Modeling and Analysis of Wave Amplification in the Cochlea

在资助期间，将对耳蜗放大器的运动方程进行系统的简化。目的是推导出一个有效的表面近似的分区，之后，多尺度将被用来推导非线性波在耳蜗中传播的渐近逼近。目标是能够实现与这些波的已知特性的定量一致，包括在低强度水平下调谐曲线的顶点位移，放大器的相对贡献随着刺激水平的增加而减少，奇阶失真音调，观察到基底膜上的零交叉点的时间位置基本上不受刺激强度的影响。在耳蜗基底部低至中等声压水平下，基底膜对纯音的反应中谐波失真的缺乏。在理解我们如何听到声音的过程中，一个基本的悬而未决的问题涉及到一个被称为耳蜗放大器的非线性反馈机制的作用。在描述导致放大的确切机制方面进展如此缓慢的原因之一是，它需要解决一个三维的、耦合的、非线性的、随时间变化的系统。PI建议开发一种近似方法，可以用来帮助研究这个问题，既包括放大的机制基础，也包括它对耳蜗中波传播的影响。这项研究的结果将提供一个严谨的框架来帮助回答放大器的问题。

During the funding period a systematic reduction of the equations of motion for the cochlear amplifier will be carried out. The objective is to derive an effective surface approximation for the partition, after which multiple-scales will be used to derive an asymptotic approximation of the nonlinear waves propagating in the cochlea. The objective is to be able to achieve quantitative agreement with the known properties of these waves, including the apical shift in the tuning curve at low intensity levels, the decrease of the relative contribution of the amplifier with increasing stimulus level, the odd-order distortion tones, the observation that the temporal position of the zero-crossings on the basilar membrane remain largely unaffected by stimulus intensity, and the dearth of harmonic distortion in the basilar membrane response to pure tones at low to moderate sound pressure levels in the basal portion of the cochlea.The fundamental open question in understanding how we hear concerns the role of a nonlinear feedback mechanism known as the cochlear amplifier. One of the reasons why progress in delineating the exact mechanism responsible for amplification is so slow is that it requires the solution of a three-dimensional, coupled, nonlinear, time-dependent system. The PI proposes to develop approximation methods that can be used to help study this problem, both the mechanistic basis for amplification as well as its effects on wave propagation in the cochlea. The results from this study will provide a rigorous framework to help answer the amplifier question.