Intensimetric detection of distortion product otoacoustic emissions with ear canal calibration

Otoacoustic emissions¹ (OAEs) are acoustic signals measurable in the ear canal, generated by the cochlear active nonlinear amplification mechanism, potentially suitable for accurate objective diagnostics of cochlear function. One of the main uncertainties still limiting the OAE diagnostic power is related to the formation of standing waves in the closed ear canal cavity. OAEs are typically measured inserting a probe into the ear canal. The probe, housing miniaturized loudspeakers and microphones, acoustically seals the ear canal cavity, terminated at the opposite end by the eardrum. Longitudinal resonant modes develop in this approximately cylindrical cavity, with frequencies critically dependent on the individual ear canal length and on the probe insertion depth. As a consequence, (1) the stimulus pressure measured at the probe position is significantly different from that fed to the eardrum, and (2) the OAE pressure measured at the probe position is different from that emitted by the eardrum. The largest differences occur near the resonance frequencies of the cavity, which depend on the probe insertion depth. Both problems, which enhance the intrinsic variability of OAE level estimates, decreasing the OAE diagnostic power, have been recently addressed by Charaziak and Shera,² who used Thévenin calibration of the sound sources both to correct the stimulus calibration and to convert the measured OAE level to that actually emitted by the eardrum.

In this study, we perform the same task in a model-independent way, using a pressure-velocity detector and suitable intensimetric physical quantities.³ Although acoustic waves consist of pressure and velocity oscillating fields, p and v, which propagate at the speed of sound, only their pressure component is typically measured in clinical applications. Recently, miniaturized intensimetric probes have become available, which simultaneously measure at the same place both the pressure and the velocity field.³ Measuring also the velocity component of the acoustic wave field does not provide redundant information; on the contrary, simultaneous pressure and velocity measurements allow one to estimate the acoustic impedances of the system constituted by the probe and the acoustic environment.³ A few studies have already used p-v measurements in the ear canal to estimate pressure at the eardrum,^4,5 mainly for headphone equalization purposes. More directly, suitable combinations of intensimetric quantities may be used to solve in a model-independent fashion the problem of obtaining calibrated OAE measurements independent of the probe insertion depth, and, more generally, of the resonant properties of the individual ear canal.

The active intensity³ of the acoustic wave field is defined, in the frequency domain, as

with ω = 2πf. It can be measured at any point inside the ear canal (e.g., at the probe position) and measures the net flow of the acoustic energy across the measurement region. Although velocity is a vector quantity, we consider here its longitudinal component only. It can be demonstrated that this quantity, measured at the stimulus frequencies f₁ and f₂, also represents the distortion product otoacoustic emission (DPOAE) stimulus intensity I_S transmitted to the middle ear. Therefore, equalizing the active intensity of the stimuli across frequencies means equalizing the acoustic intensity transmitted to the middle ear, almost equivalently to equalizing the forward pressure.⁶ 

The power density of the acoustic wave field is defined instead as

where ρ is the air density and c the speed of sound.

It may be easily demonstrated, using the acoustic potential formalism,³ that the DPOAE intensity emitted by the eardrum may be evaluated at the DP frequency, to a good approximation, as the arithmetic mean of the active intensity and the power density, measured anywhere inside the ear canal (e.g., at the probe position):

which may also be defined as the DPOAE emitted intensity. More accurate expressions of the intensity emitted by the eardrum may be computed, keeping into account multiple internal reflections in the closed ear canal cavity:

where k is the wave number, L is the length of the closed ear canal cavity, R₁, R₂ are the reflection coefficients at the eardrum and at the probe, and the last term is negligible in most ears. The length L can be estimated from the resonant pattern of the ear canal response to the stimuli. The values of R₁ and R₂ may be computed, in principle, from the same intensimetric measurements, which have been proposed indeed for measuring the impedance/reflectivity of the middle ear,³ but, for the present OAE application, the estimate of R₂ is affected by a large uncertainty, because it needs a signal coming from the eardrum. One may use the DPOAE signal itself, but its signal-to-noise-ratio (SNR) is obviously much lower than that of stimuli. Therefore, in the analysis of experimental data, the simpler approximation of Eq. (3) will be used.

A Microflown p-v detector PU-Match Probe (Microflown Technologies, Arnhem, the Netherlands) and a couple of Etymotic ER-2 loudspeakers (Etymotic Research, Inc., Elk Grove Village, IL), were housed in a teflon cylindrical cavity, terminated by a copper tube of 8 mm diameter, which was inserted a few mm into the ear canal of the subject. Deeper insertion depths could be obtained with a different kind of cavity, but the system was not optimized in this sense, also because one of the advantages of the proposed method is its insensitivity to the insertion depth. Two slow linear chirp stimuli were separately fed to the two loudspeakers (to avoid internal generation of distortion), with instantaneous frequencies in a constant ratio r = f₂(t)/f₁(t) = 1.22, which generated a DPOAE response chirp at frequency f_DP(t) = 2f₁(t)–f₂(t). The chirp sweep rates were suitably set in order to get df_DP/dt = 800 Hz/s. Complex spectra of the two stimuli and of the DPOAE response were separately obtained for the pressure and velocity detectors by applying Fourier analysis to 50% overlapping time frames of duration 50 ms, yielding a frequency resolution of 20 Hz. In the measurement frequency range, the cochlear round-trip delay was much shorter than the time frame duration, so the instantaneous DPOAE frequency coincided with f_DP(t) within a Fourier Transform frequency bin. From the pressure and velocity spectra, active intensity and power density were computed in the frequency domain.

