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

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.