Download numerical analysis of middle ear pressure effects on

NUMERICAL ANALYSIS OF MIDDLE EAR PRESSURE
EFFECTS ON PERFORMANCE OF IMPLANTABLE
HEARING DEVICES
Jiabin Tian, Jing Zhang, Zhushi Rao, Na Ta and Lifu Xu
Institute of Vibration, Shock and Noise, State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University, Shanghai 200240, China
e-mail: [email protected]
Middle ear pressure has a significant influence on the dynamic behavior of human ear. To
analyze the effect of this physiological condition on the implant performance of implantable
hearing devices, a finite element model of human ear consisting of the external ear canal,
middle ear and passive cochlea was first developed through Micro-CT imaging and reverse
engineering technology. Validation of this model was accomplished by comparing the dynamic responses with experimental data in the literature. Then the middle ear stiffening due
to static pressure varying from -2.0 to +2.0 kPa was considered by altering the elastic modulus of components in middle ear. Based on this model, a piezoelectric actuator was further
designed and attached to the incus long process. By means of acoustic-structure-fluid and
electro-mechanical coupled analysis, equivalent sound pressures (ESP) of the actuator under
different static pressure levels were finally calculated. The results show that ESPs of the actuator were decreased with the load of middle ear pressure in the frequency range of 250 to
2500 Hz, and increased at frequencies of 2500-8000 Hz. Meanwhile, negative pressure had a
greater influence on the actuator performance than positive pressure, especially at frequency
below 2500 Hz. This work will benefit the design and evaluation of implantable middle-ear
hearing devices for special physiological conditions.
1.
Introduction
Implantable middle ear hearing devices were originally designed and applied for patients with
sensorineural hearing loss. Nowadays, due to the change of excitation position, implantable hearing
devices can also be used to treat conductive and mixed hearing loss. Compared with conventional
hearing aids, implantable hearing devices have the advantages of keeping ear canal open, less feedback problem, better sound fidelity and larger gain at high frequency [1]. An implantable middle ear
hearing device usually includes three parts: a microphone, a signal processing module and a vibrating output actuator. The microphone is used to collect acoustic signals from the environment and
transform them into electrical signals, and then the electrical signals are processed by the signal
processor such as frequency division, denoising, amplitude modulation and finally transmitted to
the actuator. The actuator, which is attached to the ossicular chain or round window, takes advantage of its mechanical vibration to drive the human ear structures to compensate hearing loss. At
present, based on different implant positions of the actuator, several devices have been developed,
ICSV22, Florence (Italy) 12-16 July 2015
1
The 22nd International Congress on Sound and Vibration
such as the Vibrant Soundbridge (Med El Inc.) coupled to the incus long process, the Middle Ear
Transducer (Otologics Inc.) coupled to the incus body. Moreover, in some works [2, 3] the actuator
was also implanted onto the round window to directly drive the cochlea. In a word, implantable
middle ear hearing devices are becoming an effective mean in the treatment of hearing loss.
As a hearing equipment implanted into the human ear, the efficiency of implantable hearing devices is inevitably affected by its own performance and physiological conditions of the human ear.
Bornitz et al. [4] investigated different attachment points at the ossicular chain and calculated the
actuator performance and theoretical gain by harmonic analysis. Wang et al. [5] analyzed the effects
of coupling between ossicular chain and implantable devices on the efficiency of actuator stimulation by means of finite element (FE) method. Jenkins et al. [6] studied the intraoperative ossicular
loading to promote coupling efficiency of the actuator to ossicles by experimental method. All of
above studies mainly concentrated on coupling conditions between implantable devices and human
ear, but physiological conditions of the human ear were rarely considered. As for human ear, besides the dynamic sound pressure varying from 20 μPa at the threshold to 10 Pa at the pain threshold, the middle ear has to deal with quasi static pressure, for example caused by ambient pressure
variations, physiologic processes within the middle ear itself. Because this static pressure (±2.0 kPa)
is far greater than the dynamic sound pressure and thus has a big influence on the static and dynamic behavior of human ear [7], and furthermore affects the performance of implantable hearing devices. Lupo et al. [8] recently investigated the effect of middle ear effusion on the efficiency of
middle ear implant in human temporal bones. Their experimental results showed that the efficiency
of ossicular chain vibroplasty was not significantly affected by middle ear effusion but improved
efficiency was observed with round window vibroplasty.
