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A simple electrical lumped-element model simulates intra-cochlear sound pressures and cochlear impedance below 2 kHz
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Image of FIG. 1.
FIG. 1.

Lumped-element models of the apical cochlea explaining its principle acoustic properties below 2 kHz, as experimentally measured in the basal turn. Such models have been previously suggested by (A) Dallos (1970) , (B) Lynch (1982) , and (C) Franke and Dancer (1982) . (D) The model proposed in the current study.

Image of FIG. 2.
FIG. 2.

(A) Cochlear input impedance () derived by Lynch (1982 , Fig. 24; see also their footnote 5 for details) from physiological measurements in 29 cats (black dots). The solid green graph represents the input impedance of their model [shown in Fig. 1(B) ], which aligns generally well with the data, but does not replicate the resonance features above 100 Hz. Bold red lines show (solid), and the impedance across the BM (, dashed) of our model [Fig. 1(D) ], adjusted to fit the input impedance data by Lynch (1982) . The thin straight dotted lines show impedance functions of the model's lumped elements. All blue lines show the respective impedances of the model (bold: ; dashed: ) when fitted to the single-cat pressure data shown in (B) (pressure fits also shown in blue). The middle ear compliance ( ) and mass ( ), shown in (A) as thin straight blue dotted lines, are only relevant for fitting these pressure functions. (B) Intra-cochlear pressures measured by Nedzelnitsky (1980 , Fig. 14) in SV (, solid black) and ST (, dotted black) in one cat. The black dashed line indicates the median pressure difference across the BM ( ) for six cats and, since normalized to the ear canal pressure ( ), represents the cat's fMETF. The blue lines show simulations of these pressure functions by our model when fitted to the single cat data (i.e., and only). The predicted impedance curves with this parameter set are shown in (A) in blue.

Image of FIG. 3.
FIG. 3.

(A) Average pressure in SV and ST of two guinea pigs (black) measured by Franke and Dancer (1982) with a constant ear canal pressure of 78 dB SPL, and simulated by our model (blue). (B) Changes in the fMETF induced by sealing the helicotrema with silicone (one guinea pig; reproduced from Franke and Dancer, 1982 , Fig. 2). The shape of the fMETF is here obtained by measuring the CM, which is proportional to the pressure difference across the basal BM. The blue lines show our model fits. Additional fMETF shape data and their model fit (red) are shown for one guinea pig (dB with arbitrary reference), which exhibits a more pronounced resonance ( Marquardt , 2007 ). The latter experiments employed a non-invasive DPOAE suppression technique (described in main text, Sec. II ). Note that the measured phase values of Franke and Dancer (1982) and Marquardt (2007) were latency-compensated by 150 μs and 750 μs, respectively.

Image of FIG. 4.
FIG. 4.

Cochlear input impedance, (solid), and the impedance across the BM, (dotted), of our model, adjusted to fit the intra-cochlear pressure measured in the guinea pig by Franke and Dancer (1982) as shown in Fig. 3(A) . The dashed line shows of our model when fitted to the guinea pig data in Fig. 3(B) that were obtained by Marquardt (2007) with the DPOAE-based method and showed a more pronounced resonance feature.

Image of FIG. 5.
FIG. 5.

(A) Mean intra-cochlear pressures measured by Nakajima (2008) in SV (, solid black) and ST (, dotted black) in six human cadaveric temporal bones. Their calculated differential pressure across the BM ( , dashed black without markers) was extended toward lower frequencies by the shape of the differential pressure function of a typical human ear (dashed black with round markers) as was non-invasively obtained by Marquardt (2007) using a non-invasive DPOAE suppression technique. These relative shape data were vertically aligned with the absolute differential pressure function. The red lines show our model fits. (B) Cochlear input impedance (, solid black), the impedance across the BM (, dashed black), and the impedance seen from the ST measurement location toward the round window (, dotted black) derived for the human cochlea by Nakajima (2008) . The red lines show the impedance of our model when fitted to the intra-cochlear pressure data in (A). Note that the measured pressure phase values of Nakajima (2008) and the DPOAE suppression phases of Marquardt (2007) were latency-compensated by 83 μs and 500 μs, respectively.


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Model parameters and their physiologically derived values, where available.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A simple electrical lumped-element model simulates intra-cochlear sound pressures and cochlear impedance below 2 kHz