The effect of hair bundle shape on hair bundle hydrodynamics of inner ear hair cells at low and high frequencies

Power dissipation in the subtectorial space of the mammalian cochlea is modulated by inner hair cell stereocilia

The stereocilia bundle is the mechano-transduction apparatus of the inner ear. In the mammalian cochlea, the stereocilia bundles are situated in the subtectorial space (STS)--a micrometer-thick space between two flat surfaces vibrating relative to each other. Because microstructures vibrating in fluid are subject to high-viscous friction, previous studies considered the STS as the primary place of energy dissipation in the cochlea. Although there have been extensive studies on how metabolic energy is used to compensate the dissipation, much less attention has been paid to the mechanism of energy dissipation. Using a computational model, we investigated the power dissipation in the STS. The model simulates fluid flow around the inner hair cell (IHC) stereocilia bundle. The power dissipation in the STS because of the presence IHC stereocilia increased as the stimulating frequency decreased. Along the axis of the stimulating frequency, there were two asymptotic values of power dissipation. At high frequencies, the power dissipation was determined by the shear friction between the two flat surfaces of the STS. At low frequencies, the power dissipation was dominated by the viscous friction around the IHC stereocilia bundle--the IHC stereocilia increased the STS power dissipation by 50- to 100-fold. There exists a characteristic frequency for STS power dissipation, CFSTS, defined as the frequency where power dissipation drops to one-half of the low frequency value. The IHC stereocilia stiffness and the gap size between the IHC stereocilia and the tectorial membrane determine the characteristic frequency. In addition to the generally assumed shear flow, nonshear STS flow patterns were simulated. Different flow patterns have little effect on the CFSTS. When the mechano-transduction of the IHC was tuned near the vibrating frequency, the active motility of the IHC stereocilia bundle reduced the power dissipation in the STS.

Auditory and vestibular hair cell stereocilia: relationship between functionality and inner ear disease

The stereocilia of the inner ear are unique cellular structures which correlate anatomically with distinct cochlear functions, including mechanoelectrical transduction, cochlear amplification, adaptation, frequency selectivity and tuning. Their function is impaired by inner ear stressors, by various types of hereditary deafness, syndromic hearing loss and inner ear disease (e.g. Ménière's disease). The anatomical and physiological characteristics of stereocilia are discussed in relation to inner ear malfunctions.

The frequency response of rat vibrissae to sound

The motion of isolated rat vibrissae due to low frequency sound has been modeled and measured with good agreement (within a factor of 2) between the data and the model's predictions. As had been done in previous studies on the response of rat vibrissae to tactile stimulation [Hartmann, M. J., Johnson, N. J., Towal, R. B., and Assad, C., J. Neurosci 23, 6510-6519 (2003) and Neimark, M. A., Andermann, A. L., Hopfield, J. J., and Moore, C. I., J. Neurosci 23, 6449-6509 (2003)] the vibrissae were modeled as thin conical beams. The force of the vibrating air on a vibrissa was modeled using the exact solution for a vibrating infinite cylinder in linear fluid. A finite element method was used to model the motion of a single vibrissa fixed at its base, using the aforementioned fluid force. Values for Young's modulus and vibrissa mass density were taken from a previous study [Neimark et al. (above)]. The model had no freely fitted parameters. Motion of isolated vibrissae was measured using a video camera with microscope. The sound stimulation was created using a stereo speaker connected to a signal generator. The tuning was found to be sharp, with quality factors that varied between 3 and 7, much sharper than the motion of cricket cercal hairs or in vitro inner ear hair bundles.

Two modes of motion of the alligator lizard cochlea: measurements and model predictions

Measurements of motion of an in vitro preparation of the alligator lizard basilar papilla in response to sound demonstrate elliptical trajectories. These trajectories are consistent with the presence of both a translational and rotational mode of motion. The translational mode is independent of frequency, and the rotational mode has a displacement peak near 5 kHz. These measurements can be explained by a simple mechanical system in which the basilar papilla is supported asymmetrically on the basilar membrane. In a quantitative model, the translational admittance is compliant while the rotational admittance is second order. Best-fit model parameters are consistent with estimates based on anatomy and predict that fluid flow across hair bundles is a primary source of viscous damping. The model predicts that the rotational mode contributes to the high-frequency slopes of auditory nerve fiber tuning curves, providing a physical explanation for a low-pass filter required in models of this cochlea. The combination of modes makes the sensitivity of hair bundles more uniform with radial position than that which would result from pure rotation. A mechanical analogy with the organ of Corti suggests that these two modes of motion may also be present in the mammalian cochlea.