At this stage, there are few reports about applying theoretical methods to study the effect of middle ear pressure on the performance of implantable hearing devices. The FE method, a general numerical procedure, has been widely applied in the study of human ear biomechanics, especially
stimulation of sound transmission [9, 10] and theoretical design of implantable actuators [4]. In this
study, a FE model of human ear consisting of the external ear canal, middle ear and cochlea was
first developed. Then a piezoelectric actuator was designed and attached to the incus long process to
drive the ossicular chain under a specified input voltage. By adjusting the elastic modulus values of
middle ear soft tissues, the effect of middle ear pressure on the dynamic responses of human ear
was introduced in this model. Under different static pressure levels, the equivalent sound pressure
(ESP) of the actuator was calculated to analyze the change of implant performance due to middle
ear pressure. This study will contribute to the optimal design of implantable hearing devices under
actual physiological conditions.
2.
Methods
2.1 Finite element model of human ear
A FE model of human ear consisting of the ear canal, middle ear and cochlea was constructed.
The geometric model of the ear canal and middle ear was established through Micro-CT scanning
and reverse engineering technology. The cochlea was simplified as an uncoiled, two-chambered and
fluid-filled duct and modeled as a passive model. The detailed modeling procedure including geometric information, applied softwares and methods to couple each part was identical to the previous
work by Tian et al. [11]. Figures 1 and 2 show the whole FE model of human ear and middle ear
components respectively. To allow visualization of the basilar membrane, the fluid in cochlea is
shown to be partially transparent in the two figures. Moreover, material properties of the air in the
ear canal and cochlear components were also the same as our previous model. In the present study,
five components including tympanic membrane (TM), stapedial annular ligament, round window,
incudomalleolar and incudostapedial joints were modeled as elastic materials but not viscoelastic
ICSV22, Florence, Italy, 12-16 July 2015
2
The 22nd International Congress on Sound and Vibration
materials [11]. Young’s modulus of all the structures in middle ear were identical to our previous
model.
Figure 1. Finite element model of human ear
Figure 2. Illustration of components in middle ear
Validation of the constructed FE model was verified by comparing calculated dynamic responses
under acoustic excitation with experimental results in the literature. A sound pressure of 90 dB SPL
(0.632 Pa) was applied at the location of 2 mm away from the TM in the ear canal. The harmonic
structure-acoustic-fluid coupled analysis over the frequency range of 250-8000 Hz was conducted
in this model using Abaqus 6.10. Figure 3a shows model-derived displacements at the TM and stapes footplate along with experimental measurements by Gan et al. [12] obtained from 10 human
cadaver temporal bones. As shown in this figure, the FE results are in reasonable agreement with
published data in terms of overall trends. At frequencies below 3000 Hz, both of the two displacement curves matched well with experimental curves, but at high frequencies (f>3000 Hz), there was
some difference between the present model and experimental data. Note that stapes footplate displacement is an important parameter to evaluate the performance of implantable hearing devices,
and therefore provides the basis for the following section. Figure 3b shows the middle ear pressure
gain function defined as a ratio of the scalae pressure near the oval window to the acoustic pressure
at the TM and experimental data in the literature [13, 14]. As can be seen in the figure, the modelderived pressure gain curve was generally within the range of measured curves by Puria et al. and
ICSV22, Florence, Italy, 12-16 July 2015
3
The 22nd International Congress on Sound and Vibration
Nakajima et al. As frequency increased from 1000 Hz to 8000 Hz, the FE results were gradually
close to the experimental data by Puria et al.
Figure 3. Comparison of model-derived dynamic responses with experimental measurements. a. Displacements at the TM and stapes footplate (FP). b. Middle ear pressure gain.
2.2 Simulation of middle-ear pressure effect
In this study, the effect of middle ear pressure was considered by adjusting the Young’s modulus
values of partial middle-ear components. This method was similar to that applied by Homma et al.
[15] to investigate effects of ear-canal pressurization on middle-ear bone- and air-conduction responses. The middle-ear components to adjust Young’s modulus included the following structures
and divided into four groups: Group 1 (TM, tympanic annulus), Group 2 (superior mallear ligament,
lateral mallear ligament, anterior mallear ligament, tensor tympani tendon), Group 3 (stapes annular
ligament), Group 4 (posterior incudal ligament, posterior stapedial tendon, incudostapedial joint).
The number of groups adopted in this model was different from that by Homma et al. (three groups)
for the purpose of considering the middle-ear pressure effect in a more comprehensive way. Under a
specific static pressure, each group was assigned an initial modulus gain factor relative to the modulus at 0 kPa. By means of matching the model-calculated dynamic responses with experimental data
in the literature, each group got a final gain factor. The static pressure levels studied in this model
were -2.0 kPa, -1.0 kPa, 0 kPa, +1.0 kPa and +2.0 kPa. Table 1 lists the obtained modulus gain factors of each group under different static pressure levels.
