Download Study of the properties of the middle-ear prosthesis

A STUDY OF THE PROPERTIES OF THE
MIDDLE-EAR PROSTHESIS
Romuald Bolejko and Przemysław Plaskota
Chair of Acoustics and Multimedia, Wroclaw University of Technology,
Wybrzeze Wyspianskiego 27, 50-370 Wrocław, Poland
e-mail: [email protected]
If the auditory ossicles of the middle ear are destroyed there is often used a middle ear prosthesis. This kind of prosthesis is placed in a way that makes it something like a mechanical
link between a tympanic membrane and an oval window of a cochlea. The geometry of the
prosthesis and the material used for its production may vary. It is still required to look for
more biostable and more biocompatible materials. Therefore the evaluation of the acoustomechanical properties of the different types of prostheses is needed.
In the paper the study of the properties of the middle-ear prosthesis as well as the
measurement setup is presented. The main element of the setup is a mechanical model of the
ear. The model consists of two cavities coupled by the imitation of a tympanic membrane
and terminates in the imitation of an oval window. The acoustical properties of the prosthesis
have been investigated by measurements of acoustic pressure in the cavity of the outer ear
and vibrations of the tympanic membrane and the oval window. A laser-Doppler vibrometer
has been used for the aforementioned measurements. Different types of prosthesis have been
investigated and compared by sound transmission efficiency.
1.
Introduction
In a case of damage of auditory ossicles in human ear a middle ear prosthesis is used to prevent a
loss of hearing. Middle ear prostheses vary in shape and biostable material they have been produced
of and thus possess different mechanical properties [1]. In turn mechanical properties of the prostheses may have significant influence on transmitting the sound from the outer ear to the inner ear
and thus determine their efficiency. Furthermore, available research on the currently known prostheses [1] show that their mechanical parameters may substantially vary, whereas there are still no
clear-cut standard procedures for assessing their usefulness for patients.
In the reference literature one may generally find the results for numerical modelling of the middle ear prostheses [1] which in in some cases are supported by the results of measurements in animals. [2] Nevertheless there is still missing a clear physical model that would allow to analyse the
mechano-acoustical properties of the middle ear prostheses, and primarily their efficiency in transmitting the sound to the inner ear.
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The 22nd International Congress on Sound and Vibration
This study presents a mechanical model of the human ear which allows to measure the prosthesis’ transmittance from the outer ear to the inner ear. The proposed model has been analysed in
terms of its usefulness and limitations in measuring the efficiency of the middle ear prostheses. Also
the measurements results of the middle ear prosthesis are presented.
2.
Anatomy of the ear
Figure 1 displays a basic scheme of the human ear [3]. Concerning its anatomy and functions the
human ear can be divided into three sections: the outer ear, the middle ear, and the inner ear.
The outer ear consists of the pinna and the external auditory meatus of 2÷2.5 cm in length and
0.6÷1.25 cm3 in volume [3]. The middle ear consists of the ossicles (the hammer with a mass of ca.
23 mg (4), the anvil ca. 27 mg, and the stirrup (5) ca. 2.5 mg [3]), which are situated within the air
filled tympanic cavity of volume ca. 2 cm3 [3].
Figure 1. Schematic model of the ear [5].
The tympanic cavity is connected to the nasal cavity with the auditory tube (14) 0.1÷0.5 cm2 in
diameter [3] known as Eustachian tube, which is closed in its normal state. The outer ear is separated from the middle ear by the tympanic membrane (eardrum) (2) with a diameter of about 1 cm
and 0.1 mm thickness. [3] The basic resonance of the tympanic membrane is 1.2÷1.4 kHz. [3] The
ossicles of the middle ear mechanically connect the central part of the eardrum with the oval window (8) of the inner ear.
The main portion of the inner ear is the cochlea, which is connected to the middle ear through the
oval window (8) and the round window (9) of ca. 2 mm2 area each [3]. The cochlea is filled with
incompressible fluid of about 1 cm3 in volume [3].
Vibrations of the eardrum are transmitted by the ossicles to the oval window of the inner ear. As
a result of surface area change (the area of eardrum in comparison to the oval window) and mechanical lever formed by the ossicles the acoustic pressure in the section between the eardrum and
the oval window is increased by about 20÷24 dB [3].
