686 2014 36 1878 Helmholtz [1] 1960 Békésy [2] [3]... --. Journal of Acoustic Society of American Hearing Research. Nature, Science, Nature Neuroscien

36 6 2014 12 1) 2) (, 710049) 1970. 2 973 2 1. 2006 2009 1. /. 70 SCI 40 EI 50 2.... 20 20 000 Hz 4 000.,,,, : O428 Q66 : A doi 10.6052/1000-0879-13-477 PROGRESS IN MECHANICS OF THE COCHLEA 1) MA Fuyin WU Jiuhui 2) (School of Mechanical Engineering and State Key Laboratory for Strength and Vibration of Mechanical Structure, Xi an Jiaotong University, Xi an 710049, China) Abstract The mechanics of cochlea is the core of hearing sciences and physiological acoustics, as well as a representative biomechanics topic. The study of cochlear mechanical properties could promote the related studies of psychoacoustics. This paper reviews the mechanics of the cochlea in two parts, the macro and micro mechanics, focusing on the development trend of the cochlear mechanics and application prospects. It is suggested that the cochlea is a part of the inner ear and its mechanical response provides us with many aspects of our amazing sensitive and selective hearing, with an accurate frequency response from 20 20 000 Hz and with the stimulus signal being able to be amplified more than 4 000 times. Key words cochlea basilar membrane, traveling wave theory, hearing active feedback, cochlear amplifier, cochlear mechanics 2013 11 11 1 2014-01-16. 1) (51375362). 2) E-mail ejhwu@mail.xjtu.edu.cn

686 2014 36 1878 Helmholtz [1] 1960 Békésy [2] [3]... --. Journal of Acoustic Society of American Hearing Research. Nature, Science, Nature Neuroscience, Physic Review Letters, Annual Review Neuroscience. 2001 Robles [4] Physiological Reviews. 2008 Ashmore Physiological Reviews [5] 2008. Robles.. Helmholtz [6]. 1960 Békésy [2] Helmholtz Békésy 1961. [7] [4] [8] [9]. [10-12] -- [13-14] [15-18]. 2 [19-20]. 20 80 2 [21-23]. 2006 Dallos [24] Prestin 1948 Gold [25]. 2007 Ren [26]. [5]. -- ( )... 1 2.5 2.75.. 33 mm. 0.1 mm 20 000 Hz 0.5 mm 20 Hz. 29 000 [27].

