Elastic, Dynamic Viscoelastic and Model-Derived Fibril-Reinforced Poroelastic Mechanical Properties of Normal and Osteoarthritic Human Femoral Condyle Cartilage

Confined and unconfined articular cartilage mechanics: Effect of creep duration on estimations of mechanical properties

Recent findings suggest that cartilage mechanical function may be a biomarker for early osteoarthritis (OA) pathology. Thus, the development of methodologies for in-vivo applications has expanded. However, when creep tests are performed, inconsistency in applied stress and testing duration impede meaningful comparisons. Therefore, this study investigates the impact of creep duration on cartilage mechanics through ex-vivo confined and unconfined compression experiments on healthy bovine cartilage samples (n = 20), subjected to 1 MPa stress for 5 h. A Zener model was fitted to unconfined data and a nonlinear biphasic model was fitted to confined data using durations ranging from 15 min to 5 h. Mechanical properties were compared against the full 5-h dataset to determine relative errors (RE) associated with insufficient creep duration. Based on our findings, we aim to establish a common ground for both in vivo and ex vivo environments. Both unconfined (R2 = 0.96 ± 0.02) and confined (R2 = 0.997 ± 0.003) models fitted the data well over 5 h. For confined creep tests, the aggregate modulus (HA) was 0.34 ± 0.12 MPa after 5 h and 0.27 ± 0.12 MPa after 1 h (RE ∼ 20 %), while initial permeability (k0) increased from 0.17 × 10-15 m4N-1s-1 to 0.56 × 10-15 m4N-1s-1 (RE ∼ 49 %). The Zener model estimated the initial (E1) and steady-state (E2) modulus to be 3.6 ± 0.7 MPa and 3.2 ± 0.3 MPa after 5 h, respectively. After 1 h, these values were 4.7 ± 1.0 MPa (RE ∼ 29 %) and 3.2 ± 0.3 MPa (RE ∼ 2 %). A larger RE (∼57 %) was observed for the relaxation time constant (τ) determined after 5 h (1688 ± 556 s) and 1 h (781 ± 170 s) with the Zener model. The benefit of extended creep duration diminished after 1-1.5 h for confined compression and 2 h for unconfined compression for non-rate dependent stiffness parameters (i.e., HA, E1, E2). This aligned well with the predefined equilibrium criteria of less than 0.6 μm/min, with equilibrium reached at 71 ± 23 min for confined experiments and 94 ± 25 min for unconfined experiments. In contrast, for parameters controlling the nonlinear material response (i.e., τ, k0,M), 4 h were required for unconfined compression and 1.5 h for confined compression to achieve RE ∼ 10 %. Thus, insufficient creeping duration resulted in large RE, especially for strain-dependent parameters. Therefore, it is recommended to use a clear equilibrium definition when conducting ex vivo experiments. In the context of clinically viable testing duration (i.e., 45-60 min) RE was ∼20 % for the predicted aggregate modulus and ∼10 % for the nonlinear permeability coefficient. While these errors appear substantial, they may still estimate cartilage mechanics within reasonable limits given the associated variability in healthy and OA cartilage characteristics. Therefore, within a limited timeframe, it could be possible to estimate mechanical properties using in vivo creep experiments that may serve as biomarkers for early OA.

Comparison of site-specific tensile, compressive, and friction properties of human tibiofemoral joint cartilage and their relationship to degeneration

Site-specific differences in the compressive properties of tibiofemoral joint articular cartilage are well-documented, while exploration of tensile and frictional properties in humans remains limited. Thus, this study aimed to characterize and compare the tensile, compressive and frictional properties of articular cartilage across different sites of the tibiofemoral joint, and to establish relationships between these properties and cartilage degeneration. We cut human tibiofemoral joint (N = 5) cartilage surfaces into tensile testing samples (n = 155) and osteochondral plugs (n = 40) to determine the tensile, friction and compressive properties, as well as OARSI grades. We performed comparisons between sites using a linear mixed model and analyzed relationships with OARSI grade using Spearman's rank correlation. Cartilage samples were mostly healthy: 56 % were grade 0 or 1, 26 % grade 2, and 18 % grade 3 or higher. In tension, the medial femur was more compliant and viscous compared to the lateral femur (p < 0.05). In compression, the lateral tibia exhibited a lower equilibrium modulus than both femoral condyles (p < 0.05), while the initial friction coefficient was higher in the medial tibia compared to both femoral condyles (p < 0.05). We found no significant correlation between tensile or friction properties and OARSI grade, while compressive properties deteriorated with increasing OARSI grade. The observed site-specific differences in cartilage properties in tension, compression, and friction, demonstrate adaptations to different loading experienced by the surfaces. The comprehensive set of properties presented in this study are valuable for improving future computational knee joint models and serving as a reference for tissue engineering and prosthetic implants.

