Experimental measurements of micromechanical transfer functions in the alligator lizard cochlea

A.J. Aranyosi, C. Quentin Davis and Dennis Freeman

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Introduction

The cochlea is a remarkable organ, not only for its unparalleled sensitivity but also for its sharp frequency selectivity. In the alligator lizard, the most sharply tuned auditory nerve fibers in the low-frequency region have Q10 dB values as high as 6, and high-frequency slopes of up to 1000 dB/octave (Weiss et al, 1976). If such a fiber were tuned to middle A on a piano (440 Hz, a typical characteristic frequency in this region), it would be sensitive primarily to a frequency region only 73 Hz wide; the A# key on the piano would generate a signal in this fiber nearly 15000 times smaller than the signal generated by A natural.

Many models of the cochlea predict that this tuning arises, at least in part, from the mechanical interactions of cochlear structures such as the tectorial membrane (TM), hair bundles, and reticular lamina (RL). The drawing below shows the relative locations of these structures, as viewed from the side. The term "micromechanics" describes the motions of these structures in response to sound. Our laboratory is studying micromechanics in the alligator lizard cochlea to determine the mechanical properties of cochlear structures and their interactions, and to gain a better understanding of the mechanisms underlying sharp frequency selectivity in the cochlea.

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(Click on any image or movie to see a larger version)

The Alligator Lizard Cochlea

In comparison to mammalian cochleae, the alligator lizard cochlea is relatively simple. The drawing below, by Anne Greene, depicts the alligator lizard cochlea and some supporting structures. The structure in the center of the image is the basilar papilla, which contains the sensory hair cells. The papilla is divided into two regions. The free-standing region, which spans the top 2/3 of the papilla, contains hair cells whose hair bundles insert freely into endolymph. The tectorial region, which makes up the bottom 1/3 of the papilla, contains hair cells whose bundles insert into a tectorial membrane (the glossy structure in the image). The sensory receptor cells sit between the TM and the basilar membrane (BM), in a manner analogous to the mammalian cochlea. The frequency selectivity of hair cells in the tectorial region is similar to that of mammalian cochleae in the same frequency range. The results of this study are all from the tectorial region.

drawing of lizard cochlea

The Measurement System

We isolate the cochlea and place it in an experimental chamber as drawn below. The cochlea is clamped between two fluid spaces that can be perfused independently (e.g., to perfuse artificial endolymph apically and artificial perilymph basally). The whole chamber can be placed on the stage of a microscope for observation with brightfield Kohler microscopy and imaging with a CCD camera. The cochlea is stimulated with sound through the basal fluid; the sound pressure is calibrated with a hydrophone. Because the cochlea vibrates at the frequency of the sound stimulus, which is much faster than video cameras can take images, a strobed light source is used to stop the apparent motion of the cochlea at any desired phase of the stimulus. Images taken at several stimulus phases are then analyzed using computer vision algorithms to determine the motion of cochlear structures.

schematic of experiment chamber

The image below shows a low-magnification view of the cochlea in the stimulus chamber (on the right). The long, thin structure in the center of the image is the basilar papilla; the bright region around it is the basilar membrane. The gray region extending to the left is the auditory nerve, which fans out into individual nerve fibers near the papilla.

lizard cochlea in chamber

At a higher magnification, the tectorial region of the cochlea appears as shown below. Kohler illumination allows us to take "optical sections", so we only see structures near the plane of focus. The schematic cross-section of the cochlea on the right shows the plane of focus at which this image was taken. The image on the left shows the structures at this focal plane. In the center of the image are the bases of hair bundles of several hair cells. Note that with this preparation we can resolve individual stereocilia of the hair bundle. Towards the right, the tips of several bundles are visible. Along the right edge, the border of the TM can be seen as a wavy line.

view of cochlea through
microscope

Micromechanical Motions

To illustrate the motions we can see and measure, we will zoom in on one hair bundle, which is boxed in the image below. Although the rest of the images on this page show a single hair bundle, keep in mind that we can and do repeat this analysis for every hair bundle in the image.

zoom in on one hair bundle

The image from the boxed region above shows the base of one hair bundle. This image corresponds to the bottom of a 3D representation of the bundle, as shown in the left-hand image below. By stacking together images from successively higher focal planes, we recreate the 3D structure of the entire bundle, as shown in the right-hand image.

stacking images up... ...to make a 3D volume image

Recall that we take images at several phases of our sound stimulus. If we repeat the above process of creating 3D images for each phase, and show the resulting images in sequence, we obtain a 3D slow-motion movie of the hair bundle in motion, as shown below. From this movie, we can see that the RL at the base of the bundle moves more than the tip at this stimulus frequency. We can also see that the TM moves less than the bundle, and appears to be out of phase with the RL. The drawing on the left illustrates the motion of these structures.

moving hair bundle, inertial ref. frame

Quantifying Motions

If we take the 3D movie of the hair bundle and flatten the images, we get the movie below. In this movie we can see individual planes of focus more clearly.

