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The ear is an important sensory organ of the human body. Cochlea has a pivotal role in the hearing system of human. Nearly 300 million people around the world suffer from sensorineural deafness caused by cochlear lesions. Because the mechanism of cochlear sensing is very complex, it has not been understood completely so far, which has become one of the important problems in medicine today. The basilar membrane in the cochlear canal is the supporting structure of all microstructures, the complex coupling motion between basilar membrane and lymph in cochlear canal is the primary condition for generating the cochlear sound sensing function. Therefore, it is essential to study the dynamic behavior of the basement membranes. By dividing the length of the cochlea into a finite number of elements and giving the radial distribution, a set of governing equations is derived for coupling micromechanics with fluid. Then combining these equations with the matrix combination equation, the complete coupling response of basilar membrane and lymph is obtained. The instantaneous responses of the basilar membrane under different excitations, the time domain responses of the resonance position under different frequency excitations, and the effects of the changes of the mass and stiffness of the basilar membrane on its biomechanical properties and hearing function are analyzed. The results showthat the increase of the mass and stiffness of the basilar membrane leads to the weakening of the maximum response, and the increase of the mass causes the maximum response position to move to the bottom of the basilar membrane; the increase of the basilar membrane stiffness causes the maximum response position to move to the top of the basilar membrane; the changing basilar membrane cross-section can rapidly reduce the characteristic frequencies at the middle and top of the cochlea, thus achieving better filtering and amplification of specific frequency excitation, and enabling the cochlea to have a higher resolution in a specific frequency range of 1000–3000 Hz.This computational mathematics model can provide a numerical analysis platform for implementing the clinical evaluation of lesions in the basilar membrane of the inner ear. Compared with the existing finite element models, this method has faster calculation speed and higher efficiency of parameter analysis.
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 耳蜗形体图
Figure 1. The cochlear shape.
图 2 基底膜模型
Figure 2. The model of Basilar Membrane.
图 3 特征频率曲线
Figure 3. Characteristic frequency curve.
图 4 位移比-频率曲线
Figure 4. The curve of displacement ratio and frequency.
图 5 基底膜1/5处的时域响应
Figure 5. Time domain response at 1/5 of BM.
图 6 基底膜特征频率处的时域响应
Figure 6. Time domain response at characteristic frequency of BM
图 7 基底膜1/2处的时域响应
Figure 7. Time domain response at 1/2 of BM.
图 8 基底膜4/5处的时域响应
Figure 8. Time domain response at 4/5 of BM.
图 9 不同周期时刻响应2000 Hz
Figure 9. Response at 2000 Hz at different times.
图 10 不同周期时刻响应4000 Hz
Figure 10. Response at 4000 Hz at different times.
图 11 不同周期时刻响应8000 Hz
Figure 11. Response at 8000 Hz at different times.
图 12 不同周期时刻响应10000 Hz
Figure 12. Response at 10000 Hz at different times.
图 13 2倍质量不同周期时刻响应2000 Hz
Figure 13. Response of two times mass at different cycle times at 2000 Hz.
图 14 10倍质量不同周期时刻响应2000 Hz
Figure 14. Response of ten times mass at different cycle times at 2000 Hz.
图 15 1/5处2倍质量不同周期时刻响应2000 Hz
Figure 15. Response of two times mass at 1/5 at different cycle times at 2000 Hz.
图 16 特征频率处2倍质量不同周期时刻响应2000 Hz
Figure 16. Response of two times mass at characteristic frequency at different cycle times 2000 Hz.
图 17 2倍刚度不同周期时刻响应2000 Hz
Figure 17. Response of twice stiffness at different cycle times at 2000 Hz.
图 18 10倍刚度不同周期时刻响应2000 Hz
Figure 18. Response of 10 times stiffness at different cycle times at 2000 Hz.
图 19 1/5处2倍刚度不同周期时刻响应2000 Hz
Figure 19. Response of 2 times stiffness at 1/5 at different cycle times at 2000 Hz.
图 20 特征频率处2倍刚度不同周期时刻响应2000 Hz
Figure 20. Response of two times stiffness at characteristic frequency at different cycle times at 2000 Hz.