Table 1. Modulus gain factors of each group under different middle-ear pressure levels.
Group 1
Group 2
Group 3
Group 4
Modulus gain factor
-2.0 kPa -1.0 kPa +1.0 kPa +2.0 kPa
13
6
4
10
3
1.6
1.4
2
1.3
1.1
1.05
1.2
1.2
1.1
1
1.1
2.3 Modeling of piezoelectric actuator
A piezoelectric actuator was designed and attached to the incus long process to stimulate the ossicular chain, as shown in Fig. 4. The actuator was composed of a metal case, a piezoelectric stack
and an attachment clip which was used to couple the actuator to the incus. The two ends of the piezoelectric stack were fixed to the attachment clip and metal case respectively. At different applied
voltage levels, vibratory energy of the piezoelectric stack is transferred to the ossicles by means of
the metal case, which can be considered as an inertial mass.
ICSV22, Florence, Italy, 12-16 July 2015
4
The 22nd International Congress on Sound and Vibration
Figure 4. Coupled model of human ear and piezoelectric actuator. Dimensions of d and h represent the diameter and height of the actuator respectively.
The designed piezoelectric stack had 20 individual layers with a total height of 1.8 mm and a
cross section area of 1×1 mm2. Each layer was modeled with piezoelectric ceramic material PZT5H, which has been reported to manufacture implantable middle ear hearing devices [16]. Material
properties of PZT-5H used in the model referred to the data in the literature [17] and are listed in
Table 2. To ensure biocompatibility, material properties of the attachment clip and metal case were
assumed to the same as titanium alloy with a Young’s modulus of 116 GPa and density of 4500
kg/m3. In addition, dimensions of the actuator were 2.2 mm in diameter and 2.0 mm in height with a
total mass of 25 mg as shown in Fig. 4. The size of the actuator was small enough to be attached to
ossicular chain as a diameter of 3 mm and height of 2.4 mm were reported to be available for middle ear implants in the middle ear cavity [18].
Table 2. Material properties of PZT-5H.
Elastic Stiffnesses
(×1010 N/m2)
c11
c12
c13
c33
c44 c66
12.6 7.95 8.41 11.7 2.3 2.35
3.
Piezoelectric Coefficients
(C/m2)
e31
e33
e15
-6.5
23.3
17
Dielectric Constants
(×10-10 C/Vm)
ε11
ε33
150.3
130
Results
3.1 Effect of static pressure on human-ear dynamic responses
Figure 5. Model-derived dynamic displacements of the stapes footplate at different middle-ear static pressure levels. a. positive pressure (+1.0 kPa, +2.0 kPa). b. negative pressure (-1.0 kPa, -2.0 kPa).
Under different middle-ear static pressure levels, a sound pressure of 90 dB was consistently applied in the external ear canal 2 mm away from the TM and the displacement responses of stapes
footplate corresponding to each pressure level were obtained, as shown in Fig. 5. It is noted that
ICSV22, Florence, Italy, 12-16 July 2015
5
The 22nd International Congress on Sound and Vibration
zero static pressure means that the ear canal pressure is equal to the pressure in middle ear. As can
be seen in Fig. 5, the displacement of stapes footplate was decreased with the increase of absolute
value of middle ear pressure at frequencies below 2600 Hz. This result was consistent with the phenomenon of middle-ear stiffening due to static-pressure loading [15]. In the frequency range of
2600-8000 Hz, both of the positive and negative pressure resulted in increase of stapes footplate
displacement, which was observed in the experiment by Murakami et al. [19]. Moreover, by comparing calculated curves in Figs. 5a and 5b we can also see that the negative pressure caused more
reduction of footplate displacement than positive pressure in low frequency, especially the displacements at -1.0 kPa and +1.0 kPa. In a word, the above results indicate that the present FE model
can reflect the change of dynamic characteristics of human ear due to middle ear pressure and can
be used to evaluate implantable hearing devices in the following section.
3.2 Effect of static pressure on actuator performance
In the present study, ESP was employed to evaluate the performance of the actuator under various middle-ear pressures. By comparing the stapes displacements induced by sound pressure in the
external ear canal and the actuator, the ESP corresponding to a constant force or displacement excitation of the actuator can be obtained. The ESP level expressed as dB SPL is given as [20]
(1)
Peq  90  20 log10 (
dtr
)
d ac
where dac is the stapes footplate displacement driven by acoustic excitation of 90 dB in the ear canal and used as the baseline displacement, dtr is the stapes footplate displacement driven by mechanical excitation of the actuator and varied with static pressure levels. In this computation process,
acoustic-structure-fluid coupling in the human ear and electro-mechanical coupling in the piezoelectric stack were both taken into consideration to calculate ESP.
