Assessing time-dependent response of intact and degenerated cervical intervertebral discs by employing a poroviscoelastic model based on experimental relaxation data

Intervertebral disc (IVD) provides flexibility and shock absorption for the spine in the load transmission procedure. Disc degeneration may occur as a result of aging and inappropriate types of loading. Assessing biomechanical parameters of intact IVD in comparison to the degenerated disc with different grades of degeneration can facilitate the detection procedure and planning for suitable therapeutic treatment. In the present study, a real three-dimensional model of cercival IVD (C_5-C_6) with adjacent vertebrae is constructed by using computed tomography (CT-scan) images. In order to accurately define mechanical properties, the disc and the vertebrae are modelled as poroviscoelastic and poroelastic materials, respectively. A porous medium approach is adopted to consider the considerable water content of both media alongside the solid matrix. For the solid phase of the IVD, the related viscoelastic parameters are extracted from an experimental test on a sheep lumbar intervertebral disc and stress vs. time data are fitted to the generalized Maxwell model with two Maxwell arms. By employing the finite element method, time-dependent response of the intact IVD and three different levels of the degenerated IVD (mild, moderate, and severe) are studied in a relaxation test. Results indicate that during relaxation procedure, intradiscal fluid velocity decreases as a result of disc degeneration. This may oppositely affect the flexibility of IVD in the load bearing. It is also observed that stress relaxation of the severe degenerated IVD almost increases up to 16% relative to the intact IVD. Assessing the amount of disc bulging under load application shows enhancement for the degenerated disc compared to the intact disc.