Bone Conduction Hearing: ThreeDimensional Finite Element Model of ...

Bone Conduction Hearing: ThreeDimensional Finite Element Model of the Human Middle and Inner Ear Namkeun Kim, Kenji Homma, Sunil Puria, and Charles R. Steele Citation: AIP Conf. Proc. 1403, 340 (2011); doi: 10.1063/1.3658108 View online: http://dx.doi.org/10.1063/1.3658108 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1403&Issue=1 Published by the American Institute of Physics.

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Bone Conduction Hearing: Three-Dimensional Finite Element Model of the Human Middle and Inner Ear Namkeun Kim∗,† , Kenji Homma∗∗, Sunil Puria∗,‡ , and Charles R. Steele∗ ∗

Department of Mechanical Engineering, Stanford University † Palo Alto Veterans Administration ∗∗ Adaptive Technologies, Inc ‡ Department of Otolaryngology-HNS, Stanford University

Abstract. A finite-element (FE) simulation model of a human auditory periphery was developed to gain insight into the fundamental mechanisms of bone conduction (BC) hearing. Three dimensional geometry of middle ear and cochlea including semi-circular canal was obtained by µCT images. The simulation effectively focused on the middle ear and then the cochlea fluid-inertial BC component. The FE model was first tuned and validated against various frequency responses available from the literature. The characteristics of various cochlear response quantities such as the basilar membrane (BM) displacement, window volume velocities, and cochlear fluid pressure were examined for both BC and air conduction (AC) excitations. Especially, the decomposition analysis was applied to window volume velocities and cochlear fluid pressures to separate them into anti-symmetric and symmetric components. The preliminary result shows that the BM vibration is driven by the part of the fluid pressure that is anti-symmetric (i.e. differential slow wave) with respect to the BM, which is generated by the anti-symmetric window volume velocity. Keywords: basilar membrane, middle ear, cochlear fluid pressure, oval- and round-windows PACS: 43.64.Kc

INTRODUCTION Recently, Kim et al. [5] showed that decomposed pressures into anti-symmetric (slow) and symmetric (fast) wave in the scalae fluid were significant for the basilar membrane (BM) movement in the bone-conduction (BC) pathway as well as air-conduction (AC) pathway. However, the model had some limitations such as simplified geometry (i.e., tapered box cochlea) and lack of semi-circular canal (SCC). In this study, in order to overcome above limitations, we developed 3-D finite element (FE) human-ear model consisting of the middle ear and the cochlea including SCC based on µCT images. Then, the importance of the decomposed pressure in the scalae fluid was investigated with the coiled cochlea.

METHOD The middle-ear and cochlear finite element model An acoustic-structure-fluid-coupled FE simulation was performed using the FE simulation software ACTRAN1 , which was developed specifically for analyzing vibro1

Free Field Technologies, http://www.fft.be What Fire is in Mine Ears: Progress in Auditory Biomechanics AIP Conf. Proc. 1403, 340-345 (2011); doi: 10.1063/1.3658108 © 2011 American Institute of Physics 978-0-7354-0975-0/$30.00

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FIGURE 1. A FE model of the human auditory periphery. (A) Middle-ear structures and scalae fluid. The bony shell is represented by the transparent structure. (B) Stapes, RW, and BM. The scalae fluid including the semi-circular canal is represented by the transparent structure. Note that the middle-ear structures except stapes are masked for the visualization. In addition, different colors in the BM represent each section which has differnt local coordinates or Young’s moduli.

acoustic problems. Figure 1 shows the FE model of the human auditory periphery, consisting of the middle-ear and the cochlea including SCC. The detailed descriptions for the FE model structure can be found in the previous study [5] except the coiled cochlear geometry. Material properties. Material properties of the FE model were reported previously [5] except the RW and BM whose properties were altered from the previous one due to the modified geometry. The density of the RW was set to 1200 kg/m 3, and the Young’s modulus was set to 0.05 MPa with an 0.8 loss factor, η . In this study, we divided the BM into 35 equi-length sections. In order to model the stiffness change, the Young’s modulus of the BM gradually decreased from the base to the apex (i.e., 6.5–5.5 MPa for longitudinal direction, and 0.2–0.1 GPa for transverse direction). The density of the BM was assumed to be 1000 kg/m3, and the orthotropic material properties were determined by tuning the resulting best-frequency-to-place cochlear map. The detailed process for the tuning was described previously [5]. BC excitation simulation. The rigid-body BC excitations were simulated in the direction of the three orthogonal axes, x, y, and z (Fig. 1). In addition, the normal direction to the stapes footplate was also simulated and represented by OW direction in this study. More detailed excitation method for BC as well as AC can be found in the previous study [5].

