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Hearing Research xxx (2009) xxx–xxx
Contents lists available at ScienceDirect
Hearing Research
journal homepage: www.elsevier.com/locate/heares
Quantification of tympanic membrane elasticity parameters from in situ point
indentation measurements: Validation and preliminary study
Jef Aernouts *, Joris A.M. Soons, Joris J.J. Dirckx
Laboratory of Biomedical Physics, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
a r t i c l e
i n f o
Article history:
Received 17 July 2009
Received in revised form 4 September 2009
Accepted 17 September 2009
Available online xxxx
Keywords:
Tympanic membrane elasticity
Point indentation
Inverse modeling
a b s t r a c t
Correct quantitative parameters to describe tympanic membrane elasticity are an important input for
realistic modeling of middle ear mechanics. In the past, several attempts have been made to determine
tympanic membrane elasticity from tensile experiments on cut-out strips. The strains and stresses in
such experiments may be far out of the physiologically relevant range and the elasticity parameters
are only partially determined.
We developed a setup to determine tympanic membrane elasticity in situ, using a combination of point
micro-indentation and Moiré profilometry. The measuring method was tested on latex phantom models
of the tympanic membrane, and our results show that the correct parameters can be determined. These
parameters were calculated by finite element simulation of the indentation experiment and parameter
optimization routines.
When the apparatus was used for rabbit tympanic membranes, Moiré profilometry showed that there
is no measurable displacement of the manubrium during the small indentations. This result greatly simplifies boundary conditions, as we may regard both the annulus and the manubrium as fixed without
having to rely on fixation interventions. The technique allows us to determine linear elastic material
parameters of a tympanic membrane in situ. In this way our method takes into account the complex
geometry of the membrane, and parameters are obtained in a physiologically relevant range of strain.
Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction
Finite element modeling is a powerful method for the investigation of middle ear mechanics, (Eiber, 1999; Elkhouri et al., 2006;
Koike et al., 2002; Sun et al., 2002), studying the effect of middle
ear pathologies, (Gan et al., 2006) and predicting the behaviour
of middle ear prostheses (Eiber et al., 2006; Schimanski et al.,
2006). The technique allows to take into account the complex
shape and boundary conditions of the middle ear structure. Current finite element models are mainly restricted to acoustical
sound pressures and low acoustical frequencies, and good data
for the mechanical properties of the tympanic membrane are still
lacking. It is known, however, that tympanic membrane elasticity
has a significant influence on the resulting output (Elkhouri
et al., 2006). Furthermore, when one wants to extend finite element models to the quasi-static regime (Dirckx and Decraemer,
2001), effects such as nonlinearity and viscoelasticity of the tympanic membrane can play an important role. On the other hand,
when one considers dynamical behaviour, the strain rate dependent tympanic membrane stiffness should be taken into account.
* Corresponding author. Tel.: +32 32653435.
E-mail address: [email protected] (J. Aernouts).
URL: http://www.ua.ac.be/bimef (J. Aernouts).
Mechanical properties of the human tympanic membrane were
first measured by Békésy in 1960 (Békésy, 1960). He applied a
known force on a cut-out strip and measured the resulting displacement. Assuming the sample to be a uniform, isotropic, linear
elastic beam with a thickness of 50 lm, he calculated a Young’s
modulus of 20 MPa. Kirikae measured the ‘dynamical’ stiffness of
a strip of human tympanic membrane in 1960 (Kirikae, 1960).
From the system’s resonance frequency, he calculated a Young’s
modulus of 40 MPa based on a thickness of 75 lm. In 1980, Decraemer et al. showed a nonlinear stress–strain curve for human tympanic membrane (Decraemer et al., 1980). In the large strain
condition, starting from 8%, a Young’s modulus of 23 MPa was
proposed.