第 6 期 马富银等 耳蜗力学研究进展 底膜和每部分对应的频率如图 1(b) 所示. 内容摘自 中国数字科技馆听觉部分介绍 [27]. 图 1 耳蜗 耳蜗剖面与基底膜频率对应关系示意图 [27] 对应耳蜗的听觉功能来说 Corti 器是其核心功 能部件 决定耳蜗频率分析功能的基底膜 构成听觉 感受器的外毛细胞 构成听觉效应器的内毛细胞 与外毛细胞纤毛发生接触后产生非线性电活动的盖 膜等都位于 Corti 器内. Corti 器的结构如图 2 所示. 声音从外耳道传入后使鼓膜发生振动 鼓膜振 动会推动听骨链的运动 听骨链的终端以镫骨底板 与耳蜗相连 镫骨底板的振动会推动前庭阶内淋巴 液的运动 由于在蜗顶处 通过蜗孔 使鼓阶和前庭 阶的淋巴液流通 前庭阶流入的淋巴液会通过蜗孔 从鼓阶回流 中间以柔性基底膜分隔 基底膜两边淋 巴液的反向剪切运动使基底膜发生振动. 687 就目前耳蜗力学的研究来看 主要研究的内容 包括体外基底膜底端力学行为和顶端力学行为 (需 要说明的是 基底膜的力学行为呈现非线性变化 底端和顶端有较大差异) 耳蜗随长度变化的振动模 式 (即频率分析规律) 耳蜗行波 微观力学 两个纯 音作用下的耦合响应行为 听觉滤波器 压 -- 电转换 力学行为与听觉主动反馈 (包括耳声发射) 耳蜗放 大器等几部分. 里面也涉及了大量的神经生理活动 相关内容 增加了耳蜗力学的学科交叉性和力学行 为的复杂性. 2 基底膜力学行为 2.1 基底膜底端力学行为 目前报道的绝大多数关于正常内耳的力学行 为 都是人们在研究豚鼠 栗鼠 松鼠猴和猫等动物 的耳蜗基底膜底端的运动时获得的. 关于基底膜底 端的振动 研究者们已经在大多数问题上基本达成 共识 包括如何判断信号记录质量 精确获得特征频 率等. 然而 大量的研究表明 耳蜗顶部的力学行为 与底端的力学行为截然不同 至少在定量描述上是 完全不同的. 现阶段的耳蜗振动测试技术对基底膜 可以精确测量 对 Corti 器和盖膜则存在困难. 2.1.1 对纯音的响应 图 3 为在栗鼠耳蜗中离卵圆窗 3.5 mm 处记录 到的基底膜在纯音刺激下的速度与声压级关系 [28]. 对比图 3(a) 中小于等于特征频率的几组不同频率刺 激下的线性响应曲线 可以发现 当刺激频率接近 特征频率时 表现出高度压缩的增长过程 也就是 说 刺激强度增加到 96 db 时 响应频率却只增加了 图 2 Corti 器结构及构成 [27] 考虑到微观层次 由于毛细胞的根部是在基底 膜上的 基底膜的振动会使毛细胞发生运动 从而 使毛细胞上成排分布的纤毛与盖膜发生接触 产生 压电行为. 目前 研究者们已达成共识 外毛细胞纤 毛与盖膜发生接触 内毛细胞纤毛不与盖膜发生接 触. 由于外毛细胞纤维与盖膜发生接触后产生电信 号 与外毛细胞相连的传入神经感受到电刺激后 会将刺激传到大脑皮层的中央听区 产生听觉. 在 这个过程中 基底膜的运动可以看作是宏观力学行 为 纤毛和盖膜的接触属于微观力学行为 并带有 压 -- 电转换行为 产生电刺激的过程属于电生理行 为 电刺激传导并产生听觉属于神经动力学行为. (a) 对小于等于特征频率 (10 khz) 的纯音刺激下的响应 图 3 纯音作用下基底膜速度与声压级响应关系 (图中纵坐标 V 表示基底膜速度)

688 2014 36. (b) [4] 5... 1/3 70 90 db. 3 ( V ) ( ) 28 db. 0.2 db/db.. Mössbauer.. --. -- 80 db 90 100 db [29-30]. [31-32] 100 db 4. 80 100 db 5 ( ) [4] 6 ( )... ( ). 1/2. 4 -- ( ) [4] 6 ( ) [4]

6 689,. 7 ( ). 47 75 db. 6 db/ 200 Hz [33-34] (1) (2) ( ) (3) ( Corti )... 8 [4]... 9. 80 db 74 db. 7 [4].. 8. 6 khz. 0 90.. 1 2.5. [35] 9 [4]

690 2014 36..,. 10 db 90 db 990 µs 610 µs.... [36]. 3.5% ( 29 db). [36]. ( ).. 2.1.2... Mössbauer [37] [38]. 10 10 khz 30 ms [38]... 1 ms... 10 [4] 11.. 100 µm [38]...,. 11 [4]

6 691... [39]... 2.2. Corti... 500 1 000 Hz [40]. 2.2.1. Claudius.. 12 500 Hz ( ). 0.5 0.8 db/db 90 30 db 22 db... 12 [4] Corti. 300 400 Hz ( 12 )... 12. 1dB/dB... 13.. 0.8 8 1 1.4. 150 Hz 108 13 [4]

692 2014 36. 12.... 40 80 db 35 nm. Corti 50% [41]... 2.2.2 1 1.5 ms. 1 1.5 ms 20 50 ms... 3 3.1 Békésy... CF = A (10 αx k) (1) CF khz x 0 1 α (11.1 60 mm) 2.1. k 0.8 1 0.85. α k.. 75% x > 0.25 (1) 25%. A 0.456 0.164 0.35 0.36 0.4.. 17% 1.57 mm 3.55 mm. 0.6 mm 0.13 mm 1 mm. ( ).. (1). 3.5 mm 14 mm 1.6 0.9 14. (2).

6 693 [40]. (3) 0.7 14. 14 [4] ( ) ( ) [40]. (4)... (5)... --...... ( ) --........ ( 1 2.2 ) ( 0.8 1.4 ) ( 8 ). 0 6 khz 0 9.5 mm ( 41%). 8....