Figure 6. ESP at different middle-ear static pressure levels. a. positive pressure (+1.0 kPa, +2.0 kPa). b. negative pressure (-1.0 kPa, -2.0 kPa).
Figure 6 shows ESP of the actuator at an applied voltage of 1 V under different middle-ear static
pressure levels. As shown in this figure, ESP generated by the actuator with the input of 1 V voltage
was approximately 85 dB at frequencies below 2000 Hz and reached the maximum value of 110 dB
at frequency of 8000 Hz. However, the load of middle ear pressure resulted in the reduction of ESP,
especially in the frequency ranges of 250-800 Hz and 1000-2500 Hz. ESP of the actuator gradually
decreased as the absolute value of static pressure increased. In Figs. 6a and 6b, the maximum reduction values of ESP were 13 dB at +2.0 kPa and 14 dB at -2.0 kPa respectively, and both occurred at
the frequency of 500 Hz. This results indicated that middle-ear static pressure had a big influence
ICSV22, Florence, Italy, 12-16 July 2015
6
The 22nd International Congress on Sound and Vibration
on the performance of implantable hearing devices. Furthermore, by comparing the two figures, we
can also find that negative pressure lead to more reduction of ESP than negative pressure did in the
frequency range of 250-2500 Hz, but the difference between them was relatively small.
4.
Discussion
The derived results from the FE model of human ear consisting of ear canal, middle ear and inner ear had a reasonable agreement with experimental data in the literature and this ensured the accuracy of evaluating implantable hearing devices using this model. Meanwhile, the method of adjusting elastic modulus values of middle ear components to represent the middle-ear stiffening effect was also employed by Homma et al. [15]. In comparison with the work by Homma et al., three
components including posterior incudal ligament, posterior stapedial tendon and incudostapedial
joint were added and considered as contributing to the stiffening of middle ear structure. This was
consistent with the FE-simulation study by Wang et al. [7], which modeled middle ear structures as
hyperelastic materials and indicated that the three components were stiffened due to static pressure
load. However, because the detailed mechanism of middle ear stiffening due to static pressure is
complicated and have not been clearly understood, the present modeling method did not reveal this
mechanism but was only used to evaluate the performance of implantable hearing devices.
Middle ear effusion is usually associated with the middle ear pressure change [21] and was considered as not having a significant influence on the efficiency of implantable middle-ear hearing
devices driving ossicular bones in the human temporal bone experiment by Lupo et al. [8]. However,
analysis results in the present study show that the presence of middle ear pressure reduced the implant performance of the actuator, especially at frequencies of 250-2500 Hz, and further increased
power consumption of the device in this frequency range. Therefore, in the design of implantable
hearing devices, the potential impact of middle ear static pressure should be taken into consideration to achieve the aim of optimization design. Currently, using experimental methods to investigate
the effect of middle ear pressure on implantable devices has not been fully developed. This paper
indicates the necessity of physiological conditions in the design of implantable hearing devices
from a theoretical standpoint.
5.
Conclusion
A coupled FE model of human ear was developed and used to analyze the effect of middle ear
pressure on the performance of implantable hearing devices. Dynamic responses of the FE model
show a good agreement with experiment data in the literature. Middle ear pressure was introduced
by adjusting elastic modulus values of middle ear components and had the same influence on the
dynamic characteristics of human ear as experimental measurements. By coupling a designed piezoelectric actuator to the incus long process, ESP of the actuator under different static pressures
were calculated using this model. Analysis results indicated that ESP of the actuator was decreased
with the load of middle ear pressure in the frequency range of 250-2500 Hz and thus the implant
efficiency reduced. Meanwhile, negative pressure had a bigger impact on implantable hearing devices than positive pressure did but the difference between them was not remarkable.
REFERENCES
1 Horlbeck, D. Fully implantable ossicular stimulator, Operative Techniques in Otolaryngology-Head and Neck Surgery, 21 (3), 207-210, (2010).
2 Shimizu, Y., Puria, S. and Goode, R. L. The floating mass transducer on the round window
versus attachment to an ossicular replacement prosthesis, Otology & Neurotology, 32 (1), 98,
(2011).