In 2005, Fay et al. estimated the elastic modulus of human tympanic membrane based on the elasticity of the collagen fibers and
fiber density (Fay et al., 2005). Their data suggested an elastic modulus in the range 100—300 MPa, significant higher than previous
values. More recently, new experimental observations of the
Young’s modulus of human tympanic membrane were published
by Cheng et al. (2007). They conducted a uniaxial tensile test and
obtained a stress–strain curve which was in good agreement with
that of Decraemer et al. Describing the nonlinearity using the firstorder Ogden model, they found l1 ¼ 0:46 MPa and a1 ¼ 26:76. In
0378-5955/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.heares.2009.09.007
Please cite this article in press as: Aernouts, J., et al. Quantification of tympanic membrane elasticity parameters from in situ point indentation measurements: Validation and preliminary study. Hear. Res. (2009), doi:10.1016/j.heares.2009.09.007
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J. Aernouts et al. / Hearing Research xxx (2009) xxx–xxx
addition, preliminary stress relaxation tests were performed to
study the viscoelastic behaviour of the tissue. Two years later,
the same research group characterized more detailed the viscoelastic behaviour by in-plane and out-of-plane nanoindentations
and found Young’s relaxation moduli (Huang et al., 2008; Daphalapurkar et al., 2009). Their results show an in-plane modulus changing by 10% from 1 to 100 s with steady-state values of 37:8 and
25:73 MPa respectively for different samples. The out-of-plane
modulus seemed to reduce by 50% from 1 to 100 s with a steady-state value varying from 2 to 15 MPa over the surface. These
experiments show a wide variety and it is not straightforward
how to interpret the different moduli. Regardless Kirikae’s measurement, all previous mentioned publications report quasi-static
behaviour of the tympanic membrane. Very recently, Luo et al.
measured the Young’s modulus at high strain rates using a miniature split Hopkinson tension bar (Luo et al., 2009). Due to the viscoelastic properties of the membrane, they found that the Young’s
modulus increases with the increase in strain rate. However, they
only measured up till 2 kHz.
It should also be mentioned that in addition to human tympanic
membrane data, a lot of experiments have been performed on tympanic membranes of laboratory animals as well.
It is clear that accurate data for the mechanical properties of the
tympanic membrane, both for human and animal samples, cannot
be determined using uniaxial tensile tests. At first, when one considers the tympanic membrane to be linear elastic, which is reasonable in the acoustical regime, a Young’s modulus can only be
assigned in a physiologically irrelevant strain range starting from
8%. Moreover, small and long strips with uniform thickness of
the tympanic membrane need to be cut to perform uniaxial tensile
tests. In general, however, tympanic membrane thickness varies
with a factor 4 between periphery and the center (Kuypers et al.,
2005), making it impossible to cut long uniform samples.
Another parameter that might have an influence on the
mechanical behaviour of the tympanic membrane is the presence
of prestrain. Békésy and Kirikae are the only ones who investigated
this characteristic, but their results depended on the type of species and were not unambiguous (Decraemer and Funnell, 2008). Finally, the pars flaccida has never been examined and properties
like anisotropy, inhomogeneity, nonlinearity and viscoelasticity
are only poorly studied. These are mechanical properties that
may become important in more detailed examinations.
In order to obtain data in more realistic circumstances, we
developed a setup to determine tympanic membrane elasticity
in situ. The measurement method consists of doing a point indentation perpendicular on the membrane surface; measuring the
indentation depth, resulting force and three-dimensional shape
data; simulating the experiment with a finite element model and
adapting the model to fit the measurements using optimization
procedures. In the first part of this paper, the method of measuring
and model optimization is validated on a scaled phantom model of
the tympanic membrane with known elasticity parameters. In the
second part, preliminary results from one rabbit tympanic membrane experiment are shown.
hyperelastic material is typically characterized by a strain energy
density function W. A well known constitutive law for rubber-like
materials is the Mooney–Rivlin law (Treloar, 1975):
W¼
N
X
1
C ij ðI1 3Þi ðI2 3Þj þ K ln ðJ Þ;
2
iþj¼1
ð1Þ
with N the order of the model, I1 and I2 the strain invariants of the
deviatoric part of the Cauchy–Green deformation tensor, C ij the
Mooney–Rivlin constants, K the bulk modulus and J the determinant of the deformation gradient which gives the volume ratio.
The invariants are given as:
I1 ¼ k21 þ k22 þ k23 ;
1
1
1
I2 ¼ 2 þ 2 þ 2 ;
k1 k2 k3
ð2Þ
ð3Þ
with ki ði ¼ 1; 2; 3Þ the principal stretches. It is common to assume
that rubber materials are incompressible when the material is not
subjected to large hydrostatic loadings, so that the last term in Eq.
(1) will be neglected (Bradley et al., 2001). In this study, we will
only consider the first-order Mooney–Rivlin equation ðN ¼ 1Þ. In
this case, Eq. (1) becomes:
W ¼ C 10 ðI1 3Þ þ C 01 ðI2 3Þ:
ð4Þ
This low order strain energy function is described by two constants: C 10 and C 01 .
