Mechanical Behavior Of Cartilage Research Articles

Exploring the Multifaceted Dynamics of Cartilage: A Comparative Modeling Study

Cartilage numeric models play a vital role in advancing our understanding of cartilage mechanics, disease progression, and the development of clinical interventions. The aim of this study is to investigate the influence of different mathematical models on cartilage mechanical behavior over time. A comparative analysis was conducted across three scenarios: the single-phase, biphasic, and fibril-reinforced poroelastic models. To understand how cartilage behaves over time, a 1000-second ramp relaxation displacement was applied. The findings reveal that the single-phase model falls short of capturing the time-dependent characteristics of cartilage. Conversely, the inclusion of fluid and collagen fibrils within the cartilage model significantly enhances cartilage resilience and enables the cartilage to behave non-linearly. The results presented herein make a substantial contribution to a deeper and more holistic comprehension of cartilage's dynamic behavior under compressive loads, shedding light on the intricate interplay between fluid pressure and fibril reinforcement.

Effects of removing superficial layer of cartilage on the surface morphology and mechanical behavior of cartilage

Superficial cartilage defect is an important factor that causes osteoarthritis. Therefore, it is very important to investigate the influence of superficial cartilage defects on its surface morphology and mechanical properties. In this study, the knee joint cartilage samples of adult pig were prepared, which were treated by enzymolysis with chymotrypsin and physical removal with electric friction pen, respectively. Normal cartilage and surface treated cartilage were divided into five groups: control group (normal cartilage group), chymotrypsin immersion group, chymotrypsin wiping group, removal 10% group with electric friction pen, and removal 20% group with electric friction pen. The surface morphology and structure of five groups of samples were characterized by laser spectrum confocal microscopy and environmental field scanning electron microscopy, and the mechanical properties of each group of samples were evaluated by tensile tests. The results show that the surface arithmetic mean height and fracture strength of the control group were the smallest, and the fracture strain was the largest. The surface arithmetic mean height and fracture strength of the removal 20% group with electric friction pen were the largest, and the fracture strain was the smallest. The surface arithmetic mean height, fracture strength and fracture strain values of the other three groups were all between the above two groups, but the surface arithmetic mean height and fracture strength of the removal 10% group with electric friction pen, the chymotrypsin wiping group and the chymotrypsin soaking group decreased successively, and the fracture strain increased successively. In addition, we carried out a study on the elastic modulus of different groups, and the results showed that the elastic modulus of the control group was the smallest, and the elastic modulus of the removal 20% group with electric friction pen was the largest. The above study revealed that the defect of the superficial area of cartilage changed its surface morphology and structure, and reduced its mechanical properties. The research results are of great significance for the prevention and repair of cartilage injury.

FINITE ELEMENT ANALYSIS OF FULL-LAYER REPAIR BASED ON IMPROVED ARTICULAR CARTILAGE MODEL

In this paper, the tangential zone of cartilage is introduced into the fiber-reinforced model of articular cartilage. Considering the distribution content of the main fiber and the secondary fiber in the tangential layer of cartilage, the permeability and fiber stiffness of the layer are set in parallel and perpendicular directions, respectively, to more accurately reflect the mechanical behavior of cartilage. The parameters are set to reflect the mechanical behavior of the cartilage more realistically. We use a modified articular cartilage model to simulate the mechanical properties of implanted cartilage with different elastic modulus. The simulation results show that the selection of implants with different elastic modulus will affect the repair of cartilage. Appropriately increasing the elastic modulus of implanted cartilage, can increase the bearing capacity of the repaired area and reduce the stress concentration at the junction. The elastic modulus of the implant should be moderate, not too large or too small, and the damage of stress concentration on the repair surface should be considered. Through simulation, the mechanical state of the repaired cartilage under pressure can be obtained comprehensively, which provides a theoretical basis for clinical pathology.

Indentation mapping revealed poroelastic, but not viscoelastic, properties spanning native zonal articular cartilage.

Elucidating the time-dependent mechanical behavior of cartilage, and other biological materials, is critical to adequately recapitulate native mechanosensory cues for cells. We used microindentation to map the time-dependent properties of untreated and trypsin treated cartilage throughout each cartilage zone. Unlike conventional approaches that combine viscoelastic and poroelastic behaviors into a single framework, we deconvoluted the mechanical response into separate contributions to time-dependent behavior. Poroelastic effects in all cartilage zones dominated the time-dependent behavior of articular cartilage, and a model that incorporates tension-compression nonlinearity best represented cartilage mechanical behavior. These results can be used to assess the success of regeneration and repair approaches, as design targets for tissue engineering, and for development of accurate computational models.

