Elsevier

Journal of Biomechanics

Volume 38, Issue 8, August 2005, Pages 1665-1673
Journal of Biomechanics

Effect of dynamic loading on the frictional response of bovine articular cartilage

https://doi.org/10.1016/j.jbiomech.2004.07.025Get rights and content

Abstract

The objective of this study was to test the hypotheses that (1) the steady-state friction coefficient of articular cartilage is significantly smaller under cyclical compressive loading than the equilibrium friction coefficient under static loading, and decreases as a function of loading frequency; (2) the steady-state cartilage interstitial fluid load support remains significantly greater than zero under cyclical compressive loading and increases as a function of loading frequency. Unconfined compression tests with sliding of bovine shoulder cartilage against glass in saline were carried out on fresh cylindrical plugs (n=12), under three sinusoidal loading frequencies (0.05, 0.5 and 1 Hz) and under static loading; the time-dependent friction coefficient μeff was measured. The interstitial fluid load support was also predicted theoretically. Under static loading μeff increased from a minimum value (μmin=0.005±0.003) to an equilibrium value (μeq=0.153±0.032). In cyclical compressive loading tests μeff similarly rose from a minimum value (μmin=0.004±0.002, 0.003±0.001 and 0.003±0.001 at 0.05, 0.5 and 1 Hz) and reached a steady-state response oscillating between a lower-bound (μlb=0.092±0.016, 0.083±0.019 and 0.084±0.020) and upper bound (μub=0.382±0.057, 0.358±0.059, and 0.298±0.061). For all frequencies it was found that μub>μeq and μlb<μeq (p<0.05). Under cyclical compressive loading the interstitial fluid load support was found to oscillate above and below the static loading response, with suction occurring over a portion of the loading cycle at steady-state conditions. All theoretical predictions and most experimental results demonstrated little sensitivity to loading frequency. On the basis of these results, both hypotheses were rejected. Cyclical compressive loading is not found to promote lower frictional coefficients or higher interstitial fluid load support than static loading.

Introduction

Articular cartilage functions as the bearing material between the opposing articular surfaces of diarthrodial joints. Previous frictional studies have found that articular cartilage can have very low friction coefficients upon loading (0.002–0.02) (Jones, 1934, Jones, 1936; Charnley, 1959, Charnely, 1960; McCutchen, 1959; Barnett and Cobbold, 1962; Linn, 1967; Linn and Radin, 1968; Unsworth et al., 1975; Malcom, 1976; Forster and Fisher, 1996; Krishnan et al., 2003). But with a step load of constant magnitude (static load) applied for several hours, the coefficient becomes quite elevated (0.1–0.6) (McCutchen, 1962; Malcom, 1976; Forster and Fisher, 1996, Forster and Fisher, 1999; Ateshian et al., 1998; Krishnan et al., 2004). It has been proposed by McCutchen, 1959, McCutchen, 1962) and supported by others (Malcom, 1976; Macirowski et al., 1994; Forster and Fisher, 1996; Ateshian et al., 1998) that this transient frictional behavior is related to the fluid pressurization in the tissue. Under this hypothesis, by load transfer from the solid to the fluid phase, the interstitial fluid is able to substantially reduce the friction coefficient. When the interstitial fluid pressure within the tissue subsides to zero, the frictional coefficient reaches an equilibrium value.

Experimental measurements of the interstitial fluid pressurization of articular cartilage (Oloyede and Broom, 1991; Soltz and Ateshian, 1998, Soltz and Ateshian, 2000a; Park et al., 2003) have confirmed theoretical predictions (Ateshian et al., 1994; Macirowski et al., 1994; Ateshian and Wang, 1995; Kelkar and Ateshian, 1999) that the load supported by interstitial fluid can be in excess of 90% of the total applied load immediately upon loading, though it subsides to zero under prolonged static loading. In our recent study where measurements of cartilage interstitial fluid pressurization were performed simultaneously with frictional measurements against glass under a constant applied load (Krishnan et al., 2004), a linear correlation with a negative slope was observed between the friction coefficient and interstitial fluid load support, strongly supporting the hypothesis that interstitial fluid pressurization is a primary regulator of the frictional response of cartilage.

