Abstract
Lower back pain (LBP) is a global problem. Countless in vitro studies have attempted to understand LBP and inform treatment protocols such as disc replacement devices (DRDs). A common method of reporting results is applying a linear fit to load-displacement behaviour, reporting the gradient as the specimen stiffness in that axis. This is favoured for speed, simplicity and repeatability but neglects key aspects including stiffening and hysteresis. Other fits such as polynomials and double sigmoids better address these characteristics, but solution parameters lack physical representation. The aim of this study was to implement an automated method to fit spinal load-displacement behaviour using viscoelastic models.
Six porcine lumbar spinal motion segments were dissected to produce isolated disc specimens. These were potted in Wood's metal, ensuring the disc midplane remained horizontal, sprayed with 0.9% saline and wrapped in saline-soaked tissue and plastic wrap to prevent dehydration. Specimens were tested using the University of Bath spine simulator operating under position control with a 400N axial preload.
Specimens were approximated using representative viscoelastic elements. These models were constructed in MATLAB Simulink R2020b using the SimScape library. Solution coefficients were determined by minimizing the sum of squared errors cost function using a non-linear least squares optimization method.
The models matched experimental data well with a mean % difference in model and specimen enclosed area below 6% across all axes. This indicates the ability of the model to accurately represent energy dissipated. The final models demonstrated reduced RMSEs factors of 3.6, 1.1 and 9.5 smaller than the linear fits for anterior-posterior shear, mediolateral shear and axial rotation respectively.
These nonlinear viscoelastic models exhibit significantly increased qualities of fit to spinal load-displacement behaviour when compared to linear approximations. Furthermore, they have the advantage of solution parameters which are directly linked to physical elements: springs and dampers. The results from this study could be instrumental in improving the design of DRDs as a mechanism for treating LBP.
