Characterization and Clinical Use of Bone Conduction Transducers at Extended High Frequencies

Abstract

Measurement of bone conduction (BC) hearing thresholds at extended high frequencies (EHF; above 8 kHz) is of clinical interest but is technically complicated by limitations in standard BC transducer output, a lack of calibration standards and sparse clinical data from human subjects. A recently described calibration scheme using an artificial mastoid and interposed accelerometer is applied in this study to characterize and compare acceleration and computed force outputs over the 4–20kHz range of two standard BC transducers: the RadioEar^® B71 and B81, as well as two non-standard, commercially available BC transducers: the Tascam^® HP-F200 and the Aftershokz^® AS400. Measures of linear output growth, harmonic distortion and acoustic radiation are assessed and compared across devices. A maximum linear input voltage is established for each BC transducer using measurements of linear output growth and total harmonic distortion. At maximum linear input level, the Tascam shows superior force output by 25 to 40dB above 8kHz and the widest dynamic EHF range. Acoustic radiation per output force was lowest for the Tascam, whereas the AS400 behaved more like an air conduction earphone than a force generator. In a cohort of 15 normal hearing volunteers, BC thresholds, measured with the Tascam and reported in dB re 1 rms μN, were consistent with historical measures of EHF BC thresholds in similar subjects using an alternative BC transducer.

1. INTRODUCTION

Since the establishment of American National Standards Institute (ANSI) standards for air conducted hearing threshold measurement from 8kHz to 16kHz (ISO_389–5, 2006), there has been a growing interest in hearing function at extended high frequencies (EHF; above 8 kHz). Knowledge of hearing physiology at EHF is important for the study of aging (Mishra et al., 2022a), the assessment of ototoxic effects of noise (Fausti et al., 1981) or medications (Fausti et al., 1992) and for the study of auditory phenomena such as tinnitus or hyperacusis (Fabijanska et al., 2012). High frequency information is also important for speech recognition, speech localization and hearing in noise (Hunter et al., 2020). Routine clinical assessment of EHF hearing is increasing.

Although EHF hearing is widely recognized as important for normal communication, much remains unknown about hearing physiology in this range, particularly as it relates to bone-conducted sound. Clinically, hearing above 6 kHz is assessed exclusively via air conduction, limiting the diagnostic capabilities of threshold testing. Bone conduction (BC) testing at EHF would aid assessment of high-frequency conductive and mixed hearing loss, and better assess middle ear surgery outcomes.

BC thresholds have not historically been measured above 6 kHz because of limitations in BC transducer output. Standard clinical BC transducers, such as the Radioear B71 and B81, have excellent output level, low distortion, and limited acoustic radiation between 250Hz and 4kHz; however, above 4kHz there is rapid roll off in force output and increased acoustic radiation that limits the clinically useful range of stimulus levels to about 6kHz (Jansson et al., 2015; Lightfoot and Hughes, 1993). Although modifications of the B81 have been shown to improve EHF force output (Surendran and Stenfelt, 2022), little is known about how such modifications affect acoustic radiation and distortion across all frequencies. Finally, calibration standards for BC transducers are not published over 8KHz, and the linearity and total harmonic distortion of these devices in the EHF range are unknown.

Magnetostrictive BC transducers have been shown to generate high levels of force at EHF and may represent a viable alternative for BC testing (Popelka et al., 2010; Remenschneider et al., 2022). BC transducers, such as the Aftershokz^® have been further refined for use in military communications (Blue et al., 2013) and to improve BC sound fidelity for recreational use. The Tascam HP-F200 (Tascam) is a magnetostrictive BC transducer designed for use with an open ear canal. A prior model of this transducer (the Tascam HP-F100) was used by Popelka and coworkers (2010) to measure auditory thresholds to bone conduction in the EHF, where thresholds were reported in dB HL as referenced to a small cohort of normal hearing subjects. However, hearing at EHF, even in young individuals with normal standard frequency hearing, can be quite variable (Hemmingsen et al., 2021; Mishra et al., 2022b), which places limits on interpretation of data from small cohorts. Additionally, calibration approaches that reference test thresholds to internal cohorts of ‘normal hearing’ subjects limit the ability to compare thresholds across studies. Given that present standards for BC transducers define thresholds in terms of force (ISO_389–3, 2016), measurement and reporting of transducer force output would permit cross-study referencing of thresholds regardless of the transducer employed.

We recently described a method to determine the acceleration and force produced by BC transducers from 5 to 20kHz using an artificial mastoid and small interposed accelerometer (Remenschneider et al., 2022). In this study we use those methods to characterize the output of several BC transducers (two common clinical devices and two commercially available non-standard BC transducers sold as ‘open ear’ devices) over the 4 to 20kHz frequency range. We measure the acceleration produced by the BC transducers and convert the measurements to force using the predetermined impedance of the accelerometer and artificial mastoid. Our overarching goal is to understand the useful frequency and level range in EHF force output of a variety of BC transducers, and thereby identify suitable BC transducers for the clinical testing of EHF BC thresholds. Transducer output linearity and distortion are assessed. Measures of acoustic radiation from the different BC transducers are also made, with reference to expected impact on BC threshold measurement. Finally, we report preliminary BC threshold measurements at frequencies between 8 and 16kHz in a cohort of normal hearing subjects.

2. METHODS

Bone conducted sound thresholds are standardly obtained by using an electromechanical vibrator to generate a force over the mastoid prominence or forehead of a subject (ISO_8253–1, 2010). For the purposes of clinical testing at standard audiometric frequencies several clinical BC electromagnetic vibrators (hereon referred to as ‘BC transducers’) are available. In this study, we assess two clinical electromagnetic BC transducers: RadioEar^® B71 and RadioEar^® B81. We also assess two non-clinical, magnetostrictive transducers, (also referred to hereon as ‘BC transducers’): the Tascam^® HP-F200 and the AfterShokz^® AS400. The methods we use are similar to those described in Figure 3A of Remenschneider et al. (2022). Specifically, we used measurements of the Brüel & Kjær^® (B&K) 4393 accelerometer determined acceleration generated by the four different bone-conduction (BC) transducers against the measured mechanical impedance of a B&K 4930 Artificial Mastoid (AM) to determine the force-per-input-voltage transfer function at frequencies as high as 20 kHz. All measurements were made on a vibration isolated table in a sound-treated booth with a controlled room temperature of 68 to 72° F. While the B71 and B81 BC transducers are passive devices that were directly driven by our stimulus voltages, the Tascam and AfterShokz BC transducers come with battery-powered signal conditioning preamplifiers. For all testing, we coupled our electrical stimuli to the inputs of these preamplifiers, while ensuring the battery was fully charged and the gain was set to maximum.

Figure 3.

The stimulus-normalized force (in dB re 1 Newton/Volt) produced by four different BC transducers using broadband (0.1 to 25 kHz) chirp stimuli of different magnitudes. The magnitude of the stimuli varied between −27 to +15 dB re 1 rms Volt with a range that varied between the different BC transducers. In general, the measurements made with different levels superpose, as is consistent with a linear response, but there are levels and sound frequencies (marked by red arrows in the panel A, B and C) where level-dependent variations in the force-per-volt magnitude measurements violate linearity. A compressive non-linearity is apparent throughout the entire measured frequency range in panel C.

2.1. Measurements of the acceleration produced by BC transducers

The BC transducers drove an accelerometer (B&K 4393: 11 mm in height, 7.5 mm in diameter and mass of 2.4 gm) whose sensitivity was regularly tested against a laser-Doppler vibrometer (Remenschneider et al., 2022). The accelerometer was centered between the BC transducer and the measuring diaphragm of the AM (Figure 1A). A 0.5 kg weight (providing a static force of 4.9 N) placed on the elastic banded positioning arm of the AM stabilized the BC transducer and accelerometer and acted as a static force load on the AM measurement diaphragm. (Supplemental Information) The charge output of the accelerometer was coupled to a B&K 2525 Charge Amplifier with 20 dB of input gain, 30 Hz high-pass and low-pass filter off. The measured voltages from the amplifier were digitally compensated for the presence of the gain. The high-pass filter had no effect on the range of frequencies we present in this paper. The manufacturer determined sensitivity of the 4393 accelerometer is 0.318 pC–m⁻¹–s², consistent with the laser-Doppler measurements (Remenschneider et al., 2022). The charge amplifier with 20 dB of gain converted the sensitivity to 3.18 mv–m⁻¹–s².

