the ACL transection model of OA, similar changes in the mechanics of cartilage have been observed. In addition, changes in structure, composition, and as metabolism consistent with human OA have been found. Deterioration of the collagen-proteoglycan solid network, which appears to be focused at the articular surface, has been the earliest cartilage changes in the model. It remains to be determined if the initial disruption of the cartilage surface is a direct result of mechanical forces or a product of altered chondrocyte activity. CONCLUSIONS: These data and continued research using experimental models of OA provide a basis for our understanding of the pathogenesis and the time course of events in OA and will lead to the development of better procedures for disease intervention and treatment.
Altered mechanics of cartilage with osteoarthritis: human osteoarthritis and an experimental model of joint degeneration
Altered mechanics of cartilage with osteoarthritis
Osteoarthritis and Cartilage / OARS, Osteoarthritis Research Society
The changes in the tensile mechanical properties and biochemical composition of the superficial zone of articular cartilage were examined in a canine model of early osteoarthritis generated by transection of the anterior cruciate ligament. Sixteen weeks following ligament transection, the tensile stiffness of the articular cartilage was decreased by 44% and the ion-induced stress relaxation of the tissue was increased by 57% compared with the contralateral control. Biochemical analyses indicated that the water content of the experimental tissue was increased by 13%, which was reflected as an apparent 37% decrease in the proteoglycan content and a 36% decrease in the collagen content (expressed per wet weight). The hydroxypyridinium crosslink density was decreased in the experimental tissue by 11%. A significant negative correlation was found between the ion-induced stress relaxation and the hydroxypyridinium crosslink density in both control tissue (R = -0.56) and experimental tissue (R = -0.70). No correlation was noted between the tensile stiffness and the biochemical composition of the tissue. These results suggest that, in the superficial zone of articular cartilage, the structure of the tissue may play a more important role than the composition in the determination of its mechanical properties. A major event observed in the model of early osteoarthritis appears to be the disruption and remodeling of the collagen network in the superficial zone of the articular cartilage.
Mechanical and biochemical changes in the superficial zone of articular cartilage in canine experimental osteoarthritis
Fatigue properties of articular cartilage: a preliminary study
Fatigue properties of articular cartilage
Differential-type and integral-type formulations are two common approaches in modeling viscoelastic materials. A differential-type theory is often derived from a Helmholtz free energy function and is usually more suitable for the prediction of strain-rate dependent mechanical behavior during rapid loading, while an integral-type theory usually captures stress relaxation more efficiently than a differential-type theory. A modeling approach is needed to predict the viscoelastic responses during both rapid loading and relaxation phases. A constitutive modeling methodology based on the short and long-term internal variables was proposed in the present study in order to fully use the better features of the two types of theories. The short-term variables described the loading rate, while the long-term variables involving time constants characterized loading history and stress relaxation. The application of the methodology was demonstrated with particular formulations for ligament and articular cartilage. Model parameters were calibrated for both tissues with experimental data from the literature. It was found that the proposed model could well predict a wide range of strain-rate dependent load responses during both loading and relaxation phases. Introducing different internal variables in terms of their time scales reduced the difficulties in the material characterization process and enabled the model to predict the experimental data more accurately, in particular at high strain-rates.
Visco-hyperelastic constitutive modeling of soft tissues based on short and long-term internal variables
Articular cartilage injuries and degenerative joint diseases are responsible for progressive pain and disability in millions of people worldwide, yet there is currently no treatment available to restore full joint functionality. As the tissue functions under mechanical load, an understanding of the physiologic or pathologic effects of biomechanical factors on cartilage physiology is of particular interest. Here we highlight studies that have measured cartilage deformation at scales ranging from the macroscale to the microscale, as well as the responses of the resident cartilage cells, chondrocytes, to mechanical loading using in vitro and in vivo approaches. From these studies, it is clear that there exists a complex interplay between mechanical, inflammatory, and biochemical factors that can either support or inhibit cartilage matrix homeostasis under normal or pathologic conditions. Understanding these interactions is an important step toward developing tissue engineering approaches and therapeutic interventions for cartilage pathologies.
The Mechanobiology of Articular Cartilage: Bearing the Burden of Osteoarthritis
The Mechanobiology of Articular Cartilage
Currently, there are no clinically available tools or applications which could predict osteoarthritis development. Some computational models have been presented to simulate cartilage degeneration, but they are not clinically feasible due to time required to build subject-specific knee models. Therefore, the objective of this study was to develop a template-based modeling method for rapid prediction of knee joint cartilage degeneration. Knee joint models for 21 subjects were constructed with two different template approaches (multiple templates and one template) based on the MRI data. Geometries were also generated by manual segmentation. Evaluated volumes of cartilage degeneration for each subject, as assessed with the degeneration algorithm, were compared with experimentally observed 4 year follow up Kellgren-Lawrence (KL) grades. Furthermore, the effect of meniscus was tested by generating models with subject-specific meniscal supporting forces and those with the average meniscal supporting force from all models. All tested models were able to predict most severe cartilage degeneration to those subjects who had the highest KL grade after 4 year follow up. Surprisingly, in terms of statistical significance, the best result was obtained with one template approach and average meniscal support. This model was fully able to categorize all subjects to their experimentally defined groups (KL0, KL2 and KL3) based on the 4 year follow-up data. The results suggest that a template- or population-based approach, which is much faster than fully subject-specific, could be applied as a clinical prediction tool for osteoarthritis.
Utilizing Atlas-Based Modeling to Predict Knee Joint Cartilage Degeneration: Data from the Osteoarthritis Initiative
Utilizing Atlas-Based Modeling to Predict Knee Joint Cartilage Degeneration
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.
Sensitivities of medial meniscal motion and deformation to material properties of articular cartilage, meniscus and meniscal attachments using design of experiments methods
A common effect of arthritic disease processes in synovial joints is deterioration of the articular cartilage. Therefore, an improved understanding of the relationships between the composition and structure of articular cartilage and the mechanical behaviour is a subject of considerable interest. The numerical modelling tool of finite element (FE) analysis has been widely applied to analyse the behaviour of articular cartilage under compressive stress. FE analysis enables parameters and boundary conditions to be investigated which are not accessible experimentally or analytically. The biphasic theory describes the constitutive behaviour of soft hydrated biological tissues, such as articular cartilage, and has been successfully implemented using FE analysis. The development of successively more comprehensive biphasic models is described here detailing the use of FE analysis in modelling experimental configurations such as indentation. Key work in the area is reviewed in this paper.
Application of finite elements to the stress analysis of articular cartilage
The aim of this study was to investigate the role of the superficial zone on the mechanical behavior of articular cartilage. Confined compression of articular cartilage was modeled using a biphasic finite element analysis to calculate the one-dimensional deformation of the extracellular matrix (ECM) and movement of the interstitial fluid through the ECM and articular surface. The articular cartilage was modeled as an inhomogeneous, nonlinear hyperelastic biphasic material with depth and strain-dependent material properties. Two loading conditions were simulated, one where the superficial zone was loaded with a porous platen (normal test) and the other where the deep zone was loaded with the porous platen (upside down test). Compressing the intact articular cartilage with 0.2 MPa stress reduced the surface permeability by 88%. Removing the superficial zone increased the rate of change for all mechanical parameters and decreased the fluid support ratio of the tissue, resulting in increased tissue deformation. Apparent permeability linearly increased after superficial removal in the normal test, yet it did not change in the upside down test. Orientation of the specimen affected the time-dependent biomechanical behavior of the articular cartilage, but not equilibrium behavior. The two tests with different specimen orientations resulted in very different apparent permeabilities, suggesting that in an experimental study which quantifies material properties of an inhomogeneous material, the specimen orientation should be stated along with the permeability result. The current study provides new insights into the role of the superficial zone on mechanical behavior of the articular cartilage.
