Page 30 - Fall2020

BIOMECHANICS OF THE MIDDLE EAR
Figure 3. Eardrum structure and motion. The arrangement of radial and circumferential collagen fibers throughout the eardrum (A) and its multilayered construction (B) is depicted. Displacements of the cat eardrum relative to malleus motion as a function of frequency for a single point on the anterior (C) and posterior (D) sides of the eardrum are shown. Blue and red dashed lines indicate a measurement; black lines are model calculations (Fay et al., 2006). Spatial vibration patterns are measured on the surface of a human eardrum (E, inset) in response to a 200-Hz tone (E) and a 4-kHz tone (F), showing multiple modes (Cheng et al., 2013). Colors indicate the displacement magnitude normalized by ear canal pressure in micrometers per pascal.
collagen-fiber layers (Figure 3A) sandwiched between sub- epidermal and submucosal layers (Figure 3B). Modeling this ultrastructure has been challenging because it is difficult to know how to ascribe material properties to the layers of this complex structure. Most early finite-element models treated the eardrum as an isotropic material, with the same properties in the circumferential and radial directions. However, dynamic motion measurements combined with constitutive modeling and composite shell modeling suggest that the material properties of the two fiber layers are very different, such that an orthotropic eardrum with different properties in those two directions is more representative of the physiology (Fay et al., 2006; O’Connor et al., 2017). Now that we know that delay is involved in eardrum transduction, what does eardrum motion look like and how does it relate to this observed delay?
Discordant Eardrum Modes
Experiments have shown that eardrum motions vary sharply in amplitude above a few kilohertz for individual
points on the eardrum (Figure 3, C and D) and across the entire eardrum surface for fixed frequencies (Figure 3, E and F). Despite the seemingly chaotic motions of nearby points on the eardrum surface (see Multimedia2 at acousticstoday.org/puriamm for links to animations of the human eardrum), the motion of the malleus has been shown to be wideband and relatively smooth. This is somewhat akin to a sail on a sailboat moving in a variety of ways on its surface but nonetheless managing to propel the mast, and hence the boat, smoothly forward.
A plausible explanation for this is that all of these modes of vibration are summed together along the length of the relatively rigid malleus handle that attaches to the ear- drum. Using one of the earliest finite-element models of the eardrum, Funnell et al. (1987) showed that regardless of the complex vibration patterns of the eardrum surface, the overall sound transmission through the middle ear has smooth frequency characteristics.
Summing It All Together
Why are multiple large-amplitude eardrum modes present in the first place, and do they serve a functional purpose? This remained a mystery for many decades until model- ing studies found that the multiple seemingly discordant resonances without significant energy dissipation on the eardrum are summed together at the malleus to produce
greater sound transmission to the cochlea at high frequen- cies, resulting in greater overall hearing sensitivity but with a smooth response (Fay et al., 2006).
That discordant eardrum motions are integrated by the malleus, thus resulting in smooth but delayed middle ear transmission, has been experimentally verified through a series of cleverly designed measurements (Milazzo et al., 2017). Using a pressure-click stimulus in the gerbil ear canal, various locations on the eardrum were shown to have filtered bandlimited responses, but the click reap- peared with fidelity in the motion of the malleus after some delay. When simple mathematical models of strings of different lengths, each of which reproduces a band- limited response to a click akin to the motions on the eardrum surface, are combined, the result is similar to the original click but with a delay. These modeling stud- ies suggest that it is the radial collagen fibers that are mistuned (think of them as strings with different lengths) and are critical for high-frequency sound transmission through the middle ear.
30 Acoustics Today • Fall 2020