The two stimulus levels transmitted to the middle ear were equalized across frequency by equalizing their active intensity spectra, i.e., the voltage chirps fed to the loudspeakers were multiplied by suitable envelope functions to get equalized spectra transmitted through the middle ear. Equation (3) was used to convert the intensimetric quantities measured at the probe position to the DPOAE power emitted by the eardrum.

An Etymotic ER-10X probe, consisting of two loudspeakers and a low-noise microphone, was used for the conventional OAE measurements, in which only the pressure of the acoustic wave field is measured, both for the stimuli and for the DPOAE response. In this case, the equalization of the stimulus transmitted to the middle ear was accomplished by equalizing the forward component of the pressure wave, according to a well-established procedure.⁶ This procedure requires preliminary Thévenin calibration of the sound source in a set of tubes of different length and known impedance, which allows one to compute the forward component of the pressure by evaluating the load impedance and the reflection coefficients in the same conditions of the OAE measurements (probe inserted in the ear canal). The same signal generation and acquisition technique of the intensimetric measurements was used, but, in this case, forward pressure was equalized across frequencies for the two stimulus chirps, whereas the DPOAE spectrum emitted by the eardrum was obtained from that measured by the probe microphone at the ear canal entrance by applying the emitted pressure level (EPL) correction proposed by Charaziak and Shera.² 

Once expressed in dB units, the two OAE quantities yielded by the two experiments, I_E and EPL,² may be directly compared, if equivalent reference quantities are used for the conversion to dB units (p₀ = 20μPa for EPL and p₀²/ρc for I_E). The two measurements performed on the same ear are shown in Fig. 1. Unfortunately, the noise floor of our intensimetric setup is quite high, due to the noise level of its velocity and pressure sensors, and to its size, which makes it difficult to insert it into the ear canal with the same depth and acoustical insulation of a state-of-the-art OAE probe. Despite the much lower SNR, the intensimetric technique yields a DPOAE spectrum that is in rather good agreement with that obtained with the conventional technique, reproducing also some of the characteristic oscillating features known as the DPOAE fine-structure, although additional spectral fluctuations appear, due to the high noise floor.

It is well-known⁷ that the DPOAE spectral fine-structure is due to interference between two components with different phase-frequency relation, a (typically dominant) nonlinear distortion component, generated by a wave-fixed mechanism, with almost constant phase (as a consequence of the cochlear scaling symmetry), and a reflection component, generated by a place-fixed mechanism, with rapidly rotating phase. Time-frequency filtering⁸ allows one to separate the two DPOAE components in the time-frequency domain. Even if intensimetric quantities neglect the phase information, DPOAE amplitude spectra possess the information necessary to separate the components in the time or (better) in the time-frequency domain, because phase and amplitude fluctuations are intrinsically related to each other in causal systems. Figure 2 compares the time-frequency representations of the two spectra of Fig. 1, showing a strong zero-delay component, associated with the DPOAE nonlinear distortion component, and a fainter long-delay component, associated with coherent reflection.⁷ Even the time-frequency position of the most intense spots of the faint delayed components approximately correspond, although in the intensimetric case (right) their intensity is close to the noise floor. Because of the lack of phase information, in the intensimetric case the distribution is specular symmetric with respect to the frequency axis. The higher background luminosity is again a consequence of the higher noise level of the intensimetric probe.

The overall agreement is rather satisfactory, considering that the two methods differ as regards (1) the type of probe detector, (2) the physical quantities used to calibrate the stimuli, (3) those used to extract the DPOAE signal emitted by the eardrum, and (4) the probe insertion depth in the ear canal. Moreover, the higher order correction factors of Eq. (4) have been neglected in this analysis.

A severe limitation of the intensimetric setup of this study is clearly related to the relatively low SNR of both pressure (particularly if compared with a state-of-the-art low-noise OAE microphone, such as that used in this study) and velocity measurements performed with currently available intensimetric commercial probes, which are typically used in industrial contexts, and are therefore not optimized yet for the faint OAE signal levels. The encouraging results of this study should motivate further technological development of low-noise miniaturized intensimetric probes. Lower-noise probes would be indeed necessary for effectively using the proposed method in OAE clinical applications, which, in hearing-impaired subjects, require detection of very weak signals. The proposed technique has been tested first on DPOAEs, because of their simple acquisition technique and high SNR, but it can be straightforwardly applied to SFOAE and transient-evoked OAE (TEOAE) acquisition. In the SFOAE acquisition using the suppressor technique, the two input signals to be calibrated at the eardrum would be the probe and suppressor active intensity, whereas the residual emitted intensity would represent the SFOAE response. In the TEOAE case, equalization of the stimulus active intensity could be performed in the frequency domain as for SFOAEs and DPOAEs, and the actual calibrated transient stimulus (click, tone burst, or fast chirp) voltage to be fed to the loudspeaker would be obtained by FT. The TEOAE response would be recorded as two separate p(t) and v(t) signals, from which the TEOAE intensity emitted by the eardrum would be computed in the frequency domain.

Intensimetric techniques are used for the first time to measure high-resolution DPOAE spectra, with model-independent calibration of the transmitted power to the middle ear and reconstruction of the DPOAE power emitted by the eardrum. Despite the high noise floor of the intensimetric method, the good agreement with the results obtained with state-of-the-art conventional techniques, involving pressure measurements only, and elaborate Thévenin calibration methods, suggests that the proposed methodology could be fruitfully applied to the objective diagnostics of the cochlear function, once lower-noise and smaller-size intensimetric probes become available.