TITLE:
A Modified Right Helicoid Can Simulate the Inner Structure of the Cochlea in the Hearing Organ of Mammals
AUTHORS:
Motohisa Osaka
KEYWORDS:
Auditory Organ, Cochlea, Right Conoid, Mean Curvature
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.5,
May
19,
2021
ABSTRACT: The purpose of this study is to develop a mathematical model of the spiral basilar membrane in the center of the cochlea, which plays an important role in the mammalian auditory system. The basilar membrane transmits sound vibrations, which are converted into electrical potential changes by the inner hair cells. The basilar membrane is thought to lie on a locally undistorted curved surface because the inner hair cells, which are arranged in an orderly fashion on the basilar membrane, respond to their location-specific frequencies. In mammals, the number of rotations of this surface and the rate of change of its width with each rotation are different. It turns out that by modifying the right helicoid, we can obtain a mathematical model that satisfies these points. In conclusion, even though the three-dimensional structure of the basilar membrane varies among species, this model can reproduce this structure. This further suggests that there are common genetic determinants of cochlear development in mammals. From a practical standpoint, this may be useful for creating cochlear implants.