Effect of relaxation-dependent adhesion on pre-sliding response of cartilage

Adhesion-Lubrication Paradox of Articular Cartilage

The friction of solids is primarily understood through the adhesive interactions between the surfaces. As a result, slick materials tend to be nonstick (e.g., Teflon), and sticky materials tend to produce high friction (e.g., tires and tape). Paradoxically, cartilage, the slippery bearing material of human joints, is also among the stickiest of known materials. This study aims to elucidate this apparent paradox. Cartilage is a biphasic material, and the most cited explanation is that both friction and adhesion increase as load transfers from the pressurized interstitial fluid to the solid matrix over time. In other words, cartilage is slippery and sticky under different times and conditions. This study challenges this explanation, demonstrating the strong adhesion of cartilage under high and low interstitial hydration conditions. Additionally, we find that cartilage clings to itself (a porous material) and Teflon (a nonstick material), as well as other surfaces. We conclude that the unusually strong interfacial tension produced by cartilage reflects suction (like a clingfish) rather than adhesion (like a gecko). This finding is surprising given its unusually large roughness, which typically allows for easy interfacial flow and defeats suction. The results provide compelling evidence that cartilage, like a clingfish, conforms to opposing surfaces and effectively seals submerged contacts. Further, we argue that interfacial sealing is itself a critical function, enabling cartilage to retain hydration, load support, and lubrication across long periods of inactivity.

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.

Adhesion of fluid infused silicone elastomer to glass

Elastomers swollen with non-polar fluids show potential as anti-adhesive materials. We study the effect of oil fraction and contact time on the adhesion between swollen spherical probes of PDMS (polydimethylsiloxane) and flat glass surfaces. The PDMS probes are swollen with pre-determined amount of 10 cSt silicone oil to span the range where the PDMS is fluid free (via solvent extraction) up to the limit where it is oil saturated. Probe tack measurements show that adhesion decreases rapidly with an increase in oil fraction. The decrease in adhesion is attributed to excess oil present at the PDMS-air interface. Contact angle measurements and optical microscopy images support this observation. Adhesion also increases with contact time for a given oil fraction. The increase in adhesion with contact time can be interpreted through different competing mechanisms that depend on the oil fraction where the dominant mechanism changes from extracted to fully swollen PDMS. For partially swollen PDMS, we observe that adhesion initially increases because of viscoelastic relaxation and at long times increases because of contact aging. In contrast, adhesion between fully swollen PDMS and glass barely increases over time and is mainly due to capillary forces. While the relaxation of PDMS in contact is well-described by a visco-poroelastic model, we do not see evidence that poroelastic relaxation of the PDMS contributes to an increase of adhesion with glass whether it is partially or fully swollen.

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 of cartilage before and after articular loading in a bioreactor: assessment of length-scale dependency using two analysis methods

BACKGROUND

Microindentation is a technique with high sensitivity and spatial resolution, allowing for measurements at small-scale indentation depths. Various methods of indentation analysis to determine output properties exist.

OBJECTIVE

Here, the Oliver-Pharr Method and Hertzian Method were compared for stiffness analyses of articular cartilage at varying length-scales before and after bioreactor loading.

METHODS

Using three different conospherical tips with varying radii (20, 100, 793.75 μm), a bioreactor-indenter workflow was performed on cartilage explants to assess changes in stiffness due to articular loading. For all data, both the Oliver-Pharr Method and Hertzian Method were applied for indentation analysis.

RESULTS

The reduced moduli calculated by the Hertzian Method were found to be similar to those of the Oliver-Pharr Method when the 20 μm tip size was used. The reduced moduli calculated using the Hertzian Method were found to be consistent across the varying length-scales, whereas for the Oliver-Pharr Method, adhesion/suction led to the largest tip exhibiting an increased average reduced modulus compared to the two smaller tips. Loading induced stiffening of articular cartilage was observed consistently, regardless of tip size or indentation analysis applied.

CONCLUSIONS

Overall, geometric linearity is preserved across all tip sizes for the Hertzian Method and may be assumed for the two smaller tip sizes using the Oliver-Pharr Method. These findings further validate the previously described stiffening response of the superficial zone of cartilage after articular loading and demonstrate that the finding is length-scale independent.

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.

Transient sliding of thin hydrogel films: the role of poroelasticity

We report on the transient frictional response of contacts between a rigid spherical glass probe and a micrometer-thick poly(dimethylacrylamide) hydrogel film grafted onto a glass substrate when a lateral relative motion is applied to the contact initially at rest. From dedicated experiments with in situ contact visualization, both the friction force and the contact size are observed to vary well beyond the occurrence of a full sliding condition at the contact interface. Depending on the imposed velocity and on the static contact time before the motion is initiated, either an overshoot or an undershoot in the friction force is observed. These observations are rationalized by considering that the transient is predominantly driven by the flow of water within the stressed hydrogel networks. From the development of a poroelastic contact model using a thin film approximation, we provide a theoretical description of the main features of the transient. We especially justify the experimental observation that the relaxation of friction force Ft(t) toward steady state is uniquely dictated by the time-dependence of the contact radius a(t), independently on the sliding velocity and on the applied normal load.

Immature bovine cartilage wear by fatigue failure and delamination

This study investigated wear damage of immature bovine articular cartilage using reciprocal sliding of tibial cartilage strips against glass or cartilage. Experiments were conducted in physiological buffered saline (PBS) or mature bovine synovial fluid (SF). A total of 63 samples were tested, of which 47 exhibited wear damage due to delamination of the cartilage surface initiated in the middle zone, with no evidence of abrasive wear. There was no difference between the friction coefficient of damaged and undamaged samples, showing that delamination wear occurs even when friction remains low under a migrating contact area configuration. No difference was observed in the onset of damage or in the friction coefficient between samples tested in PBS or SF. The onset of damage occurred earlier when testing cartilage against glass versus cartilage against cartilage, supporting the hypothesis that delamination occurs due to fatigue failure of the collagen in the middle zone, since stiffer glass produces higher strains and tensile stresses under comparable loads. The findings of this study are novel because they establish that delamination of the articular surface, starting in the middle zone, may represent a primary mechanism of failure. Based on preliminary data, it is reasonable to hypothesize that delamination wear via subsurface fatigue failure is similarly the primary mechanism of human cartilage wear under normal loading conditions, albeit requiring far more cycles of loading than in immature bovine cartilage.

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.

Rate-dependent crack nucleation in cartilage under microindentation

This study investigates rate-dependent crack nucleation in cartilage under microindentation using a poroviscoelastic framework and nano/microscopic images. Localized crack failure was induced at known locations and at different loading rates via microindentation with an axisymmetric sphero-conical indenter. Finite element (FE) modeling was used to reproduce results of microindentation tests within a poroviscoelastic framework. Scanning electron microscopy (SEM) was used to examine nano- and microscale structural features of crack surfaces. Microindentation results showed rate-dependent crack nucleation in cartilage. In particular, critical total work required for crack nucleation was larger at the slow loading rate compared to the fast loading rate. FE results suggested that viscoelastic relaxation of cartilage was a major contributor to the rate dependency and that tensile stresses localized at the indenter tip was a governing factor in crack nucleation. SEM images combined with microindentation and FE results suggested that the solid matrix in the vicinity of the tip experienced relatively large relaxation and kinematic fiber rearrangement at the slow loading rate in comparison to the fast loading rate. These findings extend current understanding of rate-dependent failure mechanisms in cartilage.