3D
bundle image, flattened out

By using algorithms adopted from computer vision, we can determine the three-dimensional displacement between any pair of 3D volume images. The image below shows the results of this analysis, applied in one dimension, to the images of our hair bundle. The plots above and below each image show the position of the image as a function of time, and the numbers accompanying each plot are the magnitude and phase of the fundamental component of motion. Quantifying these motions at several stimulus frequencies allows us to examine the mechanical relationships between structures.

3D bundle
image, with motions quantified

Although the absolute motions of cochlear structures are important for understanding micromechanics, the physiologically relevant stimulus for the cell is the motion of the hair bundle about its base. We can determine this motion by jumping into the cell's reference frame. Since we know the motion of the base, we can simply shift each image to compensate for this motion, and we get a movie of relative motions. The plots above and below the images show motion estimates obtained by applying our computer vision algorithms to the shifted images. The base of the hair bundle is now stationary, and the relative motion of the bundle increases as we move upward from the base. For example, the tip of the bundle (lower-left image) moves about 0.3 micrometers peak-to-peak; this image was taken 6 micrometers above the base, so the bundle is rotating by about 3o.

3D bundle
image, motion relative to base

Micromechanical Transfer Functions

Using our measurement system, we can observe and quantify three-dimensional motions of the reticular lamnia (RL), hair bundles, and tectorial membrane (TM) in response to sound. We can examine these motions in both an absolute reference frame (left-hand image below) and in a reference frame relative to the base of the hair bundle (right-hand image).

moving hair bundle, inertial ref. frame moving hair bundle, cell ref. frame

Measuring the motions we have described is important for understanding cochlear function. However, the motions depend not only on the micromechanical properties of the cochlea, but also on the sound pressure level, the mechanical properties of the basilar membrane, etc. We can examine the contribution of micromechanics directly by examining a set of micromechanical transfer functions to relate the motions of different structures. These micromechanical transfer functions are based on the four measurements shown in the image below: in the absolute reference frame, the motions of the TM and the RL; in the relative reference frame, the shear between TM and RL (TM-RL) and the deflection of hair bundles about their base (Tips-RL).

transfer functions of relevance to cochlear micromechanics

The micromechanical transfer functions we have examined include:

  • TM/RL, which describes the displacement of the TM that results from a given RL displacement;
  • (TM-RL)/RL, which describes the shear between TM and RL that results from a given RL displacement;
  • (Tips-RL)/(TM-RL), which describes the hair bundle deflection that results from a given amount of TM shear. Each of these transfer functions provides information about the micromechanical properties of the cochlea. For example, TM/RL lets us examine whether the TM is resonant (that is, does it move more than the RL over a limited frequency range?). (TM-RL)/RL describes the transformation from absolute to relative motions, and is the output of many micromechanical models to which our results can be compared. (Tips-RL)/(TM-RL) describes the coupling between TM shear and bundle displacement; for example, if the TM and hair bundles were rigidly coupled then this ratio would have a phase near 0o; if they were coupled through fluid interactions, then the phase would be near -90o.

    The poster shows measurements of these micromechanical transfer functions as a function of frequency for 140 hair cells from cochleae of 9 lizards. In each case, both the magnitude and phase of the transfer functions were constant with frequency; consequently, they have been grouped together on the plots. The primary results are:

  • The TM did not appear to be resonant; its motion was always smaller than and in phase with RL motion.
  • The deflection of hair bundles about their base was in phase with but smaller than TM shear. This result suggests that the bundles are directly coupled to the TM, and that the TM shears throughout its length, so the relative displacement it imposes on the bundles is smaller than the relative displacement at the top of the TM.
  • None of the transfer functions shows a gain larger than 1, suggesting that there is no increase in hearing sensitivity due to micromechanics.
  • None of the transfer functions showed sharp frequency selectivity. However, we were not successful in measuring an electrical response to sound in these preparations. Although the passive mechanical properties of the tissue are unlikely to be greatly affected by this lack of an electrical response, the alligator lizard cochlea may also have physiologically-dependent mechanical properties, such as those seen in other animals.

    PDF version of the poster.
    Go To:
    Cochlear Mechanisms
    MIT Micromechanics Group
    A.J. Aranyosi (aja @ this university)
    last updated March 1999