Relative contribution of articular cartilage\u2019s constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.

Physical mechanisms underlying the strain-rate-dependent mechanical behavior of kangaroo shoulder cartilage

Due to anatomical and biomechanical similarities to human shoulder, kangaroo was chosen as a model to study shoulder cartilage. Comprehensive enzymatic degradation and indentation tests were applied on kangaroo shoulder cartilage to study mechanisms underlying its strain-rate-dependent mechanical behavior. We report that superficial collagen plays a more significant role than proteoglycans in facilitating strain-rate-dependent behavior of the kangaroo shoulder cartilage. By comparing the mechanical properties of degraded and normal cartilages, it was noted that proteoglycan and collagen degradation significantly compromised strain-rate-dependent mechanical behavior of the cartilage. Superficial collagen contributed equally to the tissue behavior at all strain-rates. This is different to the studies reported on knee cartilage and confirms the importance of superficial collagen on shoulder cartilage mechanical behavior. A porohyperelastic numerical model also indicated that collagen disruption would lead to faster damage of the shoulder cartilage than when proteoglycans are depleted.

The effect of collagen crosslinking on the biphasic poroviscoelastic cartilage properties determined from a semi-automated microindentation protocol for stress relaxation

Given the important role of the collagenous structure in cartilage mechanics, there is considerable interest in the relationship between collagen crosslinking and the mechanical behavior of the cartilage matrix. While crosslink-induced alterations to the elastic modulus of cartilage have been described, changes to time-dependent behavior have not yet been determined. The objective of the study was to quantify changes to cartilage material properties, including viscoelastic coefficients, with crosslinking via indentation. To accomplish this, a semi-autonomous microindentation stress relaxation protocol was first developed, validated and then applied to cartilage specimens before and after crosslinking. The change in mechanical properties with crosslinking was analyzed both in the unloading portions of the test via the Oliver–Pharr method and in the holding portion with an inverse iterative finite element model that represented cartilage as a biphasic poroviscoelastic material. Although both techniques suggested a similar increase in equilibrium modulus in the crosslinked specimens as compared to the controls, distinct differences in the control specimens were apparent, suggesting that the two different techniques may be capturing different aspects of the material behavior. No differences in time-dependent properties were observed between the crosslinked and the control specimens. These results give further insight into the effects of crosslinking in cartilage mechanical behavior. Additionally, the microindentation stress relaxation protocol may enable increased automation for high-throughput testing.

Temperature effects in articular cartilage biomechanics

Articular cartilage is the soft tissue that covers contacting surfaces of bones in synovial joints. Cartilage is composed of chondrocytes and an extracellular matrix containing numerous biopolymers, cations and water. Healthy cartilage functions biomechanically to provide smooth and stable joint movement. Degenerative joint diseases such as osteoarthritis involve cartilage deterioration, resulting in painful and cumbersome joint motion. Temperature is a fundamental quantity in mechanics, yet the effects of temperature on cartilage mechanical behavior are unknown. This study addressed the questions of whether cartilage stiffness and stress relaxation change with temperature. Samples of middle-zone bovine calf patellofemoral cartilage were tested in unconfined compression first at 24°C and then again after heating to 60°C. The data reveal that when temperature increases: (1) both peak and equilibrium stiffness increase by 150 and 8%, respectively, and (2) stress relaxation is faster at higher temperature, as shown by a 60% decrease in the time constant. The increases in temperature-dependent stiffness are consistent with polymeric mechanisms of matrix viscoelasticity but not with interstitial fluid flow. The changes in the time constant are consistent with a combination of both fluid flow and matrix viscoelasticity. Furthermore, we discovered a novel phenomenon: at stress-relaxation equilibrium, compressive stress increased with temperature. These data demonstrate a rich area of cartilage mechanics that has previously been unexplored and emphasize the role of polymer dynamics in cartilage viscoelasticity. Further studies of cartilage polymer dynamics may yield additional insight into mechanisms of cartilage material behavior that could improve treatments for cartilage degeneration.