694 2014 36. 3.2 3.2.1 Békésy [42]. 1 550 m/s. Wever Lawrence. Wever, Lawrence Békésy Békésy. Békésy 3 (1). 90. 300Hz Békésy. 4. (2)... ( ).. 15 khz ( 15 ). 1 mm 35 db 1.5 0.67 mm 10 m/s.. 15 15kHz [4] 100 m/s( ).. 1.7 mm 28 m/s 12.8 mm 1.55 m/s. 0.5 0.9 mm 1.2 1.6 mm. 300 2 400 Hz 2.2 mm 10% [43]... 3.5 mm 30 µs

6 695 9 10 khz [38-39]. 3 ( 14 mm 0 500 Hz) 1 1.5 ms.. 3 4 khz 1 ms 320 Hz 2.7 ms. 1 ms. 3.2.2 Békésy [42]. 1.. 2 4 Békésy. (1) Békésy.. 2. Békésy [44].. 20 3 5.. Békésy 10 000 [42]. 100 1 000 [42] 100 [45].. [45].. [45]. ( 0.2 1.1 N/m) 1 3 mm [46]. 8 mm 2 5 N/m [46] 6 11 N/m. 94 db 1 Pa 10 nm. ( 3 10 14 m 4 /N) (1.8 10 14 6.4 10 14 m 4 /N).. Békésy.. Békésy [46].. [45]. 7 N/m 11 N/m

696 2014 36 ( Corti ) 1 2 N/m. Corti.. 3.2.3 ( )....... Olson. Olson. 16.. 100 µm. 16(b) 16(d). 1 2. 16 [4] 3.2.4 Békésy... Békésy

6 697 ( ). Békésy [42]. 180. ( 2 ). Békésy Zwislocki. Peterson Bogert [44]. Lighthill. Dancer [47-48]. Dancer [47-48]. 2 3... ( 1.5 )... 16 ( 15 ). [49]. [49].... ( ) 0 ( ).. [39]. 4 1950 Peterson [44]. 17. 17 [44]. Peterson [12] Peterson. 2003 Amitava [50]

力 698 学 与 实 践 2014 年 第 36 卷 并考虑了外毛细胞的作用. 该模型如图 18 所示. 这 是目前为止提出的最为简单的耳蜗力学模型 可以 通过简单的几何关系和材料力学关于梁的理论 分 析其力学特性. 图 18 耳蜗一维梁模型 [50] [3] 建立了一种新的一维耳 蜗模型 通过该模型对耳蜗基底膜的双重放大机制 进行了研究 指出通过耳蜗内部结构与淋巴液的相 互作用 可以将声刺激信号放大 4 000 倍以上. 2010 年 Tobias 等 图 20 二自由度耳蜗理论模型 [8] 1976 年 Allen[51] 建立了一个二维耳蜗流体力 学模型 如图 19 所示. 从图中可以看出 该模型 是矩形等截面模型 存在较大的简化. 1981 年 Stephen[52] 建立了一个二维耳蜗力学模型 并通过 有限差分法进行了理论求解. 1993 年 Mammano 等 [53] 给出了一个耳蜗的二维模型 考虑了纵截面 形状的变化. 图 21 耳蜗三维矩形等截面模型 [54] 类似 都是矩形等截面模型 但是在这个模型中 考 虑了耳蜗螺旋特征带来的影响. 1998 年 Paul[55] 建立了三维耳蜗锥形截面模 图 19 矩形等截面二维耳蜗模型 2011 年 Lamb 等 [51] [8] 建立了耳蜗二自由度理论 模型. 在该模型中 综合考虑了盖膜 基底膜和淋巴 液的作用 并进行了理论求解 模型如图 20 所示. 耳蜗三维模型主要分为两类 一类是简化模 型 和一维模型一样 这类模型采用圆锥管来模拟 耳蜗 不考虑耳蜗的螺旋特性 另一类是通过 3D 断层扫描技术等建立较为精确的三维耳蜗几何模型. 无论是简化模型还是精确模型 得到三维几何模型 后 一般都借助有限元分析方法来进行分析和研究. 1981 年 Larry 等 [54] 建立了三维流体的耳蜗力学模 型 如图 21 所示. 该模型与图 19 所示的二维模型 型 完整考虑了外毛细胞纤维 盖膜 基底膜等诸多 因素的影响 模拟了耳蜗对声音的放大作用. 从上 述这些模型可以看出 基本上都是用直管代替了螺 旋管 截面也是一般用矩形 半圆形等截面 总体上 看都做了大量的简化. 此后 有大量的研究者通过 计算机 3D 断层扫描技术建立了耳蜗的精确模型 特别是对内部核心的 Corti 器实现了精确建模和分 析. 而且 有研究表明 螺旋管对耳蜗流场和基底膜 振动的影响是非常大的 但是目前还缺乏精确地考 虑螺旋管道的影响的整体耳蜗模型 精确的模型也 主要集中在对局部特征的研究上. 5 耳蜗微观力学 对应耳蜗的听觉功能来说 Corti 器是其核心功

