The influence of cochlear shape on low-frequency hearing
- Daphne Manoussaki*,†,
- Richard S. Chadwick‡,§,
- Darlene R. Ketten‡,¶,‖,
- Julie Arruda‖,**,
- Emilios K. Dimitriadis††, and
- Jen T. O'Malley**
- *Department of Mathematics, Vanderbilt University, Nashville, TN 37240;
- †Department of Sciences, Technical University of Crete, Hania, Greece 73100;
- ‡Auditory Mechanics Section, National Institute on Deafness and Other Communication Disorders, and
- ††Laboratory of Bioengineering and Physical Science, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, MD 20892;
- ¶Department of Otology and Laryngology, Harvard Medical School, Boston, MA 02114;
- ‖Woods Hole Oceanographic Institution, Woods Hole, MA 02543; and
- **Massachusetts Ear and Eye Infirmary, Boston, MA 02114
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Edited by Jon H. Kaas, Vanderbilt University, Nashville, TN, and approved February 13, 2008 (received for review October 22, 2007)
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Fig. 1.Focusing of rays by spirals. A uniform distribution of 200 rays (red) entering and filling a spiral duct (walls in blue) at the largest radius is increasingly focused toward the outer wall as the rays progress toward the apex (spiral center). The effect increases with the parameter α, which controls the rate of decrease of radius in the exponential spirals described by the formula given in the figure. Insets shown below each spiral, in an expanded scale, indicate the radial gradient of ray or energy density at the apex. These distributions should be compared with a uniform distribution of rays entering at the largest radius to see the energy density focusing effect of the spiral walls.
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Fig. 2.Land and aquatic mammalian LF hearing relationship with spiral radii ratio. The LF limit of hearing was determined in land (black dots) and marine (blue dots) mammals from behavioral audiograms at 60-dB SPL re 20 μParms. Exceptions were the behavioral audiograms in water of the bottlenose dolphin and the sea lion, which were at 120-dB SPL re 1 μParms (the sea lion audiogram in air was at 60-dB SPL). Two different mice and rat audiograms are reported because of unresolved disputes in the literature on the LF limits of hearing among strains. Cochlear radii ratios were calculated as the radius of curvature of the basilar membrane midline at the base to that at the apex, according to the technique described in Methods (data are summarized in Table 1, including abbreviations). The audiograms are strongly correlated with this dimensionless ratio and indicate that the greater the radii ratio, the lower the LF limit of hearing (r = 0.979, P < 0. 001). This relationship represents a functional anatomical correlate for the energy density focusing theory (8).
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Fig. 3.Mammalian LF hearing relationship to BM length times turns. Behavioral audiogram and cochlear data sources are listed in Table 1. This graph updates a similar data analysis by West (5). The significance level and correlation coefficient for this relationship (r = 0.827, P < 0.001; r = 0.901, P < 0.001 land mammals only) is not as strong as that for the relationship of radii ratio and LF limits shown in Fig. 2.
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Fig. 4.Schematic of cochlear spiral with five points used to determine radii of curvature. See Methods for a description of the construction procedure.
Footnotes
- §To whom correspondence should be addressed. E-mail: chadwick{at}helix.nih.gov
- © 2008 by The National Academy of Sciences of the USA
