Power Dissipation in the Cochlea Can Enhance Frequency Selectivity.

The cochlear cavity is filled with viscous fluids, and it is partitioned by a viscoelastic structure called the organ of Corti complex. Acoustic energy propagates toward the apex of the cochlea through vibrations of the organ of Corti complex. The dimensions of the vibrating structures range from a few hundred (e.g., the basilar membrane) to a few micrometers (e.g., the stereocilia bundle). Vibrations of microstructures in viscous fluid are subjected to energy dissipation. Because the viscous dissipation is considered to be detrimental to the function of hearing-sound amplification and frequency tuning-the cochlea uses cellular actuators to overcome the dissipation. Compared to extensive investigations on the cellular actuators, the dissipating mechanisms have not been given appropriate attention, and there is little consensus on damping models. For example, many theoretical studies use an inviscid fluid approximation and lump the viscous effect to viscous damping components. Others neglect viscous dissipation in the organ of Corti but consider fluid viscosity. We have developed a computational model of the cochlea that incorporates viscous fluid dynamics, organ of Corti microstructural mechanics, and electrophysiology of the outer hair cells. The model is validated by comparing with existing measurements, such as the viscoelastic response of the tectorial membrane, and the cochlear input impedance. Using the model, we investigated how dissipation components in the cochlea affect its function. We found that the majority of acoustic energy dissipation of the cochlea occurs within the organ of Corti complex, not in the scalar fluids. Our model suggests that an appropriate dissipation can enhance the tuning quality by reducing the spread of energy provided by the outer hair cells' somatic motility.

Two passive mechanical conditions modulate power generation by the outer hair cells.

In the mammalian cochlea, small vibrations of the sensory epithelium are amplified due to active electro-mechanical feedback of the outer hair cells. The level of amplification is greater in the base than in the apex of the cochlea. Theoretical studies have used longitudinally varying active feedback properties to reproduce the location-dependent amplification. The active feedback force has been considered to be proportional to the basilar membrane displacement or velocity. An underlying assumption was that organ of Corti mechanics are governed by rigid body kinematics. However, recent progress in vibration measurement techniques reveals that organ of Corti mechanics are too complicated to be fully represented with rigid body kinematics. In this study, two components of the active feedback are considered explicitly-organ of Corti mechanics, and outer hair cell electro-mechanics. Physiological properties for the outer hair cells were incorporated, such as the active force gain, mechano-transduction properties, and membrane RC time constant. Instead of a kinematical model, a fully deformable 3D finite element model was used. We show that the organ of Corti mechanics dictate the longitudinal trend of cochlear amplification. Specifically, our results suggest that two mechanical conditions are responsible for location-dependent cochlear amplification. First, the phase of the outer hair cell's somatic force with respect to its elongation rate varies along the cochlear length. Second, the local stiffness of the organ of Corti complex felt by individual outer hair cells varies along the cochlear length. We describe how these two mechanical conditions result in greater amplification toward the base of the cochlea.

Consequences of Location-Dependent Organ of Corti Micro-Mechanics.

The cochlea performs frequency analysis and amplification of sounds. The graded stiffness of the basilar membrane along the cochlear length underlies the frequency-location relationship of the mammalian cochlea. The somatic motility of outer hair cell is central for cochlear amplification. Despite two to three orders of magnitude change in the basilar membrane stiffness, the force capacity of the outer hair cell's somatic motility, is nearly invariant over the cochlear length. It is puzzling how actuators with a constant force capacity can operate under such a wide stiffness range. We hypothesize that the organ of Corti sets the mechanical conditions so that the outer hair cell's somatic motility effectively interacts with the media of traveling waves-the basilar membrane and the tectorial membrane. To test this hypothesis, a computational model of the gerbil cochlea was developed that incorporates organ of Corti structural mechanics, cochlear fluid dynamics, and hair cell electro-physiology. The model simulations showed that the micro-mechanical responses of the organ of Corti are different along the cochlear length. For example, the top surface of the organ of Corti vibrated more than the bottom surface at the basal (high frequency) location, but the amplitude ratio was reversed at the apical (low frequency) location. Unlike the basilar membrane stiffness varying by a factor of 1700 along the cochlear length, the stiffness of the organ of Corti complex felt by the outer hair cell remained between 1.5 and 0.4 times the outer hair cell stiffness. The Y-shaped structure in the organ of Corti formed by outer hair cell, Deiters cell and its phalange was the primary determinant of the elastic reactance imposed on the outer hair cells. The stiffness and geometry of the Deiters cell and its phalange affected cochlear amplification differently depending on the location.

Two-compartment passive frequency domain cochlea model allowing independent fluid coupling to the tectorial and basilar membranes.

The cochlea is a spiral-shaped, liquid-filled organ in the inner ear that converts sound with high frequency selectivity over a wide pressure range to neurological signals that are eventually interpreted by the brain. The cochlear partition, consisting of the organ of Corti supported below by the basilar membrane and attached above to the tectorial membrane, plays a major role in the frequency analysis. In early fluid-structure interaction models of the cochlea, the mechanics of the cochlear partition were approximated by a series of single-degree-of-freedom systems representing the distributed stiffness and mass of the basilar membrane. Recent experiments suggest that the mechanical properties of the tectorial membrane may also be important for the cochlea frequency response and that separate waves may propagate along the basilar and tectorial membranes. Therefore, a two-dimensional two-compartment finite difference model of the cochlea was developed to investigate the independent coupling of the basilar and tectorial membranes to the surrounding liquid. Responses are presented for models using two- or three-degree-of-freedom stiffness, damping, and mass parameters derived from a physiologically based finite element model of the cochlear partition. Effects of changes in membrane and organ of Corti stiffnesses on the individual membrane responses are investigated.