6 699 Corti [27]....... Corti.. 5.1... [56]. [56]. Corti.. (1). (2) [57]. (3). 180. [58]. [57]... (90 180 ).. 3.. Corti.. 90 db 180... ( 90 db). --. 2 3.

700 2014 36. 5.2. Corti. Corti...... (Hensen s ) 4. Hensen s. [59]. Cooper Rhode Corti.. Claudius 10 40 db.. 0.06 [59] 70 mm/pa [60]... 35 db [60-61]. [60-61]. 200 1 800 mm s 1 Pa 1... [60-61].. [19-20].. Corti.,.,,.. 6 6.1.. Corti. 6.1.1. 22 (18.8 khz).. ( 22 )

6 701 [62]. 22 [4]... 22. 500 Hz 12 khz ( )......... 600 Hz [63].......... [62].... [62]...

702 2014 36.. 1 2. [62,64]. 100 200 Hz.... 6.1.2. (f 1 f 2 f 2 > f 1 ) f 2 f 1 2f 1 f 2 2f 2 f 1. 2f 1 f 2... 23 [4] ( oct ) (f 1 f 2 ) 23 3f 2 2f 1 2f 2 f 1 2f 1 f 2 3f 1 2f 2 2f 1 2f 2 [13] f 2 f 1.. (1) (2f 1 f 2 ) 2f 1 f 2. 20 db( 15%) 16 db. 27 db 20 db. 22 15 db. 2f 1 f 2.. ( 60 db ).,.. f 2 /f 1 ( > 1.2) f 2 /f 1 200 300 db.. f 2 /f 1 3(b). 1. 1 1.06 1.25 f 2 /f 1 1.2 1.3. 1. ( ).

6 703.. 2f 1 f 2.. (2) (f 2 f 1 ) f 2 f 1. ( ) 2f 1 f 2. 23 db [58]. [58]. Corti. f 2 f 1 = CF f 1 f 2 f 2 f 1 CF. 6.2 6.2.1. Békésy 300 1 500 Hz 1 pm(10 12 m)..... 17 18 khz 34 40 µm/s 0.3 0.35 nm( ). 9 10 khz ( 10 db ) 50 100 µm/s 1 2 nm. 164 µm/s 2.7 nm 15 µm/s 0.26 nm. 30 33 khz 1 nm( 200 µm/s). [65]. -- ( ) [65]. 3 4 mm ( 17 18 khz ) 30 60 db [65] 30 db. (20 30 db) (10 20 db ) 24.. ( 400 800 Hz) ( 15 23 db ) 1 3 nm 2 7µm/s [58]. ( 350 Hz) 60 db 38 nm. 300 400Hz

704 2014 36 24 [4] 28 db. 1 11 nm. ( ).. 25 db. 39 420 µm/s. 6.2.2 20. ( ). [66]. ( ). Rhode [19-20] Rhode [66]. [66]...,. 6.2.3. 40µm/s 1 nm. 3.5 mm. 9 10 khz (0.9 nm) (50 µm/s). ( 24 ). 3 5 db. ( ). 1 1.6 khz... ( 24 ). 24 -- 400 Hz.

6 705.... ( ) ( ). ( -- ). 2011 Lamb [8]. 7 -- 7.1 Corti. Davis 1983 Gold 1948 -- [25] [23]. (, )...., 3.... Corti. 7.2 7.2.1 20 80.. -- --. Rhode. Rhode 1973 1.5. 65 81 db. Corti... 7.2.2....

