Dalhoff et al. 10.1073/pnas.0610185103. |
Fig. 7. Békésy threshold and EDPT for the conventional closed-field pressure measurements (n = 116 I/O functions from 20 subjects). Regression line has a fixed slope of 1.18 dB/dB. The standard deviation from the regression line is 11.2 dB SPL.
SI Text
SI Materials and Methods. Standard Audiometric Tests. After otomicroscopic examination, auditory status was examined ipsilaterally and contralaterally by means of: (i) pure-tone audiometry at 0.125-10 kHz (Audiometer AT 900, Auritec; Medizindiagnostische Systeme, Hamburg, Germany), (ii) tympanometry at 226 Hz and 400 daPa/s (Madsen-Zodiac 901; GN Otometrics, Münster, Germany), (iii) acoustic reflex at 0.5, 1, 2, 4 kHz and 80-100 dB SPL (Madsen-Zodiac 901; GN Otometrics), (iv) transient evoked otoacoustic emission with a 80-dB SPL click (Madsen CAPELLA; GN Otometrics), (v) brainstem-evoked response audiometry with 75- and 80-dB SPL clicks (Evoselect ERA system; Pilot Blankenfelde Medizinisch Elektronische Geräte, Blankenfeld, Germany).
Sound Delivery System for Vibration Experiments.
Experiments were performed in a double-walled sound-attenuating chamber (Industrial Acoustics Company, Niederkrüchten, Germany). The two-tone acoustic stimuli for vibration experiments were delivered free-field by two separate channels using DT 48 earphones (Beyer Dynamic, Heilbronn, Germany) coupled with acoustically dampened plastic tubes to the tip of a modified standard aural speculum, which was fitted into the subject's outer ear canal. For the vibration measurements, the subject lay supine on an examination bed used in otolaryngology, with the neck supported with a pillow. Sound pressure in the ear canal was measured with a probe-tube microphone (ER-7C; Etymotic Research, Elk Grove, IL); its silicon-tube tip was advanced into the ear canal to a distance of, with one exception, 2-4 mm from the eardrum. In the one exception, the distance was 6 mm because the subject had an exceptionally narrow ear canal. The lateral distance between the tip and the focused laser beam was 0.5-3 mm. The microphone and the speculum were mounted on a custom-built holder, coupled with an articulated arm to a plastic headband, strapped on the subject's head. This holder allowed us to fit the speculum in the subject's ear canal and keep it mechanically stable during a measurement. The sound system was calibrated with white noise at the beginning of the experiment and once during the session as a check; calibration was also made after inadvertent movement of the subject.Vibration Measurement System.
The vibration measurement set-up consisted of a custom-built LDV employing a conventional heterodyne interferometer (1), for which all optical and electronic parts were tailored to the problem of measuring picometer-sized vibrations in the presence of large, extraneous movements in the order of 0.1 mm (e.g., heart beat, breathing, or swallowing). Optical frequency shifting was performed by a Bragg-cell. The object light was coupled via a manually steerable dichroic beam splitter into the imaging path of an operational microscope used in otolaryngology (OPMI ORL; Carl Zeiss, Oberkochen, Germany). The light source was a laser diode emitting in the near infrared (l = 810 nm). The object beam (0.43 mW) was focused to a 1/e-diameter of 23 mm in the object plane of the microscope. A CCD camera provided the signal for a small TFT-monitor mounted aside the microscope oculars for visual inspection of the laser focus. The LDV together with the custom-built demodulator achieved a maximum sensitivity of 0.3 pm/ÖHz for acoustic frequencies of >1.5 kHz, when measured on a mirror, the reflectivity of which was reduced to 0.9% by means of a neutral density filter.Data Acquisition.
Stimulus generation and data acquisition were performed with custom software (LabVIEW; National Instruments, Austin, TX), running on an IBM-compatible PC equipped with a 16-bit AD/DA card (PCI 6052E; National Instruments). Simultaneously with the stimulus, both the probe-tube microphone signal and the LDV demodulator signal were low-pass-filtered with an 8-pole Bessel filter using a 20-kHz corner frequency (902LPF; Frequency Devices, Haverhill, MA), sampled by the A/D converter, and analyzed with a 2048-point Fast Fourier Transform, resulting in a 25-Hz frequency resolution (sampling rate, 51,200 Hz; time window length, 40 ms). Acquisition was interrupted by periods of insufficient laser signal strength due to extraneous movements from the subject (e.g., breathing or heart beat). The total acquisition time was no more than an order of magnitude longer than the true averaging time. Raw data were saved for processing off-line.Data Analysis for DPOAE Vibration Experiments and Estimation of SNR.
