## October - January 2014: Also 2nd- and 3rd-order intervals of spontaneous otoacoustic emissions confirm theory of local tuned oscillators

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- Category: Guest editorial
- Last Updated on Wednesday, 16 October 2013 14:27
- Written by Martin Braun, PhD : Neuroscience of Music, S-66492 Värmskog, Sweden
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### Introduction

Understanding the origin of spontaneous otoacoustic emissions (SOAEs) in mammals has been a challenge for more than three decades. Right from the beginning two mutually exclusive concepts were explored. After 30 years this has now resulted in two well established but incompatible theories, the global standing-wave theory and the local oscillator theory. The outcome of this controversy will be important for our understanding of inner ear functions, because local tuned oscillators in the cochlea would indicate the possibility of frequency analysis via local resonance also in mammals. In a recent investigation of this controversy, Braun (2013) gained new information from cases of high-multiple SOAEs in human ears. These cases, with 12 to 32 SOAEs per ear, presented large numbers of adjacent small frequency intervals. It was found that the distribution of frequency intervals of SOAEs shows no above-chance probability of multiples of the preferred minimum distance (PMD) between SOAEs. This result, together with several simulations of random-generated SOAE spacing, and a comparison of high-multiple with low- and medium-multiple SOAEs, indicated that the typical frequency spacing of human SOAEs may be due to a stochastic distribution of emitters along the cochlea plus a graded probability of mutual close-range suppression between adjacent emitters. After publication of the results, an argument was put forward that multiples of PMD in SOAE spacing might have been disguised by overlapping distribution peaks of higher-order intervals. Here, also the distribution of 2nd- and 3rd-order intervals from the same group of 18 ears with ≥ 15 SOAE per ear was analyzed. It was found that the distribution peaks were located far off from PMD multiples and that at the points of PMD multiples on the x-axis nothing of interest appeared. In conclusion, also 2nd- and 3rd-order spacing of SOAEs is consistent with the local oscillator theory of SOAE generation, and thus with intrinsic tuning of cochlear outer hair cells.

1. **Background**

The **global standing-wave theory** (GST) and the **local oscillator theory** (LOT) of SOAE generation have been extensively described and discussed (recently in: Wit and van Dijk 2012). Here the two concepts are only outlined very briefly. The GST, based on concepts of Kemp (1979), Zweig and Shera (1995), and Shera (2003), proposes coherent reflections of basilar membrane (BM) traveling waves between the stapes and points of slight functional irregularities along the cochlear duct, in analogy with the coherent wave reflections in the optical cavity of a laser. Part of the energy of the BM standing wave vibrates the stapes, and via backward middle ear transmission sound is emitted into the ear canal. The standing wave is sustained by energy input from elements of the cochlear amplifier, in particular the outer hair cells (OHC). The LOT, based on concepts of Johannesma (1980), Bialek and Wit (1984), and van Hengel et al. (1996), proposes that the same elements of the cochlear amplifier behave as local oscillators without being coupled to a standing wave. They transmit part of their vibrational energy directly through cochlea and middle ear to the ear canal.

Of the many qualities of SOAEs that the two theories have to account for, perhaps the most complex and demanding one is the observed spacing order of multiple SOAEs in one ear. Schloth (1983) and Dallmayr (1985; 1986) reported a preferred minimum distance (PMD) between spectrally neighboring SOAEs, which appears as outstanding mode in interval histograms. Later studies replicated this result, and Braun (1997) determined on the basis of a pool of 5245 intervals of human SOAEs that the mean PMD amounts to almost exactly 1 semitone (ST) = 1/12 of an octave (recently reviewed in: Wit and van Dijk, 2012).

According to the GST, “the characteristic SOAE spacing can be traced to the value of the wavelength of the traveling wave” (Shera 2003, p. 259). In other words, the GST assumes a general standing wave system that self-stabilizes as the best fit to multiple sites of irregularities. By doing so, it amplifies multiple frequencies simultaneously, leading to multiple SOAEs with a characteristic, wavelength dependent, frequency spacing.