Vibrations of the oval window induce the movement of the fluid (11) in the cochlea, which in
turn by agitating the basilar membrane (10) induces nerve impulses in the auditory nerve. The displacement of the oval window and the movement of the cochlear fluid are counterbalanced by the
defection of the round window.
In a case the ossicles are damaged the middle-ear prosthesis is provided. The middle-ear prosthesis substitutes for the ossicular system by mechanically connecting the central part of the eardrum
with the oval window of the inner ear.
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3.
Electrical model of the ear
v
c
Z
v
o
C
p
R
p
L
1
t
C
t
R
t
L
e
R
e
L
With the use of electro-mechano-acoustic analogy an electrical equivalent circuit can represent a
human ear. The reference literature [4] presents the equivalent circuit for a healthy ear, whereas
Figure 2 shows an electrical equivalent circuit for an ear without the ossicles with the middle-ear
prosthesis.
r
C
p
C
2
t
C
p
e
C
m
C
Figure 2. Electrical model of the ear without auditory ossicles with a middle-ear prosthesis.
In the electrical model the outer ear is represented by Le for mass and Ce for capacitance of the
air column present in the auditory canal. Resistance Re stands for the sound transmission losses occurring in the outer ear. Lt, Rt and Ct1,Ct2 stand for mass, loss and flexibility of the eardrum respectively. The middle-ear air ventricle produces capacitance Cm. Cp, Rp and Lp refer to the capacitance,
losses and mass of the middle-ear prosthesis. Cov and Cr stand for capacitances of the oval ear and
the round ear respectively whereas Zc denotes the impedance of the auditory cochlea.
The impedance of the cochlea represented by Zc generally is not a lumped element characterised
by resistance, mass or capacitance, but the dominating element is the fluid mass Lf inside the cochlea, which equals about 160 mg. It should be also noted that this mass is bigger than the mass of the
auditory ossicle system (ca. 50 mg) or typical mass of the prosthesis (<100 mg).
The above given model does not include the mass of the round window, the mass of the oval
window or the losses occurring in the middle ear.
Due to converting the acoustic pressure in the outer ear into the movement of the fluid within the
cochlea, transmittance v/p is significant, where p is the acoustic pressure near the eardrum, and v
stands for velocity of the inner-ear fluid. In order to compare the achieved results with the data
available in the reference literature the ratio x/p also will be analysed, where x stands for the fluid
movement within the cochlea and – taking into account the incompressibility of the fluid – the displacement of the round window.
In case there is no prosthesis, elements Cp, Rp and Lp are to be removed from the equivalent circuit, and at the same time impedance Zc is bypassed by the capacitance Ct2 that equals to infinity
(impedance equals zero). It means that there is no transmission sound energy to cochlea.
Taking into account the anatomy of the ear the following relations between the elements of the
given equivalent circuit can be defined:
C p << Ct 2
(1)
C p << Cm
L p << L f
R p << R f , where R f losses in the cochlea
As for the above given relations between the parameters of the equivalent circuit (1)assuming
that Lp and Rp tend to zero and in particular substituting the fluid mass Lf for the impedance of the
cochlea Zc, the equivalent circuit can be simplified to the form presented in Figure 3. In this circuit
the capacitance Covr=Cov/2=Cr/2 defines the resultant capacitance of the oval and round windows.
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v
p
C
p
e
C
m
C
Figure 3. Simplified electrical model of the ear without auditory ossicles and with a middle-ear prosthesis.
In the simplified equivalent circuit there are three serially connected filters placed behind the
outer ear: the middle-pass (formed by the eardrum), the low-pass filter (demarcated by the capacitance of the prosthesis) and the middle-pass (formed by the capacitance of the oval and round windows and the mass of the cochlea fluid).
It must also be clearly noted that in fact most of the ear elements can be described with the use of
the lumped elements such as resistance, induction and capacitance only within a limited frequency
range, whereas in general they are elements of disperse parameters or elements of many degrees of
freedom. For example the eardrum can be represented by three elements: the mass, capacitance and
resistance, that means by a circuit of one degree of freedom but only within the frequency below the
basic resonance frequency of the eardrum.
4.
Mechanical model and measurement set-up
As for the anatomy of the ear presented in Figure 1 and the given simplified equivalent circuit of
the ear (Figure 3) a mechanical model of the ear has been drawn up to conduct the measurement of
the efficiency of the middle ear prosthesis. Figure 4 features the structure of the mechanical model
along with the measurement scheme, whereas Figure 5 presents the constructed mechanical model
of the ear.