A biphasic finite element study on the role of the articular cartilage superficial zone in confined compression
Articular cartilage is a complex composite material in engineering terms. It is inhomogeneous, anisotropic and demonstrates a time-dependent nonlinear relationship between stress and strain. This paper reviews the application of the finite-element method to the loading of articular cartilage, and highlights the potential of this numerical technique in the investigation of osteoarthritis.
Finite-element analysis in cartilage biomechanics
Novel conical beam CT-scanners offer high resolution imaging of knee structures with i.a. contrast media, even under weight bearing. With this new technology, we aimed to determine cartilage strains and meniscal movement in a human knee at 0, 1, 5, and 30 min of standing and compare them to the subject-specific 3D finite element (FE) model. The FE model of the volunteer׳s knee, based on the geometry obtained from magnetic resonance images, was created to simulate the creep. The effects of collagen fibril network stiffness, nonfibrillar matrix modulus, permeability and fluid flow boundary conditions on the creep response in cartilage were investigated. In the experiment, 80% of the maximum strain in cartilage developed immediately, after which the cartilage continued to deform slowly until the 30 min time point. Cartilage strains and meniscus movement obtained from the FE model matched adequately with the experimentally measured values. Reducing the fibril network stiffness increased the mean strains substantially, while the creep rate was primarily influenced by an increase in the nonfibrillar matrix modulus. Changing the initial permeability and preventing fluid flow through noncontacting surfaces had a negligible effect on cartilage strains. The present results improve understanding of the mechanisms controlling articular cartilage strains and meniscal movements in a knee joint under physiological static loading. Ultimately a validated model could be used as a noninvasive diagnostic tool to locate cartilage areas at risk for degeneration.
Deformation of articular cartilage during static loading of a knee joint--experimental and finite element analysis
Computational and Mathematical Methods in Medicine
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.
Recent Advances in Computational Mechanics of the Human Knee Joint
Multiple computational models have been developed to study knee biomechanics. However, the majority of these models are mainly validated against a limited range of loading conditions and/or do not include sufficient details of the critical anatomical structures within the joint. Due to the multifactorial dynamic nature of knee injuries, anatomic finite element (FE) models validated against multiple factors under a broad range of loading conditions are necessary. This study presents a validated FE model of the lower extremity with an anatomically accurate representation of the knee joint. The model was validated against tibiofemoral kinematics, ligaments strain/force, and articular cartilage pressure data measured directly from static, quasi-static, and dynamic cadaveric experiments. Strong correlations were observed between model predictions and experimental data (r > 0.8 and p < 0.0005 for all comparisons). FE predictions showed low deviations (root-mean-square (RMS) error) from average experimental data under all modes of static and quasi-static loading, falling within 2.5 deg of tibiofemoral rotation, 1% of anterior cruciate ligament (ACL) and medial collateral ligament (MCL) strains, 17 N of ACL load, and 1 mm of tibiofemoral center of pressure. Similarly, the FE model was able to accurately predict tibiofemoral kinematics and ACL and MCL strains during simulated bipedal landings (dynamic loading). In addition to minimal deviation from direct cadaveric measurements, all model predictions fell within 95% confidence intervals of the average experimental data. Agreement between model predictions and experimental data demonstrates the ability of the developed model to predict the kinematics of the human knee joint as well as the complex, nonuniform stress and strain fields that occur in biological soft tissue. Such a model will facilitate the in-depth understanding of a multitude of potential knee injury mechanisms with special emphasis on ACL injury.
Finite element model of the knee for investigation of injury mechanisms: development and validation
Finite element model of the knee for investigation of injury mechanisms
This study is aimed at the analysis of articular contact in a three-dimensional mathematical model of the human knee-joint. In particular the effect of articular contact on the passive motion characteristics is assessed in relation to experimentally obtained joint kinematics. Two basically different mathematical contact descriptions were compared for this purpose. One description was for rigid contact and one for deformable contact. The description of deformable contact is based on a simplified theory for contact of a thin elastic layer on a rigid foundation. The articular cartilage was described either as a linear elastic material or as a non-linear elastic material. The contact descriptions were introduced in a mathematical model of the knee. The locations of the ligament insertions and the geometry of the articular surfaces were obtained from a joint specimen of which experimentally determined kinematic data were available, and were used as input for the model. The ligaments were described by non-linear elastic line elements. The mechanical properties of the ligaments and the articular cartilage were derived from literature data. Parametric model evaluations showed that, relative to rigid articular contact, the incorporation of deformable contact did not alter the motion characteristics in a qualitative sense, and that the quantitative changes were small. Variation of the elasticity of the elastic layer revealed that decreasing the surface stiffness caused the ligaments to relax and, as a consequence, increased the joint laxity, particularly for axial rotation. The difference between the linear and the non-linear deformable contact in the knee model was very small for moderate loading conditions. The motion characteristics simulated with the knee model compared very well with the experiments. It is concluded that for simulation of the passive motion characteristics of the knee, the simplified description for contact of a thin linear elastic layer on a rigid foundation is a valid approach when aiming at the study of the motion characteristics for moderate loading conditions. With deformable contact in the knee model, geometric conformity between the surfaces can be modelled as opposed to rigid contact which assumed only point contact.
Articular contact in a three-dimensional model of the knee
Cartilage was obtained from eight matched knee (tibiofemoral and femoropatellar) and ankle (talocrural) joints of five different donors (both left and right from donors 14, 22, and 38 years of age, and left only from donors 31 and 45 years of age) within 24 hours of death. All cartilage was graded as normal by the macroscopic visual Collins' scale and the histological Mankin scale. Cylindrical disks of cartilage were harvested from 10 sites within the tibiofemoral and femoropatellar joint surfaces and four sites within the talocrural joint, and uniaxial confined compression measurements were performed to quantify a spectrum of physical properties including the equilibrium modulus, hydraulic permeability, dynamic stiffness, streaming potential, electrokinetic coupling coefficient, and electrical conductivity. Matched specimens from the same 14 sites were used for complementary measurements of biochemical composition and molecular interaction, including water content, hypotonic swelling behavior, and sulfated glycosaminoglycan and collagen contents. In comparison of the top 1-mm slices of talar cartilage with the top 1-mm of tibiofemoral cartilage, the talar cartilage appeared denser with a higher sulfated glycosaminoglycan content, lower water content, higher equilibrium modulus and dynamic stiffness, and lower hydraulic permeability. The equilibrium modulus increased with increasing sulfated glycosaminoglycans per wet weight and decreased with increasing water content for all joint surfaces. Multiple linear regression showed that greater than 80% of the variation in the equilibrium modulus could be accounted for by variations in the biochemical parameters (water content, sulfated glycosaminoglycans/wet weight, and hydroxyproline content/wet weight) for each joint surface. Nonhomogeneous depth-dependent changes in the physical properties and biochemical composition of full-thickness distal femoral cartilage were consistent with previous reports. Since the compressive deformation of cartilage during cyclic loading is confined to the more superficial regions, the differences in properties of the upper regions of the talar compared with tibiofemoral or femoropatellar cartilage may be important in the etiology of osteoarthritis.
