An indentation-based approach to determine the elastic constants of soft anisotropic tissues

Characterization of the mechanical properties of tissue can help to understand tissue mechanobiology, including disease diagnosis and progression. Indentation is increasingly used to measure the local mechanical properties of tissue, but it has not been fully adapted to capture anisotropic properties. This paper presents an indentation-based method to measure elastic constants of soft anisotropic tissues without additional mechanical tests. The approach uses measurement of the indentation modulus and the aspect ratio of the elliptical contact introduced by anisotropic mechanical properties of tissue to determine the elastic constants from finite element analysis. The imprinted area imparted by a fluorescent bead-coated spherical indenter showed the aspect ratio of the contact area, giving a generalized sense of the level of anisotropy, and instrumented indentation determined the indentation modulus. A parametric study using finite element simulation of the indentation tests established the relationship between the aspect ratio of contact and the non-dimensional ratios, E_x/E_y and G_xy/E_y; here, E_x and E_y are the Young's moduli (E_x > E_y) and G_xy is the shear modulus in the xy plane. For strongly anisotropic materials (E_x/E_y > 150), aspect ratio and indentation modulus are sufficient to determine G_xy and E_y. For weakly anisotropic materials, indentation modulus in the transverse direction, E_y, and the aspect ratio of contact in the anisotropic plane can be used to determine the elastic constants. The proposed approach improves the elastic characterization of soft, anisotropic biological materials from indentation and helps to elucidate the complex mechanical behavior of soft anisotropic tissues.