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[1] Chadha S, Kamenov K, Cieza A 2021 Bull. W. H. O. 99 242
Google Scholar
[2] Taylor R R, Forge A 2005 Science 307 1056
Google Scholar
[3] Reichenbach T, Hudspeth A J 2010 Phys. Rev. Lett. 105 118102
Google Scholar
[4] Ashmore J 2008 Physiol. Rev. 88 173
Google Scholar
[5] Békésy V G 1960 Q. J. Exp. Physiol. Cogn. Med. Sci. 45 324
Google Scholar
[6] Johnstone B M, Patuzzi R, Yates G K 1986 Hear. Res. 22 147
Google Scholar
[7] Robles L, Ruggero M A, Rich N C 1991 Nature 349 413
Google Scholar
[8] Evans E, Wilson J 1975 Science 190 1218
Google Scholar
[9] Narayan S S, Temchin A N, Recio A, Ruggero, M A 1999 Science 282 1882
Google Scholar
[10] Gundersen T, Skarstein O, Sikkeland T 1978 Acta Oto-Laryngol. 86 225
Google Scholar
[11] Greenwood D D 1990 J. Acoust. Soc. Am. 87 2592
Google Scholar
[12] Warren R L, Ramamoorthy S, Ciganovic N, Zhang Y, Wilson T M, Petrie T, Wang R K K, Jacques S L, Reichenbach T, Nuttall A, Fridberger A 2016 Proc. Natl. Acad. Sci. U. S. A. 113 4304
Google Scholar
[13] 塔娜, 张景, 许立富, 周雷, 黄新生, 饶柱石 2018 振动与冲击 37 160
Google Scholar
Ta N, Zhang J, Xu L F, Zhou L, Huang X S, Rao Z S 2018 J. Vibr. Shock 37 160
Google Scholar
[14] Mammano F, Nobili R 1993 J. Acoust. Soc. Am. 93 3320
Google Scholar
[15] Kolston P J 1999 Proc. Natl. Acad. Sci. U. S. A. 96 3676
Google Scholar
[16] Ruggero M A, Narayan S S, Temchin A N, Recio A 2000 Proc. Natl. Acad. Sci. U. S. A. 97 11744
Google Scholar
[17] Duke T, Julicher F 2003 Phys. Rev. Lett. 90 158101
Google Scholar
[18] Zhang J, Zou D L, Tian J B, Ta N, Rao Z S 2019 Appl. Acoust. 145 278
Google Scholar
[19] Gan R Z, Reeves B P, Wang X 2007 Ann. Biomed. Eng. 35 2180
Google Scholar
[20] Zhang X, Gan R Z 2011 IEEE Trans. Biomed. Eng. 58 3024
Google Scholar
[21] Brown M A, Ji X D, Gan R Z 2021 Ann. Biomed. Eng. 49 757
Google Scholar
[22] Zhou K, Liu H G, Yang J H, Zhao Y, Rao Z S, Yang S G 2019 Acta Bioeng. Biomech. 21 3
[23] 周凯, 刘后广, 饶柱石, 杨善国, 赵禹, 徐丹 2017 医用生物力学 32 369
Google Scholar
Zhou K, Liu H G, Rao Z S, Yang S G, Zhao Y, Xu D 2017 J. Med. Biomech. 32 369
Google Scholar
[24] Liu H G, Xue L, Yang J H, Liu W, Yang S G, Wang W B 2020 Appl. Acoust. 169 107473
Google Scholar
[25] Yao W J, Ma J W, Luo X M, Luo B T 2014 J. Mech. Med. Biol. 14 1450051
Google Scholar
[26] Yao W J, Zhong J C, Duan M L 2018 Acta Oto-Laryngol. 138 961
Google Scholar
[27] Yao W J, Chen Y Q 2017 J. Appl. Math. Mech. 38 997
Google Scholar
[28] Ma J W, Yao W J, Hu B L 2020 J. Biomech. Eng. 142 91005
Google Scholar
[29] Yao W J, Liang J Y, Ren L J, Ma J W, Zhao Z S, Wang J K, Xie Y Z, Dai P D, Zhang T Y 2021 Commun. Nonlinear Sci. Numer. Simul. 104 106043
Google Scholar
[30] Boer E D 1996 Mechanics of the Cochlea: Modeling Efforts (New York: Springer) p258
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