In the past decade the gerbil has become very popular for middle-ear research (cf. recent work by Olson, 1998; Rosowski et al., 1999; von Unge et al., 1999). 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). Of particular interest for analyzing the mechanics of middle-ear transmission and the effects of infection are the combination of tympanometric measurements and eardrum shape and displacement measurements, made both in the normal ear and in the presence of experimental infections (von Unge et al., 1997), and also in ears with the malleus fixed.
We have previously reported the development of a 3-D finite-element model intended to permit the quantitative analysis of the mechanics of the gerbil eardrum and middle ear, including the effects of infection. Here we present an improved version of the model, as well as further comparisons with experimental measurements.
The shape of the eardrum in the model continues to be based primarily on phase-shift moiré shape measurements in the presence of varying static pressures. The ossicular geometry of the previous model was based on a 3-D reconstruction from very high-resolution MRM (magnetic resonance microscopy) data sets from UNC and The Center for In Vivo Microscopy (CIVM), Duke University. For the present model we have used additional MRI datasets and have supplemented them by serial-section histological images. The model now includes an explicit representation of the stapes and a more realistic representation of the ossicular suspension.
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 (cf. recent work by Olson, 1998; Rosowski et al., 1999; von Unge et al., 1999). 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. This poster presents further work on the model presented at ARO in 1999. The models are based on moiré shape measurements of the eardrum and on magnetic-resonance microscopic imaging of the middle ear, supplemented by observations on serial histological sections, as presented in Section 2. Section 3 presents our current finite-element model, and Section 4 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.
Figure 1 shows the moiré image for one ear with no static pressure applied (p=0). Displacement profiles are shown for p=0 and for four other pressures, demonstrating the nonlinear behaviour. The displacement profiles permit a precise delineation of the boundary of the pars tensa and pars flaccida.
Magnetic-resonance microscopy (MRM) from the Duke University Center for In Vivo Microscopy has been used to visualize auditory structures in a number of species (e.g., Henson et al., 1994, 1999). One of our MRM datasets for the gerbil middle ear is shown in Figure 2. The voxel size is 45 µm.
The MRI data are supplemented by the use of histological serial
sections to clarify certain details. For example, Figures 3 and 4
show details of the posterior incudal ligament and of the
incudostapedial joint, respectively.
Our model-creation process is now different than it was last year. For the present model, the MRM data were initially segmented using NIH Image, and then further processing was done using a suite of programmes developed by us: Fie, Tr3 and Fad (available for Microsoft Windows and Compaq Unix). Contours were extracted from the initial region-based MRM segmentation and revised in Fie, which permits explicit contour labelling and the use of open contours as well as closed ones. Figure 5 shows an example of an image being edited in Fie. Based on the contours output from Fie, the triangulated 3-D surfaces of the model were then generated using Tr3.
Tr3 generates both VRML models (for interactive visualization and distribution over the Web) and finite-element models. Figure 6 shows a model as viewed by the Cosmo Player.
Fad was used to align and combine the finite-element model of the pars tensa, pars flaccida and manubrium based on moiré data (the same model as last year) with the new model of the ossicles, ligaments, etc., generated by Tr3. The combined model is shown in Figure 7.
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 are obtained from visual inspection of the shape profiles, and a special mesh generator is then used to generate the finite-element mesh, using the moiré data to determine the z coördinates of the newly generated internal mesh nodes.
The pars tensa is modelled as a uniform, homogeneous curved shell with a Young's modulus (material stiffness) of 20 MPa. The Young's modulus of the pars flaccida has been taken as one tenth that of the pars tensa. The thicknesses of the pars tensa and pars flaccida have again been taken to be 5 µm and 15 µm, respectively, and both have a density of 103 kg m-3.
The Young's modulus and density of the ligaments and muscles in the model have all been taken to be the same as those of the pars tensa. The Young's modulus for bone has been taken to be 2 GPa, and the density to be 1.5×103 kg m-3. For convenience, the ossicles, ligaments and muscles are currently modelled as hollow shells with wall thicknesses adapted to their geometries. In particular, the malleus and incus have both been assigned 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), resulting in a combined mass of 1.7 mg (cf. an average of 1.84 mg reported by Cohen et al., 1992). The wall thickness for the stapes has been taken to be 0.1 mm.
The cochlear load is represented by springs attached to the stapes footplate. 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 1 Pa.
Figure 8 shows the simulated vibration pattern of the eardrum at low frequencies (i.e., frequencies low enough that inertial and damping effects are negligible). The colour coding represents the z component of displacement. For the parameters currently used, the displacement of the pars flaccida is much greater than that of the pars tensa.
Figure 9 shows the vibration pattern for the ossicles corresponding to the simulation of Figure 8. For the particular parameters used, the axis of rotation is consistent with the classical anatomical axis between the posterior incudal process and the anterior mallear process. The stapes footplate exhibits some rocking motion.
As an initial step towards modelling the effects of otitis media on middle-ear mechanics, the model parameters for the pars tensa and pars flaccida have been modified in line with the observations of von Unge et al. (1997). The thicknesses of both regions have been increased to 150 µm, and the Young's moduli have been decreased to 20 kPa. Figure 10 shows the resulting low-frequency vibration pattern on the eardrum. For the parameters used, the displacement amplitude of the pars flaccida has become much smaller relative to that of the pars tensa.
Figure 11 shows volume-displacement frequency responses for the two cases. For the parameters used so far, the frequency response does not match experimental observations well.
Once the computational correctness of the present model has been further checked, we shall begin to investigate what modifications may still be required for it to better match available experimental data, including the effects of infection.
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 J. Stancil for the initial segmentation of the MRM data, and Siah T.H. for his assistance with the software development.
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Copyright © 2000 Robert Funnell. All rights reserved.