Figure 1.

Methods for determining output force and artifactual sound pressures from 4 different types of BC transducers. Panel A shows the B&K #4930 Artificial Mastoid (AM) mounted on a table. A B&K #4393 accelerometer was interposed between the measuring diaphragm of the AM and each BC transducer. The 0.5 kg weight placed on the AM positioning arm kept the transducer and accelerometer stable and provided a static coupling force of 4.9 N. Also shown is the placement of the ¼ inch microphone used to measure artifactual sound pressure produced by the different BC transducers. The microphone was placed at three positions (Panel B) 1 cm above the plane of the AM diaphragm, and 4 cm away from the long axis of the 4393.

Each of the BC transducers were driven by either continuous trains of broad band voltage ‘chirps’ (0.1 to 85 kHz), a series of stepped sinusoids (1 to 20 kHz) or single sinusoids of specified audiometric frequencies with amplitudes that ranged from −27 to +15 dB re 1 rms (root-mean-square) volt (0.045 to 5.6 rms volts). The electrical stimuli to the BC transducers were generated using National Instruments^® Board 6052E (Maison et al., 2010) and the voltages produced by the accelerometer and its amplifier digitized by Analog-to-Digital convertors on a PXI 6122 board. Both stimulus generation and response measurements were controlled by custom measurement software written in LabView^® (Ravicz and Rosowski, 2013). The digitally synthesized drive signals were low pass filtered at 85 kHz and amplified by a Crest^® power amplifier (with a gain of 1). The drive output and input sampling were synchronized. The amplified drive signal was simultaneously sampled by a second analog-to-digital converter.

The chirps were presented in trains with repetition rates of 100 Hz, where each train lasted for 10 to 20s (1000 to 2000 chirps). The amplified accelerometer signal produced by the chirp segments within each train was averaged in time and converted to frequency-dependent magnitudes and phase-angles via Fourier transformation. These transforms were then normalized by the Fourier transform of the averaged drive signal to produce accelerometer voltage per input drive transfer functions. Estimates of noise in the response to the chirps were made by computing the standard deviation of the magnitude at each frequency from multiple (N=5 to 10) chirp train measurements.

The synthesized sinusoidal drive signals (of 0.5 to 20 kHz) were each harmonics of the base stimulus frequency of 0.1 kHz (a period of 10 ms) that were output with a temporal resolution of 11.8 μs (1/85 kHz) and a duration of 10ms. At least one hundred of these continuous 10ms segment of the accelerometer voltage signal (for a tonal duration of at least 1 sec) were sampled at 85 kHz synchronously with the drive and averaged. Fourier transforms of the average defined the magnitude and phase of the measured voltage at the stimulus frequency (f0) and three harmonic frequencies (2xf0, 3xf0 and 4xf0). The noise around each f0 and each harmonic was defined by averaging the spectral magnitude at six (3 lower and 3 higher) frequencies adjacent to the f0 or harmonic frequency.

The Fourier components of the measured accelerometer voltages were converted to acceleration via the above-described accelerometer sensitivity. For all measurements with either broad-band or sinusoid stimuli, the measured signal-to-noise ratio was at least 10:1 and generally greater than 100:1.

2.2. Conversions of the measured accelerations to force

The measured accelerations were converted to force using a mechanical load impedance equal to the sum of the impedance at the measurement diaphragm of the AM (Z_AM) and the impedance associated with accelerating the 2.4 gm mass of the 4393 accelerometer:

$$Z_{Load}=Z_{AM}+j2\pi f0.0024kg,$$ Eqn. 1

where j =sqrt(−1), f is the frequency in Hz, 2πf is the radian frequency and Z_AM was measured and defined by the calibration procedure described in Remenschneider et al. (2022). The results of that calibration procedure are illustrated in Figure 2. The red (gray in print) thick dot-dashed line is the average of multiple estimates of Z_AM made using a contact area between the drive and AM similar to that of the contact area between the accelerometer and the AM. The thin-dashed line illustrates the impedance of the mass of the accelerometer calculated out to 80 kHz, and the thick black line shows the sum of the two impedances where, at frequencies above 25 kHz, Z_AM is approximated by a resistance of 20 mks mechanical Ohms.

Figure 2.

The mechanical impedance in mks Ohms of the AM at its measuring diaphragm and the 4393 accelerometer. The red (gray in print) dot-dashed lines show the magnitude and angle of the impedance at the AM measurement diaphragm Z_AM, determined by Remenschneider et al. (2022). The thin dashed line shows the computed impedance of the 4393 (Z₄₃₉₃), defined from its mass of 2.4x10⁻³ kg. The thick solid black line illustrates the combination of the two, Z_AM + Z₄₃₉₃. The thin solid black line shows a model impedance fit to the combined impedance, which matches Z_AM + Z₄₃₉₃ well above 1 kHz, and is extrapolated from 25 to 80 kHz to allow conversions of harmonics of the measured acceleration to force.

Also illustrated in Figure 2 is the impedance of a three-parameter model fit to the sum of the impedances:

$$Z_{Model}(f)=R+j(2\pi fL-1/(2\pi fC)),$$ Eqn.2

where: R = 20 mks mechanical Ohms, L=2.4x10⁻³ kg, and C=4.5x10⁻⁶ m/N. The R and C values are similar to those fit to the impedance measured at the skin over the mastoid by Flottorp and Solberg (1976) that were used to define the standard impedance of the AM (IEC_60318–6, 2007). The value of L is the mass of the 4393 accelerometer in kg. The model was projected from 25kHz to 80 kHz. This projection allowed us to convert accelerations measured at harmonic frequencies (2xf0, 3xf0 and 4xf0) to force when f0 is between 4 and 20 kHz. The model impedance fits the magnitude of Z_Load (Eqn. 1) between 0.5 and 25 kHz with an error less than 10% (1 dB) and was used to convert all of our measured accelerations to force, i.e.

$$F_{earphone}(f)=\frac{A_{4393}(f)}{j2\pi f}{Z}_{Model}(f),$$ Eqn. 3

where A₄₃₉₃(f) is the complex (with magnitude and angle) sinusoidal acceleration measured at frequency f and the ratio of acceleration and j2πf is the sinusoidal velocity at f.

2.3. Tests of BC transducer linearity

A system is linear if changes in the input to the system produce proportional changes in the output. Signs of nonlinearity in a system are non-proportional growth of the output with altered input magnitude, and in cases of sinusoidal inputs, the presence of output energy at frequencies not included in the input, e.g., harmonic distortion, where an input of a pure sinusoid of frequency f0 produces output energy at frequencies of 2xf0, 3xf0, 4xf0, etc. We performed three tests to define the limits of linear behavior of the four BC transducers. The first was to define the stimulus voltage range where the chirp-defined force-to-input-voltage transfer function is independent of stimulus level. While this test provides a quick indication of broadband linear response, it quantifies the frequencies where distortion is observed, not the frequencies where it is generated.^*

The second test of linearity that we performed was to quantify the growth of the BC transducer force produced by sinusoidal input voltages. Single sinusoidal voltages of fixed frequency and varied level were used to test for the presence of either compressive (less than proportional) or expansive (greater than proportional) growth of output force at the stimulus frequency. Observations of compressions or expansions of greater than ±1 dB from linear behavior were used as the level threshold for nonlinear growth at each tested frequency.