Analysis was performed off-line with Matlab. The total time record of a DPOAE measurement was split into three equal parts to check for reproducibility. For each of the three parts, time windows with excessive noise in the frequency bands of interest were discarded; this was done iteratively by applying a noise reduction procedure to each of the three parts. The data in each time window were Fourier-transformed, and the sequence of amplitude spectra was ordered according to the maximum noise amplitude in the 100-Hz sidebands around the signal at 2f1-f2. Then, starting with the time window with the lowest sideband noise, we checked whether including the contents of the next time window in the averaging of the time signal enhanced the SNR. If not, the test was repeated by including the subsequent time window. If there was no improvement, these two time windows and the remaining time windows were discarded, and the noise-reduction procedure was terminated. If there was improvement, the two time windows were included in the record for that part and the next time window examined. After completing the noise reduction procedure for each of the three parts, the contents of the new set of time windows were time-averaged for each of the three parts. Then, the Fourier transform of the averaged time signal of each part was calculated, and the three amplitude spectra were rms-averaged. We denote the rms amplitude at 2f1-f2 by S. The unbiased standard deviation of the 2f1-f2 amplitude about S was calculated and denoted by ss. Finally, the noise, N, was calculated as the maximum amplitude in the rms average spectrum in the 100-Hz sidebands around the signal at 2f1-f2. The SNR was then calculated as 20log10(S/N).Acceptance Criteria for the Prediction of Auditory Threshold.
To be included in the data set, the conventional pressure measurements in the closed sound field were required to satisfy the acceptance criteria proposed by Boege and Janssen (2): (i) SNR for the pressure DPOAE >6 dB, (ii) for the regression line of PDP versus L2, r2 ³ 0.8 and slope ³0.2 mPa/dB SPL (see footnote in ref. 3, p. 3283), and (iii) standard deviation of the EDPT <10 dB SPL.* Of the 136 measured pressure I/O functions (Materials and Methods), 116 satisfied these criteria. (A similar proportion was reported in ref. 2.)The acceptance criteria for the vibration measurements were similar to those for the pressure measurements; the difference was as follows. If the SNR was >4 dB (see previous section), then the data were accepted. If the SNR was £4 dB, the data were nonetheless accepted if the average value of S/N and S/ss was >1.58 (i.e., >4 dB). The correlation coefficient criterion applied without changes. The slope criterion was always satisfied: The lowest slope of the corresponding pressure I/O function was 0.34 mPa/dB SPL. The EDPT standard deviation criterion applied unchanged to the v-EDPT. Of the 40 measured vibration I/O functions (Materials and Methods), 30 satisfied these criteria. (A similar proportion was reported in ref. 2 for pressure measurements).
Pure-Tone Threshold Assessment.
The psychoacoustic pure-tone threshold was measured in each subject immediately after obtaining the DPOAE vibration data. The tone signal generator (Function generator R&S AFG; Rhode & Schwarz, München, Germany) was controlled by a HP-IB-parallel-interface in a PC using custom-made software. The pure tones were delivered closed field with a DT 48 earphone (Beyer Dynamic, Heilbronn, Germany) after the signal was passed through an impedance amplitude adaptor (40-dB amplification). We were interested in the pure-tone threshold at the frequency, f2, of the second primary tone used in the DPOAE experiments. The thresholds were measured in a range of 1.7-2 kHz around f2 to guard against outliers. The recording paradigm was based on Békésy automatic audiometry: Beginning below threshold, the subject pressed a button upon hearing the tone and released it when the sensation disappeared. After the button release, the frequency was increased automatically by 100 Hz. The sound pressure was changed continuously in 1-dB steps, with a speed of 5 dB/s for each frequency. The pure-tone threshold at a given frequency was the mean value of the minimum and maximum sound pressures. The standard deviation of threshold estimates was, on average, 4 dB.SI Results and Discussion. Expected magnitude of the vibration DPOAE. It is instructive to compare the magnitudes of the measured umbo vibration DPOAEs to those that might be expected based on DPOAE vibration measured on the basilar membrane (BM) of laboratory animals. This is accomplished in three steps as follows.