Concerning the LOT, van Hengel et al. (1996) used a mathematical cochlear model to test the effect of frequency distance on mutual interaction of SOAEs. They concluded that “the resulting suppression profile leads to natural minimal distances of effective emissions, without any necessity of additional assumptions about the mechanics of the cochlea” (p. 3570).

Thus, for the LOT the PMD is a short-range effect of mutual interaction of oscillators, whereas for the GST it is a long-range effect of the wavelength of the BM traveling wave. This conflict has the advantage that it can be resolved by experimental data. The simple empirical question was, can the predicted short-range and/or long-range effects be observed in measured SOAE data?

High-multiple SOAEs (>10) in each ear of normal hearing human subjects are occasionally found in large screenings. Indications that SOAE mechanisms might vary according to emission numbers per ear had not been found, and there were no known reasons to expect such a variation. Therefore high-multiple SOAEs could reasonably be regarded as representative for all human SOAEs. Because of their large number of adjacent small SOAE intervals, ears with high-multiple SOAEs provided a unique and previously unexploited opportunity to examine the question of SOAE spacing order, and thus also the question of SOAE generation.

The results of the new investigations (Braun, 2013) led to the following conclusions. The distribution of frequency intervals of human SOAEs shows no above-chance probability of multiples of the PMD. The size of PMD is related to SOAE density. The variation in size between adjacent small intervals is not significantly different in random-generated than in measured data. Each of these three results appeared to be in conflict with the predictions of the **global standing-wave** theory (GST) but in agreement with the l**ocal oscillator theory** (LOT) of SOAE generation. After publication of the results an argument was put forward that multiples of PMD might have been disguised by overlapping distribution peaks of higher-order intervals. Therefore, also the distribution of 2nd- and 3rd-order intervals from the same group of 18 ears with ≥15 SOAE per ear was analyzed.

2. Results

** Fig.1** corresponds to **Fig.3B** of Braun (2013). Added are the distributions of 2nd- and 3rd-order intervals. 2nd-order intervals are intervals between an SOAE frequency and the frequency of its second next neighbor. 3rd-order intervals are intervals between an SOAE frequency and the frequency of its third next neighbor.

The distribution of 2nd-order intervals shows a plateau-like peak between 170 and 270 Cent. The distribution of 3rd-order intervals shows a flat peak between 330 and 350 Cent. Most importantly, both added distributions again show no relation to multiples of PMD, such as 200, 300, 400, and 500 Cent.

The right-shift of the new peaks relative to the expected locations at 200 and 300 Cent was examined further. It seemed reasonable to expect such right-shifts, in case there was a size correlation of neighboring intervals. For example, if an interval of 115 Cent has a neighbor also of 115 Cent, the 2nd-order interval is 230 Cent. In order to test this hypothesis, from the 18 ears two groups intervals were considered, >110 Cent and <90 Cent. Next, all intervals neighboring the grouped ones were extracted, separately for low-frequency and for high-frequency neighbors.

**Figure 1**

**Fig.2** shows the distribution of the four groups of neighboring intervals. The groups of intervals >110 Cent have an outstanding chance to have a neighbor of ca 110 Cent, and the groups of intervals <90 Cent have an outstanding chance to have a neighbor of ca 90 Cent. The distributions of the four subgroups in Fig.2 were compared with the respective off-group distributions for the bins 50 to 180 Cent, and the differences were tested on significance by the paired t-test. For each of the two <90 Cent groups, the difference was significant on the 0.001 level. For >110 Cent, the low-side group showed a significant difference on the 0.05 level, whereas the high-side group did not reach significance. Overall, the size correlation of neighboring interval has turned out to be highly significant, and thus the right-shift of the peaks in the 2nd-and 3rd-order interval distributions (**Fig.1**) has found a plausible explanation.

