CHARACTERIZING SPINAL LOAD-DISPLACEMENT BEHAVIOUR USING REPRESENTATIVE COMPONENTS
Authors: Hayward Samantha , Gheduzzi Sabina , Keogh Patrick , Miles Tony 
Published: November 2023

Objectives

Spinal stiffness and flexibility terms are typically evaluated from linear regression of experimental data and are then assembled into 36-element matrices. Summarising in vitro test results in this manner is quick, computationally cheap and has the distinct advantage of outputting simple characteristic values which make it easy to compare results. However, this method disregards many important experimental features such as stiffening effects, neutral and elastic zones magnitudes, extent of asymmetry and energy dissipation (hysteresis). Alternatives to the linear least squares method include polynomials, separation of the load-displacement behaviour into the neutral and elastic zones using various deterministic methods and variations on the double sigmoid and Boltzmann curve fits. While all these methods have their advantages, none provide a comprehensive and complete characterisation of the load-displacement behaviour of spine specimens. In 1991, Panjabi demonstrated that the flexion-extension and mediolateral bending behaviour of functional spinal units could be approximated using the viscoelastic model consisting of a nonlinear spring in series with a linear Kelvin element. Nowadays viscoelastic models are mainly used to describe creep and stress relaxation, rather than for cyclic loading. The aim of this study was to conclusively prove the viscoelastic nature of spinal behaviour subject to cyclic loading. Being able to describe the behaviour of spine specimens using springs and dampers would yield characterising coefficients with recognisable physical meaning, thus providing an advantage over existing techniques.

Methods

Six porcine isolated spinal disc specimens (ISDs) were tested under position and load control. Visual inspection of the load-displacement graphs from which the principal terms of the stiffness and flexibility matrices are derived suggest that the load-displacement behaviour could be idealised by a nonlinear spring system with damping. It was hypothesised that the contributions arising from non-linear spring-like behaviour and damping could be separated for each of the principal load-displacement graphs.

Results

The principal elements from position and load control tests were plotted with load on the vertical axis and displacement on the horizontal axis, and a polynomial representing spring force was fitted to the data. This polynomial was subtracted from the experimental data. The remainder - representing damping force - was plotted against displacement and velocity and compared to idealised plots for different types of damping behaviour. Applying this reasoning to the six principal load-displacement plots obtained from stiffness and flexibility tests revealed that four of six exhibit behaviour which is a combination of a nonlinear hardening spring and viscous damper. However, for flexion-extension and mediolateral bending, the damping behaviour is more akin to coulomb damping with viscous influences, characterised by a steep central linear region and near horizontal regions at the extremes. These trends were common amongst all six specimens within the study sample size.

Conclusions

The unique approach described here has allowed the characterisation of the load-displacement behaviour of ISDs in terms of characteristic mass-spring-damper systems. This is an important development which allows experimental findings to be framed in terms of mechanical contributions to a given load-displacement behaviour.

Declaration of Interest

(b) declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported:I declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research project.