The third test of linearity was to quantify the harmonic distortion produced by sinusoids of fixed frequency f0 and varied levels. Observations of the forces produced at harmonics of the stimulus frequency (2xf0, 3xf0 and 4xf0) were signs of harmonic distortion. Observed distortions in the measured force were quantified by their magnitude, and by the magnitude of the Total Harmonic Distortion Force (THDF), the root of the sum of the squares of the magnitude of the forces at the three harmonic frequencies:

$$THDF(f0)=\sqrt{F^2(2xf0)+F^2(3xf0)+F^2(4xf0)};$$ Eqn.4a

the Total Harmonic Distortion (THD) is defined by the ratio of the above quantity and the force at f0 (F(f0)):

$$THD(f0)=THDF(f0)/F(f0)$$ Eqn.4b

A common standard for allowable distortion is THD < 5% of the response at f0. While we did observe other distortions at higher harmonic frequencies, these were consistently smaller in magnitude than distortion levels observed at 2xf0, 3xf0 and 4xf0. Forces at subharmonics of f0 (f0/2, etc.) were looked for but not observed.

2.4. Intra- and inter-transducer variation of six Tascam BC transducers

Small differences in the placement of the Tascam BC transducer may introduce variability in output forces (see Fig 11, (Remenschneider et al., 2022)) and may have the potential to influence test-retest reliability during threshold testing. The magnitude and frequency dependence of intra-transducer differences observed from serial placements of the TASCAM transducer have not been thoroughly studied. Inter-transducer differences between individual standard audiometric BC transducers (e.g. Radioear^® B71 and B81) are known,(Jansson et al., 2015) and such differences represent the primary justification for regular calibration of audiometric equipment. Differences in output between individual commercial BC transducers (e.g. Tascam^® HP-F200) are unknown.

To assess intra- and inter-transducer variation in six individual Tascam BC transducers, we performed serial measurements of acceleration in the same Tascam BC transducer following each of five positionings on our accelerometer setup (Fig. 1A). With each placement, measurements of force-per-input-voltage were made using single sinusoids of each of 10 frequencies ranging from 4 to 20 kHz and a level of −23 dB re 1 rms Volt. Six individual Tascam^® HP-F200 transducers (Tascam 1, Tascam 2 and Tascam 3, each with a Left (L) and Right (R) transducer, hereafter identified by number and side, e.g Tascam 2L) were assessed to determine variation between Tascam BC transducers. A single-factor ANOVA analysis with repeated measures (Excel, Microsoft, Redmond, WA) was used to separate out variations in the repeated measurements in each transducer related to differences in the positioning of each BC transducer on the AM measurement setup from inter-transducer differences which represent variability in output across devices.

2.5. Sound pressures produced by the vibrating BC transducers

Each of the four types of BC transducers we tested produced varying levels of artifactual airborne sound, which can interfere with threshold estimation, especially in cases of asymmetric right-left hearing loss. We measured the magnitude of these sound pressures by placing the diaphragm of a Larson-Davis ¼ inch microphone at three radial positions (4 cm from the central axis of the BC transducer, accelerometer and AM) in the plane of the transducer stimulus surface (Figure 1). Broad-band chirps were used as stimuli, where the chirp level fit the linear range of operation of each BC transducer (as defined in the results section) and was large enough to produce measurable accelerations and sound pressures. The measured accelerations and computed forces did not vary with microphone placement, but the frequency dependent sound pressures S_n(f) did. These variations were all above the noise floor and can be attributed to spatially varying reverberations within the sound treated measuring space. The variations at each frequency were averaged by computing the root-mean-square (rms) of the sound pressures measure at the three measuring positions, i.e.

$$\overline{S(f)}=\sqrt{\left(S_1^2(f)+S_2^2(f)+S_3^2(f)\right)/3}.$$ Eqn. 5

The rms averaged sound pressures were converted to dB SPL (dB re 2x10⁻⁵ Pa), and the dB equivalent of the ratio of sound pressure to force (dB SPL per 1 rms μN) was used to quantify the acoustic artifact associated with force output for each BC transducer.

2.6. Human subject EHF BC threshold measurement

In 15 normal hearing subjects, BC auditory thresholds were measured from 8 to 16kHz by clinical audiologists using a single Tascam (2L) BC transducer in a double-walled sound treated booth. Subjects were included if they were between 18 and 45 years old, had a normal otoscopic exam of the external ear and TM without history of middle ear disease, air conduction (AC) thresholds ≤20dB HL at 500Hz, 1000Hz, 2kHz, 4kHz, 6kHz and 8kHz, no air-bone gaps ≥10dB at 2 or more frequencies from 250Hz to 2kHz, and no asymmetry between ears >10dB at two or more frequencies ≤ 8 kHz. All subjects provided their consent to be included in this approved human subject study (MGB institutional review board protocol# 2019P003272).

Subjects underwent EHF AC testing at 8, 9, 10, 11.2, 12.5, 14 and 16kHz in both ears using high-frequency AC earphones (Sennheiser HDA 200) in a clinical sound-treated booth using a clinical audiometer with extended high-frequency capability (Interacoustics Equinox 2.0) controlled by a custom software interface (Franck and Hultman, 2020; Thornton, 1993). The audiometer was regularly calibrated according to ANSI standards (ANSI_3.6, 2004). The left ear or the ear with 10dB lower high frequency AC thresholds at two or more frequencies was selected for BC testing. The Tascam BC transducer (with left and right ear transducers) was placed over the mastoid portion of the temporal bone of both ears but only the left channel and transducer (Tascam 2L) was used for testing. For example, if the right ear was the better hearing ear as defined above, the Tascam would be placed with the left sided transducer over the right mastoid. The form-factor of the Tascam headset provides stability and static force of about 5N over the mastoid process. The in-line preamplifier box of the Tascam was fixed at maximum gain for all testing. The Tascam was connected to high-frequency output of the audiometer with an interposed passive 10 dB of attenuation (Krohn-Hite 3940). This attenuation was accounted for when the threshold voltage to the Tascam was determined. The high frequency module of the audiometer was used to produce stimuli at identical frequencies to AC (8, 9, 10, 11.2, 12.5, 14 & 16kHz) and the audiometer attenuator was used to assess BC thresholds. Recorded threshold levels were converted to audiometer output voltages via voltage measurements at one or two suprathreshold levels at each frequency. These conversion factors were remeasured after each audiometer calibration. The attenuated audiometer voltages at each threshold were converting to force (in dB re 1 rms μN) using the calibrations described by Remenschneider et al. (2022).

3. RESULTS

3.1. Evaluation of the frequency range and range of linear behavior of four types of BC transducers

The acceleration measurement methods schematized in Figure 1A were used to evaluate the frequency and level range of linear behavior in each of four BC transducer types: one Tascam^® HP-F200, one RadioEar^® B71, one RadioEar^® B81 and one AfterShokz^® AS400. All of the accelerations were converted to forces using Eqn. 3, and the AM plus accelerometer mass load impedance described by the model in Figure 2.

3.1.1. Force-per-voltage frequency and level dependence

Our initial measurements of the frequency and level dependence of the four different BC transducer types used broadband chirp stimuli with magnitudes that varied by about 30 dB (Figure 3). The range of applied stimulus magnitudes varied between the different BC transducer types. The spectra of the measured forces were all normalized by the spectra of each stimulus. Figure 3 demonstrates significant differences in the frequency dependence of the force-per-stimulus-volt transfer functions of the four devices. All devices show frequency dependence in output; however, the Tascam displays the least frequency dependence over the 4 to 20 kHz range, with magnitudes of force-per-voltage that fall within a 16dB range. The other three BC transducers show at least 50 dB variations in this transfer function magnitude over the same frequency range.

Level-dependent variations in the force-per-voltage transfer functions indicate nonlinearity in the BC transducer output, and each of the four transducers shows small but systematic level-dependent variations in transfer-function magnitude, especially with higher level stimuli. However, it is important to note that the absolute stimulus voltage where level dependences were apparent differed between the four BC transducers: For the Tascam, level dependences were apparent with stimulus voltages above −3 dB re 1 rms Volt; for the B71 and B81 level dependences were observed with stimuli above +6 dB re 1 rms Volt, and with the AS400 level dependences were apparent with stimuli above −15 dB re 1 rms Volt. Another significant difference is the frequency extent of the observed level dependence: In the Tascam, B71 and B81, small compressive (slower than linear growth) and expansive (faster than linear growth) level dependences occurred in multiple narrow frequency ranges (arrows). In the AS400 we saw compressive growth at all frequencies when stimulus level is above −15 dB re 1 rms Volt.

