Elastic characterization of the gerbil pars flaccida from in situ inflation experiments

Abstract

In hearing science, finite element modelling is used commonly to study the mechanical behaviour of the middle ear. Correct quantitative elasticity parameters are an important input in these models. However, up till now, no large deformation elastic characterization of the pars flaccida, a small part of the tympanic membrane, has been carried out. In this paper, an elastic characterization of the gerbil pars flaccida is presented. The gerbil is used frequently as animal model in middle ear mechanics research. Characterization was done via inverse analysis of in situ static pressure inflation experiments. As a first approach, the pars flaccida was modelled as a linear homogeneous isotropic elastic membrane, which resulted in an average Young’s modulus of ${\left\langle E \right\rangle = (41.0 \pm 0.4)\,{\rm kPa}}$. It was found that linear elastic modelling cannot describe inflation stagnation at high pressures. Therefore, in a second approach, the Veronda–Westmann hyperelastic model was introduced. This was able to describe curve stagnation, the mean parameters that were found are ${\left\langle C_1 \right\rangle = (3.1 \pm 0.4)\,{\rm kPa}}$ and ${\left\langle C_2 \right\rangle = (2.5 \pm 0.2)}$. Finally, in situ strain was considered in the finite element models which resulted in a better description of the behaviour for small pressures. Incorporating this, the optimal Veronda–Westmann parameters are ${\left\langle C_1^{\varepsilon_R}\right\rangle = (2.6 \pm 0.6)\,{\rm kPa}}$, ${\left\langle C_2^{\varepsilon_R}\right\rangle = (1.4 \pm 0.2)}$ for a radial in situ strain of ${\left\langle \varepsilon_R \right\rangle = (12 \pm 2)}$. In conclusion, this paper shows that a linear elastic material is not appropriate to describe pars flaccida’s behaviour in the quasi-static pressure regime, that the currently used membrane stiffness estimates do not hold for large deformations and that incorporating an in situ strain in the models is necessary for a good description for small static pressures.