Molecular NMR T2 values can predict cartilage stress-relaxation parameters

Articular cartilage lines synovial joints and functions as a low-friction deformable tissue to enable smooth and stable joint articulation. The objective of this study was to determine the relationships between cartilage stress-relaxation properties and the collagen and GAG NMR transverse relaxation times ( T 2) toward understanding mechanisms of cartilage viscoelasticity. Stress-relaxation tests were performed on both cultured and enzymatically digested bovine cartilage, followed by measurements of both the collagen and GAG T 2 using the Call–Purcell–Meiboom–Gill pulse sequence. The peak and equilibrium stresses were correlated with the GAG T 2, and the stress-relaxation time constant was correlated with the collagen T 2. Multiple linear regression models were successful in using the specific T 2 values to predict the stress-relaxation properties. As a model of osteoarthritis, enzymatic digestion with collagenase and testicular hyaluronidase had weak effects on T 2 values. These data present a complex picture of cartilage mechanical behavior, with cartilage stiffness associated with the GAG T 2 values and the stress-relaxation time constant associated with the collagen T 2.

Thermoforming of tracheal cartilage: Viability, shape change, and mechanical behavior

Trauma, emergent tracheostomy, and prolonged intubation are common causes of severe deformation and narrowing of the trachea. Laser technology may be used to reshape tracheal cartilage using minimally invasive methods. The objectives of this study were to determine: (1) the dependence of tracheal cartilage shape change on temperature and laser dosimetry using heated saline bath immersion and laser irradiation, respectively, (2) the effect of temperature on the mechanical behavior of cartilage, and (3) tissue viability as a function of laser dosimetry. Ex vivo rabbit trachea cartilage specimens were bent and secured around a cylinder (6 mm), and then immersed in a saline bath (45 and 72 degrees C) for 5-100 seconds. In separate experiments, tracheal specimens were irradiated with a diode laser (lambda = 1.45 microm, 220-400 J/cm(2)). Mechanical analysis was then used to determine the elastic modulus in tension after irradiation. Fluorescent viability assays combined with laser scanning confocal microscopy (LSCM) were employed to image and identify thermal injury regions. Shape change transition zones, between 62 and 66 degrees C in the saline heating bath and above power densities of 350 J/cm(2) (peak temperatures 65+/-10 degrees C) for laser irradiation were identified. Above these zones, the elastic moduli were higher (8.2+/-4 MPa) than at lower temperatures (4.5+/-3 MPa). LSCM identified significant loss of viable chondrocytes within the laser-irradiation zones. Our results indicate a change in mechanical properties occurs with laser irradiation and further demonstrates that significant thermal damage is concurrent with clinically relevant shape change in the elastic cartilage tissues of the rabbit trachea using the present laser and dosimetry parameters.

Microstructural Modeling of Collagen Network Mechanics and Interactions with the Proteoglycan Gel in Articular Cartilage

Cartilage matrix mechanical function is largely determined by interactions between the collagen fibrillar network and the proteoglycan gel. Although the molecular physics of these matrix constituents have been characterized and modern imaging methods are capable of localized measurement of molecular densities and orientation distributions, theoretical tools for using this information for prediction of cartilage mechanical behavior are lacking. We introduce a means to model collagen network contributions to cartilage mechanics based upon accessible microstructural information (fibril density and orientation distributions) and which self-consistently follows changes in microstructural geometry with matrix deformations. The interplay between the molecular physics of the collagen network and the proteoglycan gel is scaled up to determine matrix material properties, with features such as collagen fibril pre-stress in free-swelling cartilage emerging naturally and without introduction of ad hoc parameters. Methods are developed for theoretical treatment of the collagen network as a continuum-like distribution of fibrils, such that mechanical analysis of the network may be simplified by consideration of the spherical harmonic components of functions of the fibril orientation, strain, and stress distributions. Expressions for the collagen network contributions to matrix stress and stiffness tensors are derived, illustrating that only spherical harmonic components of orders 0 and 2 contribute to the stress, while orders 0, 2, and 4 contribute to the stiffness. Depth- and compression-dependent equilibrium mechanical properties of cartilage matrix are modeled, and advantages of the approach are illustrated by exploration of orientation and strain distributions of collagen fibrils in compressed cartilage. Results highlight collagen-proteoglycan interactions, especially for very small physiological strains where experimental data are relatively sparse. These methods for determining matrix mechanical properties from measurable quantities at the microscale (composition, structure, and molecular physics) may be useful for investigating cartilage structure-function relationships relevant to load-bearing, injury, and repair.

