Polish J. of Environ. Stud. Vol. 15 No. 4A (2006), 140-142
Modelling of Some Mechanical Malfunctions
of the Human Tympanic Membrane
E. Skrodzka, J. Modáawska
Institute of Acoustics, A. Mickiewicz University, PoznaĔ, Poland
Abstract
Many researchers have reported mechanical damages of a human tympanic membrane (TM) in the form of
a rupture. Some forms of cicatrices and bosses were also observed on the TM. Ruptures and cicatrices can be
treated as TM’s mechanical modifications. We present numerical models of the human TM with such
modifications. The Finite Element Method was used as a numerical tool. The aim of our work was to simulate
mechanical behaviour of the TM with a rupture and with an additional mass. Results of vibrational analysis for
the structurally modified models were compared to results obtained from the physiological model. The main
characteristics predicted from the modified TM’s have shown that all modifications affected calculated curves
in all investigated cases.
Keywords: tympanic membrane, structural modifications, mechanical behaviour
Introduction
Mechanical damages or dysfunctions of a human
tympanic membrane (TM) can be acquired or related to
biochemical malfunctions [1, 2]. Many researchers have
reported acquired mechanical damages in the form of a rupture. The TM rupture may be caused by impact noise (i.e.
explosions). Some forms of cicatrices and bosses
of different origin were also observed on the TM [1]. Both
ruptures and cicatrices can be treated as mechanical
malfunctions of the TM.
There are many numerical models of the TM and the
whole middle ear in the physiological state as well as many
models including dysfunctions of the ossicular chain [3].
However, there have been no reports about modelling
of mechanical malfunctions of the TM. The aim of our
work was to numerically simulate mechanical behaviour
of the TM with a rupture and with an additional mass. Such
modelling may help better understanding of some
mechanical malfunctions of the TM.
Numerical models of the TM
with ruptures and additional mass
The human TM was modeled as a semi-conical threedimensional structure with dimensions as well as isotropic
material constants chosen to be realistic, or to be similar to
those known from experiments. Details of the physiological
model were described in our previous work, [4]. The
physiological model was structurally modified by adding
holes and mass. All ruptures and bosses were placed
anterior-inferior portion of the TM. The area of ruptures
was 2.2*10-6 m2 (small hole), 4.8*10-6 m2 (medium hole),
13.4*10-6 m2 (big hole) and 16.2*10-6 m2 (huge hole). Two
kinds of bosses were modeled. Their physical parameters
differed from those of the physiological TM (density
ȡ=1.2*103 kg/m3, pars tensa Young’s modulus of elasticity
E=3.3*107 (N/m2), total mass 8.2*10-6 kg, total area 70*10-6
m2). The thin and long bosses were modeled for the
following values of physical parameters: ȡ1=1.8*103 kg/m3
and E1 = 5.0*107 N/m2 (boss 1); ȡ2 = 2.6*103 kg/m3,
Modeling of Some Mechanical…
141
a)
b)
c)
d)
Fig. 1. (a) Input-output characteristics for models with holes; (b) input-output characteristics for models with bosses; (c) transfer
functions for models with holes; (d) transfer functions for models with bosses for selected points on the TM
142
Skrodzka E., Moádawska J.
E2= 7.2*107 N/m2 (boss 2); ȡ3=3.5*103 kg/m3, E3=9.7*107
N/m2 (boss 3). Additional mass was 9.36*10-6 kg (boss 1;
114.2% of the physiological model mass), 8.90*10-6 kg
(boss 2; 108.5 % of the physiological model mass) and
8.50*10-6 kg (boss 3; 103.7 % of the physiological model
mass) respectively. The thick and short bosses were
modeled for the following parameters: ȡ1=1.8*103 kg/m3
and E1= 5.0*107 N/m2 (boss 1a); ȡ2=2.6*103 kg/m3, E2=
7.2*107 N/m2 (boss 2a); ȡ3=3.5*103 kg/m3, E3=9.7*107
N/m2 (boss 3a). Additional mass was 9.28*10-6 kg (boss 1a;
113.2 % of the physiological model mass); 8.85*10-6 kg
(boss 2a; 107.9 % of the physiological model mass) and
8.48*10-6 kg and (boss 3a; 103.4 % of the physiological
model mass). The Finite Element Method (FEM) was
applied to modeling the dynamic behavior of the modified
TMs [5]. Frequency response analysis based on modal
superposition was used to solve the steady state response of
the structure subjected to harmonic loading. In this research
the NE/NASTRAN v.8.3K solver for FEM [6] together with
FEMAP v.8.3.0.1 pre- and post processor [7] was used, and
both programs were run on PC Pentium IV, 2.4 GHz.
Results and discussion
The TM models were tested by calculations of the
dynamic characteristics (input-output functions) and
velocity in points (model nodes). Calculations were
compared to results obtained from the normal-functioning
model of the TM, [4]. Point no. 1 was chosen on the pars
tensa portion, point no. 2 – on the pars flaccida portion,
point no. 3 – on the manubrium. The model was loaded by
sinusoidal pressure of frequency 0.5, 0.8. 1, 1.5, 2, 3, 4, 5, 6
and 7 kHz, applied perpendicular to model surface. Applied
sound pressure levels along the main axis of symmetry were
20-110 dB SPL, with 10 dB step. Examples of calculated
input-output functions are presented in Fig.1a (ruptures) and
Fig. 1b (bosses). Results are presented for chosen
frequencies 0.5 kHz and 2 kHz as the frequency band
limited by them is the most important for speech
intelligibility. All presented input-output functions show
linear behaviour, as it has been expected for the TM and the
linear model. However, results obtained from models with
holes are significantly different from those of the normal
TM model and they depend on the observation point,
frequency and the area of rupture. Results for bosses are
more consistent – for all chosen physical parameters the
input output functions are higher than the curve for the
normal TM. Examples of calculated velocity for selected
points vs. load frequency for ruptures are shown in Fig. 1c
(ruptures) and Fig. 1d (bosses). Results are presented for 60
and 90 dB SPL. All curves obtained for modified models
are generally higher than curves for the normal TM in lower
frequencies (up to 2-3 kHz). The greatest effect is observed
for big and huge holes as it could be expected [1]. For
bosses results are more uniform, the smallest effect was
observed for boss 3, the highest for boss 3a. Physical
parameters of bosses were chosen arbitrary, as no literature
data are available now. None of the chosen set of physical
parameters of bosses has secured normal functioning of the
TM. Velocities of the TM motion higher than normal may
influence signal processing on higher stages of the auditory
system.
Conclusions
Our numerical simulations have shown that all
structural modifications of the TM affected calculated
curves in most cases. It is worthwhile to add that physical
parameters of the physiological tympanic membrane are
relatively well described, but such parameters for bosses
have not been described yet. Therefore, they were estimated
to be close to reality in the best possible way. The results
seem to be reasonable and although the models have some
limitations they may be used in further investigation of the
TM malfunctions caused by physical changes or damages
like cicatrices or physiological covering of TM fistulas by
isotropic membranes after acoustic trauma. In the latter case
the fibrous structure of the tympanic membrane is probably
not recovered. The results of modelling clearly show that
the vibrations on impaired membranes are quite different
from that of the normal TM and they may be used for
improving the hearing-aid fitting process.
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