Comparison of biomechanical and biochemical properties of cartilage from human knee and ankle pairs
In a series of 103 specimens from the lateral facet of the human patella, the intrinsic mechanical properties of articular cartilage were measured using a confined compression creep test. By considering the cartilage as a porous, permeable solid filed with fluid, this experimental procedure allowed the determination of the intrinsic equilibrium modulus of the cartilage matrix and its permeability to fluid flow. The intrinsic equilibrium modulus and the permeability both were highly correlated with the water content of the tissue; as water content increased, the matrix of the tissue became softer and more permeable. There was only a marginal decrease in the equilibrium modulus of the tissue with increasing age and surface degeneration. The permeability of the cartilage matrix was not significantly correlated with age or degeneration. CLINICAL RELEVANCE: We concluded that the visual or histological appearance of a cartilage specimen may be a poor indicator of its ability to function as the bearing material in the intact joint. A more reliable indicator of the functional properties of a specimen can be obtained either by direct mechanical testing or by biochemical analysis of its composition.
Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content
The Journal of Bone and Joint Surgery. American Volume
Understanding how structural and functional alterations of individual tissues impact on whole-joint function is challenging, particularly in humans where direct invasive experimentation is difficult. Finite element (FE) computational models produce quantitative predictions of the mechanical and physiological behaviour of multiple tissues simultaneously, thereby providing a means to study changes that occur through healthy ageing and disease such as osteoarthritis (OA). As a result, significant research investment has been placed in developing such models of the human knee. Previous work has highlighted that model predictions are highly sensitive to the various inputs used to build them, particularly the mathematical definition of material properties of biological tissues. The goal of this systematic review is two-fold. First, we provide a comprehensive summation and evaluation of existing linear elastic material property data for human tibiofemoral joint tissues, tabulating numerical values as a reference resource for future studies. Second, we review efforts to model tibiofemoral joint mechanical behaviour through FE modelling with particular focus on how studies have sourced tissue material properties. The last decade has seen a renaissance in material testing fuelled by development of a variety of new engineering techniques that allow the mechanical behaviour of both soft and hard tissues to be characterised at a spectrum of scales from nano- to bulk tissue level. As a result, there now exists an extremely broad range of published values for human tibiofemoral joint tissues. However, our systematic review highlights gaps and ambiguities that mean quantitative understanding of how tissue material properties alter with age and OA is limited. It is therefore currently challenging to construct FE models of the knee that are truly representative of a specific age or disease-state. Consequently, recent tibiofemoral joint FE models have been highly generic in terms of material properties even relying on non-human data from multiple species. We highlight this by critically evaluating current ability to quantitatively compare and model (1) young and old and (2) healthy and OA human tibiofemoral joints. We suggest that future research into both healthy and diseased knee function will benefit greatly from a subject- or cohort-specific approach in which FE models are constructed using material properties, medical imagery and loading data from cohorts with consistent demographics and/or disease states.
Tissue material properties and computational modelling of the human tibiofemoral joint: a critical review
Tissue material properties and computational modelling of the human tibiofemoral joint
Kneeling is required during daily living for many patients after total knee replacement (TKR), yet many patients have reported that they cannot kneel due to pain, or avoid kneeling due to discomfort, which critically impacts quality of life and perceived success of the TKR procedure. The objective of this study was to evaluate the effect of component design on patellofemoral (PF) mechanics during a kneeling activity. A computational model to predict natural and implanted PF kinematics and bone strains after kneeling was developed and kinematics were validated with experimental cadaveric studies. PF joint kinematics and patellar bone strains were compared for implants with dome, medialized dome, and anatomic components. Due to the less conforming nature of the designs, change in sagittal plane tilt as a result of kneeling at 90° knee flexion was approximately twice as large for the medialized-dome and dome implants as the natural case or anatomic implant, which may result in additional stretching of the quadriceps. All implanted cases resulted in substantial increases in bone strains compared with the natural knee, but increased strains in different regions. The anatomic patella demonstrated increased strains inferiorly, while the dome and medialized dome showed increases centrally. An understanding of the effect of implant design on patellar mechanics during kneeling may ultimately provide guidance to component designs that reduces the likelihood of knee pain and patellar fracture during kneeling.
Patellar mechanics during simulated kneeling in the natural and implanted knee
BACKGROUND: Magnetic resonance imaging (MRI) is one of the most potential methods for non-invasive diagnosis of cartilage disorders. Several methods have been established for clinical use; T(1) relaxation time imaging with negatively charged contrast agent (delayed gadolinium enhanced MRI of cartilage, dGEMRIC) has been shown to be sensitive to proteoglycan (PG) content while T(2) relaxation time has been demonstrated to express properties of the collagen fibril network. The use of native T(1) relaxation time has received less attention. OBJECTIVE: In the present study, magnetic resonance (MR) parameters of different types of patellar cartilage were studied with respect to the mechanical properties of the tissue. The general usefulness of the parameters to predict mechanical properties was investigated using cartilage from different species and stages of maturation. METHODS: dGEMRIC, T(2) and native T(1) relaxation times of healthy mature human, juvenile porcine and juvenile bovine articular cartilage samples were measured at 9.4T at 25 degrees C. Mechanical properties (Young's modulus and dynamic modulus) of the samples were measured in unconfined compression using a material testing device. The relationships between MRI and mechanical parameters and potential differences between different types of tissues were tested statistically. RESULTS: Significant, but varying relationships were established between T(1) or T(2) relaxation time and mechanical properties, depending on tissue type. The values of mechanical parameters were in line with the results previously reported in the literature. Unexpectedly, dGEMRIC showed no statistically significant association with the mechanical properties. Variation in the assumption of native T(1) value did not induce significant differences in the calculated contrast agent concentration, and consequently did not affect prediction of mechanical properties. CONCLUSION: For patellae, a complex variation in the relationships between T(2) and mechanical properties in different groups was revealed. The results support the conclusion that juvenile animal tissue, exhibiting a highly complex collagenous architecture, may not always serve as a realistic model for mature human tissue with a typical three-zone network organization, and other than bulk metrics are required for the analysis of cartilage T(2). As the multilayered collagen network can strongly control the mechanical characteristics of juvenile tissue, it may mask the mechanical role of PGs and explain why dGEMRIC could not predict mechanical parameters in patellar cartilage.
Estimation of mechanical properties of articular cartilage with MRI - dGEMRIC, T2 and T1 imaging in different species with variable stages of maturation
Articular cartilage exhibits anisotropic mechanical properties when subjected to tension. However, mechanical anisotropy of mature cartilage in compression is poorly known. In this study, both confined and unconfined compression tests of cylindrical cartilage discs, taken from the adult human patello-femoral groove and cut either perpendicular (normal disc) or parallel (tangential disc) to the articular surface, were utilized to determine possible anisotropy in Young's modulus, E, aggregate modulus, Ha, Poisson's ratio, v and hydraulic permeability, k, of articular cartilage. The results indicated that Ha was significantly higher in the direction parallel to the articular surface as compared with the direction perpendicular to the surface (Ha = 1.237 +/- 0.486 MPa versus Ha = 0.845 +/- 0.383 MPa, p = 0.017, n = 10). The values of Poisson's ratio were similar, 0.158 +/- 0.148 for normal discs compared with 0.180 +/- 0.046 for tangential discs. Analysis using the linear biphasic model revealed that the decrease of permeability during the offset compression of 0-20 per cent was higher (p = 0.015, n = 10) in normal (from 25.5 x 10(-15) to 1.8 x 10(-15) m4/N s) than in tangential (from 12.3 x 10(-15) to 1.3 x 10(-15) m4/N s) discs. Based on the results, it is concluded that the mechanical characteristics of adult femoral groove articular cartilage are anisotropic also during compression. Anisotropy during compression may be essential for normal cartilage function. This property has to be considered when developing advanced theoretical models for cartilage biomechanics.
