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

哺乳动物内耳主动听觉过程的数学模型

• 批准号: BB/F010168/1
• 负责人: Nigel Cooper
• 金额: $ 9.07万
• 依托单位: Keele University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=BB%2FF010168%2F1
• 关键词: Mathematical; modelling; active; hearing; process

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.

人的内耳（或耳蜗）是一个非凡的装置，比任何人造系统都要出色。例如，它对亚原子长度尺度的位移敏感，比背景噪声小，可以区分以微秒为间隔的信号，可以处理超过百万倍强度范围的声音（从0dB到120dB SPL），工作频率范围超过十个八度（从20Hz到20kHz），可以区分只有0.2%的频率间隔和1dB的强度变化。总的来说，所有的哺乳动物都使用类似的听觉系统，它们的耳朵也有类似的卓越表现。虽然生理学家可以描述这种表现背后的许多过程，但他们对什么是使这一切起作用的关键因素缺乏共识。我们将利用老鼠而不是人类的数据，试图理解这一过程。耳蜗的详细结构很复杂，包括一个包裹成螺旋状的充满液体的管子。管被所谓的“基底膜”分成两部分，基底膜像鼓一样上下振动。这是一个非常奇怪的鼓。在膜上是一个被称为Corti器官的装置，它的作用就像一个非常特殊的麦克风。麦克风不仅从鼓中接收信号并通过神经细胞传递给大脑，而且它还像一个放大器一样，使鼓上下跳动得更有力。然而，每个放大器阵列在不同的距离沿着螺旋管响应不同的频率。这项拨款旨在了解耳蜗放大器的工作原理。人们普遍认为，Corti器官中负责扩增的关键部分是所谓的外毛细胞。它们上面有细小的毛发，可以打开和关闭允许钙流入细胞的小门。钙的流动被认为是触发细胞快速拉推基底膜鼓，使基底膜鼓跳动幅度更大的触发器。我们将混合使用实验测量（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，我们将确定外毛细胞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扯和推动，以及邻近外毛细胞上的毛发如何相互影响。基尔实验将观察基底膜在改变单频声音输入振幅时运动的详细图像。通过这种方式，我们可以查看特定的麦克风/放大器，并查看其活动过程的动态响应。这两组实验将用于建立一组数学方程，这些方程可以捕捉到这种情况的物理特性，并实现精确的计算机模拟，最终回答听力是如何工作的问题。首先，我们将写出控制钙浓度、毛发上通道的打开和毛细胞的拉和推之间关系的方程式。其次，我们将探索一种所谓的前馈机制，其中一个毛细胞的输出导致沿螺旋鼓面进一步放大。最后，我们将看看毛发本身如何耦合在一起，在毛细胞麦克风中引起大响应的动力学。最后，我们将使用数学模型来决定，在众多相互竞争的解释中，哪一种最能解释活动过程是如何发生的。我们希望这将使医生更容易准确地诊断听力问题，并使他们能够在一个人的听力确实下降时提出更好的治疗方法。