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.

Articular cartilage is the soft tissue that lines contacting surfaces of bones in synovial joints. Cartilage functions as a low-friction-bearing surface to enable smooth articulation during joint motion (Wright and Dowson, 1976). The primary components of articular cartilage are chondrocytes and a polymeric extracellular matrix consisting mainly of collagen, the proteoglycan aggregate, water and cations (Mow et al., 1992).

Previous studies have examined cartilage material properties in response to various experimental perturbations including enzymatic digestion (Basalo et al., 2005; Bonassar et al., 1995; DiSilvestro and Suh, 2002; Zhu et al., 1993) and ionic concentration (Dean et al., 2006; June et al., 2009; Lu et al., 2004). Static properties of articular cartilage result at least partially from electrostatic interactions between anionic glycosaminoglycans (Dean et al., 2006; Lu et al., 2004; Lux Lu et al., 2007).

Temperature is a fundamental quantity in mechanics (Holzapfel, 2000). However, the effects of temperature on cartilage material properties have not been studied. A complete understanding of cartilage mechanics requires an understanding of the effects of temperature on cartilage material properties. Hence, the first objective of this study was to determine whether cartilage mechanical properties change with temperature.

Cartilage viscoelasticity may originate from both flow-dependent and flow-independent mechanisms (Huang et al., 2001; Huang et al., 2003; Mow et al., 1980). Flow-dependent viscoelasticity results from interstitial fluid flow that is induced by pressure gradients that develop upon tissue loading (Armstrong et al., 1984; Mow et al., 1980). Flow-independent viscoelasticity is thought to originate from the macromolecules of the cartilage extracellular matrix (Huang et al., 2001; Zhu et al., 1993).

Increased cartilage temperature may affect the behavior of both the interstitial water and the extracellular matrix. Fluid viscosity decreases with temperature (http://webbook.nist.gov/chemistry/). Stress relaxation of polymeric molecules such as those of the extracellular matrix is faster at higher temperatures (Doi and Edwards, 1988). Because cartilage is a fluid-filled polymeric solid, our second objective was to test the hypothesis that cartilage stress relaxation proceeds faster at higher temperatures.

Understanding the effects of temperature on cartilage stiffness provides an experiment to discriminate between fluid flow and polymeric matrix viscoelasticity. Because fluid viscosity decreases with temperature (http://webbook.nist.gov/chemistry/), fluid-flow theories predict a decrease in dynamic stiffness upon temperature increase (Armstrong et al., 1984; Mow et al., 1980). Conversely, polymer stiffness has been shown to increase with temperature (Sneppen and Zocci, 2005). Therefore, determining how the stiffness of cartilage changes with temperature provides an experimental method for discriminating between flow-dependent and matrix mechanisms of cartilage viscoelasticity. Thus, the third objective of this study was to determine whether cartilage stiffness changes with temperature.

We tested the effects of temperature on the stress relaxation of bovine calf cartilage samples. Osteochondral explants were harvested from the patellofemoral groove, and middle-zone cartilage samples were tested in unconfined compression. Samples were tested twice, either at different temperatures or at constant temperature to control for potential effects of repeated testing. The data clearly demonstrate temperature-dependent effects in cartilage material behavior that have not previously been identified. Stress relaxation proceeded faster at higher temperatures, which is consistent with a combination of changes in fluid viscosity and polymer motion. Both dynamic and equilibrium stiffness increased at higher temperatures, consistent with polymeric viscoelasticity and inconsistent with fluid-flow theories. These data demonstrate a rich area of cartilage mechanics that has not been previously studied. Future studies may utilize these phenomena to provide additional mechanistic insight into structure–function relationships for cartilage, which may prove useful for treating diseases of cartilage degeneration.

