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.

Multilayer dielectric (MLD) gratings used in ultrahigh-intensity laser systems often exhibit a laser-induced damage performance below that of their constituent materials. Reduced performance may arise from fabrication- and/or design-related issues. Finite element models were developed to simulate stress waves in MLD grating structures generated by laser-induced damage events. These models specifically investigate the influence of geometric and material parameters on how stress waves can lead to degradation of material structural integrity that can have adverse effects on its optical performance under subsequent laser irradiation: closer impedance matching of the layer materials reduces maximum interface stresses by ~20% to 30%; increasing sole thickness from 50 nm to 500 nm reduces maximum interface stresses by ~50%.

Edwin Carstensen made significant contributions to the understanding of the interactions between ultrasound and biological tissues. He was especially interested in how acoustically-excited bubbles interact with biological systems. In his experiments, sources of these in vivo bubbles included gas in respiratory tubules of fruit fly larvae, ultrasound contrast agents, and gas in murine lung and intestine. While much of Ed’s work was experimental, he had keen insight and a unique perspective for understanding the mechanisms of the bioeffects. He realized that the shear strains in the vicinity of an oscillating bubble could be much greater than they would be if the bubble were not present. Not only was Ed a remarkable scientist, he was also a great mentor. When I first arrived at the University of Rochester, Ed introduced me to the field of biomedical ultrasound and the many outstanding researchers working in the area. It has been a great pleasure and rewarding experience to collaborate with Edwin Carstensen and his student, then close colleague, Diane Dalecki over that last 30 years. This paper will present some of our collaborative work on investigating the response of acoustically-excited bubbles and the stresses and strains induced in the surrounding media.

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.

In the cochlea, acoustic energy is transmitted toward the apex through the vibrations of a viscoelastic partition known as the organ of Corti complex. The dimensions of the vibrating structures range from a few hundred micrometers to a few micrometers. Vibrations of micro-structures 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 is believed to use cellular actuators to overcome the dissipation. We have developed a computational model of the cochlea that incorporates viscous fluid dynamics, organ of Corti micro-structural mechanics, and electro-physiology of the outer hair cells. The model is validated by comparing with experimental results in the literature, 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. Our results suggest that most energy dissipation occurs within the organ of Corti complex, not in the scalar fluids. Our results suggest that appropriate dissipation enhances the tuning quality by confining the spread of energy from the amplification site.

In the mammalian cochlea, the mechano-transduction of the inner hair cell (IHC) stereocilia occurs in a micrometer-thick fluid space between the tectorial membrane and the reticular lamina. Using a computational model of the cochlea, we analyzed how the sub-tectorial space (STS) fluid mechanics affect cochlear power dissipation and IHC mechano-transduction. Based on the simulations of a single IHC stereociliary bundle in the STS (Prodanovic et al., 2015), the fluid-induced forces of the STS were reduced to simple equations. The reduced STS response was combined with a whole cochlear model consisting of: organ of Corti structural mechanics, cochlear fluid dynamics, and outer hair cell electro-physiology. Energy dissipation in the cochlea was quantified for three categories: macro-fluidic dissipation along the cochlear scalae, micro-fluidic dissipation in the STS, and other dissipation in the organ of Corti. The phase of IHC mechano-transduction current with respect to the basilar membrane displacement was dependent on stimulating frequency and location.

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.

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.

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.

The mechano-transduction of the mammalian cochlea occurs in the micro-fluid domain between the tectorial membrane and the reticular lamina called the subtectorial space. The subtectorial fluid bathes the bundled stereocilia of the inner hair cells (IHCs). These cells are responsible for the onset of neural impulses in the auditory nerve fibers. Despite the generally accepted postulation that the IHC stereocilia are deflected by shear flow between the two layers, there have been suggestions that other flow modes exist besides the shear flow. We developed a computational model of fluid dynamics in the subtectorial space. The model simulates IHC mechano-transduction excited by different flow patterns. In order to compare different modes of fluid dynamical stimulation, the power efficiency of IHC mechano-transduction was introduced (dissipated power normalized by IHC mechano-transduction current). Besides different flow patterns, the effect of mechanical parameters (such as the gap size between the stereociliary tip and the tectorial membrane, stereociliar bundle stiffness) were investigated. The results demonstrate that the power efficiency for the IHC mechano-transduction depends on the flow pattern in the subtectorial space.

