Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models

TL;DR

This paper critiques the Ogden model for brain tissue elasticity, highlighting its non-convexity issues, and introduces an alternative family of models that better fit experimental data without these shortcomings.

Contribution

The paper proposes a new family of constitutive models that address the limitations of the Ogden model in brain tissue elasticity modeling.

Findings

Ogden model can lead to non-convex strain-energy functions.

The proposed models fit experimental data better.

The new models are robust against testing artefacts.

Abstract

The Ogden model is often considered as a standard model in the literature for application to the deformation of brain tissue. Here we show that, in some of those applications, the use of the Ogden model leads to non-convexity of the strain-energy function and mis-prediction of the correct concavity of the experimental stress-stretch curves over a range of the deformation domain. By contrast, we propose a family of models which provides a favourable fit to the considered datasets while remaining free from the highlighted shortcomings of the Ogden model. While, as we discuss, those shortcomings might be due to the artefacts of the testing protocols, the proposed family of models proves impervious to such artefacts.