Relationship between depth-wise refractive index and biomechanical properties of human articular cartilage

Significance

Optical properties of biological tissues, such as refractive index (RI), are fundamental properties, intrinsically linked to the tissue's composition and structure. We hypothesize that, as the RI and the functional properties of articular cartilage (AC) are dependent on the tissue's structure and composition, the RI of AC is related to its biomechanical properties.

Aim

This study aims to investigate the relationship between RI of human AC and its biomechanical properties.

Approach

Human cartilage samples ( n = 22 ) were extracted from the right knee joint of three cadaver donors (one female, aged 47 years, and two males, aged 64 and 68 years) obtained from a commercial biobank (Science Care, Phoenix, Arizona, United States). The samples were initially subjected to mechanical indentation testing to determine elastic [equilibrium modulus (EM) and instantaneous modulus (IM)] and dynamic [dynamic modulus (DM)] viscoelastic properties. An Abbemat 3200 automatic one-wavelength refractometer operating at 600 nm was used to measure the RI of the extracted sections. Similarly, Spearman's and Pearson's correlation coefficients were employed for non-normal and normal datasets, respectively, to determine the correlation between the depth-wise RI and biomechanical properties of the cartilage samples as a function of the collagen fibril orientation.

Results

A positive correlation with statistically significant relations ( p - values < 0.05 ) was observed between the RI and the biomechanical properties (EM, IM, and DM) along the tissue depth for each zone, e.g., superficial, middle, and deep zones. Likewise, a lower positive correlation with statistically significant relations ( p - values < 0.05 ) was also observed for collagen fibril orientation of all zones with the biomechanical properties.

Conclusions

The results indicate that, although the RI exhibits different levels of correlation with different biomechanical properties, the relationship varies as a function of the tissue depth. This knowledge paves the way for optically monitoring changes in AC biomechanical properties nondestructively via changes in the RI. Thus, the RI could be a potential biomarker for assessing the mechanical competency of AC, particularly in degenerative diseases, such as osteoarthritis.

Revealing Detailed Cartilage Function Through Nanoparticle Diffusion Imaging: A Computed Tomography & Finite Element Study

The ability of articular cartilage to withstand significant mechanical stresses during activities, such as walking or running, relies on its distinctive structure. Integrating detailed tissue properties into subject-specific biomechanical models is challenging due to the complexity of analyzing these characteristics. This limitation compromises the accuracy of models in replicating cartilage function and impacts predictive capabilities. To address this, methods revealing cartilage function at the constituent-specific level are essential. In this study, we demonstrated that computational modeling derived individual constituent-specific biomechanical properties could be predicted by a novel nanoparticle contrast-enhanced computer tomography (CECT) method. We imaged articular cartilage samples collected from the equine stifle joint (n = 60) using contrast-enhanced micro-computed tomography (µCECT) to determine contrast agents' intake within the samples, and compared those to cartilage functional properties, derived from a fibril-reinforced poroelastic finite element model. Two distinct imaging techniques were investigated: conventional energy-integrating µCECT employing a cationic tantalum oxide nanoparticle (Ta2O5-cNP) contrast agent and novel photon-counting µCECT utilizing a dual-contrast agent, comprising Ta2O5-cNP and neutral iodixanol. The results demonstrate the capacity to evaluate fibrillar and non-fibrillar functionality of cartilage, along with permeability-affected fluid flow in cartilage. This finding indicates the feasibility of incorporating these specific functional properties into biomechanical computational models, holding potential for personalized approaches to cartilage diagnostics and treatment.

Implications of using simplified finite element meshes to identify material parameters of articular cartilage

The objective of this work was to determine the effects of using simplified finite element (FE) mesh geometry in the process of performing reverse iterative fitting to estimate cartilage material parameters from in situ indentation testing. Six bovine tibial osteochondral explants were indented with sequential 5 % step-strains followed by a 600 s hold while relaxation force was measured. Three sets of porous viscohyperelastic material parameters were estimated for each specimen using reverse iterative fitting of the indentation test with (1) 2D axisymmetric, (2) 3D idealized, and (3) 3D specimen-specific FE meshes. Variable material parameters were identified using the three different meshes, and there were no systematic differences, correlation to basic geometric features, nor distinct patterns of variation based on the type of mesh used. Implementing the three material parameter sets in a separate 3D FE model of 40 % compressive strain produced differences in von Mises stresses and pore pressures up to 25 % and 50 %, respectively. Accurate material parameters are crucial in any FE model, and parameter differences influenced by idealized assumptions in initial material property determination have the potential to alter subsequent FE models in unpredictable ways and hinder the interpretation of their results.