The effect of hair bundle shape on hair bundle hydrodynamics of non-mammalian inner ear hair cells for the full frequency range

The effect of the size and the shape of the hair bundle of a hair cell in the inner ear of non-mammals on its motion for the full range of frequencies is determined thereby extending the results of a previous analysis of hair bundle motion for high and low frequencies [Hear Res. 141 (2000) 39-50]. A hemispheroid is used to represent the hair bundle because it can represent a full range of shapes, from thin, pencil-like shapes to wide, flat, disk-like shapes. Boundary element methods are used to approximate the solution for the hydrodynamics. For physiologically relevant parameters, an excellent match is obtained between the model's predictions and measurements of hair bundle motion in the free-standing region of the basilar papilla of the alligator lizard [Aranyosi, Measuring sound-induced motions of the alligator lizard cochlea. Massachusetts Institute of Technology, PhD Thesis, 2002]. Neither in the model's predictions nor in experimental measurements is sharp tuning observed. The model predicted the low frequency region of neural tuning curves for the alligator lizard and bobtail lizard, but could not predict the sharp tuning or the high frequency region. An element that represents an active mechanism is added to the hair bundle model to predict neural tuning curves, which are sharply tuned, and an excellent match is obtained for all the characteristics of neural tuning curves for the alligator lizard, and for the low and high frequency regions for the bobtail lizard. The model does not predict well the sharp tuning of the shorter hair bundles of the bobtail lizard, possibly because it does not represent tectorial sallets.

Sound-induced motions of individual cochlear hair bundles

We present motions of individual freestanding hair bundles in an isolated cochlea in response to tonal sound stimulation. Motions were measured from images taken by strobing a light source at the tone frequency. The tips and bases of hair bundles moved a comparable amount, but with a phase difference that increased by 180 degrees with frequency, indicating that distributed fluid properties drove hair bundle motion. Hair bundle rotation increased with frequency to a constant value, and underwent >90 degrees of phase change. The frequency at which the phase of rotation relative to deflection of the bundle base was 60 degrees was comparable to the expected best frequency of each hair cell, and varied inversely with the square of bundle height. The sharpness of tuning of individual hair bundles was comparable to that of hair cell receptor potentials at high sound levels. These results indicate that frequency selectivity at high sound levels in this cochlea is purely mechanical, determined by the interaction of hair bundles with the surrounding fluid. The sharper tuning of receptor potentials at lower sound levels is consistent with the presence of a negative damping, but not a negative stiffness, as an active amplifier in hair bundles.

Inner hair cell response patterns: implications for low-frequency hearing

Inner hair cell (IHC) responses to tone-burst stimuli were measured from three locations in the apical half of the guinea pig cochlea. In addition to the measurement of ac receptor potentials, average intracellular voltages, reflecting both ac and dc components of the receptor potential, were computed and compared to determine how bandwidth changes with level. Companion phase measures were also obtained and evaluated. Data collected from turn 2, where best frequency (BF) is approximately 4000 Hz, indicate that frequency response functions are asymmetrical with steeper slopes above the best frequency of the cell. However, in turn 4, where BF is around 250 Hz, the opposite behavior is observed and the steepest slopes are measured below BF. The data imply that cochlear filters are generally asymmetrical with steeper slopes above BF. High-pass filtering by the middle ear serves to reduce this asymmetry in turn 3 and to reverse it in turn 4. Apical response patterns are used to assess the degree to which the middle ear transfer function, the IHC's velocity dependence and the shunting effect of the helicotrema influence low-frequency hearing in guinea pigs. Implications for low-frequency hearing in man are also discussed.