# Three-Dimensional Vibration of the Malleus and Incus in the Living Gerbil

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## Abstract

In previous studies, 3D motion of the middle-ear ossicles in cat and human was explored, but models for hearing research have shifted in the last few decades to smaller mammals, and gerbil, in particular, has become a popular hearing model. In the present study, we have measured with an optical interferometer the 3D motion of the malleus and incus in anesthetized gerbil for sound of moderate intensity (90-dB sound pressure level) over a broad frequency range. To access the ossicles, the pars flaccida was removed exposing the neck and head of the malleus and the incus from the malleus-incus joint to the plate of the lenticular process. Vibration measurements were done at six to eight points per ossicle while the angle of observation was varied over approximately 30 ° to enable calculation of the 3D rigid-body velocity components. These components were expressed in an intrinsic reference frame, with one axis along the anatomical suspension axis of the malleus-incus block and a second axis along the stapes piston direction. Another way of describing the motion that does not assume an a priori rotation axis is to calculate the instantaneous rotation axis (screw axis) of the malleus/incus motion. Only at frequencies below a few kilohertz did the screw axis have a maximum rotation in a direction close to that of the ligament axis. A slight slippage in the malleus-incus joint developed with increasing frequency. Our findings are useful in determining the sound transfer characteristics through the middle ear and serve as a reference for validation of mathematical middle-ear models. Last but not least, comparing our present results in gerbil with those of previously measured species (human and cat) exposes similarities and dissimilarities among them.

## Keywords

middle ear ossicular chain motion measurement## Abbreviations

- AMP
Anterior mallear process

- ISJ
Incus-stapes joint (

*“incudostapedial joint”)*- LPI
Lenticular process of the incus

- LPM
Lateral process of the malleus

- MRA
Instantaneous rotation vector with maximal length (“

*maximal rotation axis*”)- MIJ
Malleus-incus joint (“

*incudomallear joint*”)- NM
Neck of the malleus

- PIP
Posterior incudal process

- PF
Pars flaccida

- SPL
Sound pressure level in decibel—\( \mathrm{SPL}=20\times \mathrm{lo}{\mathrm{g}}_{10}\left({p}_{\mathrm{rms}}/{p}_{{\mathrm{ref}}_{\mathrm{rms}}}\right)\;\mathrm{dB}\;\mathrm{with}{p}_{{\mathrm{ref}}_{\mathrm{rms}}}={2.10}^{-5}\mathrm{Pa} \)

- TARA
Time-averaged instantaneous rotation axis

## Notes

### Acknowledgments

This work was supported by the NIH/NICDC (DC003130), the Emil Capita Fund, the Fund for Scientific Research (Flanders, Belgium), the Canadian Institutes of Health Research, and the Natural Sciences and Engineering Research Council of Canada. We thank N. Maftoon (Dept. BioMedical Engineering, McGill University) for checking our inertial axis calculations using Code_Aster. The first author would also like to thank R.D. Rabbitt for insightful discussions at a few meetings, many years ago, on the description of middle-ear motion using the rigid-body concept.

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