In the past decade the gerbil has become very popular for middle-ear research. In particular, gerbils have been used in studying the effects of middle-ear infections (e.g., Fulghum et al., 1985, 1987; Fornadley & Burns, 1994; von Unge et al., 1994, 1995, 1997; Nemechek et al., 1997). Recently both tympanometric measurements and eardrum shape and displacement measurements have been made in the normal gerbil ear and in the presence of experimental infections (von Unge et al., 1997). To facilitate the quantitative analysis of such data, we are developing 3-D finite-element models of the gerbil eardrum and middle ear. The eardrum models are based on phase-shift moiré shape measurements in the presence of varying static pressures, as in our earlier work in the cat (Funnell & Decraemer, 1996). The ossicular geometry is based on 3-D reconstructions from very high-resolution MRM (magnetic resonance microscopy) data sets from UNC and The Center for In Vivo Microscopy (CIVM), Duke University.
We shall present low-frequency simulation results for the models, with preliminary comparisons to experimental moiré displacement data for normal middle ears and for fixed-malleus middle ears.
Supported by MRC Canada and the University of Antwerp. We thank Drs. M.M. and O.W. Henson (UNC) and the CIVM for providing the MRM data.
In the past decade the gerbil has become increasingly popular for middle-ear research (e.g., von Unge et al., 1991; Ravicz et al., 1992; Teoh et al., 1997). In particular, gerbils have been used in studying the effects of middle-ear infections (e.g., Fulghum et al., 1985, 1987, 1991, 1996, 1998; Fornadley & Burns, 1994; von Unge et al., 1994, 1995, 1997; Nemechek et al., 1997).
Recently both tympanometric measurements and eardrum shape and displacement measurements have been made in the normal gerbil ear and in the presence of experimental infections (von Unge et al., 1997). To facilitate the quantitative analysis of such data, we are developing 3-D finite-element models of the gerbil eardrum and middle ear. The models are based on eardrum shape measurements and on magnetic-resonance microscopic imaging of the middle ear, presented in Sections 2 and 3, respectively. Section 4 presents our current finite-element model, and Section 5 presents some preliminary simulation results.
The moiré data presented here were obtained using a phase-shift technique (as used for the cat in Funnell & Decraemer, 1996) which produces images in which the pixel values are directly related to the z coördinate, as opposed to the real-time technique (as used for the gerbil in von Unge et al., 1993) that produces fringe patterns which are more difficult to analyse.
|Fig. 1. Moiré shape data for one ear. Image shows overall shape for p=0. Black curves are horizontal and vertical profiles through the p=0 shape. Blue curves are profiles for p= -4, -2, +2 and +4 cm H2O.|
Figure 1 shows the moiré image for one ear with no static pressure applied (p=0). Note that the eardrum is viewed from the medial side and the bodies of the malleus and incus obscure the pars flaccida.
Horizontal and vertical profiles through the umbo are shown for
p=0 and for applied pressures of ±2 and
±4 cm H2O (±200 and ±400 Pa), the smallest
pressures for which measurements were made. The displacements are
nonlinear, and they are smaller for positive pressures than for
negative ones. This is also seen clearly in Figure 2.
|Fig. 2. Displacement images for ±2 and ±4 cm H2O. Displacement scale is from 0 to 0.25 mm for all four images.|
|Fig. 3. Sample MRM data. Left: one slice, showing eardrum, manubrium and stapes (Scion Image). Right: three orthogonal slices, and oblique slice along manubrium (S. Dunne's Vox).|
Magnetic-resonance microscopy (MRM) from the Duke
University Center for In Vivo Microscopy can provide 3-D
imaging with voxel sizes down to 25 µm, and has been used to
visualize auditory structures in a number of species (e.g.,
Henson et al., 1994, 1999). MRM data for a gerbil middle ear
(e.g., Figure 3) were segmented and surfaced using the
SurfDriver programme (Figure 4), and then further processed
with locally developed software to produce the finite-element
model of the gerbil malleus and incus shown in Figure 5. That
model was then joined to the finite-element model of the
eardrum which had been derived from moiré data.
|Fig. 4. Middle-ear structures reconstructed from MRM data, viewed from medial side.||Fig. 5. 3-D model of gerbil malleus and incus, derived from MRM data.|
|Fig. 6. Model outlines superimposed on moiré data.|
The shape of the pars tensa in this model was derived from the
moiré data using the same techniques that we have previously
used for the cat (Funnell & Decraemer, 1996). The outlines of the
eardrum and manubrium (Figure 6) are obtained from visual inspection
of the shape profiles, and a special mesh generator is then used to
generate the finite-element mesh (Figure 7), using the moiré
data to determine the z coördinates of the newly
generated internal mesh nodes.
|Fig. 7. Finite-element model of gerbil eardrum, malleus and incus. (a) Lateral view. (b) Medial view.|
As in our cat models, the pars tensa is modelled as a uniform, homogeneous curved shell with a Young's modulus (material stiffness) of 2 × 108 dyn cm-2, and a density of 1 g cm3. For the gerbil the thickness of the pars tensa has been taken to be 5 µm (cf. range of 3-5 µm observed histologically by von Unge et al., 1991). For the pars flaccida, the thickness has been taken to be 15 µm (cf. 10-20 µm histologically, ibid.). The Young's modulus of the pars flaccida has been taken as one tenth that of the pars tensa.
A fixed ossicular axis of rotation is assumed, running from the anterior mallear process to the posterior incudal process as determined from the MRM data. The combined ossicular and cochlear elastic load is represented at the axis of rotation by a frequency-independent rotational stiffness of 2 kdyn cm (7 times smaller than in our cat model). The mass of the ossicles is included by modelling the bodies of the malleus and incus as hollow shells with a wall thickness of 0.3 mm (cf. overall diameters of about 0.5 mm for the bodies and 0.15 mm for the long processes); this results in a mass of 1.7 mg (cf. an average of 1.84 mg reported by Cohen et al., 1992).
The damping in the system is represented by a mass-proportional
damping coefficient of 1500 s-1 (as for the cat in Funnell
et al., 1987). The acoustical input is a uniform sound
pressure of 100 dB SPL (2 Pa).
|Fig. 8. Low-frequency vibration pattern with mobile ossicles.|
Figure 8 shows the simulated vibration pattern at low frequencies
(i.e., frequencies low enough that inertial and damping effects are
negligible), with mobile ossicles. The maximal displacement on the
pars tensa is 2.5 µm and the displacement of the manubrial tip is
0.93 µm. These displacements are quite comparable to the
moiré displacement measurements.
|Fig. 9. Low-frequency vibration pattern with fixed ossicles.|
Figure 9 shows the low-frequency vibration pattern that
results when the ossicles are fixed in the model. The pars
flaccida displacements are about the same but the pars tensa
displacements have decreased by about half compared with the
The eardrum volume displacement calculated in the mobile-ossicles
case is 138 Pa/mm3. This is comparable, for example, to the
mean value of 250 Pa/mm3 (with a range of about ±50%)
obtained by Ravicz et al. (1992) measuring acoustical
impedance with the bulla open.
Supported by MRC Canada and the University of Antwerp. We thank Drs. M.M. and O.W. Henson (UNC) and the CIVM for providing the MRM data. We also thank C. Breckenridge for segmenting the MRM data; and C. Breckenridge, S. Talebinejad and P. Warrick for developing the required file-format conversions.
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Copyright © 1999 Robert Funnell. All rights reserved.