Middle Ear Modeling – A Tutorial [Hello, I am Fereshteh Kalantari. I am a Ph.D student in Electronic Engineering at K. N. Toosi University of Technology, Tehran, Iran. In this Tutorial, I want to explain Middle Ear Modeling, which is my project topic for the Neuro-Muscular System Control course. This course is instructed by Dr. Delrobaei. If you have any questions, please send me an Email ([email protected]). Now let's read and learn.] ave you ever imagined that you cannot hear your around sounds? Do you know how you hear sounds by your ears? H Have your ears ever damaged by loud sounds? Do you know how your ears are safe from annoying sounds? To understand this questions, we need to investigate different parts of an ear and their functions. The middle ear is one of them, which we explain about it in this tutorial. Where Is the Middle Ear? There are three main parts in an ear, they consist of the outer ear, the middle ear and the inner ear. As shown in Figure 1, the middle ear lies between the outer ear and inner ear. In hearing process, the middle ear is like an amplifying interface between the outer ear and the inner ear. Figure 1. The structure of an ear with three main parts. The outer ear, the middle ear and the inner ear. 1 What Does the Middle Ear Do? In Figure 2, we illustrated how we hear by an ear step by step and what the middle ear's main job is. According to Figure 2, after sound waves enter the outer ear, they travel through the ear canal and make their way to the middle ear. There is the eardrum, which is a thin piece of skin stretched tight like a drum. The eardrum separates the outer ear from the middle ear. The middle ear's main job is to take those sound waves and turn them into vibrations and amplify them. The vibrations then move to the inner ear (the cochlea). This is a fluid filled, snail shaped structure that is lined by tiny hair receptors. These hair receptors are attached to nerve endings and as the vibrations wash over the hair receptors, the nerves carry signals to the brain which interprets these stimuli as sound. How Sound waves enter our outer ear and Our eardrum vibrates with the incoming travel through the ear canal to your sound and sends the vibrations to three tiny we Hear eardrum. bones in our middle ear. Our auditory nerve carries this The bones in our middle ear amplify the sound vibrations electrical signal to the brain, and send them to our inner ear, or cochlea. The sound which translate it into a sound vibrations activate tiny hair cells in the inner ear, which in you can understand. turn release neurochemical messengers. Figure 2. The steps of hearing by an ear. The Structure of the Middle Ear The middle ear consists of an air-filled cavity called the tympanic cavity and includes the three ossicles and their attaching ligaments; the auditory tube; and the round and oval windows. The ossicles are three small bones that function together to receive, amplify, and transmit the sound from the eardrum to the inner ear. These bones also act as a protective mechanism to prevent very loud sounds from damaging the inner ear. In Figure 3, we shown the different parts of the middle ear and described about every part in the following. "The Middle Ear has the ossicles, which are three small bones that function together to receive, amplify, and transmit the sound from the eardrum to the inner ear." 2 Auditory ossicles Malleus Incus Stapes Stabilizing ligaments Oval window External acoustic meatus Round window Tympanic membrane Eustachian tube Tympanic cavity (Middle Ear) Figure 3. The structure of the middle ear. The Structure - The Auditory Ossicles The eardrum is very thin, measures approximately 8-10 mm in diameter and is stretched by means of small muscles. The pressure from sound waves makes the eardrum vibrate. The vibrations are transmitted further into the ear via ossicles that are three bones in the middle ear: the hammer (malleus), the anvil (incus) and the stirrup (stapes). The stapes is the smallest named bone in the body. These three bones form a kind of bridge, the malleus receives vibrations from sound pressure on the eardrum, where it is connected at its longest part (the manubrium or handle) by a ligament. It transmits vibrations to the incus, which in turn transmits the vibrations to the small stapes bone. The wide base of the stapes rests on the oval window. As the stapes vibrates, vibrations are transmitted through the oval window, causing movement of fluid within the cochlea. The Structure - The Oval Window The oval window is a membrane covering the entrance to the cochlea in the inner ear. When the eardrum vibrates, the sound waves travel via the hammer and anvil to the stirrup and then on to the oval window. When the sound waves are transmitted from the eardrum to the oval window, the middle ear is functioning as an acoustic transformer amplifying the sound waves before they move on into the inner ear. The pressure of the sound waves on the oval window is some 20 times higher than on the eardrum. 