Finite-element modelling of the gerbil eardrum and middle ear W.R.J. Funnell W.F.S. Decraemer M. von Unge J.J.J. Dirckx McGill University, Montréal (QC), Canada University of Antwerp (RUCA), Antwerp, Belgium Karolinska Hospital, Stockholm, Sweden 22nd Midwinter Res. Mtg., Assoc. Res. Otolaryngol., St. Petersburg Beach (1999)
Abstract

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.

1. Introduction

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.

2. Moiré shape measurements

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. Moir 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.

3. Magnetic-resonance microscopy

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 m, 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.

4. Finite-element model

Fig. 6. Model outlines superimposed on moir 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 m (cf. range of 3-5 m observed histologically by von Unge et al., 1991). For the pars flaccida, the thickness has been taken to be 15 m (cf. 10-20 m 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).

5. Simulation results

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 m and the displacement of the manubrial tip is 0.93 m. 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 mobile-ossicles case.

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.

6. Acknowledgements

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.

7. References

1. Cohen YE, Bacon CK & Saunders JC (1992): Middle ear development III: Morphometric changes in the conducting apparatus of the Mongolian gerbil. Hearing Res. 62: 187-193

2. Fornadley JA & Burns JK (1994): The effect of surfactant on eustachian tube function in a gerbil model of otitis media with effusion. Otolaryngology - Head & Neck Surgery 110: 110-114

3. Fulghum RS, Hoogmoed RP & Brinn JE (1985): Longitudinal studies of experimental otitis media with Haemophilus influenzae in the gerbil. Int. J. Ped. Otorhinolaryngol. 9: 101-114

4. Fulghum RS, Hoogmoed RP, Brinn JE & Smith AM (1985): Experimental pneumococcal otitis media: longitudinal studies in the gerbil model. Int. J. Ped. Otorhinolaryngol. 10: 9-20

5. Fulghum RS, Chole RA, Brinn JE & Branigan AE (1987): Mongolian gerbil tympanic membrane. Normal and with induced otitis media. Arch. Otolaryngol. - Head & Neck Surgery 113: 521-525

6. Fulghum RS, Beamer ME (1991): Experimental otitis media with anaerobic bacteria. Annals of Otology, Rhinology, & Laryngology Suppl. 154: 23-29

7. Fulghum RS & Marrow HG (1996): Experimental otitis media with Moraxella (Branhamella) catarrhalis. Annals of Otology, Rhinology & Laryngology 105: 234-241

8. Fulghum RS & Brown RR (1998): Purified streptococcal cell wall (PG-APS) causes experimental otitis media. Auris, Nasus, Larynx 25: 5-11

9. Funnell WRJ & Decraemer WF (1996): On the incorporation of moiré shape measurements in finite-element models of the cat eardrum. J. Acoust. Soc. Am. 100: 925-932

10. Henson MM, Henson OW Jr, Gewalt SL, Wilson JL, Johnson GA (1994): Imaging the cochlea by magnetic resonance microscopy. Hearing Res. 75: 75-80

11. Henson OW Jr, Hazel TA, Henson MM, Presson WE, St. Amour SS, Stancil JM & Gewalt SL (1999): Comparative analysis of the vertebrate ear using magnetic resonance microscopy. ARO MidWinter Meeting: Abstract #304

12. Nemechek AJ, Pahlavan N, & Cote DN (1997): Nebulized surfactant for experimentally induced otitis media with effusion. Otolaryngology - Head & Neck Surgery 117: 475-479

13. Ravicz ME, Rosowski JJ & Voigt HF (1992): Sound-power collection by the auditory periphery of the Mongolian gerbil Meriones unguiculatus. I. Middle-ear input impedance. J. Acoust. Soc. Am. 92: 157-177

14. Teoh SW, Flandermeyer DT & Rosowski JJ (1997): Effects of pars flaccida on sound conduction in ears of Mongolian gerbil: acoustic and anatomical measurements. Hearing Res. 106: 39-65

15. von Unge M, Bagger-Sjöbäck D & Borg E (1991): Mechanoacoustic properties of the tympanic membrane: a study on isolated Mongolian gerbil temporal bones. Am. J. Otol. 12: 407-419

16. von Unge M, Decraemer WF, Bagger-Sjöbäck D & Dirckx JJ (1993): Displacement of the gerbil tympanic membrane under static pressure variations measured with a real-time differential moiré interferometer. Hearing Res. 70: 229-242,

17. von Unge M & Bagger-Sjöbäck D (1994): Tympanic membrane changes in experimental otitis media with effusion. Am. J. Otol. 15: 663-669

18. von Unge M, Decraemer WF, Dirckx JJ & Bagger-Sjöbäck D (1995): Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion. Hearing Res. 82: 184-196

19. von Unge M, Decraemer WF, Bagger-Sjöbäck D & Van den Berghe D (1997): Tympanic membrane changes in experimental purulent otitis media. Hearing Res. 106: 123-136


Copyright © 1999 Robert Funnell. All rights reserved.


R.Funnell@med.mcgill.ca
Last modified: Wed Feb 24 18:24:46 1999