In the mechanical model the outer ear is a round cross-section canal of 10 mm in diameter and
34 mm in length. The canal ends with a membrane tightened to such extend that the frequency of
the basic resonance of the membrane is 1.2÷1.4 kHz. From the outside the outer-ear canal is closed
with an microphone. The lateral canal is closed with an earphone.
The middle ear is a round canal of 10 mm in diameter and 25 mm in length. The middle-ear canal is connected to the outside with a duct of ca. 1 mm diameter (imitation of the Eustachian tube).
This duct is used to balance the pressure in the middle ear, e.g. during implanting the prosthesis or
inserting the element imitating the inner ear; it may also serve as resistance element during measurements.
The inner ear has been constructed as a separate element to be inserted into the middle ear. It
contains a 0,16 cm3 volume fluid-filled canal with adjustable cross-section. The beginning and the
end of this 3 mm diameter canal are closed with tightened membranes imitating the oval and round
windows. The inner ear canal also comprises of a hole meant for filling it with the fluid and for
deaerating. The spring and micrometric screw allow to adjust the depth of the insertion of this element into the middle ear and the compressive force of the prosthesis placed between the tympanic
membrane and the oval window.
The mechanical model significantly differs from an ear anatomy by the way how middle ear cavity is taken into account. In the model middle ear cavity is placed between ear drum and an oval
window whereas in the ear the cavity is situated after the round window. The equivalent electric
circuit of the mechanical model is shown in Figure 6. However taking into account the relation
Cp<< Cm (1) the mechanical model still provides reliable results. The main difference between
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mechanical and anatomy models is that in the mechanical model there is still weak sound transmission to inner ear even for a model without a prosthesis. Such transmission depends on the ratio
Cm/Zc.
In the outer ear a 1/4” microphone recording acoustic pressure at the membrane, whereas the vibrations of the oval and round windows are measured with a laser vibrometer. The measurement
results are, in most cases, presented as the ratio of the velocity or the displacement of the round
windows to the acoustic pressure recorded by the microphone.
In
Out
POLYTEC PSV400M2
In
426B03
prostheses
oval window
tympanic membrane
ear
phone
round window
LASER HEAD
377C01
1/4 "
fluid
34
25
outer ear
middle ear
inner ear
Figure 4. Mechanical model of the ear and measurement set-up.
v
f
R
f
L
r
+
v
o
C
t
C
t
R
t
L
e
R
e
L
Figure 5. Actual mechanical model of the ear.
p
C
p
m
C
inner ear
e
C
Figure 6. Simplified electrical model of the mechanical model of an ear without auditory ossicles and
with a middle-ear prosthesis.
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5.
Results
Despite of relatively good knowledge of the human ear anatomy there is still not enough information on many parameters describing mechanical properties of the elements of the ear. It concerns
for example mechanical properties of the eardrum and the inner ear such as stiffness of the oval or
round windows, stiffness of the basement membrane, losses occurring in the middle ear or the inner
ear. Apart from that it is not entirely ascertained which parameters are important and should be absolutely taken into account while assessing the efficiency of the middle-ear prosthesis and which
could be omitted. Excluding some unimportant parameters may substantially simplify the mechanical model of the ear and thus make the measurements easier.
By analysing the simplified equivalent circuit presented in Figure 3 one may conclude that the
most important parameters as for the assessment of the efficiency of the auditory prostheses are the
mechanical parameters of the eardrum (mass, losses and stiffness of the eardrum), capacitance of
the middle-ear ventricle and the impedance of the cochlea, and above all the stiffness and mass at
the point of fastening of the prosthesis (that means in the plane of the oval window) as well as
losses in the cochlea. In the developed mechanical model the eardrum is represented by an evenly
tightened membrane, whereas in reality it is a conical element fastened with different stiffness
around the membranes edge (the eardrum is more flexible in its lower section where there is socalled pars flaccida). More over above the basic resonance frequency a tightened membrane does
not vibrate as a stiff piston. Different sections of the membrane, depending on the modes of vibrations, vibrate with varied amplitudes and phases. Additionally in special cases different sections of
the membrane vibrate in counter-phase and e.g. for the modes with odd number of node lines the air
is not compressed in the middle ear, and thus there is no capacitance Cm in the equivalent circuit.