Since the latex rubber is perfectly homogeneous in all its physical properties, a uniaxial tensile test was carried out which results
in accurate determination of the first-order Mooney–Rivlin
parameters.
The phantom model of the tympanic membrane was created by
pushing a ‘manubrium shaped rod’ in a flat circular rubber membrane which was constrained at its circumference. In this way,
the typical conical tympanic membrane shape was obtained. The
diameter of the phantom model was 50 mm and the height was
16 mm, approximately eight times the size of a human tympanic
membrane. The phantom model was placed on a translation
– and rotation stage, a schematic drawing is shown in Fig. 1. Indentations in and out in a direction perpendicular to the surface membrane were carried out using a stepper motor with indentation
depths up till 2 mm. The needle had a cylindrical ending with a
diameter of 1:7 mm and indentations were carried out slowly
ðr_ ¼ 0:125 mm s1 Þ, meaning that quasi-static behaviour was studied. The points of indentation were chosen in the undermost part
2. Materials and methods
2.1. Phantom model
In the validation experiment, we used rubber from medical
gloves, which mainly consists of natural latex. The thickness is
0:18 0:02 mm and the material is isotropic and homogeneous.
Like other rubber-like materials, natural latex exhibits very large
strains with strongly nonlinear stress–strain behaviour. For this
reason, the rubber can be described as a hyperelastic material. A
Fig. 1. Schematic drawing of the point indentation setup: (1) translation and
rotation stage, (2) phantom model: ‘manubrium shaped rod’ pushed in circular
rubber membrane, (3) needle connected to a load cell, (4) stepper motor and (5)
LVDT.
Please cite this article in press as: Aernouts, J., et al. Quantification of tympanic membrane elasticity parameters from in situ point indentation measurements: Validation and preliminary study. Hear. Res. (2009), doi:10.1016/j.heares.2009.09.007
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J. Aernouts et al. / Hearing Research xxx (2009) xxx–xxx
of the ‘cone’ (the inferior part of the ‘tympanic membrane’) because in the tympanic membrane case, it showed to be experimentally impossible to do indentations in the superior part. By doing
the indentation perpendicular to the surface and not too close to
the boundary, slippage between the needle and the rubber was
avoided. The resulting force was measured with a load cell (Sensotec Model 31). The exact indentation depth was assessed with an
LVDT (HBM KWS3071). All signal processing was done via A/D conversion in Matlab (using NI DAQPad-6015).
Three-dimensional shape data were measured with a projection
LCD-Moiré profilometer (Buytaert and Dirckx, 2008; Dirckx and
Decraemer, 1989), developed in our laboratory. The device is able
to perform topographic measurements with a height resolution
of 25 lm on a matrix of 1392 1040 pixels. The Moiré shape measurement was used to locate the exact point of indentation and to
determine if the membrane is locally at right angle with the indentation needle.
The numerical simulations were performed with the finite element code FEBio, which is specifically designed for biomechanical
applications. The rubber membrane was modeled as a first-order
Mooney–Rivlin material, triangular incompressible shell elements
were used to create a non-uniform mesh, with increased mesh
density in the contact areas. The border of the membrane was
x; y; z constrained, with x; y and z the axes of a Cartesian coordinate
system with the x; y plane parallel to the ‘annulus plane’. In the
first model steps, the ‘manubrium shaped’ rigid body was moved
vertically into the flat membrane using a combination of rigid –
and sliding contact. In the following model steps, the perpendicular needle indentation was modeled as a rigid body translation
with frictionless sliding contact.
In order to find the first-order Mooney–Rivlin parameters, we
optimized the average square force difference defined as
errorforce ¼
N
2
1X
F exp ðqj Þ F mod ðqj Þ ;
N j¼1
ð5Þ
in which N is the number of evaluated points, qj the indentation
depth, F exp ðqj Þ the experimental force and F mod ðqj Þ the simulated
force. The optimization was carried out with a surrogate modeling
toolbox (Gorissen et al., 2009; Jones et al., 1998). Using this routine,
firstly one has to specify the input domain. Then, a first surrogate
model
calculated
from
24
homogeneously
distributed
ðC 10 ; C 01 ; errorforce Þ data points is built. Afterwards, the model is refined on the basis of a gradient-optimum based sample selection in
order to localize very accurately the optimum values.
2.2. Tympanic membrane
The animal model selected for the present study was the New
Zealand white rabbit. Animals were sacrificed by injection of
120 mg/kg natrium pentobarbital and temporal bones were removed. Openings were made in the bulla so that visual access
was provided from both sides of the tympanic membrane, leaving
the tympanic membrane and entire middle ear ossicle chain intact.
