Quantitative Reappraisal of the Helmholtz-Guyton Resonance Theory of Frequency Tuning in the Cochlea

Table 1

Numerical estimates for model parameters.

Variable	Estimate	References
Length of basilar membrane (uncoiled)^#	3.5 cm	Keen [23], Miller [24]
Width, 𝑠, of basilar membrane	0.015 cm near base to 0.056 cm near apex	Givelberg [3], Bronzino-2000, Keen [23]
Radius of scala vestibuli	0.1 cm	di Fiori [25]
Radius of scala tympani	0.15 cm	di Fiori [25]
Average cross-section of scalae	0.05 cm^2	Liu and White [18] di Fiori [25]
Average thickness of basilar membrane	0.002 cm	Liu and White [18], Naidu and Mountain, [26], Wada et al. [27]
Viscosity of water at 37°C	0.0065 g/(cm-sec)	Lide [28]
Density of water	1.00 g/(cm)^3	Lide [28]
Resting strain, ε 0, of the basilar membrane	~ 0 (0.001)	Naidu and Mountain, [26]
Pressure gain from tympanic membrane to stapes	25	Puria et al. [29]
Damping ratio D/E of basilar membrane	2 × 10^−6 sec*	Summers et al. [30], Recio et al. [31, 32], Lin Guinan [33]
Young’s modulus of basilar membrane	10^9 to 10^8 dynes/cm^2	Naidu and Mountain, [26] Liu and White [18]
Ratio of axial Young’s modulus to radial Young’s modulus of basilar membrane (axial E/radial E)	1/10	Naidu and Mountain, [26] Liu and White [18]
Linear decay formula for Young’s modulus, E	𝐸=2×10^−9(1−𝑥/3.6)	Liu and White [18], Mammano and Nobili [5], Wada et al. [27]

^#Anatomic dimensions in the first five rows are for human cochleae. *Computed as (𝐷/𝐸)=(2ln(2))/(𝑡_1/2𝜔²), from transient displacement of the basilar membrane in the time domain in response to clicks, where 𝑡_1/2 is the half-life of the transient response and ω ² is the characteristic angular frequency of unforced oscillation.