The Competition between the Noise and Shear Motion Sensitivity of Cochlear Inner Hair Cell Stereocilia

Abstract

Acoustical excitation of the organ of Corti induces radial fluid flow in the subtectorial space (STS) that excites the hair bundles (HBs) of the sensory inner hair cell of the mammalian cochlea. The inner hair cell HBs are bathed in endolymphatic fluid filling a thin gap in the STS between the tectorial membrane and the reticular lamina. According to the fluctuation dissipation theorem, the fluid viscosity gives rise to mechanical fluctuations that are transduced into current noise. Conversely, the stochastic fluctuations of the mechanically gated channels of the HBs also induce dissipation. We develop an analytic model of the STS complex in a cross section of the gerbil organ of Corti. We predict that the dominant noise at the apex is due to the channel stochasticity whereas viscous effects dominate at the base. The net root mean square fluctuation of the HB motion is estimated to be at least 1.18 nm at the base and 2.72 nm at the apex. By varying the HB height for a fixed STS gap, we find that taller HBs are better sensors with lower thresholds. An integrated active HB model is shown to reduce the hydrodynamic resistance through a cycle-by-cycle power addition through adaptation, reducing the thresholds of hearing, hinting at one potential role for HB activity in mammalian hearing. We determine that a Couette flow approximation in the STS underestimates the dissipation and that modeling the entire STS complex is necessary to correctly predict the low-frequency dissipation in the cochlea. Finally, the difference in the noise budget at the base and the apex of the cochlea indicate that a sensing modality other than the shear motion of the TM that may be used to achieve low-noise acoustic sensing at the apex.

A flexible anatomical set of mechanical models for the organ of Corti

“…While there are normally three rows of OHCs, some models [17,33] assume a single OHC. However, we found ( §4.4) that a second OHC enables us to position the value of the IHB resonance frequency relative to that of the BM.…”

“…Recent measurements (in the apical region) [30,38] showed that for frequencies that are not too far from resonance, the amplitudes of the x-and of the y-component of this relative motion are of the same order of magnitude. Here we focus on the pulsatile mode [37,39], which is usually disregarded [33,36]. Accordingly, except for rotational and for fluid motion, motion will be restricted to the y-direction.…”

“…it almost touches the TM. Models for the torque exerted by the fluid on the IHB abound [19,33,37,50]. We take a simpler approach.…”

A flexible anatomic set of mechanical models for the organ of Corti

“…While there are normally three rows of OHCs, some models (24,27) assume a single OHC. However, we found (section 4D) that a second OHC enables to position the value of the IHB resonance frequency relative to that of the BM.…”

“…Recent measurements (in the apical region) (23,32) showed that for frequencies that are not too far from resonance, the amplitudes of the x-and of the y-component of this relative motion are of the same order of magnitude. Here we will focus on the pulsatile mode (31,33), which is usually disregarded (27,30). Accordingly, except for rotational and for fluid motion, motion will be restricted to the y-direction.…”