Decomposition analysis An orthogonal decomposition technique was performed on the scalae fluid pressure, pSV and pST , and the window volume velocities, UOW and URW . These pressure and volume-velocities vector quantities can be transformed [8] and the components of the


transformed vectors are: 1 1 ps (x) = √ [pSV (x) + pST (x)] , Us = √ [UOW (x) + URW (x)] 2 2 1 1 pa (x) = √ [pSV (x) − pST (x)] , Ua = √ [UOW (x) − URW (x)] , 2 2

(1)

where ps(x) and pa(x) are respective symmetric (i.e., in-phase) and anti-symmetric (i.e., out-of-phase or differential) components of the pressure vector, while U s and Ua are respective symmetric and anti-symmetric components of the volume velocity vector.

RESULTS FE model validation Middle-ear pressure-gain function. The middle-ear pressure-gain function expressed as a ratio of the scalae pressure near the OW to the acoustic pressure at the tympanic membrane (TM), pOW /pEC , obtained from the FE model, and compared with the literature [1, 2, 7, 9]. The FE results were consistent with experimental data within 5 dB difference from 0.3 kHz to 10 kHz frequency range. Cochlear input impedance. The cochlear input impedance (ZC ) in the present model alongside comparisons to measured [1, 6, 7, 9], or calculated [2] data. At the low frequnecy ranges below 0.5 kHz, the magnitude of ZC was reasonably consistent with experimental data within 10 dB difference. However, at the high frequency ranges above 1 kHz, ZC of the FE model shows 200 GΩ whereas experiemental data showed 30 GΩ. BM response. The AC and BC responses for the BM velocity, vBM , were measured at a specific BM location (12 mm from the base). The vBM was normalized by the ovalwindow (i.e., stapes-footplate) velocity, vOW , and the bone velocity, vb, for AC and BC stimulation, respectively. In AC results, vBM /vOW shows 25 dB for the maximum amplitude at 4 kHz, which was reasonably consistent with experimental data [4, 10]. In BC results, vBM /vb shows 20 dB for the maximum amplitude at 1.5 kHz. This was consistent with experimental data [10] within 3 dB difference in v BM magnitude and 0.5 kHz difference in frequency where the maximum amplitude was occurred. Cochlear map. The FE-simulated best-frequency (BF) cochlear map was calculated and compared with that obtained experimentally [3]. The BF map from the FE model is in good agreement with the data except for BFs below 200 Hz, which corresponds to locations greater than x = 30 mm. This agreement with the BF map was a result of an iterative tuning of the elastic modulus values of the BM for AC excitation.

Cochlear responses to BC and AC excitations Having validated the FE model, the next step was to simulate and analyze the symmetric (fast wave) and anti-symmetric (slow wave) response characteristics due to excitations for BC and AC excitations. In this study, only the OW directional and y-directional excitations for BC were shown to avoid the complex lines in the figures.


(A)

νBM/νOW(AC),ΔνBM/νb(BC) 40

BF

νBM/νOW(AC),ΔνBM/νb(BC)

(B) 500

BF

BF BF

20

0

BF

0

Phase(degrees)

Magnitude(dB)

−500 −20

−40

AC(0.5kHz) BCOW(0.5kHz)

−1000

BF

BC (0.5kHz) y

AC(1kHz) BCOW(1kHz)

−1500 −60

BC (1kHz) y

AC(5kHz) BCOW(5kHz)

−2000

−80

BCy(5kHz) −100

0

5

10

15 20 25 Distance from Base(mm)

30

−2500

35

0

5

10


30

35

FIGURE 2. Magnitude (A) and phase (B) of the differential BM velocity profile along the length of the BM, ΔvBM (x), normalized by the magnitude of the bone velocity (BC excitation), v b , given in two different directions (normal to OW, and y axes) at 0.5, 1 and 5 kHz. The BM-velocity response to AC excitation (normalized by stapes velocity) is also shown for comparison.

(A)

ΔνBM/Ua

(B)

0

ΔνBM/Us 0

BF

BF

BF

BF

BF

Magnitude(dB)

−50

Magnitude(dB)

−50

−100

AC(0.5kHz) BC (0.5kHz) OW

BC (0.5kHz) y

AC(1kHz) BC (1kHz)

−100

OW

BF

BC (1kHz) y

AC(5kHz) BC (5kHz) OW

BC (5kHz) y

−150

0

5

10


30

−150

35

0

5

10


30

35

FIGURE 3. The differential BM velocities distribution along the length of the BM, Δv BM (x), in response to AC and BC excitations for the frequencies 0.5, 1, and 5 kHz. The results are now normalized by (A) the anti-symmetric volume velocity (slow wave) component, U a , and (B) the symmetric volume velocity (fast wave) component, Us .

