Characterizing the ear canal acoustic impedance and reflectance by pole-zero fitting

On causality and aural impulse responses synthesized using the inverse discrete Fourier transform

Causality is a fundamental property of physical systems and dictates that a time impulse response characterizing any causal system must be one-sided. However, when synthesized using the inverse discrete Fourier transform (IDFT) of a corresponding band-limited numerical frequency transfer function, several papers have reported two-sided IDFT impulse responses of ear-canal reflectance and ear-probe source parameters. Judging from the literature on ear-canal reflectance, the significance and source of these seemingly non-physical negative-time components appear largely unclear. This paper summarizes and clarifies different sources of negative-time components through ideal and practical examples and illustrates the implications of constraining aural IDFT impulse responses to be one-sided. Two-sided IDFT impulse responses, derived from frequency-domain measurements of physical systems, normally occur due to the two-sided properties of the discrete Fourier transform. Still, reflectance IDFT impulse responses may serve a number of practical and diagnostic purposes.

Reproducing ear-canal reflectance using two measurement techniques in adult ears

Clinical diagnostic applications of ear-canal reflectance have been researched extensively in the literature, however, the measurement uncertainty associated with the conventional measurement technique using an insert ear probe is unknown in human ear canals. Ear-canal reflectance measured using an ear probe is affected by multiple sources of error, including incorrect estimates of the ear-canal cross-sectional area and oblique ear-probe insertions. In this paper, ear-canal reflectance measurements are reproduced in an occluded-ear simulator and in 54 adult ear canals using two different measurement techniques: a conventional ear probe and a two-microphone probe that enables the separation of reverse- and forward-propagating plane waves. The two-microphone probe is inserted directly into test subjects' ear canals, and the two-microphone method is distinguished by not requiring the ear-canal cross-sectional area to calculate the ear-canal reflectance. The results show a reasonable agreement between the two measurement techniques. The paper further examines the influence of oblique ear-probe insertions and the compensation for such oblique insertions, which results in an improved agreement between the two measurement techniques.

Real ear measurement (REM) and auditory performances with open, tulip and double closed dome in patients using hearing aids

OBJECTIVE

The aim of the study is to evaluate the importance of acoustic modifications generated by different commercially available ear-tips, focused on domes of receiver in the canal hearing aids using Real Ear Measurement (REM).

METHODS

We enrolled 110 people selecting 200 ears bearers of hearing aids. In every patient, we performed REM and audiological tests with three different dome types: Open, Tulip and Double Closed (DC). Data about real-ear occluded gain (REOG), Pure Tone Average (PTA), Word Recognition Score (WRS) with aids switched on in Free Field, Ear and Auditory Comfort were collected and analyzed.

RESULTS

REOG gain was statistically significant different between the three types of dome, with a DC that always closes the external auditory canal (EAC) (p < 0.001). There was no statistically significant difference between the PTA (p = 0.11). Regarding the WRS there were statistically significant differences between Open and DC dome (p < 0.001) and between Tulip and DC dome (p < 0.001), with worse discrimination when using DC. Both auditory and ear comfort are worse in the DC than in the other two domes (p < 0.001). From measured REOG gain values, in 135 cases Tulip dome does not occlude the EAC, with a statistically significant difference compared to DC (p < 0.001; Odd Ratio 0.0012; 95% CI 0.001-0.0196).

CONCLUSION

Our study confirms the necessity to perform REM to evaluate if the prescription target is achieved, especially when tulip domes are used, because they may not occlude the ear canal, causing in some cases the reduction of the vocal discrimination.

Causality-constrained measurements of aural acoustic reflectance and reflection functions

Causality-constrained procedures are described to measure acoustic pressure reflectance and reflection function (RF) in the ear canal or unknown waveguide, in which reflectance is the Fourier transform of the RF. Reflectance calibration is reformulated to generate causal outputs, with results described for a calibration based on a reflectance waveguide equation to calculate incident pressure and source reflectance in the frequency domain or source RF in the time domain. The viscothermal model RF of each tube is band-limited to the stimulus bandwidth. Results are described in which incident pressure is either known from long-tube measurements or calculated as a calibration output. Calibrations based on constrained nonlinear optimizations are simpler and more accurate when incident pressure is known. Outputs measured by causality-constrained procedures differ at higher frequencies from those using standard procedures with non-causal outputs. Evanescent-mode effects formulated in the time domain and incorporated into frequency-domain calibrations are negligible for long-tube calibrations. Causal reflectance and RFs are evaluated in an adult ear canal and time- and frequency-domain results are contrasted using forward and inverse Fourier transforms. These results contribute to the long-term goals of improving applications to calibrate sound stimuli in the ear canal at high frequencies and diagnose conductive hearing impairments.