Total preparation time was always less than 1.5 h. The study was
performed according to the regulations of the Ethical Committee
for Animal Experiments of the University of Antwerp.
The tympanic membrane was modeled as a linear isotropic
homogeneous elastic material which is described with two independent elastic constants: the Young’s modulus E and Poisson’s
ratio m. The thickness of the rabbit tympanic membrane varies
somewhat along the membrane, however, in this study the membrane was modeled with a uniform thickness. Since no data on
rabbit tympanic membrane thickness are available, we used a
mean value of 12:5 lm measured for the cat tympanic membrane
3
with confocal microscopy (Kuypers et al., 2006). In forthcoming
work, we will add a measured thickness distribution to our model.
The prepared sample was glued on a small tube so it could be
placed on a translation and rotation stage in a similar way as in
Fig. 1. In a direction perpendicular to the membrane, the indentation needle was moved back and forth from the lateral (external
ear) side with a maximal indentation depth up till 400 lm using
a piezoelectric actuator (PI P-290) in combination with an LVDT
(Solartrion) and a feed-back controller unit (PI E-509 E-507). The
needle had a cylindrical ending with a diameter of 210 lm. The
indentation was carried out in steps of 40 lm with a step time of
4 s, thus quasi-static behaviour was studied. The resulting force
was measured with a strain-gage force transducer (SWEMA SG3). Input and output signals were controlled with a computer via
A/D conversion in Matlab (using NI DAQPad-6015).
Three-dimensional shape data were measured from the medial
side with our LCD-Moiré profilometer. Because tympanic membrane dimensions are significant smaller than those of the phantom model, the setup was adjusted resulting in a height
resolution of 15 lm. Since the tympanic membrane is almost
non-reflective, it was coated with a layer of white paint mixed with
glycerin to avoid dehydration. Again, the Moiré data were used to
determine exact needle position and to verify perpendicular needle
positioning.
Moreover, a highly detailed non-uniform mesh was created on
the basis of the Moiré shape images. In the needle indentation area
and in the manubrium neighbourhood, mesh density was increased. Since in the rabbit case the pars flaccida can geometrically
be regarded as almost completely separated from the pars tensa
(Fumagalli, 1949), the influence of the pars flaccida can be ignored
so that the membrane was modeled as a homogeneous material.
The manubrium was modeled as a rigid body that is x; y; z constrained because no measurable motion was observed during
indentation (see further). The border of the tympanic membrane
was modeled as fully clamped, the perpendicular needle indentation was modeled as a rigid body translation with frictionless sliding contact. Afterwards, in a similar way as described for the
phantom model case, the errorforce was optimized in order to determine linear elasticity parameters.
3. Results
3.1. Phantom model
The mean output of the uniaxial tensile test, carried out on three
different samples, was C 10 ¼ ð43 5Þ kPa and C 01 ¼ ð159 6Þ kPa.
In Fig. 2a, the output of a force-indentation experiment is plotted (line). The indentation was carried out slowly and only a small
hysteresis is seen. The associated finite element model is shown in
Fig. 2b, with the number of membrane shell elements equal to
4337. In the first model steps, the ‘manubrium shaped rod’ rigid
body displacement was applied which results in the typical conical
shape. Next, the perpendicular point indentation was applied. The
color map represents the effective strain, which rises up to approximately 40% in the indentation area.
The resulting surrogate model is shown in Fig. 3. The evaluated
samples are plotted as white points and the color map represents
the surrogate model fitted through the errorforce values. A range
of minima lying on a linear curve can be seen (dashed line). One
can see that as a consequence of the gradient-optimum criterion
sample selection, more samples were chosen in the minimum area
in comparison to elsewhere. The force-indentation output for three
different points of ðC 10 ; C 01 Þ optimum values is plotted in Fig. 2a
(different dots). According to this plot, we see that the first-order
Mooney–Rivlin equation is able to describe the load curve quite
Please cite this article in press as: Aernouts, J., et al. Quantification of tympanic membrane elasticity parameters from in situ point indentation measurements: Validation and preliminary study. Hear. Res. (2009), doi:10.1016/j.heares.2009.09.007
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J. Aernouts et al. / Hearing Research xxx (2009) xxx–xxx
force [mN]
160
140
experimental data
model data: C10=20 kPa; C01=183 kPa
120
model data: C10=130 kPa; C01=77 kPa
model data: C10=75 kPa; C01=130 kPa
100
80
60
40
20
0
0
500
1000
1500
indentation depth [µm]
2000
Fig. 2. Phantom model: (a) plot of experimental force-indentation data (line) and best models output (different dots). (b) FE model with applied ‘manubrium shaped’ rigid
body displacement and needle indentation. The effective strain in the point indentation area after indentation rises up to approximately 40%.