BM velocity responses to BC and AC excitations. Figure 2 shows the simulated differential BM velocity distribution, Δv BM (x), in response to BC excitations at the rigid boundary bone. The results are shown for three frequencies: 0.5, 1, and 5 kHz. The BC cases are normalized with respect to the rigid bone-velocity magnitude, v b . Figure 2 also shows the BM velocity profile, vBM (x), normalized by the corresponding stapes velocity in response to AC excitation. BM velocity normalized by anti-symmetric and symmetric volume-velocity components. Figure 3 again shows the BM velocity distribution in response to both AC and BC excitations, but this time normalized by the anti-symmetric and the symmetric volume velocity components, Ua and Us, in Figs. 3A and 3B respectively. Again, the results are shown for selected frequencies of 0.5, 1, and 5 kHz.


p /U & p /U a

a

s

60

60

40

40

20 0

p (AC) a

−20 −40

p (BC a

BF

)

OW

pa(BCy) ps(AC)

−60

ps(BCOW)

−80 0

5

a

s

a

BF

0

p (AC) a

−20 −40

1kHz

a

20

p (BC a

)

OW

pa(BCy) ps(AC)

−60

ps(BCOW)

−80 0

5

p (BC ) s

p /U & p /U

(B) 80

a

Magnitude(dB)

Magnitude(dB)

(A) 80

5kHz

p (BC )

y

s

10 15 20 25 Distance from Base(mm)

30

35

y

10 15 20 25 Distance from Base(mm)

30

35

FIGURE 4. Cochlear-scalae anti-symmetric and symmetric fluid pressure components normalized by the corresponding anti-symmetric volume velocity components (A) at 1 kHz and (B) at 5 kHz. Note that all p a (AC), pa (BCOW ), and pa (BCy ) results are well-aligned to the BF location.

Decomposition of cochlear-fluid pressure vectors. Figures 4A and 4B show the antisymmetric and symmetric pressure components, pa(x) and ps(x), normalized by Ua. The results are shown for selected frequencies of 1 and 5 kHz. Here it can be seen that the magnitudes of the pa (x) for different excitation cases become aligned with one another when normalized by Ua, while this is not true for p s(x).

DISCUSSION Cochlear input impedance Discrepancy of ZC between current FE results and experimental data above 1 kHz may come from the loss of fluid viscosity. The effects of shear viscosity at the interfaces between solids and viscous fluids are not captured by the standard acoustic fluid elements available in the present FE software. Therefore, the fluid viscosity cannot be represented in the simulation while the viscosity is significant as a damping on the intersurface between scalae fluid and solid structures (BM or bony shell) in reality. The loss of viscosity may give rise to the loss of damping factor in the cochlea.

Simulated BC-induced BM vibration responses Figure 2 shows that the BM velocity responses normalized by the BC bone vibration vary significantly depending on the direction of the BC excitation. By contrast, when ΔvBM (x) is normalized by Ua, as shown in Fig. 3A, the differences in the magnitude of the BM velocity response for different excitation directions diminish significantly. In contrast, normalizing by Us, as shown in Fig. 3B, only results in further separation among the cases. These observations suggest that the BM velocity is correlated with Ua rather than Us. In other words, the BM vibration is largely driven by U a, introduced at the two windows, regardless of the method of excitation. An examination of the cochlear fluid responses in Fig. 4 provides further insight into the correlation between Δv BM (x) and Ua. Figures 4(a) and 4(b) show the magnitudes of p a (x) and ps (x) normalized


with respect to Ua. Here the pa(x)/Ua magnitudes for the different drive cases become aligned with one another from the base up to BF location. Based on these observations, we conclude that the BM vibration is primarily driven by the anti-symmetric pressure component, which is introduced by the anti-symmetric volume-velocity component at the windows, regardless of the type of excitation method used (AC or BC in any of the different directions).

CONCLUSIONS The model shows a reasonable degree of agreement with experimental BC-induced BM vibrational data from the literature, as well as with AC-induced response data, such as the BF map, pressure transfer function, and ZC . Detailed analysis of this model indicates that BM vibrational characteristics, when normalized by the anti-symmetric (i.e., differential) components of the window volume velocities, are essentially invariant for AC or BC excitations, regardless of the direction of the BC excitation. As a consequence, the BM only responds to the excitations generated at the two windows, regardless of whether these are produced via AC or BC excitation.

ACKNOWLEDGMENTS Supported in part by the Air Force Office of Scientific Research (AFOSR) STTR funding (FA9550-07-C-0088) and by grant R01 DC07910 from the NIDCD.

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