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XXIV ICTAM, 21-26 August 2016, Montreal, Canada
SPATIAL NON-UNIFORMITY IN THE YOUNG’S MODULUS OF THE HUMAN EARDRUM
S. Alireza Rohani1a), Soroush Ghomashchi2, Sumit K. Agrawal3 & Hanif M. Ladak1, 2, 3
1
Biomedical Engineering, Western University, London, Ontario, Canada
2
Medical Biophysics, Western University, London, Ontario, Canada
3
Otolaryngology - Head & Neck Surgery, Western University, London, Ontario, Canada
Summary The eardrum plays an important role in transferring sound energy to the cochlea. Several recent studies have used inverse finite
element (FE) methods to estimate the mechanical properties of the eardrum. However, the non-uniformity of the mechanical properties over the
surface of the eardrum has not yet been reported. Our objective was to develop an approach to investigate the spatial non-uniformity of the
Young’s modulus (E) of the eardrum. In this work, the shape of the eardrum before and after pressurization was imaged and compared with FE
model simulations for optimization purposes. A modified Nelder-Mead optimization technique was used in this study. The effects of two types
of eardrum partitioning on the optimization were studied and compared. Results showed that partitioning of the eardrum into 4 quadrants produces
a closer match between simulated and experimentally measured deformations compared with the assumption of uniformity or with partitioning
into concentric regions.
INTRODUCTION
The eardrum has a significant role in hearing. Sound in the environment is collected by the auricle (outer visible part of
the ear) and is focused down the ear canal where it vibrates the eardrum, a thin conical membrane. Vibration of the eardrum
causes a chain of three tiny bones (malleus, incus and stapes) to vibrate and transfer the sound energy to the inner ear,
specifically the cochlea, where mechanical vibrations of the cochlear fluids are transduced to sensorineural signals for
processing and perception. Common hearing tests, such as tympanometry, involve measurement of the acoustic properties of
the air in the ear canal under specific conditions including both static pressurization and dynamic acoustic stimulation. Finite
element (FE) modelling of these tests could potentially improve the diagnosis and treatment of hearing diseases1.
Accurate values for the mechanical properties of the eardrum are crucial for FE modelling. For physiological sound
pressure levels, a linear elastic material model characterized by the Young’s modulus (E) can be used. In current models, it is
assumed that E is either constant over the eardrum’s surface or E changes concentrically over the surface. The objective of
this work is to develop and evaluate an approach to estimate the spatial non-uniformity in Young’s modulus of the human
eardrum with the aim of improving the accuracy of FE models.
MATERIALS AND METHODS
Previously, we introduced an in situ estimation technique in which an FE model was optimized to match experimental
data acquired during eardrum pressurization in a rat model2. We have adapted this approach and applied it to a freshly frozen
cadaveric human ear. The middle-ear cavity was pressurized to 500 Pa and the deformed shape of the eardrum after
pressurization was imaged using a Fourier transform profilometer (FTP). To simulate the pressurization experiment, a
specimen-specific FE model of the eardrum at rest was defined from a 3D micro-computed tomography (micro-CT) image
(Figure 1a). E was then estimated using Nelder-Mead optimization, by minimising the cost function comparing the deformed
FE model shape to the measured shape after pressurization. The cost function is based on the differences in measured and
simulated eardrum height values (Z) relative to the XY-plane defined by the plane of the eardrum boundary at multiple points
over the eardrum. Figure 2 shows a schematic representation of the optimization technique.
Figure 1 – Imaging and modeling of the eardrum. (a)
3D micro-CT image of human middle ear. (b) FE
mesh of the eardrum and malleus.
a)
Corresponding author. Email: [email protected].
Figure 2 – Flowchart of the estimation algorithm. 𝐶 is the cost
function to be minimized in which 𝑍𝑖𝐹𝑇𝑃 and 𝑍𝑖𝑠𝑖𝑚 denote the
measured and simulated Z coordinates, respectively, for point 𝑖.
In this work, we assumed a uniform thickness of 110 um for the eardrum. The eardrum was modelled using triangular
shell elements, and the malleus was modelled using tetrahedral solid elements. All FE modelling was performed in COMSOL
Multiphysics® (Version 5.1) and optimizations were performed in MATLAB® (Release 2015a). In order to investigate the
spatial non-uniformity of E over the surface of the eardrum, results from two types of partitioning of the eardrum were
compared with results from the uniform E assumption. The two types of partitioning considered in this study included dividing
the eardrum into 4 quadrants or into 4 concentric regions; the values of E were permitted to vary from quadrant to quadrant
or from region to region when performing optimization, thus simulating non-uniformity.
RESULTS
Optimal E values for this specimen were obtained under the asumption of a single uniform E value and the two types of
partitioning and are summarized in Table 1. Figures 3a-c show the difference (i.e., error) between the simulated and measured
shapes at a pressure of 500 Pa when using the optimal E values for the simulations.
Table 1 – E estimates for each partitioning type. E_PI, E_PS,
E_AI and E_AS are the values of E in each quadrant shown in
Figure 3b. Similarly, E_1, E_2, E_3 and E_4 are E values in each
concentric region shown in Figure 3c.
Single
E (MPa)
5.39
Cost Function
0.96
Partitioning Type
Quadrants
Concentric
E_PI
9.7 E_1
16.5
E_PS
5.4 E_2
6.7
E_AI
2.4 E_3
3.6
E_AS
4.3 E_4
3.5
0.79
0.89
Figure 3 – Error maps between simulated and measured shape at a pressure of 500 Pa with simulations done using optimal
E values from Table 1. Dotted line represents the boundary of the entire eardrum obtained from micro-CT image. Colored
areas are regions within the field of view of the FTP apparatus. Simulations were performed under the following
assumptions: (a) uniform mechanical properties, (b) properties varying over 4 quadrants, and (c) properties varying over 4
concentric regions.
DISCUSSION AND CONCLUSION
Estimation of E using a pressurization technique has the advantage of being non-destructive and is easier to model
compared with tensile testing on eardrum strips or indentation testing. Results from the single-E assumption are comparable
to recent literature using indentation techniques3. The cost function decreases by 18% after partitioning into 4 quadrants, while
the reduction was only 7% with concentric region partitioning. Therefore, partitioning of the eardrum into four quadrants and
allowing E to vary from quadrant to quadrant improves the match between simulated and measured deformations.
References
[1] Daniel S. et al.: Clinical Application of a Finite-Element Model of the Human Middle Ear. J. Otolaryngology 30(6):340-345, 2001.
[2] Ghadarghadar N. et al.: Estimation of the Quasi-Static Young's Modulus of the Eardrum Using a Pressurization Technique." Comput Meth Prog Bio
110(3):231-239, 2013.
[3] Aernouts J. et al.: Mechanical Properties of Human Tympanic Membrane in the Quasi-Static Regime From in situ Point Indentation Measurements. Hearing
Res 290(1):45-54, 2012.