The rationale for the assumption of size correlation of intervals was based the mechanism of close-range suppression of a weak emitter by a stronger one, which is a necessary component of the LOT. If a strong emitter only permits neighboring emitters in a distance of >110 Cent, it is likely that this effect occurs both on the low- and the high-frequency side. This leads to a tendency of interval correlation, as seen in** Fig.2**. A corresponding effect can be expected for a weaker suppressor that permits neighbors in a distance of < 90 Cent.

**Figure 2**

The LOT also predicts a frequency dependence of interval size. **Fig.4** of Braun (2006) shows that SOAE level in humans has a clear trend of a monotonous decrease from 1000 to 4000 Hz. Over this distance of two octaves the mean SOAE level decreased from ca –3 to ca –13 dB SPL. In other words, high-frequency SOAEs tend to have lower levels and thus less strength to suppress neighbors. This prediction could be tested by comparing the mean frequencies of the two groups described above. For each interval the mean of its two frequencies was calculated. Then the grand mean per group was determined. For the group of intervals >110 Cent the grand mean was 1992 Hz. For the group of intervals <90 Cent the grand mean was 2659 Hz. According to the data in **Fig.4** of Braun (2006) the lower frequency corresponds to a mean level of ca –7.5 dB SPL, and the higher one to a mean level of ca –10 dB SPL. Thus, interval size is correlated with emission strength, and the prediction of the LOT has been confirmed.

References

Bialek W,Wit HP (1984) Quantum limits to oscillator stability: theory and experiments on acoustic emissions from the human ear. Phys Lett 104A:173-178.

Braun M (1997) Frequency spacing of multiple spontaneous otoacoustic emissions shows relation to critical bands: A large-scale cumulative study. Hear Res 114:197-203.

Braun M (2006) A retrospective study of the spectral probability of spontaneous otoacoustic emissions: Rise of octave shifted second mode after infancy. Hear Res 215:39-46.

Braun M (2013) High-multiple spontaneous otoacoustic emissions confirm theory of local tuned oscillators. SpringerPlus 2:135. http://www.springerplus.com/content/2/1/135

Dallmayr C (1985) Spontane oto-akustische Emissionen: Statistik und Reaktion auf akustische Störtöne. Acustica 59:67-75.

Dallmayr C (1986) Stationäre und dynamische Eigenschaften spontaner und simultan evozierter oto-akustischer Emissionen. Dissertation, Technische Universität München.

Johannesma PIM (1980) Narrow band filters and active resonators. Comments on papers by DT Kemp and RA Chum, and HP Wit and RJ Ritsma. In: van den Brink G, Bilsen FA (eds) Psychophysical, Physiological, and Behavioural Studies in Hearing. Delft University Press, Delft, pp 62-63.

Kemp DT (1979) The evoked cochlear mechanical response and the auditory microstructure - Evidence for a new element in cochlear mechanics. Scand Audiol Suppl 9:35-47.

Schloth E (1983) Relation between spectral composition of spontaneous otoacoustic emissions and fine-structure of threshold in quiet. Acustica 53:250-256.

Shera CA (2003) Mammalian spontaneous otoacoustic emissions are amplitude-stabilized cochlear standing waves. J Acoust Soc Am 114:244-262.

van Hengel PWJ, Duifhuis H, van den Raadt MPMG (1996) Spatial periodicity in the cochlea: The result of interaction of spontaneous emissions? J Acoust Soc Am 99:3566-3571.

Wit HP, van Dijk P (2012) Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators? J Acoust Soc Am 132:918-926.

Zweig G, Shera CA (1995) The origin of periodicity in the spectrum of evoked otoacoustic emissions. J Acoust Soc Am 98:2018-2047.

### About the Author

As a neurobiologist and a composer,
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is specialized on investigating music related auditory physiology. Since 1993 he has published original research on inner ear function, otoacoustic emissions, pitch processing in the auditory midbrain, neurophysiology of acoustical sensory consonance, precognitive absolute pitch, and the physiology of octave circularity of pitch. From 2000 he works for the independent research organization Neuroscience of Music near Karlstad in Sweden.