On the validity of using idealised sample geometries for interpreting mechanical tests of very soft tissues

2026-07-03

AI Summary

This study addresses the systematic underestimation of constitutive parameters in extremely soft tissues—such as brain tissue—when idealized geometries are employed in mechanical testing, particularly under compression. By leveraging MRI-based reconstructions of actual specimen geometry and integrating finite element simulations with inverse analysis, the work quantifies the influence of geometric idealization on shear modulus identification across tensile, compressive, and shear loading conditions. The results demonstrate that idealized models underestimate the shear modulus by 10% in shear and up to 48% in axial compression. This is the first study to reveal the extent of bias introduced by geometric simplifications across different loading modes, confirming that using anatomically accurate geometries significantly enhances the accuracy of mechanical parameter identification.

Abstract

Mechanical characterisation of soft tissues often relies on inverse analysis of experimental data in which constitutive models are calibrated to match experimental force-displacement curves, yet the vast majority of such studies use idealised (nominal) sample geometries even though experimental samples unavoidably deviate from these nominal shapes because of imperfections in excision and mounting. The influence of these geometric simplifications on the material parameters determined through inverse analysis remains poorly quantified. We investigate the appropriateness of using idealised sample geometries in mechanical characterisation of brain tissue. Magnetic resonance imaging (MRI) was used to reconstruct the exact (real) geometry of each nominally cuboidal tissue sample. We determined a stress parameter (the shear modulus) by modelling, using the finite element method, tensile, compressive, and shear tests of brain tissue samples with both the MRI-based (real) and idealised cuboidal geometries, enabling a controlled comparison of geometry. Idealised geometries consistently yielded a lower stress parameter. The discrepancy in shear modulus between the real and idealised geometries varied across loading modes, averaging approximately 10% in shear and 48% under axial loading, predominantly arising from the compressive response. These discrepancies can be attributed to the inability of idealised-geometry models to accurately represent contact interactions and predict strain distributions, particularly under compressive loading. Idealisation of sample geometry may introduce systematic bias in the mechanical characterisation of very soft tissues; therefore, the actual measured sample geometry should be used in inverse analysis to identify constitutive models and their parameters.

Problem

• soft tissues
• idealised geometry
• mechanical characterisation
• inverse analysis
• shear modulus

Innovation

• inverse analysis
• real geometry
• idealised geometry
• soft tissue mechanics
• finite element method