A comparison of ear-canal-reflectance measurement methods in an ear simulator

Ear-canal reflectance has been researched extensively for diagnosing conductive hearing disorders and compensating for the ear-canal acoustics in non-invasive measurements of the auditory system. Little emphasis, however, has been placed on assessing measurement accuracy and variability. In this paper, a number of ear-canal-reflectance measurement methods reported in the literature are utilized and compared. Measurement variation seems to arise chiefly from three factors: the residual ear-canal length, the ear-probe insertion angle, and the measurement frequency bandwidth. Calculation of the ear-canal reflectance from the measured ear-canal impedance requires estimating the ear-canal characteristic impedance in situ. The variability in ear-canal estimated characteristic impedance and reflectance due to these principal factors is assessed in an idealized controlled setup using a uniform occluded-ear simulator. In addition, the influence of this measurement variability on reflectance-based methods for calibrating stimulus levels is evaluated and, by operating the condenser microphone of the occluded-ear simulator as an electro-static speaker, the variability in estimating the emitted pressure from the ear is determined. The various measurement methods differ widely in their robustness to variations in the three principal factors influencing the accuracy and variability of ear-canal reflectance.

Pole-Zero Fitting for Transfer Function of Hearing-Aid Receiver: Evidence-Based Review

The hearing-aid transducer is ubiquitous in the hearing-aid industry. For example, the balanced armature receiver (BAR), first invented by A.G. Bell, has been used in all telephone earphones because it has the highest output and best frequency response. Nevertheless, previous electro-mechanical studies on these miniature speakers are quite primitive, given the price of the transducers. Thus, more detailed analysis is critically important for the field of hearing science. This review study was motivated by Hunt’s parameter calibration (1954), a widely used commercial hearing-aid receiver (ED series, manufactured by Knowles Electronics, Inc.). In the body of the study, the transfer function of the BAR system (i.e., pressure over voltage) was calculated from Hunt’s parameters, solely from the electrical terminals of the device. The computed transfer function was then further investigated by comparing to the pole-zero fitting method using the methods of Gustavsen and Semlyen (1999) and Prony (1975). Based on our short experiment, the better fitting result was achieved with Gustavsen and Semlyen’s method. By decomposing results of the transfer function fitting into all-pass and minimum-phase parts, the system was confirmed as a delay system. We conclude that the BAR system is linear, time-invariant, stable, and causal while providing an evidence-based understanding of the hearing-aid receiver system.

Normative Wideband Reflectance, Equivalent Admittance at the Tympanic Membrane, and Acoustic Stapedius Reflex Threshold in Adults

OBJECTIVES

Wideband acoustic immittance (WAI) measures such as pressure reflectance, parameterized by absorbance and group delay, equivalent admittance at the tympanic membrane (TM), and acoustic stapedius reflex threshold (ASRT) describe middle ear function across a wide frequency range, compared with traditional tests employing a single frequency. The objective of this study was to obtain normative data using these tests for a group of normal-hearing adults and investigate test-retest reliability using a longitudinal design.

DESIGN

A longitudinal prospective design was used to obtain normative test and retest data on clinical and WAI measures. Subjects were 13 males and 20 females (mean age = 26 years). Inclusion criteria included normal audiometry and clinical immittance. Subjects were tested on two separate visits approximately 1 month apart. Reflectance and equivalent admittance at the TM were measured from 0.25 to 8.0 kHz under three conditions: at ambient pressure in the ear canal and with pressure sweeps from positive to negative pressure (downswept) and negative to positive pressure (upswept). Equivalent admittance at the TM was calculated using admittance measurements at the probe tip that were adjusted using a model of sound transmission in the ear canal and acoustic estimates of ear-canal area and length. Wideband ASRTs were measured at tympanometric peak pressure (TPP) derived from the average TPP of downswept and upswept tympanograms. Descriptive statistics were obtained for all WAI responses, and wideband and clinical ASRTs were compared.

