Nonlinear Distortions and Parametric Amplification Generate Otoacoustic Emissions and Increased Hearing Sensitivity
Round 1
Reviewer 1 Report
p. 2 a 1D approach: please correct: an 1D approach (usw.)
p. 2 a 1D approach. My suggestion is: please, discuss shortly the possibilities of a 2D or even 3D approach (connected to the remarks on p. 8)
p. 5 using V for potential, I suggest to mention these and other new variables in Table 1 on p. 4.
p. 8 experimental data: should it be valuable to discuss your results with possible experimental data gathered in similar experiments described in literature? It is just because the results stand or fall with the experimental evidence.
Author Response
Dear reviewer. I attach the corrected text with red marks.
1. All a 1D to an 1D corrected.
2. The extended (marked red) text is: The reduction of dimensionality from 3D to 1D or 2D involves various limitations. One of these is the impossibility to calculate sound wave reflections at rigid walls or walls having limited mechanical impedance values. And even more important is the inability to simulate the 3D field generated by the superposition of propagating sound waves in a complex fluid filled geometry like the cochlea including the coupling to the elastic BM. An alternative hypothesis of a 2D approach relies on the same assumption of an 1D model concerning the structure (BM), namely representing the orthotropic elastic shell (BM) as an 1D embedded elastic beam. Therefore boundary layers and interactions of 3D sound fields cannot be calculated properly as well.
3. New Table 3 with mainly electric parameters inserted.
4. It is mainly difficult the find experimental validation for processes in the cochlea because nearly all measurements where conducted at single points whereas the numerical results enables data along the cochlea.
Nevertheless another Reference Rhode & Robles (1974) is included and discussed .
The advanced text on p. 8 discussion experimental results is marked red.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper establishes the acoustic model taking account of the stiffness of outer hair cells and parametric amplification of the input signal. The model is solved by the finite difference method and verified by several simulations. It is well written in general. I don’t find may detail to complain about. There are some points (mainly minor) that I think the authors should address better.
1. The nonlinear term kcubu3 considered as increasing displacement amplitudes is added in Eq.(2). It is better to explain the reason for using this nonlinear term.
2. All the simulations are designed for a single sinusoidal signal with a frequency of 2KHz; to verify the generalization of model, simulations for other frequencies also should be provided.
3. Can this model suit for a multi-frequencies or time-dependent frequency input signals?
Author Response
Dear reviewer. I attach the corrected text with red marks.
1. The advanced text includes the reason for the inclusion of the nonlinear term as:
With the so far mentioned physical portions, an unlimited increase of displacements would result with increasing input signal amplitude. A displacement limiting cubic nonlinear term (kcubu3) considering the stiffening of a string with increasing displacement amplitude is added. The cubic term assures the increasing restoring force for positive and negative displacements of the string representing the BM. Therefore the transversal displacements cannot grow beyond all limits as in the unphysiological linear case.
2. The use of different input frequencies is extremely desirable but very difficult, because the frequency-place transformation is limited in its reliability because of the 1D approach. In other words it is difficult to fit a realistic frequency to place map with the 1D approach. All parameters are fitted to adapt the 2 kHz case, which leads to a maximum displacement in the middle of the basilar membrane, which is the active case here and measured on human temporal bones by Bekesy initially. An additional Reference Rhode & Robles (1974) with experimental results from the squirrel monkey cochlea is included and a further discussion concerning the parametric amplification added.
3. Yes the model suits for multi-frequency signals, because of the time-domain formulation of the partial differential equation arbitrary time signals including multi-frequencies and time-dependent frequency input signals can be used.
(included im Methods p. 3 line 101 - 104, sorry this is not red marked but included)
Author Response File: Author Response.pdf
