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Structures that contribute to middle-ear admittance in chinchilla

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Abstract

We describe measurements of middle-ear input admittance in chinchillas (Chinchilla lanigera) before and after various manipulations that define the contributions of different middle-ear components to function. The chinchilla’s middle-ear air spaces have a large effect on the low-frequency compliance of the middle ear, and removing the influences of these spaces reveals a highly admittant tympanic membrane and ossicular chain. Measurements of the admittance of the air spaces reveal that the high-degree of segmentation of these spaces has only a small effect on the admittance. Draining the cochlea further increases the middle-ear admittance at low frequencies and removes a low-frequency (less than 300 Hz) level dependence in the admittance. Spontaneous or sound-driven contractions of the middle-ear muscles in deeply anesthetized animals were associated with significant changes in middle-ear admittance.

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Notes

  1. The measurements of middle-ear input admittance reported in this thesis are contaminated by a calculation error that was corrected when they were illustrated in Rosowski (1994).

  2. The equivalent volume and the acoustic compliance are related by EqVol = βA C, where C is an acoustic compliance with units of m3/pascal and βA is the adiabatic bulk modulus of an ideal gas. At standard temperature and pressure βA = 1.4 × 105 pascal.

  3. The existence of admittance angle estimates more negative than  − 0.25 periods is more likely than not related to uncertainties in the estimate of the real part of the admittance rather than the existence of sound sources within the ear.

Abbreviations

βA :

the adiabatic bulk modulus of air which equals 1.4 × 105 Pa at standard temperature and pressure

ρ0 :

the density of air, at standard temperature and pressure = 1.2 kg m−3

a :

the effective radius of the bullar hole

A TM :

the area of the TM

C :

an acoustic compliance with units of m3 Pa−1

C MEair :

the acoustic compliance of the middle-ear air spaces

C HTM :

the acoustic compliance measured lateral to the TM with 1 or 2 holes in the bullar walls

C ITM :

the acoustic compliance lateral to the TM with the middle-ear air spaces intact or bullar-holes sealed

C PTM :

the acoustic compliance lateral to the TM with bullar-holes sealed and the TM perforated

C TOC :

the acoustic compliance of the TM, ossicles and cochlea measured lateral to the TM

C TO :

the acoustic compliance of the TM and ossicles measured lateral to the TM

EqVol:

the equivalent air volume that describes the magnitude of an acoustic compliance

f :

frequency

ISJ:

the incudo-stapedial joint

l :

the thickness of the bony bullar wall

M A :

the acoustic mass associated with the open bullar hole with units of kg m−4

m TO :

the effective mechanical mass of the TM and attached ossicles

M TO :

the acoustic mass of the TM and ossicles measured lateral to the TM

Pa:

a pascal, the SI unit of pressure quivalent to 1 N m−2

S:

an acoustic siemen, a measure of acoustic admittance equivalent to 1 m3 s−1 Pa−1

SPL:

sound pressure level, a dB measure of sound level where X dB SPL = 20 log10(Y rms Pa /2 × 10−5 Pa)

TM:

the tympanic membrane or ear-drum membrane

Y :

an acoustic admittance with units of siemens

Y ASBH :

the acoustic admittance of the middle-ear air spaces with an open bullar hole

Y EC :

the acoustic admittance measured at the entrance of the ear canal coupler

Y TM :

the acoustic admittance within the ear canal just lateral to the TM

Y CDTM :

the acoustic admittance lateral to the TM with the cochlea drained of fluid

Y HTM :

the acoustic admittance lateral to the TM with 1 or 2 holes in the bullar walls

Y ITM :

the acoustic admittance lateral to the TM with the middle-ear air spaces intact or bullar-holes sealed

Y OITM :

the acoustic admittance lateral to the TM with an interrupted ISJ

Y PTM :

the acoustic admittance lateral to the TM with bullar-holes sealed and the TM perforated

Y MEair :

the admittance of the middle-ear air space

Y TOC :

the admittance at the tympanic membrane produced by the TM, ossicles (and their ligaments) and the cochlea when the admittance of the middle-ear air spaces is made infinite (Huang et al. 1997)

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Acknowledgments

This work was supported by a grant from the National Institute of Deafness and other Communicative Disorders. The experiments comply with the “Principles of animal care”, publication No. 86–23, revised 1985 of the National Institute of Health, and also with the current laws of the United States of America and the Commonwealth of Massachusetts.

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Authors and Affiliations

  1. Eaton-Peabody of Auditory Physiology, Department of Otolaryngology, Massachusetts Eye and Ear Infirmary, Boston, MA, USA

    John J. Rosowski, Michael E. Ravicz & Jocelyn E. Songer

  2. Department of Otology and Laryngology, Harvard Medical School, Boston, MA, USA

    John J. Rosowski

  3. Speech and Hearing Bioscience and Technology Program, Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, USA

    John J. Rosowski & Jocelyn E. Songer

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  1. John J. Rosowski
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  2. Michael E. Ravicz
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Correspondence to John J. Rosowski.

Appendix 1

Appendix 1

The acoustic mass of the bullar hole M A can be described in terms of the hole dimensions or the combination of the air-space compliance and the frequency of the anti-resonance:

$$M^{\rm A} = \frac{{\rho _{0} {\left({l + 1.6a} \right)}}}{{\pi\,a^{2}}} = \frac{1}{{C_{{\rm MEair}}\,{\left({2\pi\,f_{0}} \right)}^{2}}},$$
(4)

where ρ0 is the density of air, l is the thickness of the bony bullar wall (1 mm), a is the radius of the bullar hole, C MEair is the acoustic compliance of the middle-ear air spaces (the equivalent volume divided by the adiabatic compressibility of air)2, f 0 is the frequency of the anti-resonance and the factor of 1.6a represents the dual end-correction associated with flow through the bullar hole (e.g. Beranek 1986). We use the right-hand side of Eq. 4 to solve for M A using the data from our first set of 9 ears where f 0  = 1370 Hz (Table 1). Rearranging the left-hand side equality of Eq. 4 yields a quadratic relationship in a:

$$a^{2} - \frac{{1.6\,\rho _{o}}}{{\pi\,M^{\rm A}}}a - \frac{{\rho _{o} l}}{{\pi\,M^{\rm A}}} = 0$$
(5)

that when solved produces one positive root such that the calculated hole diameter (2a) is 2 mm.

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Rosowski, J.J., Ravicz, M.E. & Songer, J.E. Structures that contribute to middle-ear admittance in chinchilla. J Comp Physiol A 192, 1287–1311 (2006). https://doi.org/10.1007/s00359-006-0159-9

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