Tissue harvest and culture

Stifle joints from 1- to 3-month-old bovine calves were obtained from a local slaughterhouse and cultured in serum-free DMEM/F12 (Invitrogen 11330032; Carlsbad, CA, USA). Medium was supplemented with 0.1% bovine serum albumin (BSA; w/v, Sigma A9418; St Louis, MO, USA), insulin-transferrin-selenium (1 mg ml–1, 0.55 mg ml–1 and 0.67 μg ml–1, respectively; Invitrogen 41400045), l-ascorbic-acid-2-phosphate (50 μg ml–1; Sigma A8960) and antibiotics (penicillin at 100 units ml–1 and streptomycin at 100 μg ml–1; Invitrogen 15140155). Cylindrical samples were aseptically harvested from a standardized location on the patellofemoral groove using a 5 mm cork borer, and immersed in culture medium. The samples were trimmed to a standardized height (3.76±0.03 mm) by removing the superficial and deep zones using a custom-slicing device as described previously (Khalafi et al., 2007). Samples were rinsed three times with sterile medium, immersed in 4 ml of fresh medium in 12-well plates and maintained at 37°C in the presence of 5% CO2 in an incubator (HeraCell 150; Thermo Scientific, Milford, MA, USA).

Mechanical testing

Stress-relaxation tests were performed in unconfined compression at 24 and 60°C using an Enduratec ELF 3200 loading system (Bose Electroforce, Eden Prairie, MN, USA). The 24–60°C temperature range was the greatest possible for this system. This range was selected based on pilot experiments (supplementary material Fig. S1) that found that the variability of cartilage stress-relaxation is much greater than any differences in mechanical properties between 32 and 42°C. Temperature was controlled by a custom-built bath capable of controlling the steady-state sample temperature to within 0.1°C (supplementary material Fig. S2). Samples were removed from tissue culture and their diameters were measured using digital calipers (±0.01 mm, Absolute Digimatic; Mitutoyo, Kawasaki, Japan). Cartilage explants were then placed in the loading system, and a 12.5 kPa pre-stress (Wong et al., 2000) was applied at a displacement rate of 50 μm s–1. Immediately after the 12.5 kPa pre-stress was achieved, the loading chamber was filled with room-temperature (20–22°C) culture medium and temperature control was initiated. The initial sample height was defined as the height at which the pre-stress was achieved.

After 10 min of pre-stress equilibration, a 5% nominal compression was applied at 10 mm s–1 and held for 10 min, after which the temperature was either ramped to 60°C to examine temperature-dependence or maintained constant at 24°C for control samples to examine the effects of repeated loading. After the first test, the platens were raised, and samples were allowed to recover without any applied deformation for 5 min, followed by the same stress-relaxation testing protocol (12.5 kPa pre-stress for 10 min, 5% nominal compression, and 10 min of relaxation; Fig. 1). After the 60°C test, the specimen bath was allowed to cool for 10 min. This procedure was carried out on cartilage explants from 22 independent joints, with N=15 samples for the temperature-change protocol and N=7 samples for the control protocol.

Force data were sampled at a rate of 180 samples s–1 for stress relaxation and 1 sample s–1 for heating and cooling. Apparent stresses were calculated by dividing the compressive force by the sample cross-sectional area, which was calculated from the measured diameter. The dynamic stiffness was calculated by dividing the peak stress by the nominal strain, and the equilibrium stress was calculated by dividing the equilibrium stress by the nominal strain.

