Page 32 - Fall2020

BIOMECHANICS OF THE MIDDLE EAR
sideofthemalleusaswellasanterior–posteriordifferences in the radial-fiber lengths and material properties of the eardrum (Puria and Steele, 2010).
In the guinea pig and chinchilla, on the other hand, the malleus divides the eardrum right down the center (Figure 4, C and D, respectively) and has a cross section that distinctly resembles an I beam along most of its length. This cross section appears to be better suited for transverse motion but not for twisting or rotation of the malleus handle. Although motions of the ossicles along all three dimensions have been reported for the cat and human, a systematic study of the relationships between these diverse malleus morphologies and their three-dimensional motions remains lacking. Regardless of the type of malleus motion, it must be efficiently and smoothly transmitted to the incus and stapes.
Ossicular Axes of Rotation
Malleus motion is transferred to the incus and then the stapes, which, in turn, induces smoothly varying fluid pressure in the cochlea (Figure 2A). There are several rota- tions of the ossicles that take place to make this happen. In various species, an anterior–posterior axis passing through the center of mass of the malleus–incus complex (Axis 1, shown in Figure 5A for chinchilla; Figure 5B for human; Figure 5C for mouse) supports rocking motions that provide a small amount of leverage due to the handle of the malleus being longer than that of the incus (see Multimedia2 at acousticstoday.org/puriamm for links to animations of the human eardrum and ossicles from a finite-element model).
As previously mentioned, the round cross section of the malleus handle and asymmetrical eardrum attach- ment in human and cat could also support rotations with respect to another axis oriented along the supe- rior–inferior direction (Axis 2, shown in Figure 5B for human). Calculations of the moments of inertia of the malleus in all three perpendicular directions indicate a value that is much smaller for rotations around Axis 2 than for rotations around the two other axes. This suggests a preferred rotation around this lower-inertia inferior–superior axis for higher frequencies because the joint connecting the malleus to the incus is likely to be more flexible at higher frequencies, thus permitting more of this motion.
The anatomy of the mouse malleus–incus complex (Figure 5C) is similar in many microtype high-fre- quency-hearing mammals such as bats and mice that have a bony protuberance called the orbicular apophy- sis (Mason 2013). These animals also use Axis 1 at low frequencies but are thought to switch to Axis 2 at higher frequencies, which is orthogonal to Axis 1 and passes through the orbicular apophysis. However, the evidence for these different axes of rotation in mouse, based on one-dimensional vibration measurements at several loca- tions (Dong et al., 2013), is not strong. Bending of the malleus and incus at higher frequencies, rather than just translations or rotations of the bones as rigid bodies, is likely to play an important role in sound transmission.
Now that we have examined the biomechanics of the eardrum and ossicular chain, we return to the ques- tion of what evolutionary pressures may have led to the repurposing of jaw bones and their accompanying joints into a flexible three-ossicle linkage between the eardrum and cochlea in mammals.
Why Three Ossicles?
Themammalianmiddleearisuniqueamongvertebratesin having three ossicles with two intervening flexible joints and two dedicated muscles. What might be some advantages of this unusual design in comparison to the single-ossicle middle ear of birds and lizards? As mentioned previously, the malleus-to-incus length ratio, averaging close to a factor of two across mammals, provides some leverage to facilitate the air-to-fluid impedance-matching function of the middle ear. Although this can be considered one functional advan- tage of having three ossicles, it provides a relatively small benefit when compared with the stiletto heel-like force mul- tiplication provided by the eardrum-to-footplate area ratio. The area ratio is approximately a factor of 20 among a range of mammals, but this cannot be claimed as a mammalian advantage because birds and lizards have similar area ratios. Thus, most of the impedance matching of the middle ear is achieved by the area ratio and not the ossicular lever ratio. So, what other functional advantages might this three-piece flexible design provide?
Safety Engineering
The late surgeon and researcher at the Stanford Otolaryn- gology Department and Palo Alto VA Hospital Richard Goode (1935–2019) often quipped “The designer of the
32 Acoustics Today • Fall 2020