Time Domina One-Dimensional Cochlear Model with Integrated Tectorial Membrane and Outer Hair Cells

Abstract

Recent studies of the tectorial membrane (TM) revealed mechanical properties that are changing along the cochlear partition. In our previous cochlear model, the basilar membrane (BM) motion was derived from the cochlear fluid dynamics along with the outer hair cells (OHCs) electromotility force. In order to achieve a match between the resonances of both the BM and the OHCs gain, a set of constraints were obtained. In particular, the OHCs electrical properties were changed along the cochlear partition. However, although plausible differences found between conductance of the OHCs at different locations along the Cochlea, it seems negligible compared to the change in the characteristic frequency. In the current model the TM is included in the model. Since the OHCs are embedded in the TM, we assume that they are gaining their electromotility force from both the BM and TM. The electrical properties of the OHCs are held constant along the cochlear partition, while the TM stiffness and resistance are changing along the cochlear partition in correspondence to the BM dependence. The boundary conditions were derived from the middle ear model. A non‐linear, odd‐order, mechanism related to the OHCs motility was included in the model. The OHCs length change depends nonlinearly on its membrane electrical potential. The model was solved numerically in the time domain in response to various input signals. The basilar and tectorial membranes gain were derived for a wide range of input levels and frequencies. Both BM and TM revealed traveling waves with a maximum response for every input frequency at the same distance from the stapes. The BM sensitivity gain was greater than that of the TM. The difference between the two increased with the increase of the input level.