Cochlear Wave Propagation and Dynamics in the Human Base and Apex: Model-Based Estimates from Noninvasive Measurements

Cochlear wavenumber and impedance are mechanistic variables that encode information regarding how the cochlea works - specifically wave propagation and Organ of Corti dynamics. These mechanistic variables underlie interesting features of cochlear signal processing such as its place-based wavelet analyzers, dispersivity and high-gain. Consequently, it is of interest to estimate these mechanistic variables in various species (particularly humans) and across various locations along the length of the cochlea. In this paper, we (1) develop methods to estimate the mechanistic variables (wavenumber and impedance) from noninvasive response characteristics (such as the quality factors of psychophysical tuning curves) using an existing analytic shortwave single-partition model of the mammalian cochlea. The model we leverage in developing the estimation methods is valid at low stimulus levels, was derived using a physical-phenomenological approach, and tested using a variety of datasets from multiple locations and species. The model's small number of parameters and simple closed-form expressions enable us to develop methods for estimating mechanistic variables from noninvasive response characteristics. Developing these estimation methods involves (1a) deriving expressions for model constants, which parameterize the model expressions for wavenumber and impedance, in terms of characteristics of response variables - e.g. bandwidths and group delays of pressure across the Organ of Corti; followed by (1b) deriving expressions for the model constants in terms of noninvasive response characteristics. Using these derived expressions, we can estimate the wavenumber and impedance from noninvasive response characteristics for various species and locations along the length of the cochlea. After developing the estimation methods, we (2) apply these methods to estimate human mechanistic variables, and (3) make comparisons between the base and apex. We estimate the mechanistic variables in the human base and apex following the methods developed in this paper and using reported values for quality factors from psychophysical tuning curves and a location-invariant ratio extrapolated from chinchilla. Our resultant estimates for human wavenumbers and impedances show that the minimum wavelength (which occurs at the peak of the traveling wave) is smaller in base than the apex. The Organ of Corti is stiffness dominated rather than mass dominated, and there is negative effective damping prior to the peak followed by positive effective damping. The effective stiffness, and positive and negative effective damping are greater in the base than the apex. Future work involves studying the closed-form expressions for wavenumber and impedance for qualitative mechanistic interpretations across mammalian species as well as studying derived mechanisms such as power flux into the traveling wave and features of the cochlear amplifier. The methods introduced here for estimating mechanistic variables from characteristics of invasive or noninvasive responses enable us to derive such estimates across various species and locations where the responses are describable by sharp filters. In addition to studying cochlear wave propagation and dynamics, the estimation methods developed here are also useful for auditory filter design.