Rate-dependent crack nucleation in cartilage under microindentation

Poroviscoelastic relaxations and rate-dependent adhesion in gelatin

Hydrogels, polymeric networks swollen with water, exhibit time/rate-dependent adhesion due to their poroviscoleastic constitution. In this study, we conducted probe-tack experiments on gelatin and investigated the influence of dwelling times and unloading rates on pull-off forces and work of adhesion. We utilized in situ contact imaging to monitor separation kinematics and interfacial crack velocities. We found that the crack velocities scaled nonlinearly with the unloading rate, in a power law with an exponent of 0.8 and were independent of dwelling time. At maximum unloading rates corresponding to subsonic interfacial crack speeds, we observed an order of magnitude enhancement in the apparent work of adhesion. The enhancement of adhesion and the crack velocities were related by a power law with an exponent of 0.39. The maximum vertical extension during unloading, a measure of crack opening, exhibited linear correlation with the enhancement of adhesion. Both correlations were in line with the rate-dependent work of fracture modeled for viscoelastic solids (e.g., Persson and Brener model). We explored the links between dwelling times corresponding to varying degrees of poroelastic diffusion and the adhesion. We found 40% additional enhancement in adhesion at the highest unloading rate. This enhancement is due to the unbalanced osmotic pressure, also known as the suction effect. The influence of dwelling times on adhesion was negligible for the interfacial cracks propagating slower than the diffusive time scales. These results identify viscoelastic relaxations as the dominant mechanism governing the rate-dependent enhancement of adhesion, and hence pave the way for tuning rate-dependent adhesion in soft multiphasic materials.

Failure in articular cartilage: Finite element predictions of stress, strain, and pressure under micro-indentation induced fracture

Articular cartilage is found at the distal end of long bones and is responsible for assisting in joint articulation. While articular cartilage has remarkable resistance to failure, once initially damaged, degeneration is nearly irreversible. Thus, understanding damage initiation is important. There are a few proposed mechanisms for articular cartilage failure initiation: (A) a single collagen fibril stress-based regime; (B) a rate-dependent regime captured by brittle failure at slow displacement rates (SDR) and ductile failure at fast displacement rates (FDR); and (C) a rate-dependent regime where failure is governed by pressurization fragmentation at SDR and governed by strain at FDR. The objective of this study was to use finite element (FE) models to provide evidence to support or refute these proposed failure mechanisms. Models were developed of microfracture experiments that investigated osmolarity (hypo-osmolar, normal osmolarity, and hyper-osmolar) and displacement rate (FDR and SDR) effects. Cartilage was modeled with a neo-Hookean ground matrix, strain-dependent permeability, nonlinear fibril reinforcement with viscoelastic fibril terms, and Donnan equilibrium swelling. Total stress, solid matrix stress, Lagrange strain, and fluid pressure were determined under the indenter tip at the moment of microfracture. Results indicated significant rate dependence across multiple outputs, which does not support (A) a single failure regime. Larger solid and fluid pressures at FDR than SDR did not support (C) a rate-dependent regime split by pressurization at SDR and strain at FDR. Consistent solid shear stresses at SDR and consistent third principal solid stresses at FDR support (B) the ductile-brittle failure regime. These findings help to shed light on the underlying mechanisms of articular cartilage failure, which have implications for the development of osteoarthritis.

Instrumented nanoindentation in musculoskeletal research

Musculoskeletal tissues, such as bone, cartilage, and muscle, are natural composite materials that are constructed with a hierarchical structure ranging from the cell to tissue level. The component differences and structural complexity, together, require comprehensive multiscale mechanical characterization. In this review, we focus on nanoindentation testing, which is used for nanometer to sub-micrometer length scale mechanical characterization. In the following context, we will summarize studies of nanoindentation in musculoskeletal research, examine the critical factors that affect nanoindentation testing results, and briefly summarize other commonly used techniques that can be conjoined with nanoindentation for synchronized imaging and colocalized characterization.

