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Establishment of three-dimensional finite-element model of the whole auditory system includes external ear, middle ear, and inner ear. The sound-solid-liquid coupling frequency response analysis of the model was carried out. The correctness of the FE model was verified by comparing the vibration modes of tympanic membrane and stapes footplate with the experimental data. According to calculation results of the model, we make use of the least squares method to fit out the distribution of sound pressure of external auditory canal and obtain the sound pressure function on the tympanic membrane which varies with frequency. Using the sound pressure function, the pressure distribution on the tympanic membrane can be directly derived from the sound pressure at the external auditory canal opening. The sound pressure function can make the boundary conditions of the middle ear structure more accurate in the mechanical research and improve the previous boundary treatment which only applied uniform pressure acting to the tympanic membrane.

With the development of interdiscipline, the research that explores issues of life sciences with principles of mechanics has become a new frontier. The study of ear biological mechanics has a relatively brief history which trace back to the end of last century and the beginning of this century. Scholars mainly adopt two methods to study ear problems with mechanics: the first one is theoretical research methods, such as the use of analytical solution to eardrum vibration problem deduced by mechanical theory and analytical method of artificial ossicle detection [

However, these preliminary studies all simplified the boundary conditions, in which the sound incentive on the tympanic membrane surface was defined as uniformly distributed loads. The external load on the tympanic membrane, however, is not really uniform, because sound waves have reached external auditory canal before they reach tympanic membrane, and gas-solid coupling occurs in external auditory canal then reach tympanic membrane, and fluid-solid coupling will happen between tympanic membrane and air in the external auditory canal. After sound-solid-liquid three-phase fluid-solid coupling occurs, the pressure distribution on the tympanic membrane is shown in Figure

Load on the eardrum.

Based on the CT scan images from Zhongshan Hospital of Fudan University on the normal human middle ear (GE lights peed VCT 64 Slice spiral CT machine, Scanning parameters: collimation 0.625 mm, tube rotation time 0.4 s, reconstruction thickness 0.625 mm, interval 0.5 ~ 0.625 mm.) by further processing the image, using self-compiled program to Numerical Value the CT scans and import it into FE software Patran to reconstruct three-dimensional finite element model of ear structure, then divide into grid, we can define the boundary conditions and the material parameters, as shown in Figures

FE model of human ear.

FE model of middle ear in detail.

This paper combined the numerical analysis and theoretical analysis to study the load distribution on the eardrum deeply.

External auditory canal gas unit is divided into 7200 eight-node hexahedron (Hex8) units. The number of nodes is 7460. Tympanic membrane is divided into 330 four-node quadrilateral (Quad4) and 30 triangle (Tri3) surface units, the number of nodes is 373. Ossicular chain is divided into 21,438 four-node tetrahedral elements (Tet4), nodes 6065, Figures

Cochlea mesh: the fluid domain near stapes within vestibular is divided into Tet4 units, and other fluid domain are divided into Hex8 units, The fluid unit attributes are defined as FLUID units, the number of units produced is 4391 in total, 6817 nodes; oval window is divided into Tria3 surface units, oval window unit is defined as two-dimensional membrane structure, and the number of units is 56 in total, 37 nodes; and round window is divided into Quad4 surface units, and round window membrane unit is defined as two-dimensional structure (membrane) total 16 units, 25 nodes. Mesh is shown in Figure

The structural dynamics equation of the acoustic structural coupled system of air in external canal and tympanic membrane, stapes footplate, and perilymphatic fluid in inner ear

The assumption that elements are in no thickness

Material properties and acoustic properties of various parts of numerical models in this paper refer to experimental data in [

Material properties of the FE model.

Structure | Density (kg/m^{3}) | Young’s modulus (Pa) |
---|---|---|

Tympanic membrane (Pars tensa) | ||

Tympanic membrane (Pars flaccida) | ||

The tympanic membrane malleus attachment at the umbo | ||

The tympanic membrane malleus attachment at malleus handle | ||

Malleus head | ||

Malleus neck | ||

Malleus handle | ||

Incudomalleolar joint | ||

Incus body | ||

Incus short process | ||

Incus long process | ||

Incudostapedial joint | ||

Stapes | ||

Superior mallear ligament | ||

Lateral mallear ligament | ||

Anterior mallear ligament | ||

Superior incudal ligament | ||

Posterior incudal ligament | ||

Tensor tympani tendon | ||

Stapedial tendon | ||

Oval window | ||

Round window membrane | ||

Basilar membrane |

Acoustic properties of ear components.

