Keywords: modeling, human cochlea, basilar membrane, Reissner's membrane, harmonic analysis, ANSYS.

The modeling of the response of the ear ossicle chain movement to pressure waves in front of the external ear canal was described in previous work [1]. The goal of this work is to describe the response of basilar membrane to movements of the stapes footplate in the oval window entering the cochlea.

The finite element system ANSYS was used as for the preparation of FE model of the human cochlea as for the determination of the transient response of basilar membrane. The mathematical model was three-dimensional and it involved the hard worm of cochlea, elastic Reissner's and basilar membrane (structure elements) and acoustic subsystems of scala vestibuli, scala media and scala tympani (fluid elements). The shape of the worm and the mechanical properties were assigned from the data of the measuring of a real human cochlea [2,3]. Basilar and Reissner's membranes were tighted inside of the worm spiral (Figure 1), they separate the space inside of cochlea into three parts: scala vestibuli-upon Reissner's membrane, scala media-between Reissner's membrane and basilar and scala tympani-under basilar membrane (Figure 2). The spaces of scala vestibuli, scala media and scala tympani were filled with endolymphatic fluid medium, the material property was near to water. The spiral of cochlea had two and a half screw-heads, the height of the screw was 5mm. The moveable stapes footplate was localized in an oval window i.e. in front of scala vestibule. The spaces of scala vestibuli and scala tympani were connected through a small leak (helicoterma) on the apical end of the cochlea. From the point of view of mechanical properties the model was restricted to linear elastic material of basilar membrane, i.e. the model of the passive cochlea was used.

The basilar membrane had variable width, the lowest width (0.05mm) was on the basal end and the maximal width (0.5mm) was on the apical end. In the literature it is released lowering the stiffness of the basilar membrane from the basal end to the apical end. Material of the basilar and the Reissner's membrane was modelled as linear-elastic isotropic, the value of Young modulus was near to soft rubber. As the thickness of the basilar membrane is one of the important factors that influences their stiffness, the most difficult task from the point of view of the model checkout was the determination of the membrane thickness distribution. The logarithmically change of the basilar membrane thickness brought out the best result from the point of view of the frequency response, the thickness was maximal on the basal end and the lowest was on the apical end. The constant damping ratio was used as the damping material characteristic of basilar and Reissner's membranes. The constant value of the surface absorption coefficient was applied on all surfaces of inner walls of cochlea.

The neural sound sensors are inside of basilar membrane, the vibrations of the basilar membrane structure belong to the most important quantities from the point of view of the mechanisms of hearing. The harmonic displacements (250 Hz - 10 kHz) of stapes footplate were used as the source of basilar membrane vibrations. The responses of the basilar membrane were the travelling waves from the basal end to the apical end, the amplitude of the propagated waves significantly dropped in front of helicotrema for all frequencies. The positions of the maximal amplitude values notably depended on the frequency, the maximal values of low frequency actuation occurred on the apical end and they moved continuously to the basal end with increasing frequency. This result seems to be reasonable and it is in good agreement with the results of the well-known Békésy's measurement [4].

Acknowledgements

The investigations were supported by the Ministry of Education and Youth (Project MSM 2600001).

1

K. Pellant, K. Prikryl, P. Pejchal, D. Dušek, "Simulation of ear diseases", Proceedings of the IASTED Int. Conf. "Applied Simulation and Modeling", ACTA Press, 352-356, Marbella, Spain, 2003.

2

F. Mammano, R. Nobili, "Biophysics of the cochlea: Linear approximation", J. Acoust. Soc. Am., 93(6), 3320-3332, 1993. doi:10.1121/1.405716

3

Cochlear Fluid Space Areas, Lengths and Volumes. Public webpage: http://oto.wustl.edu/cochlea/mrhmvol.htm

4

G.v. Békésy, Experiments in Hearing In: E.G. Wewer (Ed.), McGraw-Hill, New York, 1960.

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