3.1.2. Growth of Tascam force output with varied stimulus level at different frequencies

Observations of the level dependence of the force-per-voltage transfer functions pointed to the presence of nonlinear growth of output force at higher-level stimulation in all four BC transducers; however, the chirp-induced force at each frequency represents the sum of the linear response at that frequency plus any nonlinear distortions of that frequency that are produced at other frequencies. Therefore, they do little to identify the order (quadratic, cubic, etc.,) of the nonlinearities, or how the different order distortions grow with level. A better description of the growth and order of nonlinear phenomena can be gathered using tonal stimuli with a single input frequency.

Figure 4 illustrates the forces produced by a Tascam using single tones of varied level at four different frequencies (the forces produce by each of the four stimulus frequencies are coded by different colors). The use of long duration sinusoidal stimuli allows us to quantify the forces produced at the stimulus frequency, F(f0), as well as the forces produced at the three lowest harmonic distortion frequencies (F(2xf0), F(3xf0) and F(4xf0)), where the measured harmonics are coded by different symbols and line types.

Figure 4.

Measurements of the magnitudes of force produced by a Tascam (3R) using four sinusoids of varied levels. The force magnitude at f0 and the first three harmonic frequencies are plotted vs stimulus level. The dB/dB slope of 1 is an example of linear growth of the fundamental response (solid lines and filled circles). The slope of 2 is the trajectory predicted by quadratic growth of a distortion response, as is seen in the growth of the 2xf0 components (dashed lines and open circles) over parts of the level range.

The four solid lines with filled circles demonstrate near linear growth of F(f0), the fundamental component of the force, with near dB/dB growth with stimulus level at the four stimulus frequencies. However, small deviations from precise linear growth at f0 are visible, and the presence of measurable force at the three harmonic distortion frequencies also point to the presence of nonlinearity in the Tascam force response. The observed harmonic distortions also point out frequency dependent complexities in the growth of distortion with level: At some frequencies and levels (e.g., 4 kHz above −20 dB re 1 volt) the 2xf0 components were larger than the 3xf0, but this order was reversed at other stimulus frequencies and levels (e.g., 8 kHz at all levels). Also, the 2xf0 components showed level ranges where they grew as the square of the stimulus level (log-log slopes of 2), but the 3xf0 components tended to grow at slower rates. We observed a significant increase in the magnitude of many of the distortion components at the highest level of voltage stimulation we employed. For experiments under varied stimulus levels, the harmonics in the drive were simultaneously measured and were always significantly lower than the harmonics in the transducer output.

3.1.3. Observations of harmonic distortion at different frequencies and levels in the four BC transducer types

Figure 4 indicates that at a given stimulus level the magnitude of the forces at the fundamental and the harmonic frequencies depend on frequency. This dependence is better observed in Figure 5, which illustrates the forces produced by each type of BC transducer at the fundamental and harmonic frequencies with tonal stimuli that cover the 4 to 20 kHz range at a fixed stimulus level. The chosen stimulus level for each transducer type was around the top of the linear voltage stimulus range, which we define more precisely later in this manuscript. The chosen stimulus level tended to produce more harmonic distortion in the Tascam than the other devices, but the greater output of the Tascam at f0 greatly contributes to this observation. As all mechanical stimulators will distort with high-enough stimulus level, we chose a distortion limit where THD is ≤5% of the response at f0, where the THDF defined by Eqn. 4a is included in Figure 5. The shading used in Figure 5 maps the unacceptable distortion range, where the lower limit of the shading in each plot is 5% of (− 26 dB below) the response at the stimulus frequency, and any distortions that reach into the shading are above the 5% limit.

Figure 5.

Measurements of the force at the stimulus frequency (f0) and the second through fourth harmonics (2xf0, 3xf0 and 4xf0) using sinusoidal stimuli of different frequencies of near maximum linear level. The Total Harmonic Distortion Force (THDF: Eqn. 4a) generally tracks the largest distortion component. The shaded regions illustrate the range where the measured forces are between F(f0) (the thick black lines) and 5% of F(f0) magnitude. Distortion magnitudes that reach into the shaded area describe levels of THDF that are larger than 5% of F(f0).

3.1.4. The frequency and level limits of linear response

While Figure 4 illustrates small deviations from linear growth F(f0) in the Tascam, those deviations are difficult to quantify. Figure 6 provides a sensitive graphical analysis of the frequency- and level-dependence of the growth of force at f0 in all four BC transducer types. The figure caption describes how the measured F(f0) at the different levels were first normalized by the stimulus voltage and then normalized by the magnitude of the force/Volt measured at a mid-range level, such that linear growth is coded by a 0 dB response at all levels. Dashed lines placed 1 dB above and below the 0-dB lines are used to define deviations from linear growth of more than ± 1 dB.

Figure 6.

Measurements of the force produced by four different types of BC vibrators at f0 at ten standard audiometric frequencies of 4 kHz and above as stimulus level varies. The measured forces at each f0 are normalized by the stimulus voltage and then divided by the normalized ratio measured at an intermediate stimulus level. This procedure projects linear growth as a horizontal line at 0 dB. The projected ‘0-dB lines’ at the different frequencies are staggered on the y-coordinate of the plot by 5 dB increments, where low frequencies are plotted below higher frequencies. Two horizontal dashed lines are positioned at ±1 dB around each 0-dB line. The red vertical lines show stimulus levels where the response growth first starts to deviate from linearity by more than ±1 dB. (A) Tascam (3R); (B) B71; (C) AfterShokz AS400; (D) B81.

We also used measurements like those in Figure 4 to define the growth of THD at different frequencies. Figure 7 plots THD magnitude at 10 audiometric frequencies as stimulus level varied in the four transducer types. In the Tascam (Fig. 7A) the relative magnitude of distortion fell within the −26 to −50 dB range, except at the highest stimulus levels at most frequencies and at low stimulus levels at 12 and 14 kHz. The relatively high THD magnitudes at low levels at 12.5 and 14 kHz are counterintuitive, as relative distortion level generally increases with stimulus level; however, similar THD at those frequencies were observed in multiple measurement sessions with multiple Tascam transducers. It may be that these high distortions are a result of signal processing within the Tascam preamplifier or result from resonant behavior at the distortion frequencies that contribute to THD.

Figure 7.

The Total Harmonic Distortion (THD) as a function of stimulus level at ten audiometric frequencies: (A) Tascam 3R; (B) B71; (C) AfterShokz AS400; (D) B81. The thin black dotted horizontal line at −26 dB in each panel denotes a response level where THD is 5%. The dashed blue vertical lines in panels A&C illustrate the upper stimulus limit where THD is greater than 5%. The dashed red vertical lines in panels B&D mark the limits of linear growth of F(f0) determined in Figure 6. Low-level violations of the 5% rule occur in the Tascam at 12.5 and 14 kHz and in the B71 at 16 kHz. Significant distortions are observed in the B81 at 11.2 and 16 kHz with middle stimulus levels.

In the B71 (Fig 7B) the magnitude of THD is generally lower than in the Tascam, but it also increased at the lowest and highest stimulus levels. Furthermore, we again see THD magnitudes greater than 5% (−26 dB) at low stimulus levels but only at 16 kHz. This region of increased THD matched a local minimum in F(f0) in B71 in that frequency range.

The AS400 (Fig 7C) showed relatively low THD except with the highest stimulus levels at 18 kHz. This low distortion occurred despite the obvious compressive growth of force at f0 at all frequencies in the AS400 (Fig 6C). As compression is generally associated with distortion, it is likely that signal processing within the AS400 preamplifier contributed to this unusual behavior.

The B81 generally produced THD magnitudes that were below the 5% distortion limit, except at selected frequencies: 11.2 and 16 kHz, and at the highest stimulus levels at other frequencies. These exceptional frequencies were near minima in the force-per-volt vs frequency measurements (Fig. 5D), which may contribute to the larger THD ratios.