3 The pressure is increased due to the difference in size between the relatively large surface of the eardrum and the smaller surface of the oval window. The same principle applies when a person wearing a shoe with a sharp stiletto heel steps on your foot: The small surface of the heel causes much more pain than a flat shoe with a larger surface would. The Structure - The Round Window The round window in the middle ear vibrates in opposite phase to vibrations entering the inner ear through the oval window. In doing so, it allows fluid in the cochlea to move. The Structure - The Eustachian Tube The Eustachian tube is also found in the middle ear, and connects the ear with the rearmost part of the palate. The Eustachian tube’s function is to equalize the air pressure on both sides of the eardrum, ensuring that pressure does not build up in the ear. The tube opens when you swallow, thus equalizing the air pressure inside and outside the ear. In most cases the pressure is equalized automatically, but if this does not occur, it can be brought about by making an energetic swallowing action. The swallowing action will force the tube connecting the palate with the ear to open, thus equalizing the pressure. Built-up pressure in the ear may occur in situations where the pressure on the inside of the eardrum is different from that on the outside of the eardrum. If the pressure is not equalized, a pressure will build up on the eardrum, preventing it from vibrating properly. The limited vibration results in a slight reduction in hearing ability. A large difference in pressure will cause discomfort and even slight pain. Built-up pressure in the ear will often occur in situations where the pressure keeps changing, for example when flying or driving in mountainous areas. First Mechanical Model of the Middle Ear The human middle ear is a tiny mechanical structure consisting of the tympanic membrane, three ossicles (malleus, incus, and stapes), middle ear ligaments and muscle tendons, and the middle ear cavity. In the meantime, investigations on modeling the middle ear have been developed for a better understanding of the sound transmission mechanism in the human ear. In the Figure 4, you can see a lumped model of an ear, which is proposed by Feng and Gan (2004). This model has been drawn from external ear canal to cochlea. This lumped parametric model consisting of 6 messes connected by several pairs of spring and dashpot is proposed for mechanical analysis of the ear, including the external ear canal, tympanic membrane, middle ear ossicles, and cochlea. The air inside the external ear canal was represented by the mass M1, which coupled the mass M2, the tympanic membrane (TM), through the spring K2 and dashpot C2. Spring K1 and dashpot C1 represented the TM annulus. The three ossicular bones (malleus, incus, and stapes) were represented by masses M3, M4, and M5, respectively. The malleus-incus joint and the incus-stapes joint, which connect the three ossicles and form the ossicular chain, were represented as two pairs of springs and dashpots: K5, C5 and K6, C6, respectively. The malleus (M3) was attached to the TM (M2) through K3 and C3. The middle ear suspensory ligaments and intra aural muscles supported the ossicles. Two major ligaments suspending the malleus and incus were simulated as dashpots C4 and C7. M6 represented cochlear fluid supported by dashpots C9 and C10. The stapes coupled with the cochlear fluid through the stapedial annulus (K8 and C8). All unknown parameters are identified based on the governing equations of the system and the determined through optimization and parameter-perturbation process. This lumped model serves as the starting stage for understanding the relation between the middle ear components for sound transmission. 4 The middle Ear Tympanic Malleus membrane M2 M3 Incus Stapes M5 M4 Figure 4. Lumped parametric model of the human ear. As shown in Figure 4, you can see the model of the middle ear in red dash and its different parts are represented by using different colors. In a damped mass-spring system, the equation of motion can be represented as 푚푥̈̈ + 푐푥̇̇ + 푘푥 = 푓(푡) (1) 풙̈ : Acceleration 풙̇ : Velocity Mass Stiffness 풙 : Displacement Damping parameter f(t) : Externally applied force 푥 = 푋̂ 푒푗휔푡 (2) 푥̇ = 푗푤푋̂ 푒푗휔푡 (3) 푥̈ = −푤2푋̂ 푒푗휔푡 (4) Where m is the mass, c is the damping parameter, k is the stiffness, x is the displacement, is the acceleration, is the velocity of the system matrices, and f (t) denotes an externally applied force.