ICSV22, Florence, Italy, 12-16 July 2015
7
The 22nd International Congress on Sound and Vibration
3 Schraven, S. P., Hirt, B., Goll, E., Heyd, A., Gummer, A. W., Zenner, H. P. and Dalhoff, E.
Conditions for Highly Efficient and Reproducible Round-Window Stimulation in Humans,
Audiology and Neurotology, 17 (2), 133-138, (2012).
4 Bornitz, M., Hardtke, H.-J. and Zahnert, T. Evaluation of implantable actuators by means of a
middle ear simulation model, Hearing Research, 263 (1), 145-151, (2010).
5 Wang, X. L., Hu, Y. J., Wang, Z. L. and Shi, H. Finite element analysis of the coupling between ossicular chain and mass loading for evaluation of implantable hearing device, Hearing
Research, 280 (1), 48-57, (2011).
6 Jenkins, H. A., Pergola, N. and Kasic, J. Intraoperative ossicular loading with the Otologics
fully implantable hearing device, Acta Oto-Laryngologica, 127 (4), 360-364, (2007).
7 Wang, X., Cheng, T. and Gan, R. Z. Finite-element analysis of middle-ear pressure effects on
static and dynamic behavior of human ear, The Journal of the Acoustical Society of America,
122, 906, (2007).
8 Lupo, J. E., Koka, K., Jenkins, H. A. and Tollin, D. J. Vibromechanical Assessment of Active
Middle Ear Implant Stimulation in Simulated Middle Ear Effusion: A Temporal Bone Study,
Otology & Neurotology, (2013).
9 Gan, R. Z., Reeves, B. P. and Wang, X. L. Modeling of sound transmission from ear canal to
cochlea, Annals of Biomedical Engineering, 35 (12), 2180-2195, (2007).
10 Koike, T., Wada, H. and Kobayashi, T. Modeling of the human middle ear using the finiteelement method, The Journal of the Acoustical Society of America, 111, 1306, (2002).
11 Tian, J., Huang, X., Rao, Z., Ta, N. and Xu, L. Finite element analysis of the effect of actuator
coupling conditions on round window stimulation, Journal of Mechanics in Medicine and Biology, [Online.] available:http://www.worldscientific.com/doi/abs/10.1142/S0219519415500487
12 Gan, R. Z., Wood, M. W. and Dormer, K. J. Human middle ear transfer function measured by
double laser interferometry system, Otology & Neurotology, 25 (4), 423-435, (2004).
13 Puria, S., Peake, W. T. and Rosowski, J. J. Sound-pressure measurements in the cochlear vestibule of human-cadaver ears, The Journal of the Acoustical Society of America, 101 (5),
2754-2770, (1997).
14 Nakajima, H. H., Dong, W., Olson, E. S., Merchant, S. N., Ravicz, M. E. and Rosowski, J. J.
Differential intracochlear sound pressure measurements in normal human temporal bones,
Journal of the Association for Research in Otolaryngology, 10 (1), 23-36, (2009).
15 Homma, K., Shimizu, Y., Kim, N., Du, Y. and Puria, S. Effects of ear-canal pressurization on
middle-ear bone-and air-conduction responses, Hearing Research, 263 (1), 204-215, (2010).
16 Wang, Z., Mills, R., Luo, H., Zheng, X., Hou, W., Wang, L., Brown, S. I. and Cuschieri, A. A
Micropower Miniature Piezoelectric Actuator for Implantable Middle Ear Hearing Device,
Biomedical Engineering, IEEE Transactions on, 58 (2), 452-458, (2011).
17 Five piezoelectric ceramics, Bulletin 66011/F, Vernitron Ltd., (1976).
18 Hong, E. P., Park, I. Y., Seong, K. W. and Cho, J. H. Evaluation of an implantable piezoelectric floating mass transducer for sensorineural hearing loss, Mechatronics, 19 (6), 965-971,
(2009).
19 Murakami, S., Gyo, K. and Goode, R. L. Effect of middle ear pressure change on middle ear
mechanics, Acta Oto-Laryngologica, 117 (3), 390-395, (1997).
20 Rosowski, J., Chien, W., Ravicz, M. and Merchant, S. Testing a method for quantifying the
output of implantable middle ear hearing devices, Audiology and Neurotology, 12 (4), 265276, (2007).
21 Dai, C., Wood, M. W. and Gan, R. Z. Combined effect of fluid and pressure on middle ear
function, Hearing research, 236 (1), 22-32, (2008).
ICSV22, Florence, Italy, 12-16 July 2015
8