Tomographic Reconstruction of Three-Dimensional Cochlear Motions

A. J. Aranyosi and D. M. Freeman

This poster was presented at the Twenty-Third Meeting of the Association for Research in Otolaryngology at St. Petersburg Beach, FL on February 22, 2000. The image below provides a link to a PDF file of the poster, suitable for printing. If you need a PDF viewer for Windows, MacOS, or Linux, please visit Adobe's web site.

Image of poster


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Introduction

Our group is studying cochlear micromechanics by measuring sound-induced motions of cochlear structures. These measurements allow us to obtain a better understanding of the mechanisms by which the remarkable signal-processing properties of the cochlea arise. The measurements also provide experimental data for testing and developing models of cochlear mechanics.


Drawing of alligator lizard cochlea


We measure motions of the alligator lizard (Gerrhonotus multicarinatus) cochlea, shown in the image above. The structure in the center of the image is the basilar papilla, which contains the hair cells of this organ. The basilar papilla is divided into two regions. In the tectorial region (bottom of image), hair bundles are covered by a tectorial membrane. Best frequencies of afferent nerve fibers innervating this region range from 200 to 800 Hz. Hair bundles in this region are about 8 micrometers in height. In the free-standing region (top of image), hair bundles have no overlying tectorial structure. Best frequencies of afferent nerve fibers innervating this region range from 1 kHz at the apical end (next to the tectorial region) to 4 kHz at the basal end. Hair bundle height in this region is graded from about 30 micrometers at the apical end to about 10 micrometers at the basal end. The alligator lizard cochlea has several advantageous features for studying mechanics.

  • It is planar, so we can image it in a conventional microscope while maintaining the separation of fluids seen in vivo.
  • It contains two regions - one with a tectorial membrane and one without. Thus we can attempt to determine the mechanical effect of the tectorial membrane by studying differences between the two regions.
  • The sensitivity and frequency selectivity of this cochlea are similar to those of mammals, so an understanding of the mechanical processes at work in this cochlea may provide insight into mammalian hearing.
  • Testable models of cochlear mechanics already exist for this cochlea. For example, these models predict
    1. the papilla rocks about a longitudinally-oriented line located near the neural side of the papilla
    2. motion of the papilla is independent of stimulus frequency
    3. motion of the papilla is independent of longitudinal position
    4. the rotation of free-standing hair bundles is determined by fluid motion induced by reticular lamina motion
    The measurements reported in this study were taken in the free-standing region of this cochlea (upper part of picture), which lacks a tectorial membrane.

    Methods

    Schematic of experiment chamber


    To measure sound-induced motions, we isolate the cochlea and place it in an experimental chamber, schematized above. We clamp the cochlea between two fluid spaces. To simulate the in vivo fluid environment, an artificial endolymph is perfused through the apical space, and an artificial perilymph is perfused through the basal space. Sound pressures are generated in the basal fluid with a piezoelectric disk, and are calibrated with a hydrophone (Entran). We view the cochlea from above using a Zeiss Axioplan microscope with a 63x, 0.9 NA water-immersion objective. We use stroboscopic illumination to take pictures of the cochlea at different phases of the periodic sound stimulus. Images are taken with a 12-bit CCD camera (Dalsa CA-D7-1024A). The light source is a green LED (Nichia; ceneter wavelength 525 nm) which is strobed with a 1/8 duty cycle at the same frequency as the sound stimulus. The phase of the strobe signal relative to the sound stimulus determines the phase of motion at which the image is obtained (see the poster for more details).

    Image of lizard cochlea


    The image above shows a typical image obtained with our system. In the upper left hand corner is a representation of our imaging setup; the cochlea is viewed from above, and the microscope is focused so that we are seeing structures in the focal plane indicated by the red line. The focal depth, or "thickness" of the image is highly dependent on the numerical aperture (NA) of the imaging system; our NA is about 0.9, which gives us a focal depth near 1 micrometer.

    Movie of lizard cochlea in motion


    By taking pictures at several phases of the sound stimulus and viewing them in sequence, we can generate a movie showing the cochlea in motion. Such a movie is shown above. The motion of cochlear structures is difficult to interpret from a single such movie, since structures are moving perpendicular to the plane of focus. To solve this problem, we take images at several planes of focus.

    Image of lizard cochlea at a
different focal plane


    This movie shows motions at another plane of focus (again indicated by the red line). By taking a series of such images at closely-spaced focal planes (typically 1 micrometer spacing) we obtain a three-dimensional image of the cochlea in motion. We can then view any desired cross-section by taking "slices" through this three-dimensional data set.

    3D Reconstruction

    Reconstructed cross-sectional
movie of lizard cochlea in motion


    If we take slices perpendicular to the longitudinal axis of the cochlea, we obtain images like the one above. This image was generated by reslicing 80 images taken at a 1 micrometer spacing. The large circular structure in the center of the image is the basilar papilla. Near the upper right are three hair bundles.

    The resolution in the vertical axis is determined by the axial resolution of the microscope, which for this image was near 1 micrometer. The resolution in the horizontal axis is about 300 nanometers. The thickness of the image is equal to the horizontal resolution of 300 nm; thus we do not see a horizontal view of the entire hair bundle, but a thin slice through a few stereocilia. Note that despite the high resolution in the vertical direction provided by the high NA, there are still some unusual artifacts due to the nonlinear nature of the optical system. For example, bright streaks are visible above and below the tips of each hair bundle.

    Just as in the in-plane images, we can view a sequence of these resliced images to watch the cochlea in motion. The motions in this resliced view are significantly more interpretable. For example, we can see that to a first approximation, the basilar papilla appears to rock about a point just beyond the lower-left corner of the image.

