Modeling acoustic fluid-structure interaction in the cochlea in the time-domain

The mammalian inner ear is a sensory system with high sensitivity and sharp tuning in response to low intensity sounds. These important characteristics are due to the active feedback by outer hair cells (OHCs) that amplify the vibrations of the fluid-loaded cochlear partition. In order to simulate the dynamics of the cochlea in response to sounds, many cochlear models are formulated in the frequency domain or using a one-dimensional formulation to reduce the computational cost. However, some aspects of nonlinear cochlear mechanics can only investigated using a three-dimensional time-domain model. We present here the development of a novel time-domain model of the mammalian cochlea formulated using a state-space approach. A three-dimensional model of the intracochlear fluids is coupled to a structural model of the cochlear partition using a finite element framework. Moreover, electrical degrees of freedom represent the electrical degrees of freedom in the cochlear ducts and in the OHCs. The active feedback by OHCs is modeled by linearized piezoelectric relationships, whereas the nonlinearity of the OHC mechanoelectrical transduction channels introduces nonlinearity in the model. This computational framework is used to simulate the nonlinear response of the mammalian ear to sounds. After calibration using measurements using in vivo measurements of the response of the cochlea to sounds, the model can be used to test hypotheses regarding hearing mechanics to help us to improve our understanding of the biophysics and biomechanics of the mammalian ear

Investigation of viscoelastic structures with extreme damping and high stiffness using negative stiffness layered composites

Materials that exhibit high damping are often used in structures to reduce noise and vibrations; however, most materials display an inverse relationship between stiffness and damping. Therefore, materials that display both high damping and stiffness are of great interest in many structural applications. Earlier analysis using linearized viscoelastic theory has demonstrated that high damping and high stiffness can be simultaneously achieved using viscoelastic layered composites consisting of a lossy polymer and a stiff constituent. In this research we use finite element simulations to analyze the finite deformation response of these viscoelastic layered composites in cyclic compression. We demonstrate using nonlinear finite element analysis that geometric nonlinearities affect the response of these composites at finite but moderate macroscopic strain amplitudes. In addition to the softening, the composite exhibits negative stiffness above a certain amplitude threshold, i.e., the value of the stress decreases when the strain is increased. By combining the layered composites with another constituent material, these geometric nonlinearities and the negative stiffness are exploited to obtain viscoelastic composites with higher damping than the constituents. Both analytical formulae based on composite theory and finite element simulations are used to guide the optimal choice of the geometrical parameters of the composite topology and of the material constituents to achieve extreme damping and high stiffness

High Frequency Amplification, Filtering and Nonlinearity in a Computational Model of Mammalian Cochlear Mechanics.

In this thesis the active and nonlinear dynamics of the mammalian cochlea in response to acoustic stimulation are simulated using a computational model of the physics and physiology of the cochlea. The model is based on a three-dimensional representation of the cochlear partition and intracochlear fluid and includes the electrical domain and linear feedback from outer hair cell (OHC) somatic motility. A linear version of the model of the cochlea is first used to assess the role of structural longitudinal coupling in cochlear mechanics. Longitudinal coupling in the TM and BM mechanics is found to improve the predictions compared to a locally reacting model as it broadens the frequency response of the BM to acoustic stimulation and reduces the duration of the impulse response. The linear model of the cochlea is then used to investigate the identity of the cochlear amplifier - prestin-based somatic motility or hair bundle (HB) motility. A nonlinear six-state channel model of the active HB is linearized for small harmonic perturbation around the operating point and implemented in the macroscopic model of the cochlea. A calcium binding event models fast adaptation of the transduction current and active HB force generation. The macroscopic simulations show that somatic motility underlies cochlear amplification and that the active HB force is insufficient to modulate the response of the BM to low intensity acoustic stimulation. However, the reduction of the sensitivity of the transduction channel to HB deflection due to the fast adaptation mechanism controls the energy delivered by somatic motility and thereby the sensitivity of the BM to acoustic stimulation, stabilizing the cochlea. The nonlinear dynamics of the cochlea are simulated by introducing a physiologically relevant nonlinearity in the mechanotransduction channel. An efficient alternating frequency/time method is used to compute the stationary response of the cochlea. The model predicts a realistic compressive response and generation of harmonic distortion in response to a single tone. The simulations of two tone interaction on the BM - two tone suppression and distortion products - are also in good agreement with published experimental data.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78978/1/jmeaud_1.pd

Analysis and optimal design of layered composites with high stiffness and high damping

