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.

Lower back pain (LBP) is a worldwide clinical problem and a prominent area for research. Numerous in vitro biomechanical studies on spine specimens have been undertaken, attempting to understand spinal response to loading and possible factors contributing to LBP. However, despite employing similar testing protocols, there are challenges in replicating in vivo conditions and significant variations in published results. The aim of this study was to use the University of Bath (UoB) spine simulator to perform tests to highlight the major limitations associated with six degree of freedom (DOF) dynamic spine testing.

A steel helical spring was used as a validation model and was potted in Wood's metal. Six porcine lumbar spinal motion segments were harvested and dissected to produce isolated spinal disc specimens. These were potted in Wood's metal, ensuring the midplane of the disc remained horizontal and then sprayed with 0.9% saline and wrapped in saline-soaked tissue and plastic wrap to prevent dehydration. A 400N axial preload was used for spinal specimens. Specimens were tested under the stiffness and flexibility protocols.

Tests were performed using the UoB custom 6-axis spine simulator with coordinate axes. Tests comprised five cycles with data acquired at 100Hz. Stiffness and flexibility matrices were evaluated from the last three motion cycles using the linear least squares method.

According to theory, inverted flexibility matrices should equal stiffness matrices. In the case of the spring, the matrices matched analytical solutions and inverted flexibility matrices were equivalent to stiffness matrices. Matrices from the spinal tests demonstrated some symmetry, with similarities between inverted flexibility- and stiffness matrices, though these were unequal overall. Matrix element values were significantly affected by displacements assumed to occur at disc centre.

Spring tests proved that for linear, elastic specimens, the spine simulator functioned as expected. However, multiple factors limit the confidence in spine test results. Centre of rotation, displacement assumptions and rigid body transformations are known to impact the results from spinal testing, and these should be addressed going forward to improve the replication of in vivo conditions.

Injury of the intervertebral disc (IVD) can occur for many reasons including structural weakness due to disc degeneration. A common disc injury is herniation. A herniated nucleus can compress spinal nerves, causing pain, and nucleus depressurisation changes mechanical behaviour. Many studies have investigated in vitro IVD injuries including endplate fracture, incisions, and nucleotomy. There is, however, a lack of consensus on how the biomechanical behaviour of spinal motion segments is affected. The aim of this study was to induce defined changes to IVDs of spine specimens in vitro and apply 6 degree of freedom testing to evaluate the effect of these changes.

Six porcine lumbar spinal motion segments were harvested from organically farmed pigs. Posterior structures were removed to produce isolated spinal disc specimens. Specimens were potted in Wood's metal, ensuring the midplane of the IVD remained horizontal. After potting, specimens were sprayed with 0.9% saline, wrapped in saline-soaked tissue and plastic wrap to prevent dehydration. A 400N axial preload was equilibrated for 30 minutes before testing. Specimens were tested intact and after a partial nucleotomy removing ~0.34g of nuclear material with a curette through an annular incision.

Stiffness tests were performed using the University of Bath's custom 6-axis spine simulator with coordinate axes and displacement amplitudes. Tests comprised five cycles with data acquired at 100Hz. Stiffness matrices were evaluated from the last three motion cycles using the linear least squares method.

Stiffness matrices for intact and nucleotomy tests were compared. No significant differences in shear, axial or torsional stiffnesses were noted. Nucleotomy caused significantly higher stiffness in lateral bending and flexion-extension with increased linearity and the load-displacement behaviour in these axes displayed no neutral zone (NZ).

Induced changes were designed to replicate posterolaterally herniated discs. Unaffected shear, axial and torsional stiffnesses suggest the annulus is crucial in these axes. However, reduced ROM and NZ after nucleotomy suggests bending is most affected by herniation. Increased linearity and lack of defined NZ in these axes demonstrates herniation causes major changes to the viscoelastic behaviour of spine specimens in response to loading.

Abstract