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

Abstract

An accurate estimation of tympanic membrane stiffness is important for realistic modelling of middle ear mechanics. Tympanic membrane stiffness has been investigated extensively under either quasi-static or dynamic loading conditions. It is known that biological tissues are sensitive to strain rate. Therefore, in this work, the mechanical behaviour of the tympanic membrane was studied under both quasi-static and dynamic loading conditions. Experiments were performed on the pars tensa of four gerbil tympanic membranes. A custom-built indentation apparatus was used to perform in situ tissue indentations and testing was done applying both quasi-static and dynamic sinusoidal indentations up to 8.2 Hz. The unloaded shape of the tympanic membrane was measured and used to create specimen-specific finite element models to simulate the experiments. The frequency dependent Young's modulus of each specimen was then estimated by an inverse analysis in which the error between experimental and simulated indentation data was optimised for each indentation frequency separately. Using an 8 μm central region thickness, we found Young's moduli between 71 and 106 MPa (n = 4) at 0.2 Hz indentation frequency. A standard linear viscoelastic model and a viscoelastic model with a continuous relaxation spectrum were used to derive a complex modulus in the frequency domain. Due to experimental limitations, the indentation frequency upper limit was 8.2 Hz. The average relative modulus increase in this domain was 14% and the increase was the strongest below 6 Hz.

Dynamic Properties of Tympanic Membrane in a Chinchilla Otitis Media Model Measured With Acoustic Loading

“…The modulus values of the chinchilla TM obtained in this study are significantly higher than the values reported by Zhang and Gan [5] for human TMs and Aernouts and Dirckx [16] for gerbil TMs and are only close to those in Fay et al [17] for cat TMs. The following considerations may explain this difference.…”

“…Aernouts and Dirckx used the micro-indentation measurement to estimate the Young's modulus of gerbil TM, considering an isotropic elastic membrane [16]. They reported that the Young's modulus varied between 71 and 106 MPa.…”

Optimization of a Lensless Digital Holographic Otoscope System for Transient Measurements of the Human Tympanic Membrane

“…Such measurements indicate that, even at high (i.e., >100 dB) sound pressure levels (SPL), the displacements of the surface of the TM are more than 3 orders of magnitude smaller than typical TM characteristic dimensions [20]. This suggests that the strains within the TM are in the linear regime and have negligible hysteresis [21]. We validate these assumptions as part of the development of the MPDE method.…”

“…The implementation of the MPDE method requires minimum hardware modification and utilizes a conventional camera (i.e., <20 fps) while allowing for high speed (i.e., >50 kHz) acquisition. The MPDE method utilizes the geometric linearity and repeatability [20, 21] of the acoustically induced nanometer deformations [1, 2] of the human TM. The transient displacement measurement capabilities of the DHS are verified against a laser Doppler vibrometer (LDV), on both artificial (latex membrane) and ex-vivo human TM samples, and we found samples a temporal repeatability > 96%, a time waveform correlation > 95%, and temporal and displacement difference of <10μs and <15nm, respectively.…”

A non-linear viscoelastic model for the tympanic membrane

“…The sound pressure was 80 dB sound pressure level, which is within the range of linear TM vibrations (e.g., Khanna and Tonndorf, 1972). Most recently, Aernouts and Dirckx (2012) performed in situ sinusoidal indentations on gerbil TMs at frequencies from 0.2 to 8.2 Hz. The strain magnitudes were small enough that the responses were linear.…”