    More careful measurements of the motion of the papilla reveal a more complex pattern of motion. At some frequencies, the papilla does not simply rock back and forth but moves in an elliptical pattern. The papilla itself moves more near 4 kHz than at higher or lower frequencies. These results contradict the simple models that the papilla rocks about a single axis, and that papillar motions are independent of frequency. In addition, motions of the papilla are consistently largest near the basal end, where best frequencies are near 4 kHz, and get progressively smaller for more apical regions. This effect is somewhat frequency dependent, and is most pronounced for for 4-5 kHz stimuli.

    In addition to measuring motion of the papilla as a whole, we can measure the rotation of individual hair bundles. We measure rotation by measuring displacements of both the base and the tip of a hair bundle, then subtracting motion of the base. This has the net effect of shifting us into the hair bundle's reference frame. We can compute rotation directly from the relative motion of the hair bundle. We have measured hair bundle rotation as a function of frequency at constant pressure (120 dB SPL in the fluid, which is equivalent to 94 dB SPL at the eardrum). By assuming linearity in the mechanics at this sound pressure we can convert this isopressure measurement into a predicted isoresponse curve. The poster shows this predicted curve as compared to isoresponse curves from several auditory nerve fibers. The mechanical responses are consistent with the neural responses at higher sound pressures. Further measurements are necessary to determine whether we see sharper mechanical tuning at lower sound pressures.

    Quantiative Measurements of Motion

    Measured hair bundle transfer function


    To determine how the hair bundle responds to motion of the papilla, we compute a transfer function from reticular lamina velocity to hair bundle rotation. That is, at any frequency, for a given velocity of the reticular lamina, how much does the hair bundle rotate? We have computed the magnitude and angle of this transfer function for one hair bundle and plotted it above. The magnitude is nearly constant below 1 kHz and drops with frequency above 1 kHz. The phase drops slowly with frequency. The best frequency for auditory nerve fibers innervating this bundle is expected to be near 1.5 kHz.

    Comparison to Models

    Measurements compared to
simple models


    A simple model of mammalian outer hair cell bundle mechanics predicts that the bundles rotate in proportion to reticular lamina displacement. A similar model for mammalian inner hair cell bundles predicts that the bundles rotate in proportion to reticular lamina velocity. The figure above overlays the predictions of these two models on our measured transfer function. Neither prediction matches the measured transfer function at all frequencies; rather, the bundle seems to switch from being a velocity sensor to being a displacement sensor. This transition occurs near the expected best frequency of the hair cell.

    Schematic of flap model


    A more realistic model of free-standing hair bundle mechanics must consider fluid viscosity, fluid mass, and the thickness of the viscous boundary layer of the fluid. Freeman and Weiss (Hearing Research 35, 1988) developed a two-dimensional model that takes these factors into account. The model is depicted in the figure above: a rigid hinged flap is attached by a rotational spring to a plate that moves sinusoidally with a velocity Ub. The fluid above the plate is assumed to have the properties of water. Thus the only free parameters of the model are the length of the flap L (equivalent to the height of a hair bundle) and the rotational stiffness of the spring (equivalent to the stiffness of a hair bundle).

    Movie of flap model prediction


    The animation above shows the predicted behavior of the fluid and the flap near the resonant frequency of the flap. A significant amount of fluid is moved along with the flap; the mass of the fluid dominates the hair bundle response at low frequencies. However, this mass decreases with frequency as the boundary layer gets smaller, so the resulting motion of the flap lies between that of a mass-dominated and a viscosity-dominated system. Thus for low frequencies, the bundle rotation for a given reticular lamina velocity increases with frequency at 3 dB/octave. At high frequencies, the boundary layer becomes small compared to the height of the bundle, so the fluid near the bundle tip is stationary. Thus the bundle rotates proportional to the displacement of the reticular lamina.

    Best flap model fit to
measurements


    The plot above shows the best fit of the flap model to our measured bundle motions. The fit was made by finding the two parameters (flap height and rotational spring stiffness) that minimized the error between the measured magnitude and the fit in a least-squares sense. The fit captures the trend of the magnitude measurements over the entire frequency range measured. However, the phase angle is not fit well at low frequencies. One possible reason for this is that the flap model is two-dimensional; since fluid cannot go around the hair bundle in the model, the effect of mass is overestimated. Reducing the effect of mass at low frequencies would bring the model phase into better agreement with the data.

    Comparison of model parameters
to measured values


    The two parameters of the model can be interpreted as the effective height and effective stiffness of the hair bundle. The figure above compares the parameters of the fit to measured parameters. The best-fitting flap height was 27 micrometers, almost identical to the measured 28 micrometers for the hair bundle studied. The best-fitting compliance was 3.25 x 1012 rad/N-m (this value corresponds to roughly 0.001 N/m linear stiffness). This value is slightly stiffer than the stiffest measurements from the literature. Previously measured hair bundle stiffnesses vary widely; the most compliant values (near 1000) are commonly thought to be from damaged hair cells, in which the stereocilia rootlets have been broken. Hair bundles in the alligator lizard cochlea have relatively large stereocilia, which might be expected to be on the stiff side of measured values.

    Summary

    In summary, our ability to measure three-dimensional motions in the alligator lizard cochlea has allowed us to experimentally test several models of cochlear mechanics. We have seen that the basilar papilla does not move in a pistonlike fashion, and that its motion depends on both frequency and location. In addition, we have seen that free-standing hair bundles do not behave like sensors of either velocity or displacement of the reticular lamina, but that their motions can be predicted quite well by a two-parameter hydrodynamic model. This last result illustrates the more general conclusion that fluid coupling may play an important role in cochlear mechanics in many species.