Effect of osmolarity and displacement rate on cartilage microfracture clusters failure into two regimes

Articular cartilage is a poroviscoelastic (PVE) material with remarkable resistance to fracture and fatigue failure. Cartilage failure mechanisms and material properties that govern failure are incompletely understood. Because cartilage is partially comprised of negatively charged glycosaminoglycans, altering solvent osmolarity can influence PVE relaxations. Therefore, this study aims to use osmolarity as a tool to provide additional data to interpret the role of PVE relaxations and identify cartilage failure regimes. Cartilage fracture was induced using a 100 μm radius spheroconical indenter at controlled displacement rates under three different osmolarity solvents. Secondarily, contact pressure (CP) and strain energy density (SED) were estimated to cluster data into two failure regimes with an expectation maximization algorithm. Critical displacement, critical load, critical time, and critical work to fracture increased with increasing osmolarity at a slow displacement rate whereas no significant effect was observed at a fast displacement rate. Clustering provided two distinct failure regimes, with regime (I) at lower normalized thickness (contact radius divided by sample thickness), and regime (II) at higher normalized thickness. Varied CP and SED in regime (I) suggest that failure in the regime is strain-governed. Constant CP and SED in regime (II) suggests that failure in the regime is dominantly governed by stress. These regimes can be interpreted as ductile versus brittle, or using a pressurized fragmentation interpretation. These findings demonstrated fundamental failure properties and postulate failure regimes for articular cartilage.

The intrinsic quality of proteoglycans, but not collagen fibres, degrades in osteoarthritic cartilage

The function of articular cartilage as a load-bearing connective tissue is derived primarily from a balanced interaction between the swelling proteoglycan (PG) matrix and tension-resistant collagen fibrous network. Such balance is compromised during joint disease such as osteoarthritis (OA) due to degradation to PGs and/or collagens. While the PG degradation is generally thought to be related to a loss of protein abundance, the collagenous degradation is more complex as it can be caused independently by a decrease of collagen content, disorganisation of fibrous structure and softening of individual collagen fibrils. A comprehensive understanding of the initial trajectories of degradation of PGs and collagen network can improve our chance of finding potential therapeutic solutions for OA. Here, we developed geometrically, structurally, and compositionally realistic and sample-specific Finite Element (FE) models under the framework of multiphasic mixture theory, from which the elastic moduli of collagen fibres and the PG load-bearing quality in healthy and diseased cartilages were estimated by numerical optimisation of the multi-step indentation stress relaxation force-time curves. We found the intrinsic quality of collagen fibres, measured by their elastic moduli, to stay constant for healthy and diseased cartilages. Combining with previous findings which show unaltered collagen content during early stages of OA, our results suggest the disorganisation of collagen fibrous network as the first form of collagenous degradation in osteoarthritic cartilage. We also found that PG degradation involves not only a loss of protein abundance, but also the quality of the remaining PGs in generating sufficient osmotic pressure for load bearing. This study sheds light on the mechanism of OA pathogenesis and highlights the restoration of collageneous organisation in cartilage as key medical intervention for OA. STATEMENT OF SIGNIFICANCE: Collagen network in articular cartilage consists of individual fibres that are organised into depth-dependent structure specialised for joint load-bearing and lubrication. During osteoarthritis, the collagen network undergoes mechanical degradation, but it is unclear if a loss of content, disorganisation of fibrous structure, or softening of individual fibres causes this degeneration. Using mechanical indentation, Finite Element modelling, and numerical optimisation methods, we determined that individual fibres did not soften in early disease stage. Together with previous findings showing unaltered collagen content, our results pinpoint the disorganisation of collagen structure as the main culprit for early collagenous degradation in osteoarthritic cartilage. Thus, early restoration in cartilage of collagen organisation, instead of individual fibre quality, may be key to slow osteoarthritis development.