Mechanical anisotropy of the human knee articular cartilage in compression
Previous studies have shown that stress relaxation behavior of calf ulnar growth plate and chondroepiphysis cartilage can be described by a linear transverse isotropic biphasic model. The model provides a good fit to the observed unconfined compression transients when the out-of-plane Poisson's ratio is set to zero. This assumption is based on the observation that the equilibrium stress in the axial direction (σz) is the same in confined and unconfined compression, which implies that the radial stress σr=0 in confined compression. In our study, we further investigated the ability of the transversely isotropic model to describe confined and unconfined stress relaxation behavior of calf cartilage. A series of confined and unconfined stress relaxation tests were performed on calf articular cartilage (4.5mm diameter, ∼3.3mm height) in a displacement-controlled compression apparatus capable of measuring σz and σr. In equilibrium, σr>0 and σz in confined compression was greater than in unconfined compression. Transient data at each strain were fitted by the linear transversely isotropic biphasic model and the material parameters were estimated. Although the model could provide good fits to the unconfined transients, the estimated parameters overpredicted the measured σr. Conversely, if the model was constrained to match equilibrium σr, the fits were poor. These findings suggest that the linear transversely isotropic biphasic model could not simultaneously describe the observed stress relaxation and equilibrium behavior of calf cartilage.
Confined and unconfined stress relaxation of cartilage: appropriateness of a transversely isotropic analysis
Confined and unconfined stress relaxation of cartilage
Descriptions of the mechanical behaviors of articular cartilage and their correlations with collagen, proteoglycan, water, and ions are summarized, with particular emphasis on understanding the osmotic effect inside the tissue. First, a descriptive explanation is presented of the biphasic theory required to understand how interstitial water contributes toward the viscoelastic behavior of any hydrated soft tissue. Then, the famous osmotic effect in charged, hydrated soft tissue is interpreted in light of the triphasic mixture theory framework. In the introduction of mechanical testing methods, our emphasis is on the popular indentation technique, which can determine the material properties of cartilage in situ or in vivo. The widely accepted indentation analysis solutions in cartilage biomechanics history are summarized and evaluated. At the end of this paper, a new generalized correspondence principle between charged, hydrated soft tissue and linear, isotropic, elastic material (i.e., elasticity theory) is introduced. This principle makes the employment of triphasic theory as straightforward as using an elasticity theory to solve any equilibrium problem where the elasticity theory can be used to model the material. By using this generalized correspondence principle, the fixed charge density of bovine cartilage has been simply and conveniently calculated from the indentation testing data. The results of proteoglycan content from this mechanical test are remarkably consistent with those from standard biochemical assay. This new correspondence principle significantly improves the power of indentation tests in the determination of mechanoelectrochemical properties of articular cartilage.
Biomechanics of articular cartilage and determination of material properties
Medicine and Science in Sports and Exercise
Indentation testing is widely used to evaluate the mechanical properties of articular cartilage. However, most curve-fitting solutions for indentation analysis require the deformation data of cartilage at the equilibrium state, which often takes the tissue hours to reach. The lengthy testing time reduces the efficiency of indentation, increases the chance of tissue deterioration, and prevents in vivo applications. To overcome these limitations, a novel technique based on principal component analysis (PCA) was developed in this study, which can predict the full indentation creep curve based on the first few minutes' deformation history and the principal components. The accuracy of this technique was confirmed using the indentation data from 40 temporomandibular joint condylar cartilage samples and 17 bovine knee joint samples. The mechanical properties determined by biphasic curve-fitting using predicted and experimental data are in good agreement, with the difference between the two less than 5%. For TMJ and knee cartilages, it is found that any number of full tests beyond eight will not lead to any increase larger than 1% in the accuracy, indicating a low sample number required for prediction. In addition, the principal components of indentation creep curves are consistent for the same type of cartilage tested with identical protocols, but significantly different between two distinct cartilages. Therefore PCA may also represent a new method to compare the mechanical behaviors of different cartilages, as it avoids the assumptions associated with mechanical constitutive models and relies purely on the experimental data.
Determine the equilibrium mechanical properties of articular cartilage from the short-term indentation response
Macroscopic structural damage to the cartilage articular surface can occur due to slicing in surgery, cracking in mechanical trauma, or fibrillation in early stage osteoarthrosis. These alterations may render cartilage matrix and chondrocytes susceptible to subsequent mechanical injury and contribute to progression of degenerative disease. To examine this hypothesis, single 300 microm deep vertical slices were introduced across a diameter of the articular surface of osteochondral explant disks on day 6 after dissection. Then a single uniaxial unconfined ramp compression at 7 x 10(-5) or 7 x 10(-2) s(-1) strain rate to a peak stress of 3.5 or 14 MPa was applied on day 13 during which mechanical behavior was monitored. Effects of slices alone and together with compression were measured in terms of explant swelling and cell viability on days 10 and 17. Slicing alone induced tissue swelling without significant cell death, while compression alone induced cell death without significant tissue swelling. Under low strain rate loading, no differences in the response to injurious compression were found between sliced and unsliced explants. Under high strain rate loading, slicing rendered cartilage more easily compressible and appeared to slightly reduce compression-induced cell and matrix injury. Findings highlight microphysical factors important to cartilage mechanical injury, and suggest ways that macroscopic structural damage may accelerate or, in certain cases, possibly slow the progression of cartilage degeneration.
Effects of damage in the articular surface on the cartilage response to injurious compression in vitro
Strain amplitude and strain rate dependent nonlinear behavior and load-induced mechanical property alterations of full-thickness bovine articular cartilage attached to bone were investigated in unconfined compression. A sequence of test compressions of finite deformation (ranging from 0.9% to 34.5% nominal strain) was performed at strain rates ranging from approximately 0.053%/s to 5.8%/s. Peak and equilibrium loads were analyzed to determine strain amplitude and strain rate dependence of linear versus nonlinear responses. The test protocol was designed to reveal changes in mechanical properties due to these finite deformations by interspersing small-amplitude witness ramps of approximately 1.1% deformation and approximately 0.44%/s strain rate between the test ramps ("witness" meaning to assess any mechanical property changes). We found that peak loads displayed high nonlinearity, stiffening with both increasing compression amplitude and more so with increasing strain rate. The response to witness ramps suggested that mechanical weakening occurred when compression amplitude reached 1.9-2.9% strain and beyond, and that weakening was much more significant at higher strain rate. These findings delineate regimes of linear versus nonlinear behavior of cartilage, and indicate the types of loads which can cause mechanical property alterations. Biological implications of this study are that strain amplitude and strain rate dependent stiffening may be essential to bear physiological loads and to protect cells and matrix from mechanical damage. Structural changes reflected by mechanical weakening at small compression could also initiate remodeling or disease processes.
