A linear, physiologically based, three-dimensional finite element model of the cochlea is developed. The model integrates the electrical, acoustic, and mechanical elements of the cochlea. In particular, the model includes interactions between structures in the organ of Corti (OoC), piezoelectric relations for outer hair cell (OHC) motility, hair bundle (HB) conductance that changes with HB deflection, current flow in the cross section and along the different scalae, and the feed-forward effect. The parameters in the model are based on guinea-pig data as far as possible. The model is vetted using a variety of experimental data on basilar membrane motion and data on voltages and currents in the OoC. Model predictions compare well, qualitatively and quantitatively, with experimental data on basilar membrane frequency response, impulse response, frequency glides, and scala tympani voltage. The close match of the model predictions with experimental data demonstrates the validity of the model for simulating cochlear response to acoustic input and for testing hypotheses of cochlear function. Analysis of the model and its results indicates that OHC somatic motility is capable of powering active amplification in the cochlea. At the same time, the model supports a possible synergistic role for HB motility in cochlear amplification.

The outer hair cell (OHC) is an extremely specialized cell and its proper functioning is essential for normal mammalian hearing. This article reviews recent developments in theoretical modeling that have increased our knowledge of the operation of this fascinating cell. The earliest models aimed at capturing experimental observations on voltage-induced cellular length changes and capacitance were based on isotropic elasticity and a two-state Boltzmann function. Recent advances in modeling based on the thermodynamics of orthotropic electroelastic materials better capture the cell's voltage-dependent stiffness, capacitance, interaction with its environment and ability to generate force at high frequencies. While complete models are crucial, simpler continuum models can be derived that retain fidelity over small changes in transmembrane voltage and strains occurring in vivo. By its function in the cochlea, the OHC behaves like a piezoelectric-like actuator, and the main cellular features can be described by piezoelectric models. However, a finer characterization of the cell's composite wall requires understanding the local mechanical and electrical fields. One of the key questions is the relative contribution of the in-plane and bending modes of electromechanical strains and forces (moments). The latter mode is associated with the flexoelectric effect in curved membranes. New data, including a novel experiment with tethers pulled from the cell membrane, can help in estimating the role of different modes of electromechanical coupling. Despite considerable progress, many problems still confound modelers. Thus, this article will conclude with a discussion of unanswered questions and highlight directions for future research.

. Although prestin-mediated outer hair cell (OHC) electromotility provides mechanical force for sound amplification in the mammalian cochlea, proper OHC stiffness is required to maintain normal electromotility and to transmit mechanical force to the basilar membrane (BM). To investigate the in vivo role of OHC stiffness in cochlear amplification, chlorpromazine (CPZ), an antipsychotic drug that alters OHC lateral wall biophysics, was infused into the cochleae in living guinea pigs. The effects of CPZ on cochlear amplification and OHC electromotility were observed by measuring the acoustically and electrically evoked BM motions. CPZ significantly reduced cochlear amplification as measured by a decline of the acoustically evoked BM motion near the best frequency (BF) accompanied by a loss of nonlinearity and broadened tuning. It also substantially reduced electrically evoked BM vibration near the BF and at frequencies above BF (Յ80 kHz). The high-frequency notch (near 50 kHz) in the electrically evoked BM response shifted toward higher frequency in a CPZ concentration-dependent manner with a corresponding phase change. In contrast, salicylate resulted in a shift in this notch toward lower frequency. These results indicate that CPZ reduces OHC-mediated cochlear amplification probably via its effects on the mechanics of the OHC plasma membrane rather than via a direct effect on the OHC motor, prestin. Through modeling, we propose that with a combined OHC somatic and hair bundle forcing, the upward-shift of the ϳ50-kHz notch in the electrically-evoked BM motion may indicate stiffness increase of the OHCs that is responsible for the reduced cochlear amplification. I N T R O D U C T I O NIn the mammalian cochlea, outer hair cells (OHCs) possess a unique motor capability termed "electromotility" whereby they change the somatic length in a voltage-dependent manner (Brownell et al. 1985;Santos-Sacchi 1991). The electromotility is assumed to provide mechanical force to the basilar membrane (BM), therefore locally amplifying the soundevoked traveling wave in the cochlea to ensure normal cochlear sensitivity (Dallos 1992(Dallos , 1996. Although OHC electromotility depends on the motor protein prestin (Dallos and Fakler 2002;Liberman et al. 2002;Zheng et al. 2000), proper stiffness of OHCs is also essential to the electromotile capability (Kakehata and Santos-Sacchi 1995; Santos-Sacchi et al. 2001). OHC stiffness is largely dependent on the biophysical properties of the basolateral wall, which has a unique nanoscale organization of three layers: the plasma membrane, the cortical cytoskeleton, and the subsurface cisterna Dallos 1992). The static axial stiffness of isolated OHCs has been intensively investigated (e.g., Hallworth 1995; Holley and Ashmore 1988;Iwasa and Adachi 1997;Zenner et al. 1992), and in vitro data have associated OHC stiffness with OHC electromotility (e.g., Batta et al. 2003;Borko et al. 2005;Chan et al. 1998;Dallos et al. 1997;Hallworth 1997;He and Dallos 1999;He et al. 2003;Lue and Brownell 1999;Oghalai ...

With discovery of the protein prestin and the gathering evidence linking it to outer hair cell electromotility, the working mechanism of outer hair cells is becoming clearer. Recent experiments have established the voltage-dependent stiffness of outer hair cells and given an insight into the nature of variation of stiffness with respect to voltage. These and earlier experiments are used to analyze and develop models of outer hair cell response. In this article, recent modeling efforts have been reconciled and placed into a common mechanics-based framework. The constitutive models are analyzed with regard to their capability to replicate experimental results. We extend the area motor model to include elastic constants dependent on motor state. The modified model successfully captures stiffness variations of outer hair cells and capacitance changes with respect to voltage.

We present a consistent second-order expansion of nonlinear constitutive theories for outer hair cells. For a particular theory, we will test the validity of such a model for small variations in voltage and strain about the resting state of outer hair cells. An analysis of the various terms in the simplified nonlinear model and their relevance to outer hair cell mechanics are presented. Results show that the second-order expansion is adequate for modeling outer hair cell mechanics in a global model of the cochlea. Model predictions agree with the notion that voltage nonlinearities are the dominant ones at low sound levels in vivo.

Electrically evoked otoacoustic emissions (EEOAEs) are used to investigate in vivo cochlear electromechanical function. Electrical stimulation through bipolar electrodes placed very close to the basilar membrane (in the scala vestibuli and scala tympani) gives rise to a narrow frequency range of EEOAEs, limited to around 20 kHz when the electrodes are placed near the 18-kHz best frequency place. Model predictions using a three-dimensional inviscid fluid model in conjunction with a middle ear model [S. Puria and J. B. Allen, J. Acoust. Soc. Am. 104, 3463–3481 (1998)] and a simple model for outer hair cell activity [S. Neely and D. Kim, J. Acoust. Soc. Am. 94, 137–146 (1993)] are used to interpret the experimental results. To estimate effect of viscosity, model results are compared with those obtained for a viscous fluid. The models are solved using a 2.5-D finite-element formulation. Predictions show that the high frequency limit of the excitation is determined by the spatial extent of the current stimulus. The global peaks in the EEOAE spectra are interpreted as constructive interference between electrically evoked backward traveling waves and forward traveling waves reflected from the stapes. Steady state response predictions of the model are presented.

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