Measuring absorbed energy in the human auditory system using finite element models: A comparison with experimental results

Abstract

Background: There are different ways to analyze energy absorbance (EA) in the human auditory system. In previous research, we developed a complete finite element model (FEM) of the human auditory system.

Objective: In this current work, the external auditory canal (EAC), middle ear, and inner ear (spiral cochlea, vestibule, and semi-circular canals) were modelled based on human temporal bone histological sections.

Methods: Multiple acoustic, structure, and fluid-coupled analyses were conducted using the FEM to perform harmonic analyses in the 0.1-10 kHz range. Once the FEM had been validated with published experimental data, its numerical results were used to calculate the EA or energy reflected (ER) by the tympanic membrane. This EA was also measured in clinical audiology tests which were used as a diagnostic parameter.

Results: A mathematical approach was developed to calculate the EA and ER, with numerical and experimental results showing adequate correlation up to 1 kHz. Another published FEM had adapted its boundary conditions to replicate experimental results. Here, we recalculated those numerical results by applying the natural boundary conditions of human hearing and found that the results almost totally agreed with our FEM.

Conclusion: This boundary problem is frequent and problematic in experimental hearing test protocols: the more invasive they are, the more the results are affected. One of the main objectives of using FEMs is to explore how the experimental test conditions influence the results. Further work will still be required to uncover the relationship between middle ear structures and EA to clarify how to best use FEMs. Moreover, the FEM boundary conditions must be more representative in future work to ensure their adequate interpretation.

Keywords: Finite element model; auditory system; energy absorbance.

Figure 1.

A cross-section of the ear illustrating the probe used to measure impedance when inserted into the ear canal. The probe emits a sound pressure wave that is incident to the tympanic membrane. Some of the incident sound pressure is reflected and this is then measured by the probe. The remaining incident sound pressure is absorbed by the tympanic membrane and the structures behind it.

Figure 2.

Hexahedral finite element model (FEM) for the external auditory canal based on the tympanic membrane FEM.

Figure 3.

The means for the tympanic membrane speed module for the three finite element models studied, CATIOSCO, CATI, and CATIOS. The CATI comprised the external auditory canal (EAC) and tympanic membrane (TM); CATIOS comprised the EAC, TM, ossicular chain (OC), and simplified cochlea; and CATIOSCO comprised the EAC, TM, OC, and the entire cochlea.

Figure 4.

Comparison of the three studied finite element models with an experimental model by Zhang and Gan for the module (A) and phase (B) tympanic membrane impedance (Z_TM).

Figure 5.

Comparison of the three studied finite element models for the module (A) and phase (B) external auditory canal impedance (Z_EC).

Figure 6.

Energy absorbed by the tympanic membrane for the different finite element models studied.

Figure 7.

Energy absorbed by the tympanic membrane for the finite element models and experimental results described in other publications.

Figure 8.

Phase comparison of the module (A) and phase (B) external auditory canal impedance with the findings published by Zhang and Gan (2012).