Site-specific elastic and viscoelastic biomechanical properties of healthy and osteoarthritic human knee joint articular cartilage

Articular cartilage exhibits site-specific biomechanical properties. However, no study has comprehensively characterized site-specific cartilage properties from the same knee joints at different stages of osteoarthritis (OA). Cylindrical osteochondral explants (n = 381) were harvested from donor-matched lateral and medial tibia, lateral and medial femur, patella, and trochlea of cadaveric knees (N = 17). Indentation test was used to measure the elastic and viscoelastic mechanical properties of the samples, and Osteoarthritis Research Society International (OARSI) grading system was used to categorize the samples into normal (OARSI 0-1), early OA (OARSI 2-3), and advanced OA (OARSI 4-5) groups. OA-related changes in cartilage mechanical properties were site-specific. In the lateral and medial tibia and trochlea sites, equilibrium, instantaneous and dynamic moduli were higher (p < 0.001) in normal tissue than in early and advanced OA tissue. In lateral and medial femur, equilibrium, instantaneous and dynamic moduli were smaller in advanced OA, but not in early OA, than in normal tissue. The phase difference (0.1-0.25 Hz) between stress and strain was significantly smaller (p < 0.05) in advanced OA than in normal tissue across all sites except medial tibia. Our results indicated that in contrast to femoral and patellar cartilage, equilibrium, instantaneous and dynamic moduli of the tibia and trochlear cartilage decreased in early OA. These may suggest that the tibia and trochlear cartilage degrades faster than the femoral and patellar cartilage. The information is relevant for developing site-specific computational models and engineered cartilage constructs.

Triple contrast computed tomography reveals site-specific biomechanical differences in the human knee joint-A proof of concept study

Cartilage and synovial fluid are challenging to observe separately in native computed tomography (CT). We report the use of triple contrast agent (bismuth nanoparticles [BiNPs], CA4+, and gadoteridol) to image and segment cartilage in cadaveric knee joints with a clinical CT scanner. We hypothesize that BiNPs will remain in synovial fluid while the CA4+ and gadoteridol will diffuse into cartilage, allowing (1) segmentation of cartilage, and (2) evaluation of cartilage biomechanical properties based on contrast agent concentrations. To investigate these hypotheses, triple contrast agent was injected into both knee joints of a cadaver (N = 1), imaged with a clinical CT at multiple timepoints during the contrast agent diffusion. Knee joints were extracted, imaged with micro-CT (µCT), and biomechanical properties of the cartilage surface were determined by stress-relaxation mapping. Cartilage was segmented and contrast agent concentrations (CA4+ and gadoteridol) were compared with the biomechanical properties at multiple locations (n = 185). Spearman's correlation between cartilage thickness from clinical CT and reference µCT images verifies successful and reliable segmentation. CA4+ concentration is significantly higher in femoral than in tibial cartilage at 60 min and further timepoints, which corresponds to the higher Young's modulus observed in femoral cartilage. In this pilot study, we show that (1) large BiNPs do not diffuse into cartilage, facilitating straightforward segmentation of human knee joint cartilage in a clinical setting, and (2) CA4+ concentration in cartilage reflects the biomechanical differences between femoral and tibial cartilage. Thus, the triple contrast agent CT shows potential in cartilage morphology and condition estimation in clinical CT.

