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

Coupling Active Hair Bundle Mechanics, Fast Adaptation, and Somatic Motility in a Cochlear Model

One of the central questions in the biophysics of the mammalian cochlea is determining the contributions of the two active processes, prestin-based somatic motility and hair bundle (HB) motility, to cochlear amplification. HB force generation is linked to fast adaptation of the transduction current via a calcium-dependent process and somatic force generation is driven by the depolarization caused by the transduction current. In this article, we construct a global mechanical-electrical-acoustical mathematical model of the cochlea based on a three-dimensional fluid representation. The global cochlear model is coupled to linearizations of nonlinear somatic motility and HB activity as well as to the micromechanics of the passive structural and electrical elements of the cochlea. We find that the active HB force alone is not sufficient to power high frequency cochlear amplification. However, somatic motility can overcome resistor-capacitor filtering by the basolateral membrane and deliver sufficient mechanical energy for amplification at basal locations. The results suggest a new theory for high frequency active cochlear mechanics, in which fast adaptation controls the transduction channel sensitivity and thereby the magnitude of the energy delivered by somatic motility

Response to a Pure Tone in a Nonlinear Mechanical-Electrical-Acoustical Model of the Cochlea

AbstractIn this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials

Improvement of stiffness and energy absorption by harnessing hierarchical interlocking in brittle polymer blocks

The objective of the present work is to investigate the possibility of improving both stiffness and energy absorption in interlocking, architectured, brittle polymer blocks through hierarchical design. The interlocking mechanism allows load transfer between two different material blocks by means of contact at the mating surfaces. The contacting surfaces further act as weak interfaces that allow the polymer blocks to fail gradually under different loading conditions. Such controlled failure enhances the energy absorption of the polymer blocks but with a penalty in stiffness. Incorporating hierarchy in the form of another degree of interlocking at the weak interfaces, improves stress transfer between contacting material blocks, thereby, improvement in terms of stiffness and energy absorption can be achieved. In the present work, the effects of hierarchy on the mechanical responses of a single interlocking geometry have been investigated systematically using finite element (FE) analysis and results are validated with experiments. From FE predictions and experiments, presence of two competing failure mechanisms have been observed in the interlock: the pullout of the interlock and brittle fracture of the polymer blocks. It is observed that the hierarchical interface improves the stiffness by restricting sliding between the contacting surfaces. However, such restriction can lead to premature fracture of the polymer blocks that eventually reduces energy absorption of the interlocking mechanism during pullout deformation. It is concluded that the combination of stiffness and energy absorption is optimal when fracture of the polymer blocks is delayed by allowing sufficient sliding at the interfaces