Mathematical modelling of the active hearing process in the mamalian inner ear

人类的内耳(或耳蜗)是一种非凡的设备，它的性能超过了任何人工系统。例如，它对亚原子长度尺度上的位移敏感，比背景噪声小，可以分辨以微秒为间隔的信号，可以处理超过一百万倍强度范围(从0分贝到120分贝SPL)的声音，工作在超过十个八度的频率范围(从20赫兹到20千赫)，可以区分频率仅相差0.2%，强度变化为1分贝。大体上说，所有的哺乳动物都使用类似的系统来听，它们的耳朵也有同样出色的表现。虽然生理学家可以描述这种表现背后的许多过程，但他们之间对于使这一切发挥作用的关键因素缺乏共识。使用来自老鼠而不是人类的数据，我们将试图理解这一过程。耳蜗的详细结构很复杂，包括一个被包裹成螺旋形的充满液体的管子。管子被所谓的“基底膜”一分为二，它像鼓一样上下振动。不过，这是一种非常奇怪的鼓。在薄膜的顶部是一个被称为科尔蒂器官的装置，它的作用就像一个非常特殊的麦克风。麦克风不仅从鼓上拾取信号，并通过神经细胞将信号传递到大脑，而且它还起到了放大器的作用，实际上使鼓的上下敲击更加有力。然而，沿螺旋管的不同距离处的每个放大器阵列响应不同的频率。这项资助旨在了解耳蜗放大器是如何工作的。人们普遍认为，负责放大的Corti器官的关键部分是所谓的外毛细胞。这些细胞上有细小的毛发，可以打开和关闭允许钙流入细胞的微小大门。据认为，钙离子的流动是导致细胞快速拉动和推动基底膜鼓，使其以更大幅度跳动的触发因素。我们将使用混合的实验测量(在布里斯托尔和基尔)以及数学建模和模拟。在布里斯托尔的实验中，我们将确定外部毛细胞的门的打开和关闭如何改变钙的流动，它们如何导致毛细胞本身的拉动和推动，以及邻近外部毛细胞上的毛发如何相互影响。Keele的实验将观察当一个人改变单频声音的输入幅度时，基底膜运动的详细图像。这样，我们就可以观察特定的麦克风/放大器，并看到其活动过程的动态响应。这两组实验将被用来提供一组数学方程，这些方程捕捉到了情况的物理过程，并使计算机能够进行准确的模拟，最终回答了听力是如何工作的这个问题。首先，我们将写下控制钙浓度、毛发上的门的打开和毛细胞的拉动和推动之间的关系的方程式。其次，我们将探索一种所谓的前馈机制，即一个毛细胞的输出导致沿螺旋式鼓头稍微进一步放大。最后，我们将看看毛发本身如何结合在一起，从而在毛细胞麦克风中引起巨大响应的动力学。最终，我们将使用数学模型来确定在众多相互竞争的解释中，哪一种解释对于解释活动过程如何发生是最可信的。我们预计这将使医生更容易更准确地诊断听力问题，并允许他们在一个人的听力确实失败时提出更好的补救措施。

The human inner ear (or cochlea) is a remarkable device that out-performs any human-made system. For example, it is sensitive to displacements at sub-atomic length scales, smaller than background noise, can distinguish signals separated by microseconds, can process sounds over a million-fold intensity range (from 0dB to 120dB SPL), operates over a frequency range of over ten octaves (from 20Hz to 20kHz), can discriminate frequencies only 0.2% apart, and intensity changes of 1dB. Largely speaking, all mamals use a similar system to hear, and their ears have similarly remarkable performance. While physiologists can describe many of the processes that underlie this performance, there is a lack of agreement among them about what are the key ingredients that make it all work. Using data from rats rather than humans, we will seek to understand this process. The detailed structure of the cochlea is complicated and involves a fluid filled tube that is wrapped up into a spiral. The tube is divided in two by the so-called 'basilar membrane' that vibrates up and down like a drum. This is a very strange drum though. Sitting on top of the membrane is a device known as the organ of Corti that acts like a very special microphone. Not only does the microphone pick up the signal from the drum and relay it via nerve cells to the brain, but it also acts like an amplifier that actually makes the drum beat up and down more vigorously. However, each of the array of amplifiers at different distances along the spiral tube responds to a different frequency. This grant aims to understand how the cochlear amplifier works. It is widely believed that the key parts of the organ of Corti responsible for the amplification are the so-called outer hair cells. These have small hairs on them which can open and close tiny gates that allow calcium to flow into the cell. It is thought that the flow of calcium is the trigger that causes the cell to rapidly pull and push on the basilar membrane drum to make it beat with larger amplitude. We will use a mixture of experimental measurements (at Bristol and Keele) together with mathematical modelling and simulation. In the Bristol experiments, we will determine how the opening and closing of the gates on the outer hair cells can change the flow of calcium, how they lead to the pulling and pushing of the hair cell itself, and also how the hairs on neighbouring outer hair cells influence each other. The Keele experiments will look at detailed images of the motion of the basilar membrane as one changes the input amplitude of single-frequency sounds. This way we can look at a specific microphone/amplifier and see the dynamic response of its active process. These two sets of experiments will be used to inform a set of mathematical equations that capture the physics of the situation and enable accurate computer similation and ultimately an answer to the question of how hearing works. Firstly we shall write down equations governing the relation between the concentration of calcium, the opening of the gates on the hairs, and the pulling and pushing of the hair cell. Second we shall explore a so-called feedforward mechanism where the output of one hair cell causes amplification slightly further along the spiralling drumhead. Finally we shall look at the dynamics of how the hairs themselves couple together to cause a large response in the hair-cell microphone. Ultimately we shall use the mathematical models to decide which of a number of competing explanations is the most plausible for explaining how the active process occurs. We expect that this will make it easier for doctors to diagnose hearing probelms more accurately, and will alIow them to propose better remedies when a person's hearing does fail.