Sensitivity of simulated knee joint mechanics to selected human and bovine fibril-reinforced poroelastic material properties

Fibril-reinforced poroviscoelastic material models are considered state-of-the-art in modeling articular cartilage biomechanics. Yet, cartilage material parameters are often based on bovine tissue properties in computational knee joint models, although bovine properties are distinctly different from those of humans. Thus, we aimed to investigate how cartilage mechanical responses are affected in the knee joint model during walking when fibril-reinforced poroviscoelastic properties of cartilage are based on human data instead of bovine. We constructed a finite element knee joint model in which tibial and femoral cartilages were modeled as fibril-reinforced poroviscoelastic material using either human or bovine data. Joint loading was based on subject-specific gait data. The resulting mechanical responses of knee cartilage were compared between the knee joint models with human or bovine fibril-reinforced poroviscoelastic cartilage properties. Furthermore, we conducted a sensitivity analysis to determine which fibril-reinforced poroviscoelastic material parameters have the greatest impact on cartilage mechanical responses in the knee joint during walking. In general, bovine cartilage properties yielded greater maximum principal stresses and fluid pressures (both up to 30%) when compared to the human cartilage properties during the loading response in both femoral and tibial cartilage sites. Cartilage mechanical responses were very sensitive to the collagen fibril-related material parameter variations during walking while they were unresponsive to proteoglycan matrix or fluid flow-related material parameter variations. Taken together, human cartilage material properties should be accounted for when the goal is to compare absolute mechanical responses of knee joint cartilage as bovine material parameters lead to substantially different cartilage mechanical responses.

Is the mechanical function of meniscal tissue altered in osteoarthritic knees?

BACKGROUND

Deteriorating meniscal function is thought to play a role in knee osteoarthritis. Meniscal proteoglycans maintain mechanical stiffness of the tissue through electrostatic effects. This study aimed to investigate whether the mechanical properties of macroscopically intact meniscus are preserved in osteoarthritis.

METHODS

Discs of lateral meniscal tissue two millimetres thick and of five millimetres diameter from osteoarthritic knees and from healthy donors were placed within a confined compression chamber, mounted in a materials testing machine and bathed in isotonic 0.14M PBS, hypotonic deionised water or hypertonic 3M PBS. Following equilibrium, a 10% ramp compressive strain was applied followed by a 7200 second hold. Resultant stress relaxation curves were fitted to a nonlinear poroviscoelastic model with strain dependent permeability using finite element modelling to determine mechanical parameters. All samples were assayed for proteoglycan content. Comparison of results was undertaken using multivariate ANOVA.

RESULTS

Thirty samples from osteoarthritic knees and 18 samples from healthy donors were tested. No significant differences in mechanical parameters or proteoglycan content was observed between groups. In both groups Young's modulus (E) was significantly greater, and zero-strain permeability significantly reduced, in samples tested in deionised water compared to samples tested in 0.14M or 3M PBS (all p < 0.05).

CONCLUSION

Mechanical parameters of intact lateral meniscus in osteoarthritic knees are similar to those found in healthy knees. Proteoglycan concentration and their electrostatic contribution to mechanical stiffness of the meniscus is maintained in menisci derived from osteoarthritic knees. Whilst macroscopic tears in the meniscal ultrastructure may contribute to osteoarthritis, intact meniscal tissue maintains its function.

Topographical Characterization of the Young, Healthy Human Femoral Medial Condyle

OBJECTIVE

The medial femoral condyle of the knee exhibits some of the highest incidences of chondral degeneration. However, a dearth of healthy human tissues has rendered it difficult to ascertain whether cartilage in this compartment possesses properties that predispose it to injuries. Assessment of young, healthy tissue would be most representative of the tissue's intrinsic properties.

DESIGN

This work examined the topographical differences in tribological, tensile, and compressive properties of young (n = 5, 26.2 ± 5.6 years old), healthy, human medial femoral condyles, obtained from viable allograft specimens. Corresponding to clinical incidences of pathology, it was hypothesized that the lowest mechanical properties would be found in the posterior region of the medial condyle, and that tissue composition would correspond to the established structure-function relationships of cartilage.

RESULTS

Young's modulus, ultimate tensile strength, aggregate modulus, and shear modulus in the posterior region were 1.0-, 2.8-, 1.1-, and 1.0-fold less than the values in the anterior region, respectively. Surprisingly, although glycosaminoglycan content is thought to correlate with compressive properties, in this study, the aggregate and shear moduli correlated more robustly to the amount of pyridinoline crosslinks per collagen. Also, the coefficient of friction was anisotropic and ranged 0.22-0.26 throughout the condyle.

CONCLUSION

This work showed that the posteromedial condyle displays lower tensile and compressive properties, which correlate to collagen crosslinks and may play a role in this region's predisposition to injuries. Furthermore, new structure-function relationships may need to be developed to account for the role of collagen crosslinks in compressive properties.

Intraoperative Acoustic Evaluation of Living Human Knee Cartilage-Comparison with Respect to Cartilage Degeneration and Aging

OBJECTIVE

The objective of the study was to evaluate the mechanical properties of living human knee cartilage using our ultrasonic device, and to compare the measurements with respect to cartilage degeneration and aging.