3.1.5. Definition of maximum linear drive for BC transducers

We used the data of Figures 6 and 7 to define a maximum linear drive with acceptable levels of distortion for each of the four transducer types, as summarized in Table 1. The first limit we imposed on nonlinear response came from Figure 6 and was the upper limit where the growth of F(f0) was within ±1 dB of the midrange linear growth. This limit is marked in Figure 6 by the red vertical lines and tabulated in the first data column of Table 1. The second upper limit we applied was that THD (Figure 7) should be less than 5% (−26 dB), but such limits are more complicated as the Tascam and B71 data showed violations of this limit at low as well as high stimulus levels at several stimulus frequencies (Fig.7, Table 1), and the B81 showed large THD magnitudes at several frequencies over a large part of the stimulus range. A description of potential limits and exceptions are tabulated in the second data column of Table 1. The descriptions in data columns 1 and 2 were used to decide on a ‘Nominal Maximum Linear Drive’ (data column 3 of Table 1) that is applied at all frequencies. The decision process emphasized the range of linear growth of F(f0), and ignored the exceptions to the THD criterion at low and middle stimulus levels. The chosen maximum input levels met both criteria at most of the audiometric frequencies. Limitations to this approach are addressed in the discussion.

Table 1: Linear Drive Limits.

(dB re 1 rms V)

	Stimulus Limits on ± 1 dB Linear Growth of F(f0)	Distortion Limits on Stimulus THD <5%	Nominal Maximum Linear Drive
Tascam	≤ −5 dB	≤ −5 dB*	−5
B71	≤ +10 dB	No upper limit **	+10
B81	≤ +10 dB	@4 kHz Stim ≤ +10 dB
		@11.2 kHz Stim ≤ −5 dB
		@12.5 kHz Stim ≤ +8 dB	+10
		@16 kHz Stim ≤ −12 dB
		Other Frequencies ≤+15 dB
AS400	≤ −18 dB	@18 kHz Stim ≤ −12 dB	−18
		Other Frequencies ≤ –5 dB

^*THD > 5% at 11.2 and 12.5 kHz with Stimuli < −20 dB re 1 V

^**THD > 5% at 16 kHz with Stimuli < −22 dB re 1 V

The stimulus limits defined in column 3 of Table 1 and force-per-volt chirp responses (Fig. 3) measured at a level below this limit were combined to compute the force at maximum linear drive levels over the 4 to 20 kHz range for each of the four transducer types (Fig. 8). This computation allows a comparison of both the frequency dependence and dynamic range of each transducer type. Over the pictured frequency range, the Tascam had a relatively flat frequency response with the largest maximal forces of −3 to −20 dB re 1 rms Newton. The B81 had superior output to the B71 and AS400, but all three demonstrated rapid declines in maximal linear output force with increased frequency. Because of these declines all three non-Tascam devices have outputs at 16 kHz that were 20 to 40 dB below that of the Tascam. Data taken from Frank and Ragland(1987) were used to compute the maximum force output of the Pracitronic KH70 (a historically relevant electromagnetic BC transducer with superior EHF output, but no longer obtainable) for comparison, where the frequency response over the 4 to 16 kHz range is relatively flat but the forces produced were 10 to 20dB lower than the Tascam.

Figure 8.

Estimates of the of the force at f0 produced by the four BC transducers with nominal maximum linear drive level defined in Table 1. Included is an estimate of the maximum linear force produced by the Pracitronic KH70 assuming a maximum input level of 17 dB Re 1 rms Volt (Frank and Ragland, 1987).

3.2. Output variability within and across Tascam BC transducers

Serial measurement of force output across the 4 to 20 kHz frequency range in each of six Tascam^® HP-F200 devices are shown in Figure 9. The experimental setup is shown in Fig 1A, and each measurement was repeated five times, after removing and replacing the Tascam and accelerometer each time. Figure 9A shows repeated force-per-voltage measurements with a single representative Tascam transducer (1L). Variability between positionings were generally small (± 2 to 3dB) with standard deviations in the 1 to 3 dB range (Figure 9B) except around 10kHz where the observed differences (Figure 9A) and the standard deviations (Figure 9B) were closer to 5dB. We have previously [see Fig 3A and Fig 11 of (Remenschneider et al., 2022)], observed a resonance in the Tascam output response near 10 kHz.

Figure 9.

The force-per-voltage response of six individual Tascam BC transducers during five different positionings. The stimuli were broadband voltage chirps of –23 dB re 1 rms Volt. (A). A representative force-per-voltage plot from five positionings of a single Tascam (1L). The thin solid lines show the dB value of the mean response to five 10-second-long chirp trains at each positioning. The thick black line shows the mean of the responses from the five positionings. The thin dotted lines show the noise in each of the five positionings defined by the standard deviations within the five repeated chirp trains at each positioning. This noise value is computed in linear units but plotted in dB. (B). The mean force-per-voltage from 5 positionings of each of six Tascam HP-F200 devices (thin black lines), and the overall (N=30) mean (thick black line). The response of Tascam 3L is included in the overall mean but segregated from the others due to its consistently different frequency response above 11 kHz. The standard deviations of the repeated measurements from the five positionings are plotted in thin red (gray in print) lines and scaled on the right-hand side of the plot. The standard deviation computed from all 30 measurements is plotted as a thick red (gray in print) dotted line.

When force output is assessed across six individual Tascam transducers, the inter-transducer standard deviation is similar (2 to 4dB) to the intra-transducer deviations (Figure 9B), where we see the largest standard deviations between 10 and 13 kHz in each of the individual BC transducers and across all six BC transducers with deviations approaching 5 dB (Fig 9B). For unknown reasons, one Tascam BC transducer (3L) behaved differently from the others at frequencies above 10kHz. A one-way ANOVA (Table 2) demonstrates that differences between the six BC transducers contributed significantly to the total variation in forces at all frequencies, where the mean-square variance between the different transducers is largest at 11.2, 12.5 and 20 kHz. When Tascam 3L is removed from the analysis, the variability between Tascam transducers still contributed greatly to the overall variability in force output at most frequencies, but not at 12.5 kHz (p=0.0597). This frequency is just above a minimum in the force-per-volt measurement.

Table 2.

ANOVA of five repeated measurements with six Tascams

Frequency (kHz)	MS Variance Between transducers (df = 5)	MS Variance Within transducers (df = 24)	F-Ratio	Probability
4	6.04	1.12	5.41	0.0018
6	10.68	0.76	13.98	>0.0001
8	4.29	0.80	5.31	0.0020
10	37.06	4.71	7.87	0.0002
11.2	83.44	15.27	5.46	0.0017
12.5	77.75	3.789	20.52	>0.0001
14	36.59	0.62	59.44	>0.0001
16	14.28	0.63	22.66	>0.0001
18	32.27	1.02	31.65	>0.0001
20	90.44	3.16	28.64	>0.0001

3.3. Acoustic artifact produced by the four BC transducer types

Sound pressures generated by each of the four BC transducer types were assessed with measurements from a ¼” microphone placed 4 cm from the vertical center of the accelerometer and transducer at three separate radial positions, with the microphone diaphragm co-planar to the vibrating surface of the transducer (Fig 1A&B). While the simultaneously measured accelerations were constant (less than 0.1 dB variations), the Tascam generated sound pressures measured in the three microphone positions (thin solid lines in Fig. 10A) varied but were consistently at least 20dB above the noise floor (dashed line in Fig. 10A). The source of the sound pressure variation was likely spatial variations in the sound produced within the mildly reverberant sound-treated room. The rms average of the three measurements in different locations (Eqn. 5, thick black line in Fig 10A) ‘averaged-out’ some of this spatial variation.

Figure 10.

Simultaneous measurements of forces and sound pressures produced by each of the four types of BC transducers. Sound pressure is measured at the three microphone locations described in Figure 1B. Stimuli are broadband voltage chirp trains of noted level. (A.). The Tascam generated sound pressure (in dB SPL per 1 rms Volt stimulation) at the three microphone locations. The rms average of the three sound pressures measured at each frequency (Eqn. 6) is greatly influenced by the largest responses. (B.) The ratio of sound pressure-per-force (dB SPL per 1 rms μN) for the four BC transducers.

