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 <E> = (41.0 ± 0.4) 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 <C1> = (3.1 ± 0.4) kPa and <C2> = (2.5 ± 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 <CεR1> = (2.6 ± 0.6) kPa, <CεR2> = (1.4 ± 0.2) kPa for a radial in situ strain of <εR> = (12 ± 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.

Analysis of the Mechanical Properties of the Human Tympanic Membrane and Its Influence on the Dynamic Behaviour of the Human Hearing System

“…A homogeneous and uniform isotropic strain value has been applied to the membrane, ranging from 0.1% to 1% ( ɛ 11 = ɛ 22 = 0.001 to 0.01 in the plane of the TM and ɛ 33 = − 2 ɛ 11 ). These values are very below those assumed by Aernouts and Dirckx [ 30 ] and cause a static imperceptible displacement of the umbo very below 10 μ m. The presence of prestrain must be related to the position and orientation of the fiber on the membrane. A detailed and accurate estimation of a complex prestrain pattern is difficult to do without speculations, so this approach is considered a good solution to evaluate its qualitative influence.…”

“…It is well accepted the presence of active muscles on the middle ear system [ 28 ], but apart from hypothesized active tension effects inside the TM due to smooth muscles [ 29 ], only passive prestrain has been named by several authors [ 1 , 2 ], but no quantitative estimation has been clearly made. Recently, Aernouts and Dirckx [ 30 ] assumed an in situ strain for the elastic characterization of the gerbil pars flaccida, but no other numerical model has included this effect.…”

Static versus dynamic gerbil tympanic membrane elasticity: derivation of the complex modulus

“…The pars tensa has a base diameter of approximately 4 mm and an apex height of approximately 1 mm. An elastic characterisation procedure for the gerbil pars flaccida can be found in Aernouts and Dirckx (2011).…”

Tympanic membrane pressure buffering function at quasi-static and low-frequency pressure variations

“…When the actuator moves, the volume and hence the pressure of the enclosed gas change, since the amount of gas remains constant. With a pressure sensor (PDCR 10/L, Druck, Inc., New Fairfield, CT, USA) coupled to the tube, the pressure values were measured and used in a custom-built feedback system (Aernouts and Dirckx, 2011). This way the actual pressure follows the desired values with an accuracy of better than 2% over the entire frequency and pressure range.…”