Depth-dependent Compressive Equilibrium Properties of Articular Cartilage Explained by its Composition

For this study, we hypothesized that the depth-dependent compressive equilibrium properties of articular cartilage are the inherent consequence of its depth-dependent composition, and not the result of depth-dependent material properties. To test this hypothesis, our recently developed fibril-reinforced poroviscoelastic swelling model was expanded to include the influence of intra- and extra-fibrillar water content, and the influence of the solid fraction on the compressive properties of the tissue. With this model, the depth-dependent compressive equilibrium properties of articular cartilage were determined, and compared with experimental data from the literature. The typical depth-dependent behavior of articular cartilage was predicted by this model. The effective aggregate modulus was highly strain-dependent. It decreased with increasing strain for low strains, and increases with increasing strain for high strains. This effect was more pronounced with increasing distance from the articular surface. The main insight from this study is that the depth-dependent material behavior of articular cartilage can be obtained from its depth-dependent composition only. This eliminates the need for the assumption that the material properties of the different constituents themselves vary with depth. Such insights are important for understanding cartilage mechanical behavior, cartilage damage mechanisms and tissue engineering studies.

Mechanical modulation of cartilage structure and function during embryogenesis in the chick.

The mechanical behavior of cartilage is intimately related to its biochemical composition, and tissue composition is known to be influenced by its local mechanical loading environment. Although this phenomenon has been well-studied in adult cartilage, few investigations have examined such structure-function relationships in embryonic cartilage. The goal of this work was to elucidate the role of mechanical loading on the development of cartilage composition during embryogenesis. Using an embryonic chick model, cartilage from the tibiofemoral joints of immobilized embryos was compared to that of controls. The normal time course of changes in glycosaminoglycan/DNA and hydroxyproline/DNA were significantly influenced by loading history, with the most pronounced effects observed between days 9 and 14 during the period of most rapid increase in motility in control embryos. Stress-relaxation tests conducted on samples from day 14 indicate that the effects of embryonic immobilization on cartilage matrix composition have direct consequences for the mechanical behavior of the tissue, resulting in compromised material properties (e.g. 50% reduction in E(inst)). Because embryogenesis provides a unique model for identifying key factors which influence the establishment of functional biomechanical tissues in the skeleton, these data suggest that treating mechanical loading as an in vitro culture variable for tissue engineering approaches to cartilage repair is likely to be a sound approach.

Measurement of the elastic modulus of rabbit nasal septal cartilage during Nd:YAG (lambda = 1.32 microm) laser irradiation.

The objective of this study was to quantitatively measure changes in the elastic moduli of rabbit nasal septal cartilage during laser heating. While the efficacy of laser cartilage reshaping has been established for use in nasal surgery, few studies have investigated the temperature-dependent viscoelastic behavior of cartilage. Cyclic force versus displacement curves were generated during the Nd:YAG laser (lambda = 1.32 microm, 10 second exposure time, 21.22 W/cm2) irradiation of cartilage specimens secured in cantilevered geometry. Samples were irradiated three times with 30 second cooling intervals between each laser exposure. Measurements were recorded before, during, and after laser irradiation, and then following complete rehydration in normal saline (NS) for 1 hour at 25 degrees C. Elastic modulus was calculated assuming linear viscoelastic behavior. The elastic modulus in native tissue decreased during and after successive laser exposures from about 6 to 3.5 MPa. After rehydration, the modulus returned to near-baseline value. Surface temperature reached a maximum of 65 degrees C. The laser irradiation of cartilage using parameters similar to those used in reshaping does not produce significant irreversible changes in the mechanical properties of the tissue. Measurement of the elastic modulus is an effective means of characterizing alterations in cartilage mechanical behavior during and after laser heating.

Finite element simulation of location- and time-dependent mechanical behavior of chondrocytes in unconfined compression tests.

