Radial Structure of Traveling Waves in the Inner Ear

Abstract

We develop a hybrid approach for modeling the cochlea, in which we let the WKB method determine the axial propagation of waves and restrict the numerics to transverse planes, where we solve a fluid-solid interaction eigenvalue problem. The cochlear fluid is treated as viscous and incompressible. Viscous effects are confined to oscillatory boundary layers and the thin gap between the reticular lamina (RL) and the lower surface of the tectorial membrane (TM). Our model includes axial fluid coupling and also axial elastic coupling via a basilar membrane (BM) modeled as an orthotropic clamped plate. Three-dimensional (3D) flow is solved in two-dimensional (2D) domains, with interactions with 2D elastic domains representing the organ of Corti (OC) and the TM. The OC contains inhomogeneities representing discrete cellular structures. We have computed the interaction between the BM, TM, OC, and the cochlear fluid to find the complex-valued wavenumberfrequency relation and vibrational modes. The details of the cochlear fluid flow and pressure fields are calculated, along with displacements of the elastic structures. Simulation of passive radial modes in the apical region of a guinea pig cochlea for frequencies less than 1 kHz indicates monophasic vibration of the BM and a synchronous rotation of three rows of outer hair cell stereocilia induced by a shearing motion between the RL and TM.

Finite-element model of the active organ of Corti

“…However, uncertainty remains, for example, in the volume fraction of protein in a particular component, the cross-links and in the stiffness of the ground substance. The important material properties of the model used here are listed in table 1, which are tuned to obtain the resonant frequency which is the same as the corresponding characteristic frequency, and are within the range of measurements and models reported by Cai & Chadwick [27], Steele & Puria [46], Scherer & Gummer [49], Strelioff & Flock [50] and Frank et al [51]. The parameters were manually adjusted and an order of magnitude estimate was usually sufficient, as the response of the model was robust to smaller variation in these parameters.…”

“…Similarly, Nam & Fettiplace [22] developed an elastic micromechanical model of the organ of Corti to study force transmission and elastic wave propagation [23], in which OHC somatic and hair bundle active forces were both considered. Developments of the finite-element method and in computational power have allowed newer models to study wave propagation in the cochlear partition [23][24][25], mechanical effects of OHC somatic and hair bundle motility [22,26], fluid-solid interaction [27,28] and detailed motion patterns within the organ of Corti in response to static pressure loading [29]. The active amplification process within the cochlea has also been studied using either lumped-parameter models [30 -32], or simplified three-dimensional models [21,[33][34][35][36].…”

A wave finite element analysis of the passive cochlea

“…Steele (1999) also describes how multi-chamber models give rise to multiple modes. Cai et al (2003Cai et al ( , 2004 discuss how a more detailed numerical model of slices of the cochlea can be used to describe wave propagation. In this case a finite element (FE) model of the 2D cross-section was constructed and used to calculate multiple values of the wavenumber, from which the one with the least-negative imaginary part is selected for a WKB solution over the length of the cochlea.…”

Auditory Nerve Excitation via a Non-traveling Wave Mode of Basilar Membrane Motion

“…Between BM motion and ANF responses lies HC excitation. Several theoretical studies have explored the relationship between BM and hair bundle motion, and this relationship is far from well understood (Neely and Kim 1986;Steele and Lim 1999;Cai and Chadwick 2003;Cai et al 2004;Steele and Puria 2005;Reichenbach and Hudspeth 2010). These models and in vitro experimental results (Nowotny and Gummer 2006) indicate that BM motion is not a direct predictor of hair bundle motion.…”

“…These models and in vitro experimental results (Nowotny and Gummer 2006) indicate that BM motion is not a direct predictor of hair bundle motion. For example, the model developed by Chadwick and colleagues shows a frequency-dependent sheer gain that quantifies the amount of hair bundle bending due to BM deflection (Cai and Chadwick 2003;Cai et al 2004). Such a model could be employed to explore whether the sheer gain is different in the plateau versus the traveling wave frequency region, and the results presented here inform and constrain such efforts.…”