Abstract
Summary Statement
Creep behaviour can only be quantified accurately when the testing time exceeds the estimated time constant of the creep process. The new parameters obtained in this paper can be used to describe normal behaviour up to 24 hrs.
Background
Diurnal loading on the human spine consists of 16hrs loading and 8hrs rest. After an initial load increase, due to rising in the morning, an axial loading is maintained throughout the day. As a consequence subsidence of the intervertebral disc (IVD) occurs during the day while disc height recovers during the night. This behaviour is time dependent (non-linear). In literature different constitutive equations have been used to describe creep. A stretched exponential (Kolraush-Wilson-Watts, KWW) and a double Voight (DV) model have both been used to quantify the creep behaviour. Using these models, time constants and the deformation at equilibrium are estimated. It is unsure whether these different approaches yield to valid predictions. In this study we compared the validity of different equations for the prediction of creep behavior.
Materials and Methods
IVDs (T9-T12) were obtained from 5 human spines. IVD's with osteophytes and/or disc narrowing were excluded from the test. The transverse area of each disc was measured and used to calculate the required compression load. IVDs were preloaded at 0.1MPa for 12hrs, compressed (0.8MPa, 24hrs) and finally unloaded (0.1MPa, 24hrs). Tests were performed in a saline bath. A KWW model and a DV model were fitted to the measured creep data (least squares method). Model parameters, e.g. the time constant and maximum deformation, were calculated for a test duration of 4, 8, 12, 16, 20 and 24hrs.
Results
4hours loading: KWW model: Time constant = 70hrs. Deformation = 3.0 mm.
DV model: Time constant = 5hrs, Deformation = 1.7 mm.
24hours loading: KWW model: Time constant = 17hrs. Deformation = 3.2 mm
DV model: Time constant =12.5hrs, Deformation = 2.1 mm
Discussion
Both models described the measured data well but the model parameters were highly sensitive to test duration. For both models the estimated time constant varied with test duration. When extrapolating the measured data beyond test duration, the DV model under-estimated and the KWW model over-estimated creep behaviour. The 24hrs experiment was still too short for an accurate determination of the parameters. The upper and lower limits of the parameters can be estimated using a KWW and Voight model.
Conclusions
Creep behaviour can only be quantified accurately when test duration exceeds the estimated time constant of the creep process. All reported time constants in current literature are based upon experiments that lack sufficient test duration. The new parameters obtained in this paper can be used to describe normal behaviour up to 24 hrs., but are not suitable for extrapolation beyond the test duration.
