Biophysics and OAEs



 

One source for distortion productotoacoustic emissions generated by low- and high-level primaries.

 

Paper Summarised from:

Lukashkin et al. (2002),J. Acoust. Soc. Am. 111, 2740-2748.

 

Andrei N. Lukashkin, Victoria A. Lukashkina and Ian J. Russell,

School of Biological Sciences, University of Sussex, Falmer,Brighton, BN1 9QG, UK.

 

e-mail :A.Lukashkin@sussex.ac.uk



1.    Introduction

 

The vulnerabilityof the distortion product otoacoustic emission (DPOAE) to various cochleartraumas is level dependent. In rodents, DPOAEs elicited by low-level tones (thelevels of primaries, L1and L2, are below 60-70 dBSPL) are significantly more sensitive to hypoxia, reduction of the endocochlearpotential and post-mortem conditions1-5. The level dependence of theDPOAE vulnerability led to speculation that the sources of DPOAEs generated byprimaries below 60-70 dB SPL were different from those generated for levelsabove 60-70 dB6. It was proposed that the vulnerable, low-levelDPOAEs were associated with the active cochlear process, whereas the relativelyrobust high-level DPOAE component was attributable to passive, non-linearmacromechanical properties of the cochlear partition.

 

However, differencesin the vulnerability of the low- and high-level DPOAEs may be a naturalconsequence of the way the cochlear operates at low and high sound pressurelevels. Basilar membrane (BM) vibrations are boosted by an active process whosecontribution to the BM mechanical response, in absolute terms, increases withincreasing SPL until saturation of the outer hair cell (OHC) transducerconductance7. However its relative contribution is greatest at lowSPLs.  At high SPLs, responses of the BMare dominated by the passive mechanical properties of the cochlea.Consequently, any reduction in the magnitude of the active cochlear feedbackwill have greatest effect on BM vibrations and DPOAE characteristics at lowSPLs.

 

2.    Theoretical consideration

 

In a model thathas been published previously8 we took as a first approximation, thebasolateral membrane potential, which drives the OHC motility9 to beconsidered proportional to the total charge flow through the mechanoelectricaltransducer channels. Hence, the non-linearity of the mechanoelectricaltransducer can be assumed to be the main contributor to the cell’s non-linearvoltage responses7,10 and is the dominant DPOAE producingnon-linearity. The two-exponentialBoltzmann function N(x)11 (Fig. 1) is usedin this paper to model the OHC mechanoelectrical transducer.

 

The simplest way tomimic the presence of the cochlear active process is to introduce a positivefeedback as shown in Fig. 1. At this stage we consider feedback as aformal description of the cochlear amplification without specifying particularmechanisms. Figure 1 gives examples of the resultant DPOAE producingnon-linearity, N’(x), for a few values of the relativegain, Kr.

 

 

Figure 1. Non-linearity, N’(x), of the mechano-electricaltransducer with a positive feedback. The non-linearity was normalised formaximum transducer conductance and modified by moving its operating point intothe point of inflection of the function. N(x) is the OHC transducer function measuredby Géléoc et al.12. H is the feedback gain constant. Relative gain,Kr, for each curve is indicated in decibels re gain without feedback(Kr=0 dB). Note that each curve has the same asymptote for large hairbundle displacements x.

 

When two sinusoidalsignals (with frequencies f1and f2 and amplitudes L1 and L2 respectively) used as an input to the non-linearity N’(x)then distortion component at frequency 2f1-f2 can be calculated at theoutput of N’(x) (Fig. 2). The amplitude of the 2f1-f2component depends strongly on Kr,i.e. on the efficiency of the feedback, when the amplitudes of the primaries atthe input of the non-linearity N’(x) are small. However, there is nosizeable alteration of the DP amplitudes calculated for different Kr for the highest amplitudesof the primaries, when the output of the non-linearity saturates strongly.

 

 

Figure 2. Calculated amplitude growthfunctions for 2f1-f2 components at the output of thenon-linearity N’(x) for different efficiency of the feedback. Relative gain, Kr,for each curve is indicated in decibels re gain without feedback (Kr=0dB). 2f1-f2 amplitudes are calculated for equally growingamplitudes of the primaries L1=L2. The labels indicatethe phase angle for each part of the curve limited by the notch. Amplitudes, L1and L2, of both primaries are given in decibels re 0.01nm. Theamplitude of the 2f1-f2 component is expressed indecibels re maximal transducer conductance.