Increasing strain and strain rate strengthen transient stiffness but weaken the response to subsequent compression for articular cartilage in unconfined compression
OBJECTIVE: To investigate the mechanical properties and morphological characteristics of articular cartilage on the tibial plateau of human knees, including the region covered by the meniscus. DESIGN: Using a 1-mm diameter flat-ended cylindrical probe to apply a constant load (0.6 MPa) at specific sites on the tibial plateau, the mechanical properties of articular cartilage were studied using seven cadaver knees. Comparison was made between data obtained by the cartilage covered by the meniscus and that not covered. This was done for both the medial and lateral plateaus. Histological sections of the articular cartilage were also performed to study differences between cartilage from these regions of the tibial plateau. RESULTS: Compared to cartilage that was not covered by the meniscus, the articular cartilage beneath the meniscus showed a significantly (P<0.05) larger modulus by as much as 70%, and was less thick by about 40%. Also, the subchondral bone quantity and calcified layer thickness were observed to be significantly lesser in the regions covered by the meniscus. CONCLUSIONS: Our findings revealed a significant difference between the mechanical properties and associated structures of articular cartilage in the region covered by the meniscus compared with the articular cartilage not covered by the meniscus.
Mechanical properties of articular cartilage covered by the meniscus
We measured the in situ biomechanical properties of knee joint cartilage from five species (bovine, canine, human, monkey, and rabbit) to examine the biomechanical relevance of animal models of human knee joint injuries and osteoarthritis. In situ biphasic creep indentation experiments were performed to simultaneously determine all three intrinsic material coefficients (aggregate modulus, Poisson's ratio, and permeability) of the cartilage as represented by the linear KLM biphasic model. In addition, we also assessed the effects of load bearing on these intrinsic properties at "high" and "low" weight-bearing regions on the distal femur. Our results indicate that significant differences exist in some of these material properties among species and sites. The aggregate modulus of the anterior patellar groove within each species is the lowest among all sites tested, and the permeability of the patellar groove cartilage is the highest and does not vary among species. Similarly, the Poison's ratio in the patellar groove is the lowest in all species, except in the rabbit. These results lead to the conclusion that patellar groove cartilage can undergo greater and faster compression. Thus, under high compressive loads, the cartilage of the patellar groove surface can more rapidly compress to create a congruent patellofemoral joint articulation. For any given location, no differences were found in the aggregate modulus among all the species, and no correlation was found between aggregate modulus and thickness at the test site. Thus, in the process of selecting a suitable experimental animal model of human articular cartilage, it is essential to consider the significant interspecies differences of the mechanical properties.
Interspecies comparisons of in situ intrinsic mechanical properties of distal femoral cartilage
The stiffness of articular cartilage is a nonlinear function of the strain amplitude and strain rate as well as the loading history, as a consequence of the flow of interstitial water and the stiffening of the collagen fibril network. This paper presents a full investigation of the interplay between the fluid kinetics and fibril stiffening of unconfined cartilage disks by analyzing over 200 cases with diverse material properties. The lower and upper elastic limits of the stress (under a given strain) are uniquely established by the instantaneous and equilibrium stiffness (obtained numerically for finite deformations and analytically for small deformations). These limits could be used to determine safe loading protocols in order that the stress in each solid constituent remains within its own elastic limit. For a given compressive strain applied at a low rate, the loading is close to the lower limit and is mostly borne directly by the solid constituents (with little contribution from the fluid). In contrast, however in case of faster compression, the extra loading is predominantly transported to the fibrillar matrix via rising fluid pressure with little increase of stress in the nonfibrillar matrix. The fibrillar matrix absorbs the loading increment by self-stiffening: the quicker the loading the faster the fibril stiffening until the upper elastic loading limit is reached. This self-protective mechanism prevents cartilage from damage since the fibrils are strong in tension. The present work demonstrates the ability of the fibril reinfored poroelastic models to describe the strain rate dependent behavior of articular cartilage in unconfined compression using a mechanism of fibril stiffening mainly induced by the fluid flow.
Strain-rate dependent stiffness of articular cartilage in unconfined compression
We evaluated whether the use of cartilage thickness measurement would improve the ability of the arthroscopic indentation technique to estimate the intrinsic stiffness of articular cartilage. First, cartilage thickness and ultrasound reflection from the surface of bovine humeral head were registered in situ using a high-frequency ultrasound probe. Subsequently, cartilage was indented in situ at the sites of the ultrasound measurements using arthroscopic instruments with plane-ended and spherical-ended indenters. Finally, full-thickness cartilage disks (n=30) were extracted from the indented sites (thickness=799-1654microm) and the equilibrium Young's modulus was determined with a material testing device in unconfined compression geometry. We applied analytical and numerical indentation models for the theoretical correction of experimental indentation measurements. An aspect-ratio (the ratio of indenter radius to cartilage thickness) correction improved the correlation of the indenter force with the equilibrium Young's modulus from r(2)=0.488 to r(2)=0.642-0.648 (n=30) for the plane-ended indenter (diameter=1.000mm, height=0.300mm) and from r(2)=0.654 to r(2)=0.684-0.692 (n=30) for the spherical-ended indenter (diameter=0.500mm, height=0.100mm), depending on the indentation model used for the correction. The linear correlation between the ultrasound reflection and the Young's modulus was r(2)=0.400 (n=30). These results suggest that with large indenters, knowledge of the cartilage thickness improves the reliability of the indentation measurements, especially in pathological situations where cartilage thickness may be significantly lower than normal. Ultrasound measurements also provide diagnostically important information about cartilage thickness as well as knowledge of the integrity of the superficial zone of cartilage.
Estimation of the Young's modulus of articular cartilage using an arthroscopic indentation instrument and ultrasonic measurement of tissue thickness
Nonlinear, linear and failure properties of articular cartilage and meniscus in opposing contact surfaces are poorly known in tension. Relationships between the tensile properties of articular cartilage and meniscus in contact with each other within knee joints are also not known. In the present study, rectangular samples were prepared from the superficial lateral femoral condyle cartilage and lateral meniscus of bovine knee joints. Tensile tests were carried out with a loading rate of 5mm/min until the tissue rupture. Nonlinear properties of the toe region, linear properties in larger strains, and failure properties of both tissues were analysed. The strain-dependent tensile modulus of the toe region, Young's modulus of the linear region, ultimate tensile stress and toughness were on average 98.2, 8.3, 4.0 and 1.9 times greater (p<0.05) for meniscus than for articular cartilage. In contrast, the toe region strain, yield strain and failure strain were on average 9.4, 3.1 and 2.3 times greater (p<0.05) for cartilage than for meniscus. There was a significant negative correlation between the strain-dependent tensile moduli of meniscus and articular cartilage samples within the same joints (r=-0.690, p=0.014). In conclusion, the meniscus possesses higher nonlinear and linear elastic stiffness and energy absorption capability before rupture than contacting articular cartilage, while cartilage has longer nonlinear region and can withstand greater strains before failure. These findings point out different load carrying demands that both articular cartilage and meniscus have to fulfil during normal physiological loading activities of knee joints.
Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus
Aims of the present study were to test the hypotheses that (1) the compressive properties of articular cartilage are affected more by changes in the medium ionic concentration than the tensile properties, (2) collagen network controls the compression-tension nonlinearity of articular cartilage, and (3) proteoglycan (PG) and collagen contents are primary determinants of the compressive and tensile properties of cartilage, respectively. These hypotheses were experimentally tested by axial compressive and tensile tests (perpendicular to the cartilage surface) of bovine articular cartilage samples immersed in 0.005 M (n=6), 0.15M (n=12) and 1.0M (n=6) saline solutions. Compressive and tensile behaviour was analyzed by a nonlinear fibril-reinforced poroelastic model. Tissue PG and collagen contents were measured using Fourier transform infrared imaging spectroscopy (FT-IRIS). The compressive modulus of cartilage varied significantly (n=6, p<0.05) as the medium concentration changed. The tensile modulus changed significantly only as the medium concentration was reduced from 0.15 to 0.005 M (n=6, p<0.05). The fibril-reinforced poroelastic model with stiff, nonlinear collagen fibrils predicted the experimentally measured compression-tension nonlinearity of cartilage. Tissue PG and collagen contents accounted for the compressive and tensile properties of cartilage.