706 2014 36. 0.5 [16]. ( ).. 7.2.3 --. -- [67]... 25. 25 [4] ( ).... ( ) [68].. ( 60 db). 0 50% 6 db ( ).... 15 db. ( ). 2.5 10 3 5 10 3 mol/l( ). 45 db 10 db.. 7.2.4

6 707 ( ).... ( ) [57]. (27kHz) (270 ). 2.2 1.5. [57]. Rhode.... 17 khz 80 18kHz 270. 7.2.5.. ( ).. f 1 f 2 2f 1 f 2. 2f 1 f 2. 2f 1 f 2 2f 1 f 2.. [62,64]. 7.2.6...... 7.3... ( ).. --

708 2014 36 30 db. 50 75 db 90 db 10 db....... /........ 7.4 ( )...... ( ) Corti. Corti 15 khz. Corti...... [69] ( 2 )..,,. Moxon Nuttall [69] Corti. ( ). ( ). Corti [68]. ( )

6 709.... [69] ( ). [68].. ( ).. 7.5 --. /. Corti....... --. 2010 Jiang Grosh 26. 2011, Szalai [18]. 26 [16,18] 8 8.1 Corti........ ( ).

710 2014 36... 8.2 ( ).... 69 db (36 db)... 22 db 0 21 db. ( ) ( )... 17 18 khz 78 db 9 10 khz 81 db. ( 1/2 ) ( ). 3. 9 10 khz 35 58 db 17 18 khz 35 db [58]. 8.3 1 mm ( )....... 97% 0.5 mm 1.3 mm. 0.5 1.3 mm. Alexander.,. 2012 Saaid..... 9 10 khz 1.5

6 711 1/3. ( 2.5 mm/ ) 1.3 mm 0.8 mm 2.1 mm.. 1 2 mm... 1.25 mm. 15 khz 2 mm 5.5 khz 3.5 mm 9 10 khz. 15. ( ). 8.4 Corti ( ). Brownell... Prestin [17]. ( [5] ). ( ) 30 nm/mv. 79 khz. ( ). 1.2 khz 6 db. 15 mv 16 khz 15 db. 1 nm.. 2011 Chen [70].... ATP (adenosine triphosphate).. 2011 Andrei [13]. Szalai [18]. /. --. ( ) [71]. 50 nm [72-73]. 2005 Dylan Hudspeth.. ( ).

712 2014 36 ( ).,.. /Corti /. ( 6 11 N/m) ( 0.002 0.005 N/m ). 8.5 --.... ( ).. ( ) --. (= 1/CF )... ( ). 9....... ( ).. (0.2 0.3 db/db). (120 db) (30 40 db). Corti. Corti.

6 713. 400 800 Hz.. ( ).. ( ).,. [74-76] [77-80]....... 1 000 4 000. [4] ( 3 9 ) 2001.. [4] 2001... 1 Helmholtz H. The theory of sound. Nature, 1878, 19(476): 117-118 2 Békésy. Experiments in Hearing. New York: McGraw, 1960 3 Tobias R, Hudspeth AJ. Dual contribution to amplification in the mammalian inner ear. Physical Review Letters, 2010, 105(11): 118102 4 Robles L, Ruggero MA. Mechanics of the mammalian cochlea. Physiological Review, 2001, 81(3): 1305-1352 5 Ashmore Jonathan. Cochlear outer hair cell motility. Physiological Review, 2008, 88: 173-210 6. Corti. [ ]., 2009 7 Zwicker E, Fastl H. Psychoacoustics: Facts and Models. Berlin: Springer-Verlag, 1999 8 Lamb S Jessica, Chadwick S Richard. Dual traveling waves in an inner ear model with two degrees of freedom. Physical Review Letters, 2011, 107(8): 088101 9 Karen B Avraham. Sounds from the cochlea. Nature, 1997, 390(11): 559-560 10 Adjemian BC. A three-chamber hydroelastic model of the cochlea. [PhD Thesis]. California: University of California, 1981 11 Mahmoud Hamadiche. Fluid and structure interaction in cochlea s similar geometry. In: Proceedings of the ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting and 8th International Conference on Nanochannels, Microchannels, and Minichannels, Montreal, Canada,

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