RESULTS

Mean absorbance at ambient pressure and TPP demonstrated a broad band-pass pattern typical of previous studies. Test-retest differences were lower for absorbance at TPP for the downswept method compared with ambient pressure at frequencies between 1.0 and 1.26 kHz. Mean tympanometric peak-to-tail differences for absorbance were greatest around 1.0 to 2.0 kHz and similar for positive and negative tails. Mean group delay at ambient pressure and at TPP were greatest between 0.32 and 0.6 kHz at 200 to 300 μsec, reduced at frequencies between 0.8 and 1.5 kHz, and increased above 1.5 kHz to around 150 μsec. Mean equivalent admittance at the TM had a lower level for the ambient method than at TPP for both sweep directions below 1.2 kHz, but the difference between methods was only statistically significant for the comparison between the ambient method and TPP for the upswept tympanogram. Mean equivalent admittance phase was positive at all frequencies. Test-retest reliability of the equivalent admittance level ranged from 1 to 3 dB at frequencies below 1.0 kHz, but increased to 8 to 9 dB at higher frequencies. The mean wideband ASRT for an ipsilateral broadband noise activator was 12 dB lower than the clinical ASRT, but had poorer reliability.

CONCLUSIONS

Normative data for the WAI test battery revealed minor differences for results at ambient pressure compared with tympanometric methods at TPP for reflectance, group delay, and equivalent admittance level at the TM for subjects with middle ear pressure within ±100 daPa. Test-retest reliability was better for absorbance at TPP for the downswept tympanogram compared with ambient pressure at frequencies around 1.0 kHz. Large peak-to-tail differences in absorbance combined with good reliability at frequencies between about 0.7 and 3.0 kHz suggest that this may be a sensitive frequency range for interpreting absorbance at TPP. The mean wideband ipsilateral ASRT was lower than the clinical ASRT, consistent with previous studies. Results are promising for the use of a wideband test battery to evaluate middle ear function.

Effects of Negative Middle Ear Pressure on Wideband Acoustic Immittance in Normal-Hearing Adults

OBJECTIVES

Wideband acoustic immittance (WAI) measurements are capable of quantifying middle ear performance over a wide range of frequencies relevant to human hearing. Static pressure in the middle ear cavity affects sound transmission to the cochlea, but few datasets exist to quantify the relationship between middle ear transmission and the static pressure. In this study, WAI measurements of normal ears are analyzed in both negative middle ear pressure (NMEP) and ambient middle ear pressure (AMEP) conditions, with a focus on the effects of NMEP in individual ears.

DESIGN

Eight subjects with normal middle ear function were trained to induce consistent NMEPs, quantified by the tympanic peak pressure (TPP) and WAI. The effects of NMEP on the wideband power absorbance level are analyzed for individual ears. Complex (magnitude and phase) WAI quantities at the tympanic membrane (TM) are studied by removing the delay due to the residual ear canal (REC) volume between the probe tip and the TM. WAI results are then analyzed using a simplified classical model of the middle ear.

RESULTS

For the 8 ears presented here, NMEP has the largest and most significant effect across ears from 0.8 to 1.9 kHz, resulting in reduced power absorbance by the middle ear and cochlea. On average, NMEP causes a decrease in the power absorbance level for low- to mid-frequencies, and a small increase above about 4 kHz. The effects of NMEP on WAI quantities, including the absorbance level and TM impedance, vary considerably across ears. The complex WAI at the TM and fitted model parameters show that NMEP causes a decrease in the aggregate compliance at the TM. Estimated REC delays show little to no dependence on NMEP.

CONCLUSIONS

In agreement with previous results, these data show that the power absorbance level is most sensitive to NMEP around 1 kHz. The REC effect is removed from WAI measurements, allowing for direct estimation of complex WAI at the TM. These estimates show NMEP effects consistent with an increased stiffness in the middle ear, which could originate from the TM, tensor tympani, annular ligament, or other middle ear structures. Model results quantify this nonlinear, stiffness-related change in a systematic way, that is not dependent on averaging WAI results in frequency bands. Given the variability of pressure effects, likely related to intersubject variability at AMEP, TPP is not a strong predictor of change in WAI at the TM. More data and modeling will be needed to better quantify the relationship between NMEP, WAI, and middle ear transmission.

