Sustained loading on the intervertebral disc leads to loss of disc height. The generally accepted explanation for this is that the disc loses height due to an unbalance between the external load on the disc and the osmotic pressure in the disc. Consequently, water is expelled from the disc until the osmotic attraction reaches an equilibrium with the pressure applied. In this study, we compared the time course of loss of disc height with loss of pressure in the nucleus. We expected to see a similar time course of disc height and intra-discal pressure. Fifteen caprine lumbar discs were tested in a saline bath. Of each motion segment both vertebral bodies were cut-off close to the endplate. After a preload of 6 hours at 10N, an axial compressive load of 150N was applied to the discs for 18 hours by an Instron testing device. An 1.33mm pressure needle was inserted in the nucleus to measure hydrostatic pressure. Both change of disc height and change of nucleus pressure were measured at 2 samples/s. A double Kelvin–Voigt model was fitted to estimate the time constants of both hydrostatic pressure and disc height loss. The model comprises two time constants: the first modelling a fast change, the second a slow change. A paired t-test was used to compare the time constants of both the pressure and the disc height.Introduction
Methods
The main load on the disc is a compression load. In humans this leads to a 16hrs loading phase followed by 8hrs of rest. Loads due to daily activities are superimposed on this diurnal pattern. The mechanical effect of the diurnal loading part is a slow, time dependent, change of disc height. This time dependent deformation can be described by a four parameter model (Double Kelvin-Voigt). This model describes the mechanical behaviour in a slow and a fast regime. In the present research we describe the changes during the loading phase with a constant load or constant deformation. We expect these changes to be dependent on disc size. Ten motion segments (L2L3 and L4L5) of rabbits, rats and pigs were tested in a saline bath. The posterior part of the motion segment was removed. Both outer endplates of the motion segment were embedded in bone cement and connected to the loading device. The maximum load was half of the body weight (bw). Protocol for rat and rabbit: Step1: preload (5%bw, 4hrs) Step2: Creep test (load 50%bw, 4hrs) Step3: preload (5%bw, 4hrs) Step4: Stress relaxation test (the deformation at 50%bw was maintained for 4hrs.). Protocol porcine: Due to the large disc size of the porcine samples duration of each test phase was increased to 12hrs. The applied load and the change of disc height was measured at 2/s. The time dependent mathematical model (Matlab) consists of two spring-damper combinations: the first modelling a fast mechanical change, the second a slow mechanical change. Both the time dependent behaviour of the creep experiment and of the stress relaxation experiment were determined. The influence of disc size was expressed in terms of volume, periphery, disc height, cross sectional area, wet area and ratio volume vs wet area. We found a large difference of time constants between the creep experiment and the stress relaxation experiment. In both, the time constants increased with disc size for the slow regime but decreased with disc size for the fast regime. Time constants of the slow regime (hrs) vs fast regime (hrs):
rat: 0.65 (slow creep)/0.18 (slow relaxation) vs 0.09 (fast creep)/0.03 (fast relaxation), rabbit: 0.91 (slow creep)/0.38 (slow relaxation) vs 0.06 (fast creep)/0.01 (fast relaxation), pig: 1.32 (slow creep)/0.40 (slow relaxation) vs 0.03 (fast creep)/0.01 (fast relaxation). The relation between time constants and disc height was almost linear (R2=0.98). We found a relation between mechanical behavior and disc size. The time constants of both the fast and the slow regimes changed with disc size. Animal discs can be used as a model for human discs under sustained loading but the results need to be corrected for the disc size. The difference between creep and stress relaxation could be attributed to the nonlinear spring constant of the disc. An increasing disc size leads to a larger time constant of the slow regime in a Kelvin-Voigt model but to a smaller time constant in the fast regime of the model.
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. 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.Summary Statement
Background