Early impairment of cartilage poroelastic properties in an animal model of ACL tear

BACKGROUND

In more than 50% of cases, anterior cruciate ligament (ACL) lesions lead to post-traumatic osteoarthritis. Ligament reconstruction stabilizes the joint, but the tear seems to impair the poroelasticity of the cartilage: synovial membrane fluid inflammation is observed 3 weeks after tearing. There have been some descriptions of visible cartilage changes, but poroelasticity has never been analyzed at this early stage. The present animal study aimed to determine (1) whether cartilage showed early poroelastic deterioration after ACL tear; (2) whether an impairment correlated with macroscopic changes; and (3) whether cartilage poroelasticity deteriorated over time.

HYPOTHESIS

In the days following trauma, cartilage poroelasticity is greatly impaired, without macroscopically visible change.

MATERIAL AND METHODS

ACL tear was surgically induced in 18 New-Zealand rabbits. Cartilage poroelasticity was assessed on indentation-relaxation test in 3 groups: "early", at 2 weeks postoperatively (n=6), "mid-early" at 6 weeks (n=6) and in a non-operated control group ("non-op"). Macroscopic changes were scored in the same groups.

RESULTS

Poroelastic impairment was greatest at the early time-point (2 weeks). Permeability ranged from a mean 0.08±0.05×10^-15 m⁴/Ns (range, 0.028-0.17) in the "non-op" group to 1.03±0.60×10^-15 m⁴/Ns (range, 0.24-2.15) in the "early" group (p=0.007). Shear modulus ranged from 0.53±0.11MPa (range, 0.36-0.66) to 0.23±0.10MPa (range, 0.12-0.43), respectively (p=0.013). Macroscopic deterioration, on the other hand, differed significantly only between the "mid-early" and the "non-op" groups: p=0.011 for cartilage deterioration and p=0.008 for osteophyte formation. At the "mid-early" time point, poroelastic deterioration was less marked, with 0.33±0.33×10^-15 m⁴/Ns permeability (range, 0.06-1.06) and shear modulus 0.30±0.10MPa (range, 0.13-0.41: respectively p=0.039 and p=0.023 compared to the "non-op" group.

DISCUSSION

The severe rapid deterioration in poroelasticity following ACL tear in an animal model, as notably seen in increased permeability, corresponds to changes in cartilage microstructure, with easier outflows of interstitial fluid. This mechanical degradation may underlie onset of microcracks within the cartilage, leading to physiological loading that the cartilage by its nature is unable to repair. Further investigations are needed to correlate these experimental data with clinical findings.

LEVEL OF EVIDENCE

III; comparative study with control group.

Effects of solvent osmolarity and viscosity on cartilage energy dissipation under high-frequency loading

Articular cartilage is a spatially heterogeneous, dissipative biological hydrogel with a high fluid volume fraction. Although energy dissipation is important in the context of delaying cartilage damage, the dynamic behavior of articular cartilage equilibrated in media of varied osmolarity and viscosity is not widely understood. This study investigated the mechanical behaviors of cartilage when equilibrated to media of varying osmolarity and viscosity. Dynamic moduli and phase shift were measured at both low (1 Hz) and high (75-300 Hz) frequency, with cartilage samples compressed to varied offset strain levels. Increasing solution osmolarity and viscosity both independently resulted in larger energy dissipation and decreased dynamic modulus of cartilage at both low and high frequency. Mechanical property alterations induced by varying osmolarity are likely due to the change in permeability and fluid volume fraction within the tissue. The effects of solution viscosity are likely due to frictional interactions at the solid-fluid interface, affecting energy dissipation. These findings highlight the significance of interstitial fluid on the energy dissipation capabilities of the tissue, which can influence the onset of cartilage damage.

Microindentation Technique to Create Localized Cartilage Microfractures

Articular cartilage is a multiphasic, anisotropic, and heterogeneous material. Although cartilage possesses excellent mechanical and biological properties, it can undergo mechanical damage, resulting in osteoarthritis. Thus, it is important to understand the microscale failure behavior of cartilage in both basic science and clinical contexts. Determining cartilage failure behavior and mechanisms provides insight for improving treatment strategies to delay osteoarthritis initiation or progression and can also enhance the value of cartilage as bioinspiration for material fabrication. To investigate microscale failure behavior, we developed a protocol to initiate fractures by applying a microindentation technique using a well-defined tip geometry that creates localized cracks across a range of loading rates. The protocol includes extracting the tissue from the joint, preparing samples, and microfracture. Various aspects of the experiment, such as loading profile and solvent, can be adjusted to mimic physiological or pathological conditions and thereby further clarify phenomena underlying articular cartilage failure. © 2021 Wiley Periodicals LLC. Basic Protocol 1: Harvesting and dissection of the joint surfaces Basic Protocol 2: Preparation of samples for microindentation and fatigue testing Basic Protocol 3: Microfracture using microindentation Basic Protocol 4: Crack propagation under cyclic loading.