The capacitance of the prosthesis Cp bypasses the inner-ear section and thus can substantially reduce transmission of the sound to the inner ear in case ossicles are not presented. Moreover for the
model based on the scheme that is presented in Figure 6 because of a Cm the sound pressure is still
transmitted to inner ear even for the model without prosthesis.
The above-described relations as well as their influence on the sound transmission from the outer
ear to the inner ear are confirmed by the calculation presented in Figure 7.
Figure 7. Calculation results (E-M-A model) of the transmission v/p from the outer ear to the round
window for model without prosthesis (blue), and with prosthesis (red).
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In case of the model without a prosthesis in the transmittance characteristic there is one specific
resonances for approximately 1.9 kHz. The resonance is characterised by the basic vibrations resonance of the tympanic membrane. In higher frequencies a rapid drop in round window displacement
occurs, which is about 60 dB/octave. Furthermore, based on the presented results (Figure 7) it can
be observed that the greatest efficiency of the middle-ear prostheses is observed in this frequency
range, for the frequencies above the basic resonance of the tympanic membrane with the transmittance decrease of 60dB/octave
In Figure 8 the transmission v/p from the outer ear to the round window for the actual mechanical model without prosthesis is presented. It can be observed good agreement between calculation
(Figure 7) and measurement results. The first resonance for approximately 2.1kHz is identified by
measurement as a basic whereas for c.a. 4.2kHz second eardrum vibrations resonances.
Figure 8. Measurement result of the transmission v/p from the outer ear to the round window obtained
using the actual mechanical model without a prosthesis.
In Figure 9 the measurement results for the model with three different types of prosthesis are
presented. The shapes of transmission curves are quite similar but there are significant differences
in their amplitude. At this moment it is difficult to define the reasons of such differences. . It should
be noticed, that the way a prosthesis is placed can also influence measurement results.
Figure 9. Measurement result of the transmission x/p from the outer ear to the round window obtained
using the actual mechanical model with 3 different types of the prosthesis.
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Figure 10. Measurement result of the transmission x/p from the outer ear to the round window obtained for the model with the prosthesis compressed between eardrum and oval window. Arrows show
the direction of the changes caused by compression of the prosthesis. The lower curve – results for the
model without prosthesis.
In Figure 10 the measurement results for the prosthesis compressed with different forces between
eardrum and oval window are presented. It can be observed that as force is increased the transmission is decreased by several dB at around 2 kHz and at the same time increased even by 6 dB at
higher frequencies.
6.
Summary
The work presents a measurement system meant for conducting the studies on the mechanoacoustic properties of the middle-ear prostheses. The basic element of this system is a mechanical
model of the human ear. The model comprises of three elements/ventricles imitating the outer ear,
the middle ear and the inner ear. With the use of electro-mechano-acoustic analogy the electric
equivalent circuit of the ear model has been developed and its basic properties defined. With the use
of the developed mechanical model the measurements were conducted to assess the influence of the
chosen elements of the model on the achieved outer-ear acoustic pressure transmission to the vibrations of the inner-ear round window.
The mechanical model of the ear can be used in the assessment of the efficiency of the middleear prosthesis. Three different types of the prosthesis are measured and compared using developed
mechanical model. The influence of compression of a prosthesis between eardrum and oval window
on its efficiency are presented.
References
1 Zenner H.P., Freitag H.G.,Linti C.,Steihardt U., Rodriguez J., Preyer S., Mauz P.S., Surth M.,
Planck H., Baumann I., Lehner R., Eiber A. Acoustomechanical properties of open TTP titaniummiddle ear prodtheses. Hearing Research, 192, 36-46, 2004.
2 Mojallal H., Stieve M., Turck C., Krueger I., Witteck N., Sub B., Mueller P.P., Behrens P.,
Lenarz T., Functional evaluation of middle ear prostheses. IFMBE Proceedings, vol.14/1,
139-141, 2007.
3 Skudrzyk E., Die grundlagen der akustik, Springer-Verlag, Wien, 1954.
4 Onchi Y., Mechanism of the Middle Ear, J.Acoust.Soc.Amer., vol.33, 794-805, 1961.
5 Bekesy G., Experiments in hearing. ASA, 1986.
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