AbstractIn this paper we investigate the design of composite materials with simultaneously high stiffness and high damping. We consider layered composite materials with parallel plane layers made of a stiff constituent and a lossy polymer. We analyze the response of these composites to a dynamic load with an arbitrary direction. Using the viscoelastic correspondence principle and linear frequency domain viscoelastic models, we derive an expression for the effective complex modulus of layered composites of infinite size at infinitesimal strains. The dependence of the effective dynamic modulus and loss factor on the geometrical parameters and on the tensile and bulk loss factors of the lossy constituent is analyzed. Moreover we determine the magnitude of the strains in the lossy constituent and demonstrate that the combination of high stiffness and high damping of these composites is due to the high normal and/or shear strains in the lossy material. We use nonlinear constrained optimization to design layered composites with simultaneously high stiffness and high damping while constraining the strains in the polymer. To determine the range of validity of the linear viscoelastic model, simulations using finite deformations models are compared to the theoretical results. Finally, we compute the effective properties of composites of finite size using finite element methods and determine the minimum size required to approach the formulae derived for composites of infinite size

A tectorin-based matrix and planar-cell-polarity genes are required for normal collagen-fibril orientation in the developing tectorial membrane

The tectorial membrane is an extracellular structure of the cochlea. It develops on the surface of an epithelium and contains collagen fibrils embedded in a tectorin-based matrix. The collagen fibrils are oriented radially with an apically-directed slant - a feature considered critical for hearing. To determine how this pattern is generated, collagen-fibril formation was examined in mice lacking a tectorin-based matrix, epithelial cilia, or the planar-cell-polarity genes Vangl2 and Ptk7. In wild-type mice, collagen-fibril bundles appear within a tectorin-based matrix at E15.5 and, as fibril-number rapidly increases, become co-aligned and correctly oriented. Epithelial-width measurements and data from Kif3acKO mice suggest, respectively, radial stretch and cilia play little, if any, role in determining normal collagen-fibril orientation, but evidence from tectorin-knockout mice indicates confinement is important. PRICKLE2 distribution reveals the planar-cell-polarity axis in the underlying epithelium is organised along the length of the cochlea and, in mice in which this polarity is disrupted, the apically-directed collagen offset is no longer observed. These results highlight the importance of the tectorin-based matrix and epithelial signals for precise collagen organisation in the tectorial membran

Drug diffusion along an intact mammalian cochlea

Intratympanic drug administration depends on the ability of drugs to pass through the round window membrane (RW) at the base of the cochlea and diffuse from this location to the apex. While the RW permeability for many different drugs can be promoted, passive diffusion along the narrowing spiral of the cochlea is limited. Earlier measurements of the distribution of marker ions, corticosteroids and antibiotics demonstrated that the concentration of substances applied to the RW was two to three orders of magnitude higher in the base compared to the apex. The measurements, however, involved perforating the cochlear bony wall and, in some cases, sampling perilymph. These manipulations can change the flow rate of perilymph and lead to intake of perilymph through the cochlear aqueduct, thereby disguising concentration gradients of the delivered substances. In this study, the suppressive effect of salicylate on cochlear amplification via block of the outer hair cell (OHC) somatic motility was utilized to assess salicylate diffusion along an intact guinea pig cochlea in vivo. Salicylate solution was applied to the RW and threshold elevation of auditory nerve responses was measured at different times and frequencies after application. Resultant concentrations of salicylate along the cochlea were calculated by fitting the experimental data using a mathematical model of the diffusion and clearing of salicylate in a tube of variable diameter combined with a model describing salicylate action on cochlear amplification. Concentrations reach a steady-state at different times for different cochlear locations and it takes longer to reach the steady-state at more apical locations. Even at the steady state, the predicted concentration at the apex negligible. Model predictions for the geometry of the longer human cochlea show even higher differences in the steady-state concentrations of the drugs between cochlear base and apex. Our findings confirm conclusions that achieving therapeutic drug concentrations throughout the entire cochlear duct is hardly possible when the drugs are applied to the RW and are distributed via passive diffusion. Assisted methods of drug delivery are needed to reach a more uniform distribution of drugs along the cochlea

Analyse multi-échelle des connexions par collage : application aux éléments structuraux multimatériaux fléchis