 

Theoreticalanalysis also reveals a distinguishing feature of the 2f1-f2growth functions generated by a single, saturating, non-linearity with built-inamplification. That is an upward shift of the notch with corresponding phasechange when the system amplification becomes less efficient (Fig. 2). Ashift in the opposite direction would be expected if the notch were dueto phase cancellation between the vulnerable “active” emission prevailing atlow levels of the primaries, and the robust “passive” emission dominating atthe high primary levels. Indeed, if a cochlea insult affects the activecochlear process and decreases the amplitude of the “active” emission, then the“passive” emission would dominate at even lower levels of the primaries. Hencedirection of the notch transition during reduction of the active cochlear processcan be a reliable criteria to distinguish between “single source” and “two sources”hypotheses.

 

3.    Methods

 

DPOAE was recorded from pigmented guinea pigs. Sound wasdelivered to the tympanic membrane by a closed acoustic system comprising two microphonesfor delivering tones and a single microphone for measuring acoustical responses.Amplitudes and phase angles of the DPOAEs were obtained by performing an FFT ona time-domain averaged signal 4096 points in length sampled at 200 kHz. Furosemide(100 mg/kg b. w.) was injected intraperitoneally. All procedures involvinganimals were performed in accordance with UK Home Office regulations.

 

4.   Results

 

The main ototoxic action of furosemide is based on its abilityto suppress the endocochlear potential13 and the OHC motility14.Both effects result in a decrease in the efficiency of the cochlearamplification.

 

Similar results were obtained from 8 guinea pigs for f2 of 8, 12, 20 kHz and f2/f1 ratio of 1.21-1.25. Injection of furosemide leads toa shift to higher levels of the DPOAE amplitude notch and a corresponding phasetransition in the growth functions of the 2f1-f2 and f2-f1components (Fig. 3) as predicted by the “single source” hypothesis.

 

 

Figure 3. Dependence of the DPOAE amplitude (left) and phase angle (right)on the levels L1 and L2 of the primaries recorded from aguinea pig before and after injection of furosemide (100 mg/kg b. w.). Thethickest curves show response before the injection (0 minutes). Time after theinjection is indicated inside the left panel. f2 is fixed at 8kHz.  f2/f1 ratiois1.24. L2 is 10 dB SPL below L1. Double arrows betweentwo dotted vertical lines show maximal upward shift DL of the notch position.

 

Changes in the 2f1-f2 amplitude and phase angledepend on the level of the primaries (Fig. 3). The amplitude and phaseangle of 2f1-f2 was stable during thewhole experiment (up to 2 hours after furosemide injection) for the highestlevels of primaries used (L1=75dB SPL). For low-level primaries (L1=35dB SPL, Fig. 7, top left) the 2f1-f2 amplitude dropped belowthe noise floor of about –20 dB SPL and eventually partially recovered.

 

5.   Conclusions

Behaviour of theDPOAE after the cochlear active process is compromised by furosemide injectionprovide evidence in favour of one source of the DPOAE generated by low- andhigh-level primaries up to at least 75 dB SPL.

 

The unambiguous concept of a saturating non-linearity withassociated amplification, together with data that supports the importance ofOHC motility for generating high-level DPOAEs5, has significantbasic and diagnostic implications. We can deduce that the non-linear cochlearamplifier, which depends on OHC activity, is the main source of DPOAEs recordedfor levels of primaries below about 75 dB SPL. We can also conclude that anypathology leading to the generation of “passive-like” DPOAEs is not due to dysfunction of the OHC mechanoelectricaltransducer. Emissions of this kind appear because cochlear amplification isimpaired due to, for example, a reduction in the endocochlear potential13or to feedback desynchronisation15.

 

This work wassupported by the Wellcome Trust.

 

References

 

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12.  Géléoc, GSG et al. (1997). “Aquantitative comparison of mechanoelectrical transduction in vestibular andauditory hair cells of neonatal mice,” Proc. R. Soc. London, Ser. B 264,611-621.

 

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