# Nonlinear viscoelastic models improve characterisation of 6 DOF intervertebral disc load response at low strain rates

## TL;DR

Nonlinear viscoelastic models better capture the behavior of spinal discs under low-rate loading compared to traditional linear methods.

## Contribution

A new method using nonlinear viscoelastic models is introduced for more accurate spinal disc load response characterization.

## Key findings

- Nonlinear models reduced RMSE by 60% compared to linear stiffness models.
- Nonlinear models replicated experimental hysteresis area within 17%.
- Three-element nonlinear viscoelastic models effectively capture key load response features.

## Abstract

Graphical abstract

The viscoelastic characteristics of the intervertebral disc (IVD) govern spinal response to applied dynamic loading which is important in understanding how the spine responds to loads experienced in everyday activity. The common method of reporting experimental load response data in terms of linear stiffnesses represents a significant oversimplification of this behaviour. This study presents a method yielding substantially increased accuracy for principal direction load-displacement response of porcine lumbar spine segments. It compares quality of fit to experimental data of nonlinear viscoelastic models and the typical linear stiffness method. Experimental load response data were recorded from six porcine lumbar spine segments tested under 6 DOF cyclic displacement control at low strain rates (0.1 Hz). Model spring and damper coefficients were determined using an optimisation procedure to minimise the differences between model and experimental load response vectors in each axis. Experimental hysteresis area cannot be reproduced using the linear method but was replicated to within 17% by nonlinear viscoelastic models. Fit quality was substantially improved by nonlinear models compared to the linear stiffness model, with RMSE reduced by 60%. Results indicate that three-element nonlinear viscoelastic models are well-suited for characterisation of principal direction load response to cyclic loading, replicating key features.