The study was designed to produce DPOAE level changes when calibration method was unreliable in controlling stimulus level in the ear canal (i.e. when standing-wave minima were present at the emission probe). Unfortunately, DPOAEs are doubly affected by insertion depth. Even if input level is controlled at the eardrum and the response from the cochlea is the same, the measured response in the ear canal will depend on insertion depth because DPOAE level measured with the ER-10C probe some distance from the eardrum depends on the impedance of the volume of air in the ear canal, which acts as an acoustic load for the emitted sound. Increasing the volume by moving the probe to a more shallow insertion decreases ear-canal impedance. Assuming that the volume velocity of the eardrum (due to the DPOAE traveling out of the cochlea) remains constant for an ideally calibrated stimulus, a shallower insertion will cause pressure of the DPOAE to decrease at the emission probe. Consequently, a cochlear response (DPOAE level) measured with a deep probe placement will be larger than a response of the same size measured with a shallow probe placement. This level difference (i.e., incidental change) will occur in conjunction with any changes in emission level caused by calibration errors. Since the study design introduced the additional, incidental change in DPOAE level unrelated to stimulus level, it was important to try to eliminate this variable prior to analysis. Isolating the effects of calibration errors on DPOAE level allows a more accurate comparison among calibration methods. It is acknowledged that predicting the incidental effect of ear-canal impedance on measured emission level is more complicated than addressed in our estimate (described below), which reflects the gross effects on emission level and is more accurate for low frequencies1.
Because ear-canal impedance is similar to the impedance of a tube, the incidental change in DPOAE level can be estimated using the relationship between length and impedance in Eq. 1. When kL is small, cot(kL) ≈ 1/kL . Wavenumber ( k ) is small at low frequencies because k ≈ ω/c (Beranek, 1954 ). Accordingly, low-frequency impedance approximates inverse proportionality to length of the ear canal between the probe and the eardrum: Zc≈−iZ0kL.
Impedance of the ear canal was calculated from 4 to 15996 Hz (in 4-Hz increments) during each in-situ SIL and FPL calibrations. For each subject, four of the calibrations were used to assess changes in probe-insertion depth during data collection: two representing deep probe placement and two representing shallow placement. Each of the four representative load estimates was reduced to a single value by averaging impedance magnitude across 250 to 500 Hz2. This frequency range is both high enough to have a good SNR and low enough to have the expected proportional relationship between impedance and length. The resulting mean impedance values for the two deep-insertion and the two shallow-insertion calibrations were averaged. The incidental change in DPOAE level due to changes in probe-insertion depth was assumed to be equal to the decibel difference in impedance magnitude between the two depths over the selected low-frequency range.
Figure 2 shows low-frequency impedance magnitudes used to estimate the incidental change in DPOAE level for three subjects. The top panel represents a favorable case in which the estimate appeared ideal. Note the consistency in the dB difference (the estimated, incidental change due to changes in volume) for both sets of measurements. The middle panel illustrates a less favorable case in which the two deep-insertion impedance levels are separated, indicating an unintentional change in insertion depth over time within the same probe placement. Furthermore, the dB differences between insertion depths for the lowest frequencies are larger than the dB differences at the highest frequencies, indicating a change in estimated impedance difference between insertions over the frequency range for which the impedance difference was assumed to be constant. The bottom panel shows the worst case from the subject in whom the largest volume change with (supposedly) the same probe placement occurred. Results from this subject were atypical but were not excluded from analysis.