Characterization of mouse artery tissue properties using experimental testing combined with finite element modelling

Abstract

Indentation tests have been widely used to determine the material properties of arterial tissue. However, it remains a challenge to extract the relevant material parameters from the force-indentation curves that result from indentation tests. This paper presents a detailed procedure for determining the first-order Ogden parameters, $\mu$ and $\alpha$, for mouse arterial tissue using a method that combines indentation tests with numerical simulations. The method builds on a previous study (Li and Masen, 2024) and has been expanded to account for the surface roughness of the indented specimen. It is assumed that hyperelastic material behaviour can be linearized for small strain increments, ${\varepsilon }_{ji}\le$ 1%, allowing the model developed by Hayes (Hayes et al., 1972) to be applied to accommodate the contact behaviour in each increment. However, mouse arterial specimens have an irregular or rough surface which complicates the use of Hayes’ model, as the thickness of the specimen is an input parameter into the model. To solve this, we introduce an ‘equivalent thickness’ that can be applied in Hayes’ model by identifying the thickness that yields the smallest variance $S^2$ of the shear moduli among a range of possible specimen thickness values. The shear moduli obtained for the equivalent thickness, denoted as the equivalent shear moduli $G_i^{\ast }$, along with the corresponding principal strains ${\varepsilon }_j$ obtained from simulations, were used to calculate the principal stresses ${\sigma }_j$ using Hooke’s law. By combining the principal stresses ${\sigma }_j$ across all increments, a nonlinear stress ${\sigma }_j$ versus strain ${\varepsilon }_j$ curve was generated, from which the first-order Ogden parameters $\mu$ and $\alpha$ were obtained. The proposed method is demonstrated by applying it to simulated force-indentation curves, successfully recovering the input parameters for both thickness and Ogden parameters. The method was subsequently applied to 26 experimentally obtained curves, yielding an average shear modulus $G$ of 1.22 kPa for the indented mouse arterial tissue specimens, with values ranging from 0.27 to 5.02 kPa. Numerical simulations of the indentation process with the obtained values were used to verify the obtained material parameters.