Relaxation capacity of cartilage is a critical factor in rate- and integrity-dependent fracture

Articular cartilage heals poorly but experiences mechanically induced damage across a broad range of loading rates and matrix integrity. Because loading rates and matrix integrity affect cartilage mechanical responses due to poroviscoelastic relaxation mechanisms, their effects on cartilage failure are important for assessing and preventing failure. This paper investigated rate- and integrity-dependent crack nucleation in cartilage from pre- to post-relaxation timescales. Rate-dependent crack nucleation and relaxation responses were obtained as a function of matrix integrity through microindentation. Total work for crack nucleation increased with decreased matrix integrity, and with decreased loading rates. Critical energy release rate of intact cartilage was estimated as 2.39 ± 1.39 to 2.48 ± 1.26 kJ m-2 in a pre-relaxation timescale. These findings showed that crack nucleation is delayed when cartilage can accommodate localized loading through poroviscoelastic relaxation mechanisms before fracture at a given loading rate and integrity state.

Bi-component T2 mapping correlates with articular cartilage material properties

Non-invasive estimation of cartilage material properties is useful for understanding cartilage health and creating subject-specific computational models. Bi-component T2 mapping measured using Multi-Component Driven Equilibrium Single Shot Observation of T₁ and T₂ (mcDESPOT) is sensitive for detecting cartilage degeneration within the human knee joint, but has not been correlated with cartilage composition and mechanical properties. Therefore, the purpose of this study was to investigate the relationship between bi-component T₂ parameters measured using mcDESPOT at 3.0 T and cartilage composition and mechanical properties. Ex-vivo patellar cartilage specimens harvested from five human cadaveric knees were imaged using mcDESPOT at 3.0 T. Cartilage samples were removed from the patellae, mechanically tested to determine linear modulus and dissipated energy, and chemically tested to determine proteoglycan and collagen content. Parameter maps of single-component T₂ relaxation time (T₂), the T₂ relaxation times of the fast relaxing macromolecular bound water component (T_2F) and slow relaxing bulk water component (T_2S), and the fraction of the fast relaxing macromolecular bound water component (F_F) were compared to mechanical and chemical measures using linear regression. F_F was significantly (p < 0.05) correlated with energy dissipation and linear modulus. T₂ was significantly (p ≤ 0.05) correlated with elastic modulus at 1 Hz and energy dissipated at all frequencies. There were no other significant (p = 0.13-0.97) correlations between mcDESPOT parameters and mechanical properties. F_F was significantly (p = 0.04) correlated with proteoglycan content. There were no other significant (p = 0.19-0.92) correlations between mcDESPOT parameters and proteoglycan or collagen content. This study suggests that F_F measured using mcDESPOT at 3.0 T could be used to non-invasively estimate cartilage proteoglycan content, elastic modulus, and energy dissipation.

Effect of collagen fibril distributions on the crack profile in articular cartilage

BACKGROUND AND OBJECTIVE

Cartilage cracks and fissures may occur due to certain daily life activities such as sports practice, blunt trauma, and matrix fibrillation during early osteoarthritis. These cracks could further grow at the macroscopic level, alter the load distribution pattern in the matrix, limit the joint range of motion, and disturb chondrocytes synthesis. Cracks' shape and deformations in the loaded cartilage may affect the subsequent mechanobiological processes in the long term, likely because of the altered fluid exchange and excessive local deformations in the vicinity of the damage site. The fibrillar structure of the cartilage matrix appeared to have a protective effect against excessive deformations and tissue failure. Hence, in the present study, a fibril reinforced biphasic cartilage model was used to assess the potential role of different fibril orientations on the profile of a vertical crack in cartilage after applying a compressive load.