5
x 10
2000
0.2
baseline
model data: C10=31 kPa; C01=172 kPa
1800
0.15
model data: C =11 kPa; C =191 kPa
2
10
01
model data: C =51 kPa; C =153 kPa
0.05
1200
1.4
1000
1.2
800
error_z [mm]
1400
[mN2]
0.1
force
C_01 [Pa]
1.6
1600
10
01
0
−0.05
error
1.8
−0.1
600
1
−0.15
400
0.8
−0.2
200
25
0.6
2
4
6
8
C_10 [Pa]
10
12
30
35
40
45
50
r [mm]
14
4
x 10
Fig. 3. Phantom model: contour plot with result of errorforce optimization after 119
samples. The samples are plotted as white dots, the color map represents the fitted
surrogate model and the resulting range of local minima is highlighted with a
dashed line.
Fig. 4. Phantom model: plot of difference between experimental and model
deformation data along a point indentation section line for different Mooney–Rivlin
parameters. In the case of C 10 ¼ 31 kPa and C 01 ¼ 172 kPa, the difference error is the
smallest.
2.5
3.2. Tympanic membrane
Fig. 5 shows an experimentally measured section plot of tympanic membrane deformation during indentation. This experiment
shows no manubrium movement, so the manubrium can be
regarded as fixed.
without indentation
with indentation
2
height [mm]
well. It is not possible, however, to extract a unique set of Mooney–
Rivlin parameters only on the basis of a load curve optimization.
Therefore, also a shape analysis was carried out in which the average square difference between model – and experimental deformation (conform Eq. (5)) along a point indentation section was
optimized so that the final optima were filtered out of the range
of force minima. In Fig. 4, the difference between model and experimental shape data is shown for different Mooney–Rivlin parameters. The final output after shape optimization was C 10 ¼ 31 kPa
and C 01 ¼ 172 kPa. The final output for a second indentation experiment was C 10 ¼ 33 kPa and C 01 ¼ 163 kPa.
1.5
1
0.5
0
−0.5
0
1
2
3
section axis [mm]
4
5
Fig. 5. Rabbit tympanic membrane (right): experimentally measured section plots
before and after indentation to show fixed behaviour of manubrium.
The finite element model of the perpendicular point indentation
experiment is shown in Fig. 6, with the number of membrane shell
elements equal to 5988. The perpendicular point indentation re-
Please cite this article in press as: Aernouts, J., et al. Quantification of tympanic membrane elasticity parameters from in situ point indentation measurements: Validation and preliminary study. Hear. Res. (2009), doi:10.1016/j.heares.2009.09.007
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J. Aernouts et al. / Hearing Research xxx (2009) xxx–xxx
Fig. 6. Rabbit tympanic membrane (right): FE model with indentation: the effective strain in the point indentation area after indentation rises up to approximately 15%.
sults in an effective strain of approximately 15% in the point indentation area and due to manubrium fixation, no deformation in the
opposite membrane part can be seen.
In Fig. 7a, the associated force output of the experiment is plotted (dotted line). When doing slow indentations, only a small hysteresis can be seen. Using the finite element model and the
experimental force-indentation data, the surrogate model was calculated. The input interval was set to E ¼ ½20; 40 MPa and
m ¼ ½0:2; 0:49, the resulting surrogate model is shown in Fig. 7b.
The evaluated samples are plotted as white points and the color
map represents the surrogate model fitted through the errorforce
values. In total, 118 samples were evaluated to guarantee an accurate determination of the model.
Inspecting the resulting output, one can see that the optimum
value for the Young’s modulus E in the Poisson’s ratio interval
m ¼ ½0:2; 0:45 is practically constant: E ¼ 30:4 MPa. For higher
Poisson’s ratio’s, the optimum value decreases. For a Poisson’s ratio
m ¼ 0:49, towards the theoretical upper limit m ¼ 0:5 that represents incompressibility, the optimum value is E ¼ 26:4 MPa. In
Fig. 7a, the force-indentation curve is plotted for the optimum values with respectively m ¼ 0:2; 0:45 and 0:49. The simulated curves
show good agreement with the experimental one. For all these
optimum values, models show practically no difference in model
deformation, so that a shape analysis is not under discussion.
