A Two-Mode Model of Motion of the Alligator Lizard Basilar Papilla

A. J. Aranyosi and D. M. Freeman

This poster was presented at the Twenty-Fifth Meeting of the Association for Research in Otolaryngology at St. Petersburg Beach, FL in February, 2002. 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


Abstract

Most cochlear mechanical models assume the cochlea has multiple modes of motion, but the number and nature of modes has not been determined. We present such a characterization for the alligator lizard basilar papilla. Early measurements of basilar papilla motion revealed a simple rocking motion (Frishkopf and DeRosier, 1983; Holton and Hudspeth, 1983), which has been modeled as a single mode (Weiss and Leong, 1985; Freeman and Weiss, 1990). We have recently shown that the basilar papilla has a resonant peak near 5 kHz (Aranyosi and Freeman, 2000), and that each location moves elliptically. These results cannot be explained by single-mode models, but a functional interpretation of anatomy leads to a two-mode model. The basilar papilla rests off-center on the basilar membrane, between two regions of different thicknesses. This arrangement allows both a translational and a rotational mode of motion. At each longitudinal position, the magnitude and phase of both modes and the center of rotation of the rotational mode were determined by finding the least-squares fit of the sum of modes to the measured motions. The rotational mode has a center of rotation that runs roughly parallel to the longitudinal axis on the neural side of the papilla. The translational mode is perpendicular to the basilar membrane (BM). At low frequencies, the magnitude and phase of both modal fits are independent of position, and the two modes are in phase. These results imply that the basilar papilla moves as a rigid body at these frequencies. The peak in motion at 5 kHz is reflected in both the translational and rotational modes. Above 5 kHz, both modes show a relative phase lag at the basal end, suggesting that the basilar papilla is both twisting and bending. Since both modes drive deflection of hair bundles, we conclude that multi-modal motions are significant to the function of the alligator lizard cochlea.

Introduction

Although hair cells are the mechanical receptors of the cochlea, they do not act in isolation. Acoustic signals cause macromechanical vibrations of the cochlea, and these vibrations in turn induce deflections of the sensory hair bundles of hair cells. In recent years our understanding of the transverse component of motion of the BM has greatly increased (for review, see Robles and Rugerro, Phys Rev 81:3, 2001). However, the relation between this motion and the motion of the entire cochlea is still unclear.

In the alligator lizard cochlea, the transverse motion is relatively simple. Velocity of the BM is proportional to and in phase with velocity of the extrastapes (attached to the tympanic membrane) over a wide frequency range (Peake and Ling, J Acoust Soc Am 67:5, 1980). This observation led to the hypothesis that in response to sound stimulation, the basilar papilla (homologous to the organ of Corti in mammals) simply rotates, as shown in the figure below. The left side of the figure shows a cross-section through the basilar papilla. The right side schematizes this image, and illustrates the hypothesized motion of the organ.

In this "rotational" model of basilar papilla motion, the excitatory drive to the hair cells varies significantly across the width of the organ. In the basal region of the alligator lizard cochlea, the hair bundles project freely into endolymph. Consequently the shearing component of displacement at the level of the reticular lamina is the primary drive for hair bundle deflection. The figure below plots this shearing displacement as a function of angular position on the surface of the basilar papilla in response to rotation about a point near the neural edge. This shearing displacement is largest at the abneural edge, and drops to zero at some location near the neural edge. At this location, rotation of the papilla causes displacements normal to the reticular lamina surface, so a hair bundle at this location would not be subjected to any shear. In other words, hair bundles near the abneural edge could be subjected to trauma-inducing displacements before hair bundles near the neural edge reach threshold levels of excitation.

Based on the statements above, it seems clear that understanding the relation between motion of the BM and motion of the basilar papilla is important for understanding cochlear function. We have previously reported measurements of the motion of the basilar papilla in three dimensions. In this poster, we place those results in the context of a simple mechanical model that allows the basilar papilla to undergo two simultaneous modes of motion. The addition of a second mode of motion elminates the notch in sensitivity in the figure above; consequently, both modes are important for hair bundle deflection.