METHODS

A 20 × 20 × 1.5 mm³ cartilage model was developed with a 0.7 mm length V-shape cut at the center. Using an impermeable indenter, a 27% compression was applied to immature, mature, and isotropic cartilage models. Each of immature and mature groups had 4 different split line directions with respect to the cut edges, including 90°, 45°, 0°, and random orientation. The latter represented the disrupted collagen fibril orientations in early osteoarthritis. The model was verified with the experimental results in the literature.

RESULTS

In the superficial zones, the larger angle between the split lines and cut edges resulted in a wider cut opening. In the absence of collagen fibrils, the isotropic model resulted in a closed edge profile. Also, under a consistently applied compression, the OA model, with random collagen fibril distribution on its surface, had the smallest load-bearing capacity compared to the other models.

CONCLUSIONS

Findings highlighted a primary role of collagen fibrils on the cut profile, which was more pronounced at dynamic rather than static conditions. Split lines perpendicular to the cut edges had some protective effects against the large dislocation of cut edges. These findings could be utilized to develop engineered tissues less susceptible to rupture. Moreover, the outcome of the present study can explain the potential causes of the crack propagation path reported in the literature.

Glycosaminoglycan depletion increases energy dissipation in articular cartilage under high-frequency loading

High-frequency material behavior of cartilage at macroscopic lengths is not widely understood, despite a wide range of frequencies and contact lengths experienced in vivo. For example, cartilage at different stages of matrix integrity can experience high-frequency loading during traumatic impact, making high-frequency behavior relevant in the context of structural failure. Therefore, this study examined macroscopic dissipative and mechanical responses of intact and glycosaminoglycan (GAG)-depleted cartilage under previously unexplored high-frequency loading. These dynamic responses were complemented with the evaluation of quasi-static responses. A custom dynamic mechanical analyzer was used to obtain dynamic behavior, and stress relaxation testing was performed to obtain quasi-static behavior. Under high-frequency loading, cartilage energy dissipation increased with GAG depletion and decreased with strain; dynamic modulus exhibited opposite trends. Similarly, under quasi-static loading, equilibrium modulus and relaxation time of cartilage decreased with GAG depletion. The increased energy dissipation after GAG depletion under high-frequency loading was likely due to increased viscoelastic dissipation. These findings broaden our understanding of fundamental properties of cartilage as a function of solid matrix integrity in an unprecedented loading regime. They also provide a foundation for analyzing energy dissipation associated with cartilage failure induced by traumatic impact.

Rate-dependent adhesion of cartilage and its relation to relaxation mechanisms

Cartilage adhesion has been found to play an important role in friction responses in the boundary lubrication regime, but its underlying mechanisms have only been partially understood. This study investigates the rate dependence of adhesion from pre-to post-relaxation timescales of cartilage and its possible relation to relaxation responses of the tissue. Adhesion tests on cartilage were performed to obtain rate-dependent cartilage adhesion from relaxed to unrelaxed states and corresponding relaxation responses. The rate dependence of cartilage adhesion was analyzed based on experimental relaxation responses. Cartilage adhesion increased about 20 times from relaxed to unrelaxed states. This rate-dependent enhancement correlated well with the load relaxation responses in a characteristic time domain. These experimental results indicated that the degree of recovery (or relaxation) in the vicinity of contact during unloading governed the rate dependence of cartilage adhesion. In addition, the experimentally measured enhancement of adhesion was interpreted with the aid of computationally and analytically predicted adhesion trends in viscoelastic, poroviscoelastic, and cohesive contact models. Agreement between the experimental and predicted trends implied that the enhancement of cartilage adhesion originated from complex combinations of interfacial peeling and negative fluid pressure generated within the contact area during unloading. These findings enhance the current understanding of rate-dependent adhesion mechanisms explored within short time scales and thus could provide new insight into friction responses and stick-induced damage in cartilage.