The cochlea is a spiral-shaped, fluid-filled organ in the inner ear that converts sound with high resolution over a large frequency range to neurological signals that can then be interpreted by the brain. The organ of Corti, supported below by the basilar membrane and attached above to the tectorial membrane, plays a major role in the amplification of small signals. In early fluid-structure interaction models of the cochlea, the mechanical properties of the organ of Corti were neglected and only the basilar membrane was considered, approximated by a series of springs. Recent experiments suggest that the mechanical properties and property gradients of the tectorial membrane may also be important for frequency response of the organ of Corti and that separate waves may propagate along the basilar and tectorial membranes. Therefore, a two-dimensional two-chamber finite difference model of the cochlea was developed to investigate the independent responses of the basilar and tectorial membranes. Responses are compared for models using one-, two-, or three-degree-of-freedom approximations for the organ of Corti, with parameters derived from a physiologically based finite element model. The effects of independent coupling of the fluid to the tectorial and basilar membranes and longitudinal coupling along the membranes are investigated.

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%.

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.

The dynamic response of bubbles in a liquid that are partially constrained by a surrounding tube or channel is important in a variety of fields, including diagnostic and therapeutic biomedical ultrasound and for microfluidic devices. In this study, numerical simulations, lumped parameter models, and experiments are used to investigate the effects of a surrounding tube on a bubble’s response to acoustic excitation. In particular, a coupled boundary element and finite element model and COMSOL MULTIPHYSICS models have been developed and used to investigate the nonlinear interactions of this three-phase system. Simulation results were compared to experimental measurements obtained using a scaled balloon model. The effects of tube parameters and bubble interactions on a bubble’s natural frequency important for proposed clinical applications of ultrasound are investigated. Resonance frequencies agree well with one-dimensional lumped parameter 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 the aspherical oscillations and induced tube stresses at higher amplitudes. [Work supported by NIH and NSF CMMI.]

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.

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.

An understanding of biotissue–bubble interactions and the stresses induced in the tissue is needed to identify potential mechanisms of tissue damage, such as vessel rupture, by acoustically excited bubbles. Interactions between acoustically excited bubbles and nearby rigid structures have been studied effectively using the boundary element method. However, if the nearby structure is a biotissue, structure deformations will affect the bubble response. In this paper a coupled finite element and boundary element code, developed to investigate the interactions between an acoustically excited bubble and a deformable structure, is presented. In particular, this model was developed to investigate the response of bubbles within deformable tubes. This code is validated by comparison to other simulation and experimental results and employed to obtain the response of an acoustically excited bubble centered within a tube. General characteristics of bubble–tube interactions and stresses induced in the tube wall are described by considering typical simulation results.

UltraForm. Finishing (UFF) is a new deterministic subaperture computer numerically controlled (CNC) polisher. Because UFF uses compliant tools with large contact patches, the depth of removal is prescribed by adjusting the tool crossfeed velocity. The equations for the depth of removal as the tool traverses an axisymmetric part are derived. The form correction problem consists in solving these equations by adjusting the tool crossfeed velocity to achieve a desired removal profile. The solution must satisfy constraints on the tool velocity and acceleration. Solutions for flats, spheres and aspheres are achieved by treating the problem as a constrained optimization after writing the depth of removal equations in matrix form. The solutions were validated experimentally. The removal function is evaluated by making a removal spot for one set of process parameters. Its variations, as a function of the process parameters, are predicted by using Hertz contact theory and the Preston equation. To prevent tool-part collisions and to analyze part and spot measurements, algorithms were developed for the tool path and evaluation of metrology inputs.

UltraForm Finishing (UFF) is a new deterministic subaperture computer numerically controlled (CNC) polisher. Because UFF uses a compliant tool, the desired depth of removal is achieved by adjusting the tool crossfeed velocity. Algorithms for determining an optimum crossfeed velocity profile that satisfies tool velocity and acceleration constraints have been derived for flats, spheres, and mild aspheres. The solutions were validated experimentally. The removal function that characterizes the interaction between a particular tool and part material is evaluated by making a removal spot for one set of process parameters. Its variations, as a function of the process parameters, are predicted by using Hertz contact theory and the Preston equation. Additional algorithms were developed for the evaluation of part and spot metrology inputs and for tool path generation to prevent tool-part collisions.

Various independent investigations indicate that the presence of microbubbles within blood vessels may increase the likelihood of ultrasound-induced hemorrhage and endothelial cell damage. To explore potential damage mechanisms, an axisymmetric coupled finite element and boundary element code was developed to simulate the response of an acoustically excited bubble centered within a compliant tube. Results will be presented to show the influence of acoustic excitation parameters, tube dimensions, and material properties on bubble response, tube dilation, and stresses induced within the tube wall. Tube dilation occurs during the tensile portion of the acoustic excitation, when the external pressure is lower than the internal pressure. The hoop stress is the maximum induced principal stress. Its peak value occurs as the bubble is expanding, well before the bubble reaches its maximum radius. As the tube thickness, tube radius, and acoustic frequency decreases, the maximum hoop stress increases, indicating a higher potential for tube rupture and hemorrhage. [Work supported by NIH research grant R01HL69824.]