Introduction

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.

Daytime spinal loading is twice as long as night time rest, but diurnal disc height changes due to fluid flow are balanced. A direction-dependent permeability of the endplates, favouring inflow over outflow, has been proposed to explain this; however, fluid also flows through the annulus fibrosus. This study investigates the poro-elastic behaviour of entire intervertebral discs in the context of diurnal fluid flow.

Caprine discs were preloaded in saline for 24 hours under different levels of static load. Under sustained load, we modulated the disc's swelling pressure by replacing saline for demi-water and back again to saline, both for 24h intervals. We measured the disc height creep and used stretched exponential models to determine the respective time constants.

Reduction of culture medium osmolality induced an increase in disc height, and the subsequent restoration induced a decrease in disc height. Creep varied with the mechanical load applied. No direction-dependent resistance to fluid flow was observed. In addition, time constants for mechanical preloading were much shorter than for osmotic loading, suggesting that outflow is faster than inflow. However, a time constant does not describe the actual rate of fluid flow: close to equilibrium fluid flow is slower than far from equilibrium. As time constants for mechanical loading are shorter and daytime loading twice as long, the system is closer to the loading equilibrium than to the unloading equilibrium. Therefore, paradoxically, fluid inflow is faster during the night than fluid outflow during the day.

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.

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.