Inverse finite element analysis of indentation tests to determine hyperelastic parameters of soft-tissue layers

Abstract

Indentation is being used increasingly to probe the mechanical behaviour of cells, the extra-cellular matrix, and organs. Multiple hyperelastic parameters have been extracted from indentation data, but their accuracy has not been evaluated. Consequently, this paper examines whether two non-linear hyperelastic parameters or even a single generalized elastic modulus E can be extracted accurately from atomic force microscopy and nanoindentation force–depth data. Tissue was modelled as incompressible isotropic Mooney–Rivlin (MR), polynomial (POLY), or exponential (EXP) layers. For each model, n = 9 sets of the two hyperelastic parameters (all with R² > 0.99) were extracted from an artificial ‘benchmark’ by running our inverse finite-element-based extraction algorithm multiple times. Error between the mean extracted E and the known ‘benchmark’ value was 5.5 per cent for an MR layer, 3.6 per cent for a POLY layer, and 20.6 per cent for an EXP layer. Errors in at least one of the two hyperelastic parameters reached 75 per cent for the MR layer, 33 per cent for the POLY layer, and 400 per cent for the EXP layer, indicating that indentation has limited potential to extract two or more hyperelastic parameters accurately. However, the generalized elastic modulus extracted from indentation could be used as a quantitative measure to evaluate the influence of altered processing conditions, pathology, etc.