In Figure 10B we normalize the spatially averaged sound pressures by the forces produced by the different transducers. Over much of the illustrated frequency range the Tascam had the smallest acoustic artifact per force output. Conversely, the AS400 generated a relatively large acoustic artifact over the 4 to 20 kHz range. The B71 and B81 produced relatively low sound pressures-per-force at the lowest frequencies, but the acoustic artifact associated with force generated by these BC transducers increased at higher frequencies. The consequences of these different levels of acoustic artifact to BC and AC threshold testing will be a point of later discussion.

3.4. EHF BC threshold measurement in human subjects with normal hearing

Fifteen normal hearing subjects, 6 female, mean age of 32 yrs (stdev of ± 7yrs, and range of 18 to 45), completed EHF BC threshold testing using the Tascam 2L BC transducer. Median thresholds for all subjects are plotted in dB re 1 rms μN in Figure 11. The full range of thresholds demonstrated an increased variability with increasing frequency. In the ± 25% range, thresholds were generally within 5 to 10dB of the median below 12kHz. Tascam measured thresholds are compared to Pracitronic KH70 measured EHF BC median thresholds reported by Hallmo et al. (1994) for two different age groups: 18–24yrs and 30–39yrs, and mean thresholds in 21–49 year old subjects reported by McDermott et al. (1990). Although the two earlier studies obtained BC thresholds with the Pracitronic KH70 transducer, there is significant similarity in EHF BC force thresholds in our cohort where the Tascam BC transducer was used.

Figure 11.

Measurements of BC thresholds using Tascam 2L transducer in 15 human subjects with normal standard frequency hearing. The subjects ranged in age from 18 to 45 years. The solid black line shows the median threshold in dB re 1 rms μN. The cross-hatching describes the inter-quartile range around the median and the stippling describes the total range of the measured thresholds. Included are thick dotted and dot-dashed lines that describe the median thresholds measured by Hallmo et al. (1994) in subjects within two different age ranges, and the solid lines with filled-circles to describe the thresholds measured by McDermott et al. (1990) The thin-dotted line approximates the highest thresholds measured by Hallmo et al. The thin solid line represents the calculated maximum linear output of the Tascam.

The output limits of the KH70 can be described from the clinical report of Hallmo et al 1994. Median thresholds are only reported when at least 50% of the subject population had measurable thresholds, and subjects were tested at each frequency up to the maximal output of the BC vibrator. Therefore, the highest thresholds measured by Hallmo et al. (1994) indicate the output limits of the KH70. We have included our defined ‘nominal maximum linear output’ for the Tascam (driven at −5dB re 1rms V) for comparison. When compared to the KH70, the Tascam demonstrated a wider dynamic range (highest output level relative to normal thresholds), by 20–30dB across the 8–16kHz range. EHF BC thresholds were obtained for all subjects at all frequencies using the Tascam transducer in our study while in Hallmo’s 1994 study, some subjects in both the 18–24 and the 30–39-year-old age groups had non-measurable thresholds at 14 and 16kHz. Notably, using the Tascam, we were able to measure BC thresholds in all our subjects at 14 and 16kHz and at levels higher than permissible with the KH70 (Fig 11, stippled range). When we compare the median threshold level from our cohort of 15 subjects to the maximum linear output of the Tascam, there appears to be 40dB of dynamic range at 16 kHz and at least 60 dB at 14 kHz and lower.

4. DISCUSSION

We assess linearity, harmonic distortion and acoustic artifact in clinical and non-clinical BC transducers at EHF and provide nominal maximum linear drive input limits to define the suitability of tested BC transducers for clinical use in the EHF range. To accomplish these tasks, we utilize a recently described calibration scheme (Remenschneider et al., 2022) that determines the frequency dependent output force at EHF for clinical and non-standard BC transducers. A priori, we set stimulus limits on linear growth of the force at f0 to ±1dB, and relative distortion magnitudes of THD <5% to determine the nominal maximum linear drive for each BC transducer. These parameters are used to guide selection of a maximal linear output force and dynamic range of each of the BC transducers in the EHF range. We demonstrate a relatively flat and superior maximum output force of the Tascam device between 4 and 20kHz, which supports its use as an EHF BC transducer. We subsequently employed the Tascam for the measurement of EHF BC force thresholds in a small cohort of normal hearing subjects and compare measured force thresholds to historical data collected using alternate BC transducers. Although some limitations were found, the Tascam is useful for the measurement of BC thresholds in the EHF range.

4.1. Linearity and distortion define transducer output limits

Our measurements assess force output, transducer linearity and output distortion, factors that have recently motivated improvements for clinical BC transducers in the standard frequency range.(Eichenauer et al., 2014; Jansson et al., 2015) The assessment of BC transducer force output is essential for comparisons of the efficacy and suitability of different transducer types in the clinical environment. Determination of the output range with linear growth and low distortion is also relevant for clinical testing and use. When assessing force per drive using chirp stimuli (Fig. 3) there are different frequency dependences in the output across devices: the B71, B81 and the AS400 demonstrated decreased output force per voltage (up to 50dB) with increasing frequency, while the Tascam maintained a relatively similar output force (decreasing by only 16dB) across EHF. Across the stimulus ranges employed in Figure 3, it can also be observed that each of the transducers behave non-linearly at higher input levels – the B71, B81 and Tascam deviate from linearity in multiple narrow frequency ranges. The AS400 exhibits a frequency-independent compressive non-linearity that is likely related to signal processing within the AS400 preamplifier, which will be discussed later.

Using variations in the stimulus level of pure tones, we evaluated the growth of force output with voltage input at a set of clinically relevant EHF frequencies and used deviations from linear growth of more than ±1dB to determine a nominal maximum input level for each BC transducer. The range of input voltages that resulted in linear behavior varied substantially by device. The AS400 exhibited compressive growth of the force output at relatively low stimulus levels of −18dB. While the onset of nonlinear behavior is certainly rooted in the physics and mechanics of the different transducer types (the B71 and B81 are electromagnetic devices, and the Tascam and the AS400 are magnetostrictive), the device preamplifiers that coupled our inputs to the Tascam and the AS400 likely contributed to the onset of nonlinear behavior. Future investigation of magnetostrictive transducer outputs when directly driven by controlled voltages can be used to separate out the influence of the preamplifiers on the behaviors we describe in this report.

We investigated distortion in the force output by measurement of the force at the first (2xf0), second (3xf0) and third (4xf0) harmonic distortion frequencies during tonal stimulation for each BC transducer and found increasing distortion with increasing stimulus levels. The input/output level functions of Figure 4 describe small non-linearities in the growth of force at f0 that are accompanied by measurable distortion at the first three harmonic frequencies (2xf0, 3xf0 and 4xf0) for the Tascam. Distortion level varies with frequency and input level for the Tascam where 3xf0 distortion dominates in some frequency-level combinations, and 2xf0 distortion dominates at other combinations. Figure 5 demonstrates that the relative amplitudes of the harmonic distortion for all BC transducers depends on the frequency, with higher levels of distortion seen where force output drops off (B71 and AS400).

