A family of hyperelastic models for human brain tissue

L Angela Mihai,Silvia Budday,Gerhard A Holzapfel,Ellen Kuhl,Alain Goriely

doi:10.1016/j.jmps.2017.05.015

Abstract

Experiments on brain samples under multiaxial loading have shown that human brain tissue is both extremely soft when compared to other biological tissues and characterized by a peculiar elastic response under combined shear and compression/tension: there is a significant increase in shear stress with increasing axial compression compared to a moderate increase with increasing axial tension. Recent studies have revealed that many widely used constitutive models for soft biological tissues fail to capture this characteristic response. Here, guided by experiments of human brain tissue, we develop a family of modeling approaches that capture the elasticity of brain tissue under varying simple shear superposed on varying axial stretch by exploiting key observations about the behavior of the nonlinear shear modulus, which can be obtained directly from the experimental data.

Highlights

The study of the mechanical response of biological systems within a continuum framework relies on constitutive equations relating stresses to strains (Holzapfel, 2000)
The analysis presented in this paper is based on the data of human brain tissues tested under finite uniaxial and multiaxial loading reported in Budday et al (2017)
In Appendix B, we summarize the constitutive behavior of the calibrated model, which shows excellent agreement with the experimental results at more than 5% shear and offers reliable predictions of the elastic behavior at less than 5% shear

Summary

Introduction

The study of the mechanical response of biological systems within a continuum framework relies on constitutive equations relating stresses to strains (Holzapfel, 2000). Our objective is to build a family of isotropic hyperelastic strain-energy functions, with a small number of parameters, that exhibit the characteristic behavior under combined shear and compression or tension. This observation is used to identify a generic strain-energy function capable of predicting the physical behavior of human brain tissues subjected to combined shear and tension or compression.

Finite shear superposed on axial stretch

Modeling strategy

Preliminary considerations

Model calibration

Findings

Discussion