A Cochlea-Slice Model using Floquet Boundary Conditions shows Global Tuning

Abstract

ABSTRACTA common assumption about the cochlea is that the local characteristic frequency (CF) is determined by a local resonance of basilar-membrane (BM) stiffness with the mass of the organ-of-Corti (OoC) and entrained fluid. We modeled the cochlea while avoiding sucha prioriassumptions by using a finite-element model of a 20-μm-thick cross-sectional slice of the middle turn of a passive gerbil cochlea. The model had anatomically accurate structural details with physiologically appropriate material properties and interactions between the fluid spaces and solid OoC structures. The longitudinally-facing sides of the slice had a phase difference that mimicked the traveling-wave wavelength at the location of the slice by using Floquet boundary conditions. A paired volume-velocity drive was applied in the scalae at the top and bottom of the slice with the amplitudes adjusted to mimic experimental BM motion. The development of this computationally efficient model with detailed anatomical structures is a key innovation of this work. The resulting OoC motion was greatest in the transverse direction, stereocilia-tip deflections were greatest in the radial direction and longitudinal motion was small in OoC tissue but became large in the sulcus at high frequencies. If the source velocity and wavelength were held constant across frequency, the OoC motion was almost flat across frequency,i.e., the slice showed no local resonance. A model with the source velocity held constant and the wavelength varied realistically across frequency, produced a low-pass frequency response. These results indicate that tuning in the gerbil middle turn is not produced by a resonance due to local OoC mechanical properties, but rather is produced by the characteristics of the traveling wave, manifested in the driving pressure and wavelength.STATEMENT OF SIGNIFICANCEThe sensory epithelium of hearing, the organ of Corti, is encased in the bone of the fluid-filled cochlea and is difficult to study experimentally. We provide a new method to study the cochlea: making an anatomically-detailed finite-element model of a small transverse slice of the cochlea using Floquet boundary conditions and incorporating global cochlear properties in the slice drive and the wavelength-frequency relationship. The model shows that the slice properties do not show a mechanical resonance and therefore do not produce the frequency-response tuning of the cochlea. Instead, tuning emerges from global cochlear properties carried by the traveling wave.