The active basilar membrane nonlinearity for generating multi-component DPOAEs can be modelled by a polynomial power series model at mid-lower stimulus levels (Cheng, 1999). The present study demonstrates that the degree of basilar membrane nonlinearity for generating specific multi-component DPOAEs can be quantified as , whereis a correlation coefficient derived from the input-output function of the basilar membrane nonlinearity. The 'bounce' phenomenon on the active cochlear nonlinearity was investigated after the ears were exposed to a loud, but not traumatic lower frequency tone, which showed a similar recovery pattern as the psychophysical 'bounce' (Hirsh and Ward, 1952; Kirk and Patuzzi,1997; Kirk et al., 1997) and the transient evoked otoacoustic emission 'bounce' (Kemp, 1986). The analysis of the 'bounce' recovery pattern from an individual ear will give information on the individual ability to recover from a temporal threshold shift objectively.

At mid-lower stimulus levels the basilar membrane nonlineariry for generating multi-component DPOAEs can be modelled by a polynomial power series model (Pickles, 1988). Here only a short description of the model is given, and the details can be found elsewhere (Cheng, 1999). The multi-component DPOAEs generated by primary tones at a location on the basilar membrane, x, can be described as a polynomial power series model:

, n = 1, 2, ...N, (1).

For a fixed position on the basilar membrane, the question turns to how to find the model's coefficients to match the levels of the odd order multi-component DPOAEs at lower frequencies. The even order multi-component DPOAEs were discussed (Cheng, 1999) as well. When the model's coefficients are decided, the input-output function of the basilar membrane nonlinearity to generate the specific multi-component DPOAEs can be calculated.

Fig. 1 shows an example of the computer program for measuring the multi-component DPOAEs and modelling the basilar membrane nonlinearity. The left side of uppermost panel shows ear canal response while measuring the multi-component DPOAEs and the right side demonstrates the frequencies, levels and phases of different orders of DPOAEs. The middle panel demonstrates spectrum of multi-component DPOAEs. The lowest panel shows the input-output function of the basilar membrane nonlinearity, the polynomial power series model and quantifying basilar membrane nonlinearity.

Fig.1

The input-output function can be calculated from the multi-component DPOAEs at mid-lower stimulus levels by applying a polynomial power series model. For a nonlinear system, as a result of the system nonlinearity, the error energy between model's output y(n) and model's input x(n) of the system can be estimated as:

, (2)

where a is a scale factor. Let to get the minimum error energy. Then the degree of cochlear nonlinearity for generating specific multi-component DPOAEs can be calculated as a normalized minimal error energy:

, (3)

whereis a correlation coefficient between the model's output and the input. Equation 3 represents the basilar membrane nonlinearity to generate specific multi-component DPOAEs, which is a number between 0.0 (full linear) and 1.0 (full nonlinear), and will refer to basilar membrane nonlinearity in this investigation.

a
b

Fig. 2. (a) Two examples of the 'bounce' phenomenon after the normal-hearing ears are exposed to a low-frequency tone for 1 minute. The nonlinearity at -1 minute post-exposure time indicated the basilar membrane nonlinearity before the low-frequency tone exposure and the nonlinearity from 20 second to 5.0 minutes indicated the basilar membrane nonlinearity after the low-frequency tone exposure. (b) Reliability of the measurement of the basilar membrane nonlinearity for the ear of the lower curve in Fig. 2a. The measurement was done for the post-exposure time without the low-frequency tone exposure.

Fig. 3. 'Bounce' phenomenon on the basilar membrane nonlinearity as a function of stimulus parameters: a (left panel)as a function of stimulus levels; b (middle panel)as a function of exposure tone frequencies; and c (right panel) as a function of F2 frequency.

Cheng, J. (1999). "Estimation of active cochlear nonlinearity by multi-component distortion-product otoacoustic emissions," Acustica 85, 721-727.

Hirsh, I. J., and Ward, P. H. (1952). "Recovery of the auditory threshold after strong acoustic stimulation," J. Acoust. Soc. Am. 24, 131-141.

Kemp, D. T. (1986). "Otoacoustic emissions, travelling waves and cochlear mechanism," Hearing Res. 22, 95-104.

Kirk, D. L., Moleirinho, A., and Patuzzi, R. B. (1997). "Microphonic and DPOAE measurements suggest a micromechanical mechanism for the 'bounce' phenomenon following low-frequency tones," Hearing Res. 112, 69-86.

Kirk, D. L., and Patuzzi, R. B. (1997). "Transient changes in cochlear potentials and DPOAEs after low-frequency tones: the 'two minute bounce' revisited," Hearing Res. 112, 49-68.

Pickles, J. O. (1988). An introduction to the physiology of hearing (Academic Press, London, 2nd ed.), pp. 106-109.