Cartilage interstitial fluid load support in unconfined compression

Abstract

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than in compression, and theoretical analyses have suggested that this tension-compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone. Ten human cartilage samples from six patellofemoral joints, and 10 bovine cartilage specimens from three calf patellofemoral joints were tested in unconfined compression. The peak fluid load support was measured at 79 +/- 11% and 69 +/- 15% at the articular surface and deep zone of human cartilage, respectively, and at 94 +/- 4% and 71 +/- 8% at the articular surface and deep zone of bovine calf cartilage, respectively. Statistical analyses confirmed both hypotheses of this study. These experimental results suggest that the tension-compression nonlinearity of cartilage is an essential functional property of the tissue which makes interstitial fluid pressurization the dominant mechanism of load support in articular cartilage.

Figure 1

(a) Testing chamber for unconfined compression. The cylindrical cartilage sample (diameter b = 6 mm) is flush against a recessed free-draining porous filter (diameter a = 4.78 mm) communicating with a piezoresistive microchip pressure transducer. (b) The non-uniform pressure distribution at the interface of the cartilage and filter is averaged into a single time-varying value p₀(t) measured by the pressure transducer over the footprint of the porous filter. In the annular region a/≤r≤b/2 the pressure is assumed to drop linearly to zero, producing a trapezoidal pressure profile p(r,t) along r.

Figure 2

(a) Typical response for the total load, W(t), and the load supported by interstitial fluid pressure, W^p(t), for a human Specimen in Experiment 1, with the articular surface facing the pressure transducer. Both W(t) and W^p(t) rise during the compressive phase of loading (0 ≤ t ≤ s) conducted at a constant strain rate (20% over 100 s), and reduce to zero during the unloading phase when the platen recedes at the same rate (100 ≤ t ≤ 200 s), because loading platen lift-off typically occurs during unloading. (b) Plot of W^p(t) versus W(t) during the loading phase (0 ≤ t ≤100 s), using the same data set as in (a). Linear regression on the data provides the slope dW^p/dW which remains nearly constant during the entire loading phase.

Figure 3

(a) Typical response for W(t) and W^p(t), for a bovine Specimen in Experiment 2, with the articular surface facing the pressure transducer. Both W(t) and W^p(t) rise during the compressive phase of loading (0 ≤ t 500 s) conducted at a constant strain rate (10% over 500 s). For t > 500 s the applied deformation is maintained constant and W(t) relaxes to its equilibrium value while W^p(t) reduces to zero. (b) Plot of W^p(t) versus W(t) during the early portion of the loading phase (0 ≤ t ≤ 180 s), using the same data set as in (a). Linear regression on the linear portion of the data provides the slope dW^p/dW and the load W₀ where the compliance is approximately overcome.

Figure 4

(a) Fluid load support W^p/W' as a function of time (W'(t) = W(t) − W₀) for the four tests of Experiment 2. (b) Theoretical fluid load support W^p/W predicted from the biphasic-CLE theory for the same loading protocol as in (a), using typical material properties H_−A =0.64 MPa, λ₂=0.48 MPa, k=0.6×10⁻¹⁵ m⁴/N.s (Soltz and Ateshian, 2000b), and varying the ratio of the tensile to compressive moduli H_+A − λ₂/H_−A − λ₂ from 30 down to 1.

Figure 5

Testing configuration and results for finite element analyses of contact analysis of a spherical indenter on a cartilage layer (physiologic contact condition), unconfined compression and confined compression of a cylindrical cartilage sample, and indentation of a cartilage layer with a flat porous permeable probe. Results include (a) the interstitial fluid pressurization, with arrows indicating the relative interstitial fluid flux; (b) the minimum principal effective stress, with lines and arrows indicating their principal direction; and (c) the maximum principal effective stress, with lines and arrows indicating their principal directions.

Figure 6

Theoretical analysis of confined compression of a biphasic cylindrical cartilage plug, taking into account pressure transducer impedance. (a) Schematic of loading configuration. (b) Theoretical prediction of interstitial fluid load support for various ratios of the pressure transducer sensor and cartilage compressive aggregate moduli ($H_A^t/H_{-A}$).