We observed that the compressive stress increased with temperature, including a local maximum in the temperature–stress curve that occurred at ∼57°C (Fig. 4). To examine this phenomenon further, we subjected additional samples (N=8) to the same temperature protocol while under low-stress cyclical loading. (Note that peak stresses reached almost 500 kPa in the stress-relaxation tests.) Dynamic sinusoidal compression was applied at 1 cycle s–1 using a different loading system capable of reaching 65°C. Samples were removed from culture, measured for height and diameter, and placed in a dynamic mechanical analyzer (DMA 7, Pyris Software Ver. 7.0.0.0110; Perkin Elmer, Waltham, MA, USA). The specimen bath was filled with medium, the temperature was set to 24°C and load-control sinusoidal loading was initiated at an average compressive stress of 6.5 kPa and an amplitude of 5.5 kPa. Samples were preconditioned at 24°C for 5 min, followed by a temperature increase to 65°C at a rate of 3.6°C min–1 (the same heating rate as in the stress-relaxation experiments), held for 5 min and cooled to 24°C. The cyclical loading parameters (phase angle and storage modulus) were calculated using the proprietary software on the dynamic mechanical analyzer.

Analysis

Stress relaxation was quantified by two methods. First, data were normalized to a range between one, representing the peak stress, and zero, representing the equilibrium stress and plotted on a semilog scale. Second, stress-relaxation data were fitted with a stretched exponential model (Eqn 1) of stress relaxation, which has been used previously (June et al., 2009):
formula
(1)
where σpeak and σeq are the peak and equilibrium stresses, respectively, which were defined by the experimental data; t is time; τ is the time constant; and β (0≤β<1) is the stretching parameter with decreases in β representing increasingly heterogeneous relaxation dynamics (Lindsey and Patterson, 1980). τ and β were adjusted to fit the data using nonlinear minimization techniques (Boyd and Vandenberghe, 2004; June et al., 2009). The fitted model parameters were used to quantify differences in cartilage stress relaxation.

Statistical analysis was performed using repeated-measures ANOVA to compare each stress-relaxation parameter between control and treatment groups. Bonferroni post hoc tests were used to make comparisons between: (1) the first and second tests, and (2) treatment and control groups. Linear correlation between temperature and stress was used to assess temperature–stress relationships for the heating and cooling data. All data are expressed as means ± s.e.m.

Increased temperature had marked effects on cartilage stress relaxation (Figs 2, 3, Table 1). Peak stress increased by 150% and equilibrium stress by 8% at 60°C compared with 24°C in the temperature-change group (both P<0.01, N=15). Stress relaxation proceeded faster with increased temperature as shown by the normalized stress-relaxation data (Fig. 2) and the 60% decrease in the time constant τ (P<0.01, N=15). Both the dynamic and equilibrium stiffness increased with temperature (both P<0.01, N=15; Fig. 4). Increased temperature also resulted in a decrease in the stretching parameter, β, from 0.43 at 24°C to 0.33 at 60°C (P<0.01, N=15). No statistically significant differences were found in any stress-relaxation parameters for control samples subjected to repeated tests at the same concentration.

We found novel temperature-dependent behavior in cartilage: during heating, the compressive stress increased with increasing temperature and, during cooling, the stress decreased with decreasing temperature (Table 2, Fig. 5). The temperature dependence of the equilibrium stress was 77% greater for cooling (0.78±0.07 kPa °C–1) than for heating (0.44±0.07 kPa °C–1, P<0.01, N=15; Table 2). During the heating phase, a peak in the temperature–stress curve was observed at 57±0.1°C (Fig. 5). Cyclical loading under lower stresses (mean compressive stress of 6.5 kPa) revealed a temperature transition at 64±0.3°C, demonstrated by a phase lag peak (Fig. 6).

Linear regression on the last 2 s of the stress-relaxation data found no statistically significant slopes in any data set at the 99% confidence level, demonstrating that 10 min of stress relaxation were sufficiently long to produce an equilibrium to the applied 5% compression. To assess the unloaded recovery period between stress-relaxation tests, we performed linear regression of the final 2 s of preload stress-time data for the second stress-relaxation test. No significant slopes were found in any data set at the 99% confidence level, demonstrating that the recovery period between tests was sufficient. Furthermore, the difference between sample heights at 24 and 60°C was not statistically significant (P=0.37).