Compressive and tensile properties of articular cartilage in axial loading are modulated differently by osmotic environment
Knowledge of the extent to which tibial plateau cartilage displays non-uniform mechanical topography under physiologically relevant loading conditions is critical to evaluating the role of biomechanics in knee osteoarthritis. Cartilage explants from 21 tibial plateau sites of eight non-osteoarthritic female cadaveric knees (age: 41-54; BMI: 14-20) were tested in unconfined compression at 100% strain/s. The elastic tangent modulus at 10% strain (E(10%) ) was calculated for each site and averaged over four geographic regions: not covered by meniscus (I); covered by meniscus-anterior (II); covered by meniscus-exterior (III); and covered by meniscus-posterior (IV). A repeated-measures mixed model analysis of variance was used to test for effects of plateau, region, and their interaction on E(10%) . Effect sizes were calculated for each region pair. E(10%) was significantly different (p<0.05) for all regional comparisons, except I-II and III-IV. The regional pattern of variation was consistent across individuals. Moderate to strong effect sizes were evident for regional comparisons other than I-II on the lateral side and III-IV on both sides. Healthy tibial cartilage exhibits significant mechanical heterogeneity that manifests in a common regional pattern across individuals. These findings provide a foundation for evaluating the biomechanical mechanisms of knee osteoarthritis.
Heterogeneity of tibial plateau cartilage in response to a physiological compressive strain rate
Tensile stiffness of articular cartilage is much greater than its compressive stiffness and plays an essential role even in compressive properties by increasing transient fluid pressures during physiological loading. Recent studies of nonlinear properties of articular cartilage in compression revealed several physiologically pertinent nonlinear behaviors, all of which required that cartilage tensile stiffness increase significantly with stretch. We therefore performed sequences of uniaxial tension tests on fresh bovine articular cartilage slices using a protocol that allowed several hours to attain equilibrium and measured longitudinal and transverse tissue strain. By testing bovine cartilage from different ages (6 months to 6 years) we found that equilibrium and transient tensile modulus increased significantly with maturation and age, from 0 to 15 MPa at equilibrium and from 10 to 28 MPa transiently. Our results indicate that cartilage stiffens with age in a manner similar to other highly hydrated connective tissues, possibly due to age-dependent content of enzymatic and nonenzymatic collagen cross links. The long relaxation period used in our tests (5-10 hours) was necessary in order to attain equilibrium and avoid a very significant overestimation of equilibrium modulus that occurs when much shorter times are used (15-30 minutes). We also found that equilibrium and transient tensile modulus increased nonlinearly when cartilage is stretched from 0 to 10% strain without any previous tare load. Although our results estimate a nonlinear increase in tensile stiffness with stretch that is an order of magnitude lower than that required to predict nonlinear properties in compression, they are in agreement with previous results from other uniaxial tension tests of collagenous materials. We therefore speculate that biaxial tensile moduli may be much higher and thereby more compatible with observed nonlinear compressive properties.
Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth
An optimized digital image correlation (DIC) technique was applied to investigate the depth-dependent mechanical properties of articular cartilage and simultaneously the depth-dependent nonlinear viscoelastic constitutive model of cartilage was proposed and validated. The creep tests were performed with different stress levels and it is found that the initial strain and instantaneous strain increase; however the creep compliance decreases with the increase of compressive stress. The depth-dependent creep strain of cartilage was obtained by analyzing the images acquired using the optimized DIC technique. Moreover the inhomogeneous creep compliance distributions within the tissues were determined at different creep time points. It is noted that both creep strain and creep compliance with different creep times decrease from cartilage surface to deep. The depth-dependent creep compliance increases with creep time and the increasing amplitude of creep compliance decreases along cartilage depth. The depth-dependent and stress rate dependent nonlinear stress and strain curves were obtained for articular cartilage through uniaxial compression tests. It is found that the Young's modulus of cartilage increases obviously along cartilage depth from superficial layer to deep layer and the Young's modulus of different layers for cartilage increases with the increase of stress rate. The Poisson's ratio of cartilage increases along cartilage depth with given compressive strain and the Poisson's ratio of different layers decreases with the increase of compressive strain. The depth-dependent nonlinear viscoelastic constitutive model was proposed and some creep data were applied to determine the parameters of the model. The depth-dependent compressive behaviors of cartilage were predicted by the model and the results show that there are good agreements between the experimental data and predictions.
Depth and rate dependent mechanical behaviors for articular cartilage: experiments and theoretical predictions
Depth and rate dependent mechanical behaviors for articular cartilage
Materials Science & Engineering. C, Materials for Biological Applications
OBJECTIVE: To examine the functional behavior of the surface layer of the meniscus by investigating depth-varying compressive strains during unconfined compression. DESIGN: Pairs of meniscus and articular cartilage explants (n=12) site-matched at the tibial surfaces were subjected to equilibrium unconfined compression at 5, 10, 15, and 20% compression under fluorescence imaging. Two-dimensional (2D) deformations were tracked using digital image correlation (DIC). For each specimen, local compressive engineering strains were determined in 200 μm layers through the depth of the tissue. In samples with sharp strain transitions, bilinear regressions were used to characterize the surface and interior tissue compressive responses. RESULTS: Meniscus and cartilage exhibited distinct depth-dependent strain profiles during unconfined compression. All cartilage explants had elevated compressive engineering strains near the surface, consistent with previous reports. In contrast, half of the meniscus explants tested had substantially stiffer surface layers, as indicated by surface engineering strains that were ∼20% of the applied compression. In the remaining samples, surface and interior engineering strains were comparable. 2D Green's strain maps revealed highly heterogeneous compressive and shear strains throughout the meniscus explants. In cartilage, the maximum shear strain appeared to be localized at 100-250 μm beneath the articular surface. CONCLUSIONS: Meniscus was characterized by highly heterogeneous strains during compression. In contrast to cartilage, which consistently had a compliant surface region, meniscal explants were either substantially stiffer near the surface or had comparable compressive stiffness through the depth. The relatively compliant interior may allow the meniscus to maintain a consistent surface contour while deforming during physiologic loading.
Meniscus and cartilage exhibit distinct intra-tissue strain distributions under unconfined compression
BACKGROUND: Differential-type and integral-type formulations are two common approaches in modeling viscoelastic materials. A differential-type theory is often derived from a Helmholtz free energy function and is usually more suitable for the prediction of strain-rate dependent mechanical behavior during rapid loading, while an integral-type theory usually captures stress relaxation more efficiently than a differential-type theory. A modeling approach is needed to predict the viscoelastic responses during both rapid loading and relaxation phases. METHODS: A constitutive modeling methodology based on the short and long-term internal variables was proposed in the present study in order to fully use the better features of the two types of theories. The short-term variables described the loading rate, while the long-term variables involving time constants characterized loading history and stress relaxation. RESULTS: The application of the methodology was demonstrated with particular formulations for ligament and articular cartilage. Model parameters were calibrated for both tissues with experimental data from the literature. It was found that the proposed model could well predict a wide range of strain-rate dependent load responses during both loading and relaxation phases. CONCLUSION: Introducing different internal variables in terms of their time scales reduced the difficulties in the material characterization process and enabled the model to predict the experimental data more accurately, in particular at high strain-rates.