Experimental evidence suggests that cells are extremely sensitive to their mechanical environment and react directly to mechanical stimuli. At present, it is technically difficult to measure fluid pressure, stress, and strain in cells, and to determine the time-dependent deformation of chondrocytes. For this reason, there are no data in the published literature that show the dynamic behavior of chondrocytes in articular cartilage. Similarly, the dynamic chondrocyte mechanics have not been calculated using theoretical models that account for the influence of cell volumetric fraction on cartilage mechanical properties. In the present investigation, the location- and time-dependent stress-strain state and fluid pressure distribution in chondrocytes in unconfined compression tests were simulated numerically using a finite element method. The technique involved two basic steps: first, cartilage was approximated as a macroscopically homogenized material and the mechanical behavior of cartilage was obtained using the homogenized model; second, the solution of the time-dependent displacements and fluid pressure fields of the homogenized model was used as the time-dependent boundary conditions for a microscopic submodel to obtain average location- and time-dependent mechanical behavior of cells. Cells and extracellular matrix were assumed to be biphasic materials composed of a fluid phase and a hyperelastic solid phase. The hydraulic permeability was assumed to be deformation dependent and the analysis was performed using a finite deformation approach. Numerical tests were made using configurations similar to those of experiments described in the literature. Our simulations show that the mechanical response of chondrocytes to cartilage loading depends on time, fluid boundary conditions, and the locations of the cells within the specimen. The present results are the first to suggest that chondrocyte deformation in a stress-relaxation type test may exceed the imposed system deformation by a factor of 3-4, that chondrocyte deformations are highly dynamic and do not reach a steady state within about 20 min of steady compression (in an unconfined test), and that cell deformations are very much location dependent.

Muscle-ligament interactions at the human knee (II)

In part I of this paper, a three-dimensional model of the human knee joint was incorporated into a detailed human musculoskeletal lower extremity model. The model was used to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans extend/flex in an isometric state. Part II investigates the sensitivity of the model calculations to changes in the parameters which describe the mechanical behavior of cartilage and the ligaments of the knee. The ligament function in the real knee was most sensitive to changes in ligament reference lengths or strains, less sensitive to changes in cartilage stiffness, and least sensitive to changes in ligament stiffness.

Compressive behavior of articular cartilage is not completely explained by proteoglycan osmotic pressure

It has been hypothesized that applied mechanical or osmotic loads which decrease cartilage volume by 5% or more are sufficient to relieve all collagen tensile forces, and that further changes in the applied load are completely supported by changes in proteoglycan osmotic pressure. In thisview, cartilage should behave mechanically like a concentrated solution of proteoglycans. We tested this hypothesis by measuring the equilibrium axial and radial stresses in bovine articular cartilage during uniaxial confined compression. If the hypothesis is correct, the observed changes in the radial and axial stresses in confined compression should be equal for compression greater than 5%. However, the observed change in axial stress was always substantially greater than the change in radial stress over the range of strains (5–26%) and saline concentrations (0.05–0.15 M) tested. This indicates that the mechanical behavior of cartilage in confined compression cannot solely be explained by changes in proteoglycan osmotic pressure even for strains as large as 26%. A linear isotropic model was found to describe the observed equilibrium behavior adequately. In addition, the inferred shear modulus was found to be independent of saline concentration and similar to measurements by others of the flow-independent shear modulus. Our results have implications regarding the relative contribution of the proteoglycans and collagen to the mechanical properties of the tissue in compression, and suggest that tensile forces in the collagen network may play an important role in determining tissue behavior in confined compression even for relatively large volume changes.

Load partitioning influences the mechanical response of articular cartilage.

The role of the fluid within articular cartilage as affected by the load-sharing mechanism and its potential, beneficial effects were assessed with the u-p finite element method. The mechanical behavior of cartilage as it covers the surface of a diarthrodial joint was evaluated when the partitioning of an applied stress to the solid and fluid phases of the tissue was varied. Comparisons were made in the response of the cartilage when 0%, 25%, 50%, or 75% of the applied stress was supported by the fluid at the surface. Substantial changes in the behavior of the tissue were observed for each load case. As the fluid sustained a larger portion of the applied stress, several parameters were affected; the fluid pressure within the cartilage layer remained at a higher value, the stress and strain generated in the solid matrix decreased while the compression of the cartilage layer decreased. These findings indicate that an increased load-partitioning to the fluid phase in cartilage may perform the function of shielding the solid matrix from excessive stresses. This could also potentially alter the mechanical environment around the chondrocytes, influencing metabolic activity and homeostasis.