Procedures for ambient-pressure and tympanometric tests of aural acoustic reflectance and admittance in human infants and adults

Procedures are described to measure acoustic reflectance and admittance in human adult and infant ears at frequencies from 0.2 to 8 kHz. Transfer functions were measured at ambient pressure in the ear canal, and as down- or up-swept tympanograms. Acoustically estimated ear-canal area was used to calculate ear reflectance, which was parameterized by absorbance and group delay over all frequencies (and pressures), with substantial data reduction for tympanograms. Admittance measured at the probe tip in adults was transformed into an equivalent admittance at the eardrum using a transmission-line model for an ear canal with specified area and ear-canal length. Ear-canal length was estimated from group delay around the frequency above 2 kHz of minimum absorbance. Illustrative measurements in ears with normal function are described for an adult, and two infants at 1 month of age with normal hearing and a conductive hearing loss. The sensitivity of this equivalent eardrum admittance was calculated for varying estimates of area and length. Infant-ear patterns of absorbance peaks aligned in frequency with dips in group delay were explained by a model of resonant canal-wall mobility. Procedures will be applied in a large study of wideband clinical diagnosis and monitoring of middle-ear and cochlear function.

Reflectance measurement validation using acoustic horns

Variability in wideband acoustic reflectance (and absorbance) measurements adversely affects the clinical utility of reflectance for diagnosis of middle-ear disorders. A reflectance standard would encourage consistency across different measurement systems and help identify calibration related issues. Theoretical equations exist for the reflectance of finite-length exponential, conical, and parabolic acoustic horns. Reflectance measurements were repeatedly made in each of these three horn shapes and the results were compared to the corresponding theoretical reflectance. A method is described of adjusting acoustic impedance measurements to compensate for spreading of the wave front that propagates from the small diameter sound port of the probe to the larger diameter of the acoustic cavity. Agreement between measured and theoretical reflectance was less than 1 dB at most frequencies in the range from 0.2 to 10 kHz. Pearson correlation coefficients were greater than 0.95 between measured and theoretical time-domain reflectance within the flare region of the horns. The agreement suggests that the distributed reflectance of acoustic horns may be useful for validating reflectance measurements made in human ear canals; however, refinements to reflectance measurement methods may still be needed.

Equalization of loudspeaker response using balanced model truncation

Traditional loudspeaker equalization algorithms cannot decide the order of an equalizer before the whole equalization procedure has been completed. Designers have to try many times before they determine a proper order of the equalization filter. A method which solves this drawback is presented for loudspeaker equalization using balanced model truncation. The order of the equalizer can be easily decided using this algorithm and the error between the model and the loudspeaker can also be readily controlled. Examples are presented and the performance of the proposed method is discussed with comparative experiments.

Investigation of bacterial biofilm in the human middle ear using optical coherence tomography and acoustic measurements

Children with chronic otitis media (OM) often have conductive hearing loss which results in communication difficulties and requires surgical treatment. Recent studies have provided clinical evidence that there is a one-to-one correspondence between chronic OM and the presence of a bacterial biofilm behind the tympanic membrane (TM). Here we investigate the acoustic effects of bacterial biofilms, confirmed using optical coherence tomography (OCT), in adult ears. Non-invasive OCT images are collected to visualize the cross-sectional structure of the middle ear, verifying the presence of a biofilm behind the TM. Wideband measurements of acoustic reflectance and impedance (0.2-6 [kHz]) are used to study the acoustic properties of ears with confirmed bacterial biofilms. Compared to known acoustic properties of normal middle ears, each of the ears with a bacterial biofilm has an elevated power reflectance in the 1 to 3 [kHz] range, corresponding to an abnormally small resistance (real part of the impedance). These results provide assistance for the clinical diagnosis of a bacterial biofilm, which could lead to improved treatment of chronic middle ear infection and further understanding of the impact of chronic OM on conductive hearing loss. This article is part of a special issue entitled "MEMRO 2012".