The viscoelastic behavior of the non-degenerate human lumbar nucleus pulposus in shear

Abstract

The viscoelastic behavior of the nucleus pulposus was determined in shear under transient and dynamic conditions and was modeled using a linear viscoelastic model with a variable amplitude relaxation spectrum. During stress-relaxation tests, the shear stress of the nucleus pulposus relaxed nearly to zero indicative of the fluid nature of the tissue. Under dynamic conditions, however, the nucleus pulposus exhibited predominantly 'solid-like' behavior with values for dynamic modulus (magnitude of G*) ranging from 7 to 20 kPa and loss angle (delta) ranging from 23 to 30 degrees over the range of angular frequencies tested (1-100 rad s-1). This frequency-sensitive viscoelastic behavior is likely to be related to the highly polydisperse populations of nucleus pulposus molecular constituents. The stress-relaxation behavior, which was not linear on a semi-log plot (in the range t1 << t << t2), required a variable amplitude relaxation spectrum capable of describing this frequency sensitive behavior. The stress-relaxation behavior was well described by this linear viscoelastic model with variable amplitude relaxation spectrum; however, the dynamic moduli were underpredicted by the model which may be related to non-linearities in the material behavior.