The combined magnitude of the different distortions is described by the THDF (Eqn. 4a), and the relative value (THD, eqn. 4b) is used to summarize the growth of distortion with stimulus level for each BC transducer (Fig. 7). The four BC transducers differ greatly in THD produced. The Tascam (Fig. 7A) demonstrated a relatively high level of THD across the EHF range, but Figures 3 and 5 demonstrate the overall force generated by the Tascam is also greater. The AS400 (Fig. 7C) has the lowest relative distortion, except at the highest stimulus levels; however, the force output of the AS400 is relatively low. The B71 (Fig. 7B) and B81 (7D) have intermediate levels of relative distortion in the EHF, though the data suggests the B71 produces less distortion, but also less drive. The B71 has also been shown to have high levels of distortion at low frequencies (100–300Hz) when compared to the B81. (Jansson et al., 2015)

A common limit on the presence of harmonic distortion in audiometric devices is that THD is ≤ 5% of the response at the fundamental frequency. We investigated whether a −26dB (or 5%) limit on THD can help define easily generalizable upper limits on the stimulus level but were unable to define such limits for the Tascam, B71 and the B81. The Tascam and the B71 both showed THD levels that were greater than −26 dB at some frequencies when the stimulus was below some level (Fig. 7A and B), while the B81 at several audiometric frequencies had THD levels that were greater than −26 dB for a wide range of moderate stimulus magnitude (Fig 7D). We can only speculate about the causes for high THD at low input level for selected frequencies. These irregularities in the level dependence of THD lead us to rely on the growth of the force at f0 to define the Nominal Maximal Linear Drive Levels described in Table 2 and mostly to ignore the observed THD at low input levels. Although some of the transducers (notably the Tascam and B81) occasionally break the predefined rules for linear growth and THD, the defined Nominal Maximum Linear Drive appear to be reasonable across the relevant audiometric frequencies. An alternate approach to optimize the linear dynamic range, and minimize frequency specific THD, would be to select frequency specific maximum input levels as is currently performed for the B71 and B81 in standard clinical practice.

Clinically, calibration of BC transducers typically assesses transducer output at several levels close to the maximum of the defined dynamic range with assumptions about linearity of output at lower input levels (i.e.: audiometer attenuation). Due to known challenges in measurement of BC transducer output at very low input drives, we also assume linear behavior at levels below the nominal maximum input for the Tascam and acknowledge that we are ignoring the evidence of increased THD in the Tascam at lower input levels for 12.5 and 14kHz (Figure 7A).

Given that the generally accepted range of human hearing extends to 20kHz, one may ask whether higher level harmonics at EHF are relevant for audiometric testing. That is, if we test a 12kHz threshold, would it even matter if there were significant stimulus energy at the 2^nd harmonic frequency of 24kHz? Although air conducted sound is frequently not audible above 20kHz, several publications have demonstrated that humans perceive ultrasonic (25 kHz < f < 130 kHz) bone-conducted stimuli (Corso, 1963; Lenhardt et al., 1991; Nishimura et al., 2021; Pumphrey, 1950). This sensitivity to BC ultrasound could complicate EHF BC threshold measurements in humans made with transducers that produce measurable harmonic distortion. Since all the low and moderate level distortions we observed were at least 10 dB below the force at f0 (18 dB for the Tascam), these complications would be reduced if the thresholds for sensing ultrasonic BC stimuli were much higher than those for BC vibrations at stimulus frequencies less than 20 kHz. Corso (1963) compared thresholds in the EHF and ultrasonic high frequency (UHF) ranges and found that thresholds for ultrasonic BC simulation were 20 to 30 dB greater than those for 16 kHz and less, but possible errors in his calibration techniques could reduce these differences. To our knowledge, no one has reported ultrasonic BC thresholds in terms of force, although Lenhardt et al. (1991) reports acceleration thresholds of 82 to 112 dB re 1 mm/s² over the 25 to 85 kHz range (their Figure 1B and text). If we assume the impedance of the head at the mastoid at those high frequencies can be predicted by the model of Flottorp and Solberg (1976), those accelerations translate into forces (Eqn. 3) of 75 to 110 dB re 1 rms μN, which are 15 to 50 dB higher than the median thresholds we observed at 16 kHz (Fig. 11). These projected increases in threshold in the ultrasonic BC range, make it unlikely that the ultrasonic harmonics produced with f0 between 10 and 16 kHz, with forces <−20 dB re the force at f0, produce greater than threshold stimulation at ultrasonic frequencies.

4.2. Comparison of BC transducer force at maximum linear drive

Using our determined Nominal Maximum Linear Drive (Table 1) for each BC transducer, we can directly compare the maximal force output across devices (Fig. 8). As noted previously, the maximal force output of the Tascam is relatively independent of frequency in the EHF range, while the frequency response for the B71, B81 and the AS400 demonstrate decreasing force with increasing frequency. Above 8kHz, the maximum linear Tascam output is between 20 and 40dB greater than the other tested transducers and remains relatively flat across EHF. We also find that force output of the AS400 is inferior to both the Tascam and B81. The B71 demonstrates the sharpest roll-off in force output across the EHF range, indicating poor suitability for EHF threshold measurement.

Historically, the no-longer-available Pracitronic KH70 BC transducer was used for measurement of EHF BC thresholds, up to 16kHz, because it had a relatively flat output from 5–13kHz (Frank and Ragland, 1987). We calculated the maximal linear force from the KH70 (Fig 8) from the force-per-voltage function in Frank and Ragland (1987) with the maximal input level of 17 dB re 1 rms Volt described in that paper. This computed maximal linear force from the KH70 is superior to the B71 and B81, but the Tascam has a 10 to 20dB higher maximum force output than the KH70 at most EHF.

Hallmo et al. (1994) used the KH70 to measure EHF BC thresholds in subjects aged 8 to 79 yrs but had difficulty obtaining BC thresholds in the EHF range for most individuals above 40 years. Included in Figure 11 are the highest thresholds Hallmo et al. measured in their study (expressed in dB re 1 μN), which are 10–15dB lower than the defined output limits of the KH70 as defined by Frank and Ragland (1987), expressed in dB re 1N. (Figure 8) As the distortion of the KH70 at an input of 17 dB re 1 rms Volt is unknown, it is possible that Hallmo’s lower ‘maximal’ thresholds represent a clinical limit of the KH70 at EHF. Regardless, these maximum force thresholds determined with the KH70 are about 20 dB lower in force than the maximal linear force we estimate for the Tascam. Consistent with this difference, the range of measured thresholds in our 15 subjects at 16 kHz include thresholds that are 15 dB higher than those measured by Hallmo et al.

Other studies using the KH70 have focused only on subjects with normal hearing, perhaps due to its limited dynamic range. In contrast, Popelka and colleagues (2010) used an earlier version of the Tascam (HP-F100) with its amplifier box and were able to obtain BC thresholds up to 16kHz even in subjects with high frequency hearing loss. This provides preliminary evidence of the suitability of the Tascam for assessment of elevated EHF thresholds in subjects with known standard frequency hearing loss.

Modifications to current BC transducers may improve their output characteristics and should be further explored. Surendran and Stenfelt (2022) describe a modified B81 BC transducer where the motor unit was encased in a plastic housing and connected to a bone anchored hearing aid attachment. They report improved output (over 10kHz), but the distortion also appears to increase. The degree of acoustic radiation of the transducer (outside of its casing) is also unknown. Modifications of the Tascam HP-F100 BC transducer headpiece (Howey, 2019) have also been described, but force response curves are unknown for this device. Finally, the Tascam and AS400 preamplifier boxes may contribute to non-linearities and distortions at high (and potentially low) drive levels. The compressive non-linearity of the AS400 is likely due to signal processing within the preamplifier box, which has not been described. Future studies should evaluate these transducers without an in-line preamplifier.

4.3. Force output is affected by Tascam positioning and differs with Tascam transducer

Clinical testing with BC transducer requires a stereotypical positioning of the transducer over the mastoid. The degree to which the BC transducer output changes as a function of positioning (or repositioning) will determine if relevant differences would be expected in human subject’s measured thresholds. We investigated the degree to which Tascam transducer output differed as a function of positioning the transducer in our calibration scheme (Fig. 9A). When the same transducer is repositioned, we find small but detectable deviations in the output force (±2 to 3dB) across most frequencies, with increased deviations (around 5dB) in the 10–12kHz range. While such positioning-dependent BC transducer output variability may impact the accuracy and consistency of subject EHF BC threshold measures, such differences are similar to test-retest variability seen in clinical testing (typically ~5dB).