Cartilage is a complex tissue containing a heterogeneous three-dimensional extracellular matrix composed of multiple biopolymers, cations and water. The in vivo function of cartilage is primarily mechanical: to provide a smooth surface for joint articulation. Because cartilage function is mechanical, understanding the mechanical properties of cartilage is necessary to understand cartilage function. As such, the objectives of this study were to: (1) determine whether the mechanical properties of cartilage changed with temperature, and test the hypotheses that (2) cartilage stress relaxation is faster at higher temperature and (3) cartilage stiffness increases with temperature.

We found that stress relaxation was markedly different between 24 and 60°C. Furthermore, we discovered novel cartilage behavior: at 5% stress-relaxation equilibrium, compressive stress was proportional to temperature. The stress-relaxation testing protocol applied a 5% nominal compression in less than 20 ms whereas previous experiments have used loading times ranging from ∼1 (Huang et al., 2003) to 500 s (Basalo et al., 2004; Park et al., 2003). Our rapid load application revealed fast relaxation dynamics that have not previously been emphasized: about 80% of the stress-relaxation occurred during the first 100 s (Fig. 2). These data add a novel experimental phenomenon to an already complex picture of cartilage mechanics (Dean et al., 2006; Federico et al., 2005; Julkunen et al., 2008; Neu et al., 2007; Park et al., 2003).

Cartilage stress relaxation was faster at 60°C than at 24°C, as shown by both the normalized stress-relaxation data (Fig. 2) and the 60% decrease in τ. Neither of the putative mechanisms of cartilage viscoelasticity (flow-dependent or flow-independent) can solely explain this observation. However, the combination of flow-dependent and flow-independent mechanisms does explain the data. Between 24 and 60°C, the viscosity of water decreases by 49% (http://webbook.nist.gov/chemistry/). Thus, faster fluid flow would predict a 49% decrease in τ, assuming a linear relationship between the stress-relaxation time constant and water viscosity. The remaining decrease in τ may result from changes in the dynamics of the extracellular matrix biopolymers, which are predicted to be inversely proportional to the change in absolute temperature (Doi, 1995; Doi and Edwards, 1988). Absolute temperature increased by 12% in our experiments. The combination of a decrease in viscosity (49%) and an increase in polymer motion (12%) may explain the total observed decrease in τ (60%). Individually, neither mechanism can explain the experimentally observed changes; only the combination of flow-dependent viscosity decrease and flow-independent polymer motion explains the data.

By mass, cartilage is ∼60–80% water, 10–20% collagen and 4–7% proteoglycan aggregate (Mankin et al., 2000). The interactions between these components are paramount to tissue function. For example, in cartilage the proteoglycan aggregate is compressed to a small fraction of its free-swelling volume (Kuettner and Kimura, 1985). Additionally, water in cartilage can be separated into fibrillar and intrafibrillar compartments (Wachtel and Maroudas, 1998). The physics of polymers such as those of the cartilage extracellular matrix is strongly dependent on interactions with the solvent, which in cartilage is assumed to be water (Doi and Edwards, 1988). Despite these complexities, the correlation between the experimental data (60% change in τ) and the combined theoretically predicted changes in dynamics (49% change in water viscosity and 12% change in polymer motion) is remarkable.

Both the dynamic and equilibrium stiffnesses of cartilage increased with temperature. Because fluid viscosity decreases with temperature, the increases in stiffness cannot represent a flow-dependent phenomenon. Polymer stiffness is known to increase with temperature (Sneppen and Zocci, 2005), and the solid matrix of articular cartilage is mainly composed of biopolymers. The reason for the temperature-induced stiffening of polymers is that the end-to-end distribution of polymer lengths is primarily driven by entropy, which increases with temperature. The temperature-induced increases in stiffness are probably caused by increases in the stiffness of the extracellular matrix biopolymers, consistent with previously developed theoretical models of cartilage (Kovach, 1995; Kovach, 1996).