This PhD thesis investigates the connection of steel-flexural members by bonding and focuseson static and instantaneous behavior. First, experimental and numerical analyses are performed. A push out test is used : two concrete blocks are connected to steel members. The influence of the concrete blocks and bonding joint geometry is examined. Cohesive shear failure appears in concrete near the interface. Failure can occur when the average shear strain is twice the tension limit of concrete, which can be explained by favorable slipping between the concrete block and the support. In this case, the bonding joint is not only solicited in shear but also in compression. Results depend on the length of bonding joint and concrete blocks geometry. So, push out test cannot be now used to characterize the bonding connection between steel and concrete in order to design structures. The second is about the analysis of the behavior of steel concrete composite beams. A precast beam with compressive concrete was tested. Results show that a bonding connection can be an alternativesolution regardless of the slab manufacturing. We develop two numerical models. The first one is based on multi-layer beam modeling and the second one is a nonlinear 3D finite element model. The stress distribution close to the interface and near failure is more accurate with the finite element model than with the generalized model. Bonding joint geometry and plastification of steel girder have an influence on the failure region in the concrete.Ce travail de recherche est axé sur la compréhension du comportement en flexion, statique et instantané, des structures multimatériaux acier-béton collées du génie civil. La première étape consiste à mener une analyse expérimentale et numérique par éléments finis non linéaire sur la caractérisation de la connexion. L’essai Push-Out a été retenu : deux dallettes de béton C25/30 sont connectées à un profilé métallique. Nous faisons varier la géométrie des dallettes et du joint de colle. La ruine est cohésive dans le béton proche de l’interface par cisaillement. Un effet favorable du frottement entre dallette et presse peut se développer et induire le développement de contraintes de compression et augmenter la contrainte de cisaillement moyenne à l’interface. Les dimensions des éprouvettes et du joint de colle influent sur la charge de ruine. Ainsi, l’essai Push-Out est, dans l’état actuel de connaissances, difficile à utiliser pour la caractérisation de la connexion collée acier-béton en vue du dimensionnement de structures. La seconde partie est consacrée à l’analyse du comportement de poutres mixtes acier béton collées. Un essai sur poutre constituée de prédalles et d’une dalle de compression confirme que le collage est une alternative aux connexions traditionnelles. Nous développons aussi un modèle de calcul en variables généralisées et en variables locales en 3D non linéaire. La modélisation par éléments finis apporte plus de précisions, notamment sur l’état de contraintes à proximité de l’interface et à l’approche de la ruine. Les dimensions du joint de colle et la plastification du profilé influent sur la zone de rupture dans le béton

Multi-scale analysis of bonding connexion : applied to steel concrete structures tested by flexure

Ce travail de recherche est axé sur la compréhension du comportement en flexion, statique et instantané, des structures multimatériaux acier-béton collées du génie civil. La première étape consiste à mener une analyse expérimentale et numérique par éléments finis non linéaire sur la caractérisation de la connexion. L’essai Push-Out a été retenu : deux dallettes de béton C25/30 sont connectées à un profilé métallique. Nous faisons varier la géométrie des dallettes et du joint de colle. La ruine est cohésive dans le béton proche de l’interface par cisaillement. Un effet favorable du frottement entre dallette et presse peut se développer et induire le développement de contraintes de compression et augmenter la contrainte de cisaillement moyenne à l’interface. Les dimensions des éprouvettes et du joint de colle influent sur la charge de ruine. Ainsi, l’essai Push-Out est, dans l’état actuel de connaissances, difficile à utiliser pour la caractérisation de la connexion collée acier-béton en vue du dimensionnement de structures. La seconde partie est consacrée à l’analyse du comportement de poutres mixtes acier béton collées. Un essai sur poutre constituée de prédalles et d’une dalle de compression confirme que le collage est une alternative aux connexions traditionnelles. Nous développons aussi un modèle de calcul en variables généralisées et en variables locales en 3D non linéaire. La modélisation par éléments finis apporte plus de précisions, notamment sur l’état de contraintes à proximité de l’interface et à l’approche de la ruine. Les dimensions du joint de colle et la plastification du profilé influent sur la zone de rupture dans le béton.This PhD thesis investigates the connection of steel-flexural members by bonding and focuseson static and instantaneous behavior. First, experimental and numerical analyses are performed. A push out test is used : two concrete blocks are connected to steel members. The influence of the concrete blocks and bonding joint geometry is examined. Cohesive shear failure appears in concrete near the interface. Failure can occur when the average shear strain is twice the tension limit of concrete, which can be explained by favorable slipping between the concrete block and the support. In this case, the bonding joint is not only solicited in shear but also in compression. Results depend on the length of bonding joint and concrete blocks geometry. So, push out test cannot be now used to characterize the bonding connection between steel and concrete in order to design structures. The second is about the analysis of the behavior of steel concrete composite beams. A precast beam with compressive concrete was tested. Results show that a bonding connection can be an alternativesolution regardless of the slab manufacturing. We develop two numerical models. The first one is based on multi-layer beam modeling and the second one is a nonlinear 3D finite element model. The stress distribution close to the interface and near failure is more accurate with the finite element model than with the generalized model. Bonding joint geometry and plastification of steel girder have an influence on the failure region in the concrete