Structure | Density (kg/m^{3}) | Speed (m/s) |
---|---|---|

Air | 1.21 | 340 |

Perilymphatic fluid | 1000 | 1400 |

Because of the sensitivity of displacement of microstructure to the dynamical response of ear structure, the connection between soft tissue and temporal bone was regarded as fixed constraint, which is to say its displacement in all three orthogonal directions is zero. The defined boundary condition is listed below.

90 dB SPL (0.632 Pa, from 200 Hz to 8000 Hz) was set on the opening surface of external auditory canal.

The displacement of connection between soft tissues and temporal bone was defined to be zero in three orthogonal directions.

The displacement of outer edge of tympanic membrane annular ligament was defined to be zero in three orthogonal directions.

The displacement of outer edge of stapes annular ligament was defined to be zero in three orthogonal directions.

The displacement of outer edge of oval window and round window was defined to be zero in three orthogonal directions.

The displacement of external auditory canal wall and the inner ear bony labyrinth wall was defined to be zero in three orthogonal directions.

Eardrum and Oval window are fluid-structure coupling interface.

Figures

Comparison of the displacement of umbo between the FE model-predicted and the experimental data of Gan et al. [

Comparison of the displacement of stape footplate between the FE model-predicted and the experimental data of Gan et al. [

Aibara et al. [

Comparison of the stapes footplate velocity transfer function between the FE model-predicted and the experimental data.

The displacement of soft tissue in the boundary condition and the elastic modulus of Table

The simulation results show that SVTF reaches the average maximum when the frequency is 1 KHz, gets 0.33 mm s^{−1}/Pa, has a slope of about 7 dB/octave in the range of 100–1000 Hz frequency, and has a slope of about −7 dB/octave above 1000 HZ. Figure

This paper makes use of finite element model to impose sound incentive on external auditory canal, and results are compared with those of sound pressure imposed on tympanic membrane in the vicinity, the comparison shows that when the range of frequency is between 3 and 4 kHz, the effect that impose sound incentive on external auditory canal is higher than that of Eardrum with an increase of 10 dB. The increase reaches the maximum when the frequency is 3700 Hz; see Figure

The pressure gain of external auditory canal for various frequencies.

Figure

Distribution of sound-pressure level in the external auditory canal at frequencies of 500–8000 Hz (90 dB).

Figure

Frequency response curves of the sound pressure at six locations along the external auditory canal (90 dB).

Figure

The variation of sound-pressure level at the eardrum for various frequencies (90 dB).

According to calculation results, piecewise function of sound pressure which varies with frequency in different points of the surface of tympanic membrane was fitted using least-square method

The paper achieves the following conclusions by numerical simulation and theoretical analysis.

The finite element model containing external auditory canal, middle ear, and inner ear hearing system was established, made use of this model to do the frequency response analysis containing gas external auditory canal, middle ear structure, and inner ear fluid coupling, and get the response curves of tympanic membrane and stapes footplate. In the paper, the curves obtained by calculation results using this model and experiment data of was in very good agreement, and prove that the model is correct.

In consideration of the sound transmission role of external auditory canal, middle ear structures occurs resonance at the frequency 3000 Hz–4000 Hz, and close to the conclusions of medical science [

The calculation results showed that in the low frequency (<4500 Hz), the sound pressure that transmits uniform sound pressure of external acoustic foramen into the surface of tympanic membrane by external auditory canal mainly varies with frequency, the effects of changes in distance can be ignored, in the high frequency (>4500), the situation is different; the sound pressure of the surface of tympanic membrane does not only vary with frequency, but also relates to distance. Thus, according to simulation results, functional formula of sound pressure of the surface of tympanic membrane was fitted using least-square (

Previous studies usually defined a constant sound pressure in simplified model of tympanic membrane, taking no consideration of the influence of external auditory canal. Since (

The authors gratefully acknowledge national natural science foundation of China (11072143) and foundation research key project of shanghai science committee (08jc1404700).