Under static loading, in laboratory conditions, the equilibrium cartilage friction coefficient achieved when fluid pressurization has subsided (μeq0.10.6) is typically too high to provide functionally effective lubrication. For example, if the peak load transmitted across the hip joint during gait is approximately five times normal body weight (∼5×750 N=3750 N), this would result in friction forces ranging between 375 and 2250 N. Such elevated friction forces can lead to rapid wear and degeneration of the surfaces (Forster and Fisher, 1996). It is therefore expected that the normal environment in diarthrodial joints would maintain the friction coefficient in a low range (e.g., ∼0.02 or less) over the range of activities of daily living. This study begins to address the question of what makes the friction coefficient stay sufficiently low under physiological loading conditions in vivo.

Under physiological activities such as walking and running, the loading environment in the lower extremities is cyclical (Dillman, 1975; Paul and McGrouther, 1975), yet few studies have investigated the frictional characteristics of articular cartilage under such conditions. Malcom observed that the effect of dynamic loading, compared to static loading, was to reduce the friction coefficient of cartilage and keep it lower over a wider range of normal stresses (Malcom, 1976). Results from our previous measurements of interstitial fluid load support under dynamic confined compression loading (Soltz and Ateshian, 2000a) indicate that substantial interstitial fluid pressurization persists at frequencies as low as 10−4 Hz. Based on these observations, the hypothesis of the current study is that under cyclical loading rates and physiological stresses, normal articular cartilage always maintains high interstitial fluid load support and low friction coefficient, never achieving the zero-pressure/high friction equilibrium conditions typical of prolonged static loading under laboratory conditions. More specifically, (1) the steady-state friction coefficient is significantly smaller under cyclical compressive loading than the equilibrium friction coefficient under static loading, and decreases as a function of loading frequency; (2) the steady-state interstitial fluid load support remains significantly greater than zero under cyclical compressive loading and increases as a function of loading frequency. These hypotheses are tested using a combination of experimental and theoretical studies.

Section snippets

Materials and methods

In the experimental study, friction measurements between bovine articular cartilage and glass were performed in unconfined compression under three dynamic loading frequencies representative of physiological conditions (0.05, 0.5 and 1 Hz), and under a static load. In the theoretical study, cartilage interstitial fluid load support was predicted under similar conditions of static and dynamic loading, using the previously described biphasic-conewise linear elasticity (CLE) mixture model of

Statistical analyses

A one-way analysis of variance (ANOVA) with repeated measures was performed to detect differences in the experimentally measured values of μmin in all four friction tests. Similarly, ANOVA with repeated measures was used to detect differences between μeq from the static loading test and μub and μlb from the three dynamic loading tests. Statistical significance was accepted for p0.05, with α=0.05. Post-hoc testing of the means was performed using Bonferroni correction.

Results

Representative experimental results for the applied load W and measured frictional force F are shown in Fig. 2a–d under static loading and dynamic loading at 0.05 Hz. The friction force is observed to increase with time, both for static and dynamic loading configurations. The corresponding effective friction coefficient μeff is shown in Fig. 2e,f along with a trace of the corresponding lower bound and upper bound responses under dynamic loading. For this specimen, the rise in μeff occurs at a

Discussion

Cyclical compressive loading is an important testing configuration as it is frequently encountered in our joints during activities of daily living such as walking or running. The experimental results presented in Fig. 2 and Table 1 demonstrate that the friction coefficient under cyclical compressive loading oscillates above and below the response to static loading, with the upper bound steady-state friction coefficient considerably higher than the equilibrium friction coefficient, μlb>μeq.

Acknowledgements

This study was supported by funds from the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health (AR43628).

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