At stress-relaxation equilibrium, compressive stress increased with temperature by a mean of 8% between 24 and 60°C. Between these temperatures, the specific volume of water increases by only 1.4% (http://webbook.nist.gov/chemistry/), so the expansion of water might have minimally contributed to the temperature-dependent increase in equilibrium stress. Polymers such as those of the cartilage matrix are known to swell with temperature (Doi, 1995), and expansion of the polymeric extracellular matrix might also have contributed to the temperature-dependent increase in equilibrium stress.

Cyclical loading revealed a phase-lag peak that is indicative of a temperature transition at 64°C, which is consistent with previous research on collagen thermodynamics. Previous research on the thermodynamics of solution-phase type I collagen has found that, upon heating, crystalline regions melt at 64°C (Flory and Garrett, 1958). Although cartilage contains mostly type II collagen, the collagens are highly conserved proteins – bovine types I and II have substantial sequence homology (supplementary material Fig. S4) – justifying comparison between the two types.

The 64°C transition observed in these cyclical loading experiments probably represents melting of crystalline regions of collagen, which has previously been found at 63–64°C in type I collagen (Flory and Garrett, 1958). The 57°C local maximum in the stress-temperature heating data may also result from melting of crystalline collagen, albeit at a lower temperature owing to the additional strain energy resulting from the 5% compression. This interpretation is supported by our observation that the stress-temperature dependence (Table 2) is stronger for cooling (after the melting would have happened) than for heating (while the crystalline regions may have been intact); melted regions will have higher mobility than crystalline regions, resulting in faster molecular motion to relieve the stress associated with the applied compression.

In the stress-relaxation experiments, the decrease in β demonstrates increasing heterogeneity of the relaxation processes with increased temperature (Lindsey and Patterson, 1980). This is consistent with collagen melting: the melted crystalline regions of collagen will exhibit distinct dynamics, which may partially explain the decreases in β. Melted crystalline regions of collagen may also enable altered dynamics within the noncollagenous components of cartilage (e.g. water and the proteoglycan aggregate may behave differently), which may also explain the decreases in β.

When considering these data, some limitations should be noted. First, we used cartilage explants maintained in tissue culture, and the temperature increase may have affected chondrocyte biology (e.g. by inducing the release of proteolytic enzymes). It is unknown whether altered chondrocyte biology could have substantially altered cartilage material properties during the time scale of this experiment (∼60 min). However, the half-lives of collagen and aggrecan are on the order of years (Maroudas et al., 1998; Maroudas et al., 1992; Verzijl et al., 2000), suggesting that substantial induced proteolysis would be needed to induce major changes in these matrix molecules during the relatively short experimental time course. Additionally, the maximum temperature used in this study was well above physiological temperature. Despite this limitation, we believe that the resulting data provide an improved picture of cartilage mechanics. Understanding the dynamics of the matrix biopolymers may yield important insight for novel therapeutic targets and strategies for the treatment and/or prevention of osteoarthritis. Future studies may provide further insight into the nature of cartilage mechanics by using the temperature-dependent behavior discovered in this study.

We determined the mechanical properties of articular cartilage explants at different temperatures. Stress relaxation was faster at higher temperatures, consistent with a combination of changes in fluid viscosity and extracellular matrix polymer dynamics. Both the dynamic and equilibrium stiffness increased with temperature, consistent with polymer mechanisms. Novel temperature-dependent increases in equilibrium stress were observed and may result from the swelling of water and matrix polymers. These data clearly demonstrate the presence of temperature-dependent effects in cartilage mechanics. Future studies may utilize these effects toward a better understanding of structure–function relationships in cartilage mechanics.

We gratefully acknowledge Professor A. H. Reddi for providing the cartilage samples. We thank Professor T. L. Kuhl and Dr G. S. Shapiro for helpful comments on the manuscript.

We thank the David Linn Chair and NIH 5F31AR05086 for funding. Deposited in PMC for release after 12 months.

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