4. Discussion
If large enough samples of a material are available, tensile tests
on a strip can be performed to determine elasticity parameters. On
small samples like the tympanic membrane, it becomes very difficult to control the exact size and extension of a strip. In this case, it
becomes inevitable to perform in situ measurements because specimens are too small and the natural shape of the membranes are
complex.
In this paper, a new approach is presented in which elasticity
parameters are determined by inverse modeling of an in situ point
indentation experiment.
At first, the characterization method was validated on a latex
rubber phantom model. Measuring the first-order Mooney–Rivlin
elasticity parameters with a uniaxial tensile test, carried out on
three different samples, the output was C 10 ¼ ð43 5Þ kPa and
C 01 ¼ ð159 6Þ kPa. Applying the point indentation method, the
output of a first point indentation experiment was C 10 ¼ 31 kPa
and C 01 ¼ 172 kPa. The output of a second experiment on a different location was C 10 ¼ 33 kPa and C 01 ¼ 163 kPa. One can see that
there is a good agreement between the two approaches. However,
there is approximately a 25% relative error for the C 10 values. It is
known that the C 10 parameter has a small influence on the stress–
strain curve for strains smaller than 50%. Since effective strains in
16
experimental data
model data: E=30.4 MPa; v=0.2
model data: E=30.4 MPa; v=0.45
model data: E=26.4 MPa; v=0.49
14
10
9
0.45
12
8
5
6
4
0.3
4
[mN2]
force
0.35
error
6
8
v
force [mN]
7
0.4
10
3
2
2
0.25
1
0
0
50
100
150
200
250
indentation depth [µm]
300
350
400
0.2
2
0
2.5
3
E [Pa]
3.5
4
7
x 10
Fig. 7. Rabbit tympanic membrane (right): (a) plot of experimental force-indentation data (line) and best models output (different dots). (b) Contour plot with optimization
output after 118 evaluated samples: the samples are plotted as white dots and the color map represents the fitted surrogate model.
Please cite this article in press as: Aernouts, J., et al. Quantification of tympanic membrane elasticity parameters from in situ point indentation measurements: Validation and preliminary study. Hear. Res. (2009), doi:10.1016/j.heares.2009.09.007
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J. Aernouts et al. / Hearing Research xxx (2009) xxx–xxx
the indentation experiments go only up to approximately 80% and,
this apparently high relative error can be argued.
Having validated the method, a preliminary experiment on a
right rabbit tympanic membrane was performed. Indentations
were carried out slowly, so that quasi-static behaviour was studied. In this first approach, the tympanic membrane was considered
to be a linear isotropic homogeneous elastic material. Although we
know this is not the best choice, it allows a comparison with previous studies.
From our Moiré shape measurements, we learned that the
manubrium does not move under influence of a small point indentation on the tympanic membrane. This is a very important result,
as it shows that no complex procedures are needed to fixate the
manubrium in order to obtain well defined boundary conditions.
Since there was practically no difference in model deformation
for different force-indentation optimum values, we cannot filter
out one optimum value for the Young’s modulus. In contrast, it will
depend on the choice of Poisson’s ratio. In most of the middle ear
finite element models, a Poisson’s ratio in the range m ¼ ½0:3; 0:4
is proposed (Elkhouri et al., 2006; Koike et al., 2002; Sun et al.,
2002), with a corresponding optimum value of E ¼ 30:4 MPa. However, it might be argued that the Poisson’s ratio should be close to
0.5 because soft tissues are thought to be nearly incompressible. In
this case, the corresponding optimum value is E ¼ 26:4 MPa. In
both cases, the optimum values are close to those found in previous studies.
In future work, more point indentation experiments will be performed and a measured tympanic membrane thickness distribution will be added to the finite element models. Simultaneously,
we will investigate the behaviour under dynamic load conditions
and the influence of nonlinearity, inhomogeneity, anisotropy, viscoelasticity and the possible presence of prestress.
Acknowledgments
This work was supported by the Institute for the Promotion of
Innovation through Science and Technology in Flanders (IWTVlaanderen).
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Please cite this article in press as: Aernouts, J., et al. Quantification of tympanic membrane elasticity parameters from in situ point indentation measurements: Validation and preliminary study. Hear. Res. (2009), doi:10.1016/j.heares.2009.09.007