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

TL;DR

This paper addresses the challenge of noninvasively estimating cochlear mechanistic variables that govern wave propagation and Organ of Corti dynamics. It uses a parsimonious short-wave single-partition model parameterized by three constants to derive closed-form expressions for the wavenumber $k(x,\omega)$ and effective impedance $Z(x,\omega)$, and inverts macromechanical and noninvasive response characteristics to estimate these variables in humans. The authors show that base regions have shorter minimum wavelengths and greater damping and stiffness compared to apex regions, reflecting location-dependent mechanics. The methods enable cross-species and region-specific comparisons from noninvasive data and have potential utility for auditory filter design and biomimetic cochlear devices.

Abstract

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 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. We then apply these methods to estimate human mechanistic variables 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. 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.

Figures (2)

• Figure 1: We develop methods for estimating mechanistic variables which encode how a box representation of the cochlea works (purple star) from noninvasive response characteristics (purple triangle). To do so, we leverage an analytic model of the healthy mammalian cochlea in which a set of three model constants ($b_p, A_p, B_u$) parameterizes the model mechanistic variables, $k(x,\omega), Z(x,\omega)$, as well as the model macromechanical response variables, $P(x,\omega), V(x,\omega)$. The magnitude and phase of the response variables may be described by filter characteristics such as peak frequencies, quality factors, and group delays that are reported from invasive experiments in some animals. Our objective (following the red text and arrows from the purple triangle to the purple star) is to develop methods for estimating the mechanistic variables from characteristics of noninvasive responses such as quality factors of psychophysical tuning curves. To do so, we first derive a parameterization of model constants in terms of noninvasive response characteristics by deriving then 'inverting' expressions for noninvasive response characteristics in terms of model constants. For species where invasive measurements are reported, we may alternatively parameterize the model constants in terms of (invasive) response characteristics such as the quality factors and group delays of experimental mechanical (or neural) measurements that provide both magnitude and phase information.
• Figure 2: Estimated wavenumbers and impedances in the human base and apex: The top panel shows the real and imaginary parts of the model generated human wavenumber, and the bottom panel shows the real and imaginary parts of the impedance. The blue solid lines are for a point in the apex (CF = 1 kHz, where $Q_{psych-erb} \approx 12.7$) which has estimated model constants $A_p = 0.11, B_u = 7$, and the dashed green lines are for a point in the base (CF = 10 kHz, where $Q_{psych-erb} \approx 25.34$) which has estimated model constants $A_p = 0.055, B_u = 7$. The values for $A_p, B_u$ are estimated from noninvasive response characteristics in the previous section.