The mechanical movements of the tympanic membrane are transmitted through three small bones known as “ossicles”, comprising the “malleus”, “incus” and “stapes”—more commonly known as the
“hammer”, “anvil” and “stirrup”—to the oval window of the cochlea (see Figure 2.1). The oval window forms the boundary between the middle and inner ears.
The malleus is fixed to the middle fibrous layer of the tympanic membrane in such a way that when the membrane is at rest, it is pulled inwards. Thus the tympanic membrane when viewed down the auditory canal from outside appears concave and conical in shape. One end of the stapes, the stapes footplate, is attached to the oval window of the cochlea. The malleus and incus are joined quite firmly such that at nor-mal intensity levels they act as a single unit, rotating together as the tympanic membrane vibrates to move the stapes via a ball and socket joint in a piston-like manner. Thus acoustic vibrations are transmitted via the tympanic membrane and ossicles as mechanical movements to the cochlea of the inner ear.
The function of the middle ear is twofold: (1) to transmit the movements of the tympanic membrane to the fluid which fills the cochlea without significant loss of energy, and (2) to protect the hearing system to some extent from the effects of loud sounds, whether from external sources or the individual concerned.
In order to achieve efficient transfer of energy from the tympanic membrane to the oval window, the effective pressure acting on the oval window is arranged by mechanical means to be greater than that acting on the tympanic membrane. This is to overcome the higher resistance to movement of the coch-lear fluid compared with that of air at the input to the ear. Resistance to movement can be thought of fIgure 2.1
The main structures of the human ear showing an overall view of the outer, middle and inner ears (left) and a detailed view of the middle and inner ear (right).
31 as “impedance” to movement and the impedance of fluid to
move-ment is high compared with that of air. The ossicles act as a mechani-cal “impedance converter” or “impedance transformer” and this is achieved essentially by two means:
n the lever effect of the malleus and incus, and
n the area difference between the tympanic membrane and the stapes footplate.
The lever effect of the malleus and incus arises as a direct result of the difference in their lengths. Figure 2.2 shows this effect. The force at the stapes footplate relates to the force at the tympanic membrane by the ratio of the lengths of the malleus and incus as follows:
F1L1F2L2
where
F1 force at tympanic membrane F2 force at stapes footplate L1 length of malleus and L2 length of incus Therefore:
F F L
2 1 L1
2 (2.1)
The area difference has a direct effect on the pressure applied at the stapes footplate compared with the incoming pressure at the tympanic membrane since pressure is expressed as force per unit area as follows:
Pressure Force
Area (2.2)
The areas of the tympanic membrane and the stapes footplate in humans are represented in Figure 2.2 as A1 and A2 respectively. The pressure at the tympanic membrane (P1) and the pressure at the stapes footplate (P2) can therefore be expressed as follows:
P F The forces can therefore be expressed in terms of pressures:
F1(P1A1) (2.3)
The function of the ossicles of the middle ear.
32
Substituting Equations 2.3 and 2.4 into Equation 2.1 gives:
(P A ) (P A ) L
Pickles (1982) describes a third aspect of the middle ear which appears relevant to the impedance con-version process. This relates to a buckling motion of the tympanic membrane itself as it moves, result-ing in a twofold increase in the force applied to the malleus.
In humans, the area of the tympanic membrane (A1) is approximately 13 times larger than the area of the stapes footplate (A2), and the malleus is approximately 1.3 times the length of the incus. The buckling effect
Base Apex (a) The spiral nature of the cochlea. (b) The cochlea
“unrolled”. (c) Vertical cross-section through the cochlea.
(d) Detailed view of the cochlear tube.
examPle 2.1
Express the pressure ratio between the stapes footplate and the tympanic membrane in decibels.
The pressure ratio is 33.8:1. Equation 1.20 is used to convert from pressure ratio to decibels:
dB(SPL) P
20 P2
10 1 log
Substituting 33.8 as the pressure ratio gives:
20log [1033 8. ]30 6. dB
33 of the tympanic membrane provides a force increase by a factor of 2. Thus the pressure at the stapes
foot-plate (P2) is about (13 1.3 2 33.8) times larger than the pressure at the tympanic membrane (P1).
The second function of the middle ear is to provide some protection for the hearing system from the effects of loud sounds, whether from external sources or the individual concerned. This occurs as a result of the action of two muscles in the middle ear: the tensor tympani and the stapedius muscle. These muscles con-tract automatically in response to sounds with levels greater than approximately 75 dB(SPL) and they have the effect of increasing the impedance of the middle ear by stiffening the ossicular chain. This reduces the efficiency with which vibrations are transmitted from the tympanic membrane to the inner ear and thus protects the inner ear to some extent from loud sounds. Approximately 12–14 dB of attenuation is provided by this protection mechanism, but this is for frequencies below 1 kHz only. The names of these muscles derive from where they connect with the ossicular chain: the tensor tympani is attached to the “handle” of the malleus, near the tympanic membranes, and the stapedius muscle attached to the stapes.
This effect is known as the “acoustic reflex”. It takes some 60–120 ms for the muscles to contract in response to a loud sound. In the case of a loud impulsive sound such as the firing of a large gun, it has been suggested that the acoustic reflex is too slow to protect the hearing system. In gunnery situations, a sound loud enough to trigger the acoustic reflex, but not so loud as to damage the hearing systems, is often played at least 120 ms before the gun is fired.