Characterizing the mechanical properties of soft biological tissues presents a formidable challenge. In order to ensure that the structure of the specimens is at a repeatable reference state, preconditioning is commonly performed before the actual test. However, the exact mechanisms of preconditioning remain unclear and more research on this issue needs to be undertaken so that the methods for preconditioning can be refined to reduce experimental variability. Previous studies have suggested that the choice of preconditioning strain may influence the measured properties. In this study, uniaxial tests were performed on three groups of spinal cord tissues. Two groups (Groups 1 and 2) were preconditioned at 5% strain and tested to 5% and 2% each, while the third (Group 3) was preconditioned at 2% strain and tested to 2%. The peak stress measured at 2% strain for group 3 was 0.0054+/-0.0035MPa and this was significantly higher than group 2 (134%; p=0.015) and group 1 (p=0.005). However, the ratio of peak to equilibrium stress and the relaxation time were similar for both preconditioning strains. This study suggests that in future work, the preconditioning strain should be reported and the highest strain being used in the study should be used for preconditioning. This is important to allow meaningful comparison of test data within the study and also with other studies.
The effects of preconditioning strain on measured tissue properties
Mechanical characterization of soft tissues such as ligaments remains challenging. There is variability in the measured material parameters of ligaments, most of which is related to natural tissue variability, but some of it can be a result of using different testing protocols. Generally preconditioning (cyclic loading-unloading) is performed prior to actual tests to reduce the experimental variability. Commonly, preconditioning protocols for ligaments with a small strain level and 10 sinusoidal loading-unloading cycles are used. The effect of preconditioning and its parameters including strain level, number of cycles and number of preconditioning repetitions on the repeatability of tensile stress-relaxation tests are poorly known for knee ligaments. In the present study, forty-eight dumbbell-shaped bovine anterior cruciate ligament (ACL) samples were used to evaluate the repeatability of stress-relaxation response. Different preconditioning protocols with 2% and 6% strain levels and 1, 5 or 10 preconditioning repetitions were applied. After preconditioning, one-step stress-relaxation test was carried out twice with an hour resting period in between the tests. The equilibrium stress showed no systematic bias when only one preconditioning repetition was applied (2.0 ± 3.1% difference and p > 0.05 between repeated tests). Systematic bias in the peak-to-equilibrium stress ratio was not observed when higher strain level and number of repetitions were used (0.5 ± 1.6% difference and p > 0.05 between repeated tests). In conclusion, the commonly used preconditioning protocol is capable of producing repeatable equilibrium stress levels of bovine ACLs from stress-relaxation tests in tension. However, if repeatable peak-to-equilibrium stress ratio is desirable, higher strain and number of preconditioning repetitions are recommended.
The effect of different preconditioning protocols on repeatability of bovine ACL stress-relaxation response in tension
Journal of the Mechanical Behavior of Biomedical Materials
It is known that initial loading curves of soft biological tissues are substantially different from subsequent loadings. The later loading curves are generally used for assessing the mechanical properties of a tissue, and the first loading cycles, referred to as preconditioning, are omitted. However, slow viscoelastic phenomena related to fluid flow or collagen viscoelasticity are initiated during these first preconditioning loading cycles and may persist during the actual data collection. When these data are subsequently used for fitting of material properties, the viscoelastic phenomena that occurred during the initial cycles are not accounted for. The aim of the present study is to explore whether the above phenomena are significant for articular cartilage, by evaluating the effect of such time-dependent phenomena by means of computational modeling. Results show that under indentation, collagen viscoelasticity dominates the time-dependent behavior. Under UC, fluid-dependent effects are more important. Interestingly, viscoelastic and poroelastic effects may act in opposite directions and may cancel each other out in a stress-strain curve. Therefore, equilibrium may be apparent in a stress-strain relationship, even though internally the tissue is not in equilibrium. Also, the time-dependent effects of viscoelasticity and poroelasticity may reinforce each other, resulting in a sustained effect that lasts longer than suggested by their individual effects. Finally, the results illustrate that data collected from a mechanical test may depend on the preconditioning protocol. In conclusion, preconditioning influences the mechanical response of articular cartilage significantly and therefore cannot be neglected when determining the mechanical properties. To determine the full viscoelastic and poroelastic properties of articular cartilage requires fitting to both preconditioning and post-preconditioned loading cycles.
How preconditioning affects the measurement of poro-viscoelastic mechanical properties in biological tissues
Articular cartilages and menisci are generally considered to be elastic in the published human knee models, and thus the fluid-flow dependent response of the knee has not been explored using finite element analysis. In the present study, the fluid pressure and site-specific collagen fiber orientation in the cartilages and menisci were implemented into a finite element model of the knee using fibril-reinforced modeling previously proposed for articular cartilage. The geometry of the knee was obtained from magnetic resonance imaging of a healthy young male. The bones were considered to be elastic due to their greater stiffness compared to that of the cartilages and menisci. The displacements obtained for fast ramp compression were essentially same as those for instantaneous compression of equal magnitude with the fluid being trapped in the tissues, which was expected. However, a clearly different pattern of displacements was predicted by an elastic model using a greater Young's modulus and a Poisson's ratio for nearly incompressible material. The results indicated the influence of fluid pressure and fiber orientation on the deformation of articular cartilage in the knee. The fluid pressurization in the femoral cartilage was somehow affected by the site-specific fiber directions. The peak fluid pressure in the femoral condyles was reduced by three quarters when no fibril reinforcement was assumed. The present study indicates the necessity of implementing the fluid pressure and anisotropic fibril reinforcement in articular cartilage for a more accurate understanding of the mechanics of the knee.
A human knee joint model considering fluid pressure and fiber orientation in cartilages and menisci
This paper describes a technique and apparatus for measuring the compressive modulus of articular cartilage under physiological loading rates. The compressive modulus is the most relevant property to the primary function of articular cartilage i.e., load carriage. It has been determined previously from measurement of cartilage deformation under slow or almost static loading conditions. The modulus was based on deformations occurring 2 s after the initial application of load which greatly reduces its relevance since in physiological conditions joint loading occurs within 10-150 ms. Five human knee joints have been used to test the apparatus before a major study is undertaken. The preliminary results from these joints show that the compressive modulus of articular cartilage measured within physiological loading time intervals was much greater than previously reported. The compressive modulus at 20 ms was in the range 4.4-27 MPa and was between 32 and 75 per cent greater than its value obtained at 2 s after loading.
A technique for measuring the compressive modulus of articular cartilage under physiological loading rates with preliminary results
Summary Objective To determine if differences in biomechanical properties and biochemical composition exist between human patellar articular cartilage and the opposing femoral articular cartilage. Design The biomechanical properties and biochemical composition of the articular cartilage of 17 knees from 13 donors were determined for four sites on the patella and three sites on the femur represting regions of contact at 30° and 90° of flexion. The material properties were determined by biphasic indentation testing, yielding the compressive aggregate modulus, HA, permeability, k, and Poisson's ratio, vs. The thickness of the cartilage at the indentation site, h, was also measured using a needle probe. Full-thickness samples of cartilage adjacent to each indentation site were used for wet weight, sulfated glycosaminoglycan content and hydroxyproline content determinations. Results The patellar cartilage was found to have a lower compressive aggregate modulus by 30% (P<0.001), higher premeability to fluid flow by 66% (P<0.001) and greater thickness by 23% (P=0.017) than that of the opposing femoral cartilage. The Poisson's ratios for both surfaces were found to be nearly zero. The water content of the patella was higher by 5% (P=0.031) and the proteoglycan content lower by 19% (P=0.030) than that of the femur. However, no differences were found between the collagen contents of the cartilages. Conclusions Significant differences were found between the intrinsic material properties of the patellar cartilage and those of the femoral-trochlear cartilage. This variability of cartilage material properties with the patellofemoral joint may help explain why patellar cartilage has been frequently observed clinically to exhibit earlier and more severe fibrillation changes than the opposing femoral cartilage.