Basilar Papilla Motion

Observations of basilar papilla motion in vitro (Frishkopf and DeRosier, Hear Res 12, 1983; Holton and Hudspeth, Science 222, 1983) are to a first approximation qualitatively consistent with the rotational model, although both studies noted that basilar papilla motion increased at the basal end for frequencies higher than about 3 kHz. More recently, we reported that in vitro, the basilar papilla moves elliptically in response to sound, as shown in the figure above. In addition, the motion was dependent on both frequency and location, as shown in the figure below.

The Model

From the measured motion of the basilar papilla, and from anatomical considerations, we derived the simple mechanical model shown in the figure below. The mass m represents the basilar papilla. The springs k_n and k_a represent the transverse stiffness of the BM on the neural and abneural sides, respectively. The histological cross-section at the top of this page shows the anatomical basis for these two stiffnesses. The BM underneath the papilla is not connected to the tissue on either side; rather, the papilla and BM are supported by hyaline epithelial cells. The cells on the neural edge are short and thick, while those on the abneural edge are longer and thinner. Consequently, we expect the stiffnesses on the two sides to differ.

In addition to the difference in stiffnesses on the two sides, note that the center of mass of the basilar papilla is closer to the neural edge of the thin region of the BM. Consequently, pressure on the BM exerts a torque on the basilar papilla. Thus in response to sound stimulation, the basilar papilla simultaneously exhibits a translational and a rotational component of motion. The consequence of these two modes of motion is shown in the figure below, which plots shearing displacement at the surface of the basilar papilla as a function of angular position. When the basilar papilla simply rotates about a point near the neural edge, the relative shearing displacement magnitude looks as plotted with a dashed line (this plot is simply repeated from the one above). When the basilar papilla simultaneously translates and rotates, the detailed shape of the plot depends on the relative magnitudes and phases of the two modes of motion. For one particular set of values (the best-fit values to the measured motion of one basilar papilla in response to a 5 kHz tone), the plot looks as shown. The addition of the second mode has two important consequences: first, the zero (at which rotation exerts no shear) is eliminated, because translation exerts shear at that location; second, over most of the basilar papilla, the relative shearing displacement is more uniform.

Finally, based on the mechanical model above, the anatomical constraints, and the measured motion of the basilar papilla as a function of frequency, we derived an electric-circuit analogy of the basilar papilla. In this model, schematized below, the input stimulus is pressure at the BM. This pressure acts on the area A of the BM to exert a force. In the translational domain (center part of circuit), the impedance is dominated by the compliance C_b of the basilar membrane. If the impedance of the rotational branch is relatively large (based on our best estimates for the parameter values, it is at least ten times larger at all frequencies), then the input impedance of the system is dominated by the translational compliance C_b. This result is consistent with basilar membrane impedance estimates from measurements of BM motion using the Mössbauer method (Peake and Ling, 1980), and with measurements of cochlear input impedance made at the tympanic membrane (Rosowski et al, 1985). In the rotational domain, the impedance is dominated by the rotational compliance C_r at low frequencies, and by the inertia J_p of the basilar papilla at high frequencies. At an intermediate frequency (typically near 5 kHz), these two impedances cancel each other to create a resonance; near the resonant frequency, the impedance is dominated by the damping element R_r. Note that all of the damping in this circuit occurs in the rotational domain.

In summary, by combining 3D measurements of basilar papilla motion with anatomically based mechanical modeling, we have shown that the basilar papilla of the alligator lizard exhibits two simultaneous modes of motion. Although both modes play a role in driving hair bundle deflection, only the translational mode has been observed at the level of the basilar membrane. Although the translation of the basilar membrane is largely independent of frequency, the rotation exhibits a second-order resonance which presumably increases the high-frequency slope of tuning curves of auditory nerve fibers innervating this cochlea.

Supported by NIH Grant R01-DC00238