First, restricting our comparison to BM recordings in the basal turn, as opposed to recordings near the extreme basal or apical ends of the cochlea, we note that for both chinchilla (figure 2A in ref. 4 and figure 4B in ref. 5) and guinea pig (figure 3H in ref. 6), the DPOAE displacement amplitude at the DPOAE place on the BM is ≈150-200 pm for the low-to-moderate SPLs used here and for f2/f1 = 1.1-1.2.† According to Greenwood's (7) map of frequency to place along the cochlea and anatomical observations (8), our range of 2f1-f2 values corresponds to about the 6-mm central part of the basal turn in the human cochlea. Therefore, because of the similarity of DPOAE displacement amplitudes in the basal turn of chinchilla and guinea pig, we simply assume the same value of DPOAE displacement amplitude for the human BM under similar stimulus conditions.
Second, we need the ratio of DPOAE displacement amplitude at the stapes relative to that on the BM. An estimate can be obtained from the experiments of Ren (9) in the gerbil: For our range of DP frequencies (2.7-6.4 kHz), the DPOAE at the gerbil stapes is attenuated in a frequency-dependent manner by ≈12-26 dB, with the larger value at the higher frequency (figure 2A in ref. 9). Assuming the same attenuation for the human cochlea, a 150-pm DPOAE reduces to a stapes DPOAE displacement of amplitude 38 pm at 2.7 kHz, decreasing to ≈8 pm at 6.4 kHz.
Third, to estimate umbo vibration in response to stapes vibration, we need the transfer gain for middle-ear vibration when driven in reverse from the stapes. To this end, we consider the middle ear to be a two-port system describable by an ABCD matrix relating ear-canal pressure and volume velocity (UEC) to vestibule pressure and stapes volume velocity (UST), as presented in ref. 10. To (very roughly) estimate an upper bound for the velocity ratio, we assume that the middle ear obeys reciprocity and that the output impedance at the umbo is approximately zero for our open sound field and probe-tube configuration. Then, one can readily show that UEC/UST = -M1[1 + (M3/ZC)], where, using the notation in ref. 10, M1 is the forward pressure gain, M3 is the reverse middle-ear impedance, and ZC is the cochlear input impedance. By using values measured for fresh cadaver material, M1 and ZC from Aibara et al. (11) and M3 from Puria (10), we find that UEC/UST ranges from 10.9exp(j32°) at 2.7 kHz to 3.1exp(-j6°) at 6.4 kHz. To convert from volume, U, to point, V, velocities, we divide in the usual manner by the respective effective areas of the eardrum, ATM, and stapes footplate, AST; namely, VEC/VST = (UEC/UST)(AST/cos(qST)ATM), where qST = 55° is the stapes angle (10). By using AST = 3.2 mm2 and ATM = 55 mm2 (12), the magnitude of VEC/VST ranges from 1.1 at 2.7 kHz to 0.3 at 6.4 kHz. These factors yield upper bounds for the umbo displacement amplitudes of 42 pm and 2 pm at 2.7 and 6.4 kHz, respectively, for a DPOAE displacement amplitude of 150 pm at the DPOAE place on the BM.
In conclusion, the range of DPOAE displacement amplitudes (1-8 pm) reported here from vibration measurements of the human umbo is consistent with DPOAE umbo displacement amplitudes (2-42 pm) estimated from DPOAE displacement amplitudes (150 pm) measured at the DPOAE place on the BM of laboratory animals. The agreement is extremely good when one considers some of the assumptions involved: cross-species comparisons, frequency independence of the effective eardrum area, middle-ear transfer functions from cadaver material, no correction for angle between laser axis and umbo normal (35-50°), to mention just a few.
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*The standard deviation of the EDPT was computed as the standard deviation of the ordinate intercept of the regression line for the data with axes interchanged. Although not mentioned explicitly in (2), this was also their method of estimation (P. Boege, personal communication).
†
Compared with the basal turn, the amplitudes are considerably larger near the extreme apical end [chinchilla, 1,000 pm at 2f1-f2 = 500 Hz (6)] and smaller near the extreme basal end [guinea pig (6) and cat (13)], where the amplitudes are < 40 pm for 2f1-f2 = 30-34 kHz and low-to-moderate SPLs.