Limitations of the standard linear solid model of intervertebral discs subject to prolonged loading and low-frequency vibration in axial compression

The purpose of this study was to answer the following questions: (1) Can the standard linear solid model for viscoelastic material simulate the influence of disc level and degeneration on the ability of a disc to withstand prolonged loading and low-frequency vibration? (2) How well does the SLS model explain the relationship between the ability of a disc to resist prolonged loading and its ability to resist dynamic loads and dissipate energy when subjected to low-frequency vibration? Responses of human thoracic and lumbar discs were measured in axial compression under a constant load, and for cyclic deformations at three frequencies. Parameters of the SLS model for each disc were determined by a least-squares fit to the experimental creep response. The model was subsequently used to predict the disc's response to cyclic deformations. The SLS model was able to qualitatively simulate the effects of disc level and degeneration on the ability of an intervertebral disc to resist both prolonged loading and low-frequency vibration. However, the model underestimated the stress relaxation, dynamic modulus and hysteresis of thoracic and lumbar discs subjected to low-frequency vibration. The SLS model was unable to explain the relationship between the ability of a disc to resist prolonged loading and its ability to resist dynamic loads and dissipate energy when subjected to low-frequency vibration. Although in the lumbar discs the steady-state predictions of the SLS model were significantly correlated to the experimental response, the strength of model predictions decreased with increasing frequency, particularly for hysteresis.