DESIGN

A total of 95 knees which had undergone arthroscopic knee surgery, from 88 patients, were included in the study, with informed consent. All procedures were reviewed and approved by the ethical committee of our hospital. In the study group, there were 41 men, 47 women, 39 right knees, and 56 left knees. The conditions primarily included knee osteoarthritis and anterior cruciate ligament rupture. The mean operative age was 44.1 years old (range = 10-83). We compared mechanical properties of the knee cartilage with respect to aging and gender, in comparison with normal cartilage. A P value of <0.05 represented statistical significance.

RESULTS

In the context of the International Cartilage Repair Society (ICRS) classification of cartilage degeneration (grade 0-3), the signal intensity in grade 0 was significantly larger than that in grade 1, 2, or 3. The thickness in grade 0 was significantly higher than that in grade 1, 2, or 3. Normal cartilage in older women had the lowest signal intensity and the least cartilage thickness among all the groups.

CONCLUSION

The ultrasonic system we developed was able to detect early degenerative changes in living cartilage in knees. The lowest signal intensity and least cartilage thickness in normal cartilage among older women were correlated to a large prevalence of knee osteoarthritis in women.

LEVEL OF EVIDENCE

Level IV, case series.

Using a poroelastodynamic model to investigate the dynamic behaviour of articular cartilage

BACKGROUND AND OBJECTIVE

There is still a few studies about the poroelastic model that performed dynamic behaviour, especially for the case of the poroelastic cartilage model. Therefore, this study is aimed to use the poroelastodynamic model to simulate the dynamic behaviour of cartilage.

METHODS

The governing equations of the poroelastodynamic model is firstly established. The validation of the model is initialised by modifying the equations into the static poroelastic model. The modified equations are then discretised using the finite element method. Mandel's problem is used to validate the discretised equations. The numerical solution calculated using FreeFEM++ is validated with the analytical solution for the quasi-static state and compared with the results generated using COMSOL Multiphysics software. Finally, the quasi-static solution is compared with the dynamic solution to discuss the difference in pore pressure and displacement variations of the poroelastic cartilage model.

RESULTS

The dynamic solution showed transient behaviour at the beginning of the excitation. When the compressive force acts on the cartilage, there are obvious fluctuations during the initial stage and then the dynamic numerical solution gradually approaches the quasi-static value over a period of time. The deduced results of the analytical solution were approximately the same as the numerical simulation results.

CONCLUSION

This study was able to use the poroelastodynamics equation to simulate the dynamic behaviour of the poroelastic cartilage model. The comparison between the result coming from poroelastodynamics equation with that of the validated numerical solution was satisfactorily compared. The approximate similarity between the results of quasi-static and dynamic solutions underscored the importance of performing the dynamic solution for a more realistic simulation. This dynamic solution can be further used for the analysis of vibration or stress waves in future research.

Characterizing site-specific mechanical properties of knee cartilage with indentation-relaxation maps and machine learning

Knee cartilage experiences site-specific focal lesion and degeneration, which is likely associated with tissue inhomogeneity and nonuniform mechanical stimuli in the joint, for which a complete picture remains to be depicted. The present study aimed to develop a methodology to quantify knee cartilage inhomogeneity using porcine knee specimens. Automated indentation-relaxation and needle probing were performed on fully intact cartilage to obtain data that essentially represent continuous distributions of cartilage properties in the knee. Machine learning was then introduced to approximate the tissue inhomogeneity with several regions via clusters of indentation locations, and finite element modeling was used to obtain poromechanical properties for each region using indentation-relaxation and thickness data. Significant region dependence was established from the full time-dependent mechanical response. Seventeen regions, or clusters, were found to best approximate the site-specific poromechanical properties of articular cartilage for femoral groove, lateral and medial condyles and tibial plateaus, after up to eight clusters were tested for each of the five cartilage sections. The region partitions recommended, and tissue properties acquired would facilitate implementation of tissue inhomogeneity in future applications, e.g., contact modeling of the knee joint. The results obtained from 14 porcine knees revealed interesting region differences, for example, the two condyles have the same effective stiffness when responding to slowly applied mechanical loadings but substantially lower stiffness in the medial condyle when responding to fast loadings. This mechanical behavior may be associated with the fact that medial femoral cartilage is more prone to focal lesions than the lateral one.