Viscoelastic properties of bovine articular cartilage attached to subchondral bone at high frequencies

Abstract

Background: Articular cartilage is a viscoelastic material, but its exact behaviour under the full range of physiological loading frequencies is unknown. The objective of this study was to measure the viscoelastic properties of bovine articular cartilage at loading frequencies of up to 92 Hz.

Methods: Intact tibial plateau cartilage, attached to subchondral bone, was investigated by dynamic mechanical analysis (DMA). A sinusoidally varying compressive force of between 16 N and 36 N, at frequencies from 1 Hz to 92 Hz, was applied to the cartilage surface by a flat indenter. The storage modulus, loss modulus and phase angle (between the applied force and the deformation induced) were determined.

Results: The storage modulus, E', increased with increasing frequency, but at higher frequencies it tended towards a constant value. Its dependence on frequency, f, could be represented by, E' = Alog(e) (f) + B where A = 2.5 +/- 0.6 MPa and B = 50.1 +/- 12.5 MPa (mean +/- standard error). The values of the loss modulus (4.8 +/- 1.0 MPa mean +/- standard deviation) were much less than the values of storage modulus and showed no dependence on frequency. The phase angle was found to be non-zero for all frequencies tested (4.9 +/- 0.6 degrees ).

Conclusion: Articular cartilage is viscoelastic throughout the full range of frequencies investigated. The behaviour has implications for mechanical damage to articular cartilage and the onset of osteoarthritis. Storage modulus increases with frequency, until the plateau region is reached, and has a higher value than loss modulus. Furthermore, loss modulus does not increase with loading frequency. This means that more energy is stored by the tissue than is dissipated and that this effect is greater at higher frequencies. The main mechanism for this excess energy to be dissipated is by the formation of cracks.

Figure 1

Sinusoidally varying force A) at 92 Hz (rise time 5.4 ms); B) at 1 Hz (rise time 500 ms).

Figure 2

Storage and loss moduli against frequency, for frequencies of up to 92 Hz.

Figure 3

Storage and loss moduli against frequency, for frequencies of up to 18 Hz.