The Mechanics of Hearing

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1 The Mechanics of Hearing Dr Lim Kian Meng Mechanical Engineering Department, NUS Introduction We are constantly surrounded by sound that provides information about the objects around us. Determining the sources of sound is an important biological trait and our ears enable us to collect such vital information in the air. An animal's ability to find food or avoid a predator and our communication by speech depends on the ear's functions of collecting and conditioning such signals for processing by the brain. The ear can be divided into three distinct regions based on their function and location in the peripheral auditory system. Figure 1 shows a cross-section of the human ear divided into the three distinct regions. The acoustic signals manifested as pressure fluctuations in the air are collected by the external ear and transmitted through the middle ear towards the inner ear for transduction into electrical neural impulses to the brain. Figure 1: Cross-section of the human ear divided into three regions: [E] External ear, [M] Middle ear and [I] Inner ear. Outer Ear The external or outer ear consists of the visible part of the ear (pinna) and the ear canal leading to the eardrum. The pinna provides a sense of direction to the incoming sound, especially in animals where it is large and under muscular control. Sound in the air is collected by the outer ear and directed down the ear canal towards the

2 middle ear. The length of the ear canal is believed to provide resonance that enhances the sensitivity of hearing over a band of frequency. The human ear canal s length of about 3cm has a resonant frequency of about 3kHz (based on a quarter wavelength model) and this coincides with the prominent frequency used in speech. Middle Ear The middle ear is an air-filled cavity in the temporal bone. Its purpose is to provide impedance matching between the acoustic waves in air and the fluid vibration in the inner ear. The middle ear consists of the eardrum (tympanic membrane) and three ossicles, namely the malleus, incus and stapes, which are three tiny bones connected in series. The malleus is attached to the eardrum and the stapes to the oval window in the cochlea. The eardrum responds to the acoustic sound wave collected by the ear canal, and its vibration is transmitted down the series of ossicles to the inner ear. The ossicles are suspended and connected by ligaments forming a lever system. The lever ratio, together with the area ratio of the eardrum to the oval window, provides an amplification of pressure transmitted to the inner ear. Active muscle tissues attached to the ossicles guard against loud sound which may cause damage to the delicate inner ear, and they also have a role in sound localization. Inner ear The inner ear is a fluid-filled cavity in the temporal bone consisting of the semicircular canals, the vestibule and the cochlea. The semicircular canals provide us the sense of balance, and the cochlea is responsible for our sense of hearing. A crosssection of the cochlea is shown in Figure 2. It is a long narrow chamber coiled around a bony core (modiolus) into a conical helix resembling the snail shell. The chamber houses three separate fluid ducts: the scala vestibule, scala media and scala tympani. Figure 2: Cross-section of the cochlea showing the fluid being set into motion when sound is transmitted to the stapes.

3 The fluid chamber has a taper along its length, wider around the base and narrower at the apex. The stapes attaches to the cochlea at the oval window which closes the basal end of the scala vestibule. At the apex, the scala vestibule connects with the scala tympani via a small hole called the helicotrema. A flexible round window connects to the basal end of the scala tympani, providing pressure relief when the incompressible fluid in the duct is set in motion. The scala media is a self-contained duct that terminates just before the helicotrema. The partition separating the scala tympani and scala media consists of the basilar membrane which is the main vibrating structure. It is supported by the bony osseous spiral lamina near the central modiolus and the spiral ligament at the outer edge. The membrane consists of dominantly transverse fibers embedded in an amorphous ground substance. It is thick and narrow at the base and broad and thin at the apex. This unique construction gives the basilar membrane distinct tuning behavior when it is set into motion. Figure 3 shows a schematic drawing of the cochlea with the fluid chamber uncoiled to depict the essential components and mechanics. Here, the scala media has been collapsed and represented together with the basilar membrane for simplicity. Figure 3: Schematic drawings of the uncoiled cochlea showing a typical basilar membrane response when the stapes is set in motion. Mechanical vibrations from the stapes set up pressure waves in the fluid duct. The fluid-structure interaction between the scalae and the basilar membrane results in a traveling wave along the length of the cochlea. Due to the tuning property of the basilar membrane, different frequency components in the sound give rise to response peaks occurring at different locations along the length of the cochlea. The vibration response is picked up by the organ of Corti, a complicated structure of cells on the basilar membrane responsible for the transduction of the mechanical vibration to electrical pulses in the auditory nerve for interpretation by the brain. It is also at this stage where further conditioning and amplification of the signal is performed. A cross-sectional view of the fluid duct showing the organ of Corti is given in Figure 4.

4 Among the elaborate array of cells in the organ of Corti, the inner hair cells are the primary sensory cells that detect the motion of the basilar membrane based on the shear on the stereocillia (tiny hair-like structures) at the top of the hair cells. The outer hair cells are also sensory cells, but they have a dual role as actuation cells due to their electro-motility. When the basilar membrane vibrates, these outer hair cells sense the motion and push back on the basilar membrane to amplify its motion. Figure 4: Cross-section of the fluid duct showing the organ of Corti with the inner and outer hair cells. It can be seen that the acoustic signal is in fact processed in terms of its intensity and frequency contents at the peripheral stage of the hearing process. These complicated functions are accomplished through interactions between a labyrinth of fluid ducts and an elaborate organization of cell structures, cleverly crafted in the cochlea. Engineering Applications The cochlea has evolved over many generations of optimization to be an excellent signal transducer, amplifier and analyzer all build into a tiny package. The human cochlea has a remarkable performance of broadband frequency coverage of 10 octaves (20Hz to 20kHz) wide dynamic range of 6 orders of magnitude (0 to 120dB SPL) low power consumption (tens of microwatts) fine time resolution (6 to 10 microseconds) It is desirable to build a transducer that can mimic some, if not all, the performances of the cochlea. To achieve that, it is important to first understand the mechanics and

5 working principles in the cochlea. Many researchers have studied cochlear mechanics through analytical and numerical modeling and simulations, such as 1D lumped parameter models, 2D and 3D finite difference and finite element models. Although there is a general agreement in the working principles in the cochlea, there are still many fine details of cochlear mechanics that remained to be resolved, especially the active amplification process and mechanism due to the outer hair cells. Some physical models of the cochlea have also been constructed, and they probably serve as a preliminary prototype of a transducer that would inherit some of the behaviors of the cochlea. Figure 5 shows a cochlear model prototype that is developed at the Mechanical Engineering Department (NUS). It is a half-model of the cochlea consisting of a single fluid chamber with a tapered basilar membrane at the top. At one end, it is connected to a vibration shaker that pushes (like the stapes) on the fluid in the chamber. The vibration motion of the membrane at the top is then measured using a laser vibrometer. Figure 5: A cochlear model prototype developed at NUS consisting of a tapered membrane at the top and it is connected to a vibration shaker that acts like the stapes. This prototype is a preliminary model which is able to reproduce the gross behavior of the cochlea. There are many modifications that need to be added to improve its performance including better frequency selectivity and significant amplification of response while maintaining stability. Such design improvements may best be assisted by good mathematical models that provide various design parameter studies. Good designs may also be inspired by careful study of the construction of the cochlea found in many animals. We definitely have quite a lot to learn from Nature in making such a high performance sensor that mimics the ear. For more information see:

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