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.

Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results.

Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.

Shear strain from irrotational tissue displacements near bubbles.

Particle displacements can be much greater near bubbles than they would be in a homogeneous liquid or tissue when exposed to an acoustic wave. In a plane wave, shear and bulk strains are of the same order of magnitude. In contrast, for a bubble oscillating close to its resonance frequency, the shear strain in the medium near the bubble is roughly four orders of magnitude greater than the bulk strain. This can lead to shear strains of a few percent even with acoustic excitation pressures far below the pressure thresholds required to cause inertial cavitation. High shear strains near oscillating bubbles could potentially be the cause of bioeffects. After acoustic exposures at audio frequencies, hemorrhages in tissues as diverse as lung, liver, and kidney have been observed at shear strains on the order of 1%.

Natural frequency of a gas bubble in a tube: experimental and simulation results.

Use of ultrasonically excited microbubbles within blood vessels has been proposed for a variety of clinical applications. In this paper, an axisymmetric coupled boundary element and finite element code and experiments have been used to investigate the effects of a surrounding tube on a bubble's response to acoustic excitation. A balloon model allowed measurement of spherical gas bubble response. Resonance frequencies match one-dimensional cylindrical model predictions for a bubble well within a rigid tube but deviate for a bubble near the tube end. Simulations also predict bubble translation along the tube axis and aspherical oscillations at higher amplitudes.

Ultrasonic excitation of a bubble inside a deformable tube: implications for ultrasonically induced hemorrhage.

Various independent investigations indicate that the presence of microbubbles within blood vessels may increase the likelihood of ultrasound-induced hemorrhage. To explore potential damage mechanisms, an axisymmetric coupled finite element and boundary element code was developed and employed to simulate the response of an acoustically excited bubble centered within a deformable tube. As expected, the tube mitigates the expansion of the bubble. The maximum tube dilation and maximum hoop stress were found to occur well before the bubble reached its maximum radius. Therefore, it is not likely that the expanding low pressure bubble pushes the tube wall outward. Instead, simulation results indicate that the tensile portion of the acoustic excitation plays a major role in tube dilation and thus tube rupture. The effects of tube dimensions (tube wall thickness 1-5 microm), material properties (Young's modulus 1-10 MPa), ultrasound frequency (1-10 MHz), and pressure amplitude (0.2-1.0 MPa) on bubble response and tube dilation were investigated. As the tube thickness, tube radius, and acoustic frequency decreased, the maximum hoop stress increased, indicating a higher potential for tube rupture and hemorrhage.

A unified view of imaging the elastic properties of tissue.

A number of different approaches have been developed to estimate and image the elastic properties of tissue. The biomechanical properties of tissues are vitally linked to function and pathology, but cannot be directly assessed by conventional ultrasound, MRI, CT, or nuclear imaging. Research developments have introduced new approaches, using either MRI or ultrasound to image the tissue response to some stimulus. A wide range of stimuli has been evaluated, including heat, water jets, vibration shear waves, compression, and quasistatic compression, using single or multiple steps or low-frequency (<10 Hz) cyclic excitation. These may seem to be greatly dissimilar, and appear to produce distinctly different types of information and images. However, our purpose in this tutorial is to review the major classes of excitation stimuli, and then to demonstrate that they produce responses that fall within a common spectrum of elastic behavior. Within this spectrum, the major classes of excitation include step compression, cyclic quasistatic compression, harmonic shear wave excitation, and transient shear wave excitation. The information they reveal about the unknown elastic distribution within an imaging region of interest are shown to be fundamentally related because the tissue responses are governed by the same equation. Examples use simple geometry to emphasize the common nature of the approaches.

Ultrasonic excitation of a bubble near a rigid or deformable sphere: implications for ultrasonically induced hemolysis.

A number of independent studies have reported increased ultrasound bioeffects, such as hemolysis and hemorrhage, when ultrasound contrast agents are present. To better understand the role of cavitation in these bioeffects, one- and two-dimensional models have been developed to investigate the interactions between ultrasonically excited bubbles and model "cells." First, a simple one-dimensional model based on the Rayleigh-Plesset equation was developed to estimate upper bounds for strain, strain rate, and areal expansion of a simulated red blood cell. Then, two-dimensional boundary element models were developed (with DynaFlow Inc.) to obtain simulations of asymmetric bubble dynamics in the presence of rigid and deformable spheres. The deformable spherical "cell" was modeled using Tait's equation of state for water, with a membrane approximated by surface tension that increases linearly with areal expansion. The presence of a rigid or deformable sphere had little effect on the bubble expansion, but caused an asymmetric collapse and jetting for the conditions considered. Predicted membrane areal expansions were found to be below critical values for hemolysis reported in the literature for the cases considered near the inertial cavitation threshold.