Differences in patellofemoral joint cartilage material properties and their significance to the etiology of cartilage surface fibrillation
In vitro electromechanical and biomechanical testing of articular cartilage provide critical information about the structure and function of this tissue. Difficulties obtaining fresh tissue and lengthy experimental testing procedures often necessitate a storage protocol, which may adversely affect the functional properties of cartilage. The effects of storage at either 4°C for periods of 6 days and 12 days, or during a single freeze-thaw cycle at -20°C were examined in young bovine cartilage. Non-destructive electromechanical measurements and unconfined compression testing on 3 mm diameter disks were used to assess cartilage properties, including the streaming potential integral (SPI), fibril modulus (Ef), matrix modulus (Em), and permeability (k). Cartilage disks were also examined histologically. Compared with controls, significant decreases in SPI (to 32.3±5.5% of control values, p<0.001), Ef (to 31.3±41.3% [corrected] of control values, p=0.046), Em (to 6.4±8.5% of control values, p<0.0001), and an increase in k (to 2676.7±2562.0% of control values, p=0.004) were observed at day 12 of refrigeration at 4°C, but no significant changes were detected at day 6. A trend toward detecting a decrease in SPI (to 94.2±6.2% of control values, p=0.083) was identified following a single freeze-thaw cycle, but no detectable changes were observed for any biomechanical parameters. All numbers are mean±95% confidence interval. These results indicate that fresh cartilage can be stored in a humid chamber at 4°C for a maximum of 6 days with no detrimental effects to cartilage electromechanical and biomechanical properties, while one freeze-thaw cycle produces minimal deterioration of biomechanical and electromechanical properties. A comparison to literature suggested that particular attention should be paid to the manner in which specimens are thawed after freezing, specifically by minimizing thawing time at higher temperatures.
Effects of refrigeration and freezing on the electromechanical and biomechanical properties of articular cartilage
The relationship between the tensile properties of articular cartilage and age has been investigated in vitro in the human knee joint. Specimens orientated parallel to the articular surface were excised from the superficial and deep zones of the femoral condyles of knee joints of persons in the age range from 8 to 91 years. The results showed that the tensile strength of the superficial zone increased with age to reach a maximum value in the third decade. Thereafter the strength decreased markedly with increasing age. The tensile strength of cartilage from the deep zone did not show an increase in the early years but decreased continuously with age. The tensile stiffness of the superficial layer at stresses of 5 MN/m2 and 10 MN/m2 increased to maximum values in the third decade and thereafter decreased with increasing age. The stiffness of the deep zone decreased continuously with age. It is suggested that these results reflect changes in the organisation of the collagen fibre mesh with age and possibly also changes in the collagen cross-links.
Relationship between the tensile properties of articular cartilage from the human knee and age
Although the contribution of the circumferential collagen bundles to the anisotropic tensile stiffness of meniscal tissue has been well described, the implications of interactions between tissue components for other mechanical properties have not been as widely examined. This study compared the effects of the proteoglycan-associated osmotic swelling stress on meniscal fibrocartilage and articular cartilage (AC) mechanics by manipulating the osmotic environment and tissue compressive offset. Cylindrical samples were obtained from the menisci and AC of bovine stifles, equilibrated in phosphate-buffered saline solutions ranging from 0.1× to 10×, and tested in oscillatory torsional shear and unconfined compression. Biochemical analysis indicated that treatments and testing did not substantially alter tissue composition. Mechanical testing revealed tissue-specific responses to both increasing compressive offset and decreasing bath salinity. Most notably, reduced salinity dramatically increased the shear modulus of both axially and circumferentially oriented meniscal tissue explants to a much greater extent than for cartilage samples. Combined with previous studies, these findings suggest that meniscal proteoglycans have a distinct structural role, stabilizing, and stiffening the matrix surrounding the primary circumferential collagen bundles.
Comparison of osmotic swelling influences on meniscal fibrocartilage and articular cartilage tissue mechanics in compression and shear
Isotropic hyperelastic models have been used to determine the material properties of normal human cartilage, but there remains an incomplete understanding of how these properties may be altered by osteoarthritis. The aims of this study were to (1) measure the material constants of normal and osteoarthritic human knee cartilage using isotropic hyperelastic models; (2) determine whether the material constants correlate with histological measures of structure and/or cartilage tissue damage; and (3) quantify the abilities of two common isotropic hyperelastic material models, the neo-Hookean and Yeoh models, to describe articular cartilage contact force, area, and pressure. Small osteochondral specimens of normal and osteoarthritic condition were retrieved from human cadaveric knees and from the knees of patients undergoing total knee arthroplasty and tested in unconfined compression at loading rates and large strains representative of weight-bearing activity. Articular surface contact area and lateral deformation were measured concurrently and specimen-specific finite element models then were used to determine the hyperelastic material constants. Structural parameters were measured using histological techniques while the severity of cartilage damage was quantified using the OARSI grading scale. The hyperelastic material constants correlated significantly with OARSI grade, indicating that the mechanical properties of cartilage for large strains change with tissue damage. The measurements of contact area described anisotropy of the tissue constituting the superficial zone. The Yeoh model described contact force and pressure more accurately than the neo-Hookean model, whereas both models under-predicted contact area and poorly described the anisotropy of cartilage within the superficial zone. These results identify the limits by which isotropic hyperelastic material models may be used to describe cartilage contact variables. This study provides novel data for the mechanical properties of normal and osteoarthritic human articular cartilage and enhances our ability to model this tissue using simple isotropic hyperelastic materials.
Mechanical properties of normal and osteoarthritic human articular cartilage
METHODS: The instantaneous compressive modulus of articular cartilage was surveyed in 11 sets of human lower limb joints obtained from the ipsilateral side. The average modulus for the entire joint surface of each joint and the topographical variations in the modulus within each joint were examined for all 11 sets, and subjected to statistical analysis. RESULTS: Within each set of joints (hip, knee and ankle), the ankle always had a significantly greater mean compressive modulus than the hip and knee (P < 0.001-P < 0.05). In seven sets of joints, there was no significant difference between the mean compressive moduli of the knee and hip joints. In three sets of joints, the compressive modulus of the knee was significantly greater than that of the hip (P < 0.001-P < 0.01), while in only one set of joints was the compressive modulus of the hip significantly greater than that of the knee (P < 0.01). CONCLUSION: The topographical variations in the cartilage instantaneous compressive modulus over the surfaces of the lower limb joints were matched by differences in the stresses occurring in different areas of each joint. The results of the present study corroborate previous findings and show that the site-specific stresses and corresponding values of the instantaneous cartilage compressive modulus over the surfaces of lower limb joints were correlated (r = 0.82 at P < 0.01), thus adding credence to the conditioning hypothesis of cartilage by prevalent stress.
The 'instantaneous' compressive modulus of human articular cartilage in joints of the lower limb