Standard clinical BC transducers such as the B71 and B81 have strict manufacturing requirements that ensure consistent output across devices (ISO_389–3, 2016) but with non-standard BC transducers such as the Tascam, output consistency across BC headphones is unknown. In our evaluation of 6 different Tascam transducers, we found inter-transducer standard deviations of 2 to 4dB, similar to the positioning related intra-transducer deviations. We also found larger differences around the 10 to 12 kHz resonance, with inter-transducer standard deviations near 5dB. Device specific calibration prior to clinical use will remove inter-Tascam differences, particularly at the resonant frequency of each device. Practically, however, while the positioning and inter-transducer dependent variations we observed are detectable, the magnitude of these variations are generally about ±5 dB or less. Figure 11 demonstrates the wide range of EHF BC thresholds in our ‘normal hearing’ subjects. In the future, serial testing on different days in the same subject will better define test-retest variability for EHF BC thresholds with particular attention to thresholds in the 10–12kHz frequency band.

4.4. BC transducers demonstrate large differences in acoustic artifact

Acoustic artifact from BC transducers can complicate threshold measurements, particularly in the case of hearing asymmetry. We analyzed the acoustic radiation from each of the 4 BC transducers to determine whether the amount of sound generated with each device would be relevant for threshold testing. All BC transducers produce measurable acoustic radiation, although with varied intensities and frequency dependence. Our measurements suggest the Tascam produces less sound per unit force than the other BC transducers (Fig 10B). However, it is difficult to know if the amount of radiated sound (here in dB SPL) is relevant at hearing thresholds given the frequency dependence of reference equivalent AC and BC threshold levels at EHF.

To assess if the acoustic radiation produced from each BC transducer can complicate BC threshold testing, we compute the difference between transducer produced BC and AC hearing levels across the 0.5 to 16 kHz frequency range, in five steps. 1). We first assume that the sound pressures we measure 4 cm away from the different BC transducers (Fig 1A) approximate the sound at the entrance of the open ear canal when the different transducers stimulate the mastoid. 2) We then define the transducer-induced force at 0dB HL BC over the 0.5 to 4 kHz range using ISO standards (ISO_389–3, 2016), and extend the definition of force at 0 dB HL BC to 16 kHz using the BC thresholds reported by Hallmo et al. (1994) for their 18–28 year old group. 3). We next use the forces at 0 dB HL, together with the data in Figure 10B to define the sound pressure in dB SPL at the ear canal when a force level of 0 dB HL is applied at different frequencies with the different transducers. 4). We next convert the calculated ear canal SPL levels at 0dB HL BC to dB HL for AC using the ISO standard for threshold at normal and extended high frequencies (ISO_389–1, 2017) 5). Finally, we invert these dB HL AC values to represent the difference between the transducer producer dB HL BC levels and the dB HL AC levels (dB HL_BC – dB HL_AC, Figure 12).

Figure 12.

Computations of the ratio of BC to AC hearing levels produced by a linear-range stimulus voltage applied to 4 different BC transducers. The computations were performed at the normal audiometric test frequencies between 0.5 and 20 kHz. As described in the text, a positive number implies the BC stimulus is larger than the AC stimulus.

In Figure 12, a positive dB value occurs when the BC stimulus produced by the BC transducer has a larger predicted effect on the hearing percept than the transducer produced AC sound artifact. Note that positive dB values are seen with the Tascam, B71 and B81 at frequencies below 5 kHz. However, we only see positive dB HL values in the Tascam and B81 at higher frequencies, where the difference at EHF between BC and AC output with the Tascam is equal to or superior to that of the B81. The Tascam is better by more than 5 dB at 8 & 9 kHz and at frequencies of 12, 14 and 16 kHz. The consistent negative difference values produced by the AS400 suggests it produces larger AC stimuli than BC stimuli at most of our tested frequencies.

While the results of Figure 12 are clear, they only approximate what happens when the transducers are applied to human subjects and patients. One difference between our measurements and the application to real subjects are related to differences between the acoustics of our testing arrangement and the acoustic effect of the head and pinna in real subject measurements. While these anatomical structures will have little effect on sound transmission between the transducer and the ear canal at frequencies < 1 kHz, their effects can be significant at higher frequencies (Shaw, 1974; Teranishi and Shaw, 1968), and it is likely when the BC transducer is placed on the mastoid, the sound pressures at the entrance to the ear canal at EHF in live patients are lower than we describe. A second difference is that our techniques approximate the sound pressure at the entrance to the ear canal when the ear canal is open, while the standard for AC threshold measurements we employ (ISO_8253–1, 2010) describes the sound pressure at the entrance to the ear canal under headphones. The consequences of this difference are more complicated as the presence of the earphones can have a frequency-dependent effect on ear canal sound transmission.

4.5. Utility of Tascam in human subject threshold measurements

Using the Tascam BC transducer, we successfully measure EHF BC thresholds in 15 normal hearing subjects. All individuals met strict inclusion criteria and possessed normal auditory thresholds in the standard frequency range, but there was variability in subject age (18–45 years old). Results of EHF BC threshold testing demonstrated variability between subjects that increased with increased frequencies. At 14 and 16kHz differences in individual BC thresholds between subjects were around 40 and 60dB, respectively. Our data suggests that even in a population of individuals with normal standard frequency hearing there can be large differences in BC thresholds at EHF. Table 3 shows the mean and standard deviation (SD) of EHF BC thresholds for all subjects at audiometric frequencies. It also shows the AC thresholds and the SD for each and the magnitude of the standard deviations observed with repositioning a single Tascam BC transducer. The size of the calibration SDs are less than 2dB at all frequencies except for 11.2 where it is 6.87. The BC threshold SD at 11.2kHz is not notably different from the SDs at the other measured audiometric frequencies, suggesting little impact on BC threshold variability. Additionally, the size of the SDs for both AC and BC thresholds are comparatively large and they both increase with increasing frequency, suggesting that the variability in BC thresholds is organic to subject hearing sensitivity. Given prior reports of wide variability in EHF AC thresholds (Hemmingsen et al., 2021; Hunter et al., 2020), we have reason to believe that EHF BC thresholds, measured with the Tascam, reflect true variability between subjects in bone conducted hearing sensitivity.

Table 3.

Mean and Standard Deviations of AC and BC Thresholds at EHF with Calibration Standard Deviation for Comparison.

Frequency (kHz)	Calibrations N=5	AC Thresholds N=15		BC Thresholds N=15
	StDev (dB)	Mean (dB HL)	StDev (dB)	Mean (dB re 1 μN)	StDev (dB)
8.0	0.78	7.0	5.61	40.1	4.57
9.0	0.32	7.7	5.63	53.3	7.79
10.0	1.10	7.0	7.27	45.4	8.96
11.2	6.87	8.7	10.43	43.7	8.96
12.5	1.60	7.7	9.80	37.3	12.7
14.0	0.78	10.3	13.02	44.4	15.3
16.0	0.75	16.3	16.95	63.2	18.8

Although the Tascam has been used in other studies to measure HF BC thresholds, values have been reported in dB HL defined by a small internal group of ‘normal hearing’ control subjects (Howey, 2019; Popelka et al., 2010). The use of small internal reference populations for defining 0 dB HL limits the ability to compare thresholds across studies. In addition, there is evidence that even in ‘normal hearing’ subjects there is a wide range of EHF BC thresholds. EHF BC thresholds shown in Fig 11 in this study in ‘normal hearing’ subjects (a population defined similar to Popelka et al. (2010)) show variability of as much as 40 and 60dB at 14 and 16kHz, respectively. As such, reference 0 dB HL may vary significantly depending upon the ‘normal’ hearing subjects selected. In order to promote cross study comparisons of EHF BC thresholds in the future, we recommend reporting thresholds in units of force (e.g. dB re 1µ) while using standard, (ISO_8253–1, 2010), (or defined) transducer contact surface area and static force.

Our BC threshold values are similar to prior studies reporting EHF BC thresholds in similarly aged subjects. Hallmo et al. (1994) used the KH70 to measure EHF BC thresholds and found that EHF BC thresholds increased as a function of age. Figure 11 shows thresholds for 2 of his groups with similar ages to our cohort. We find similar thresholds (±5 to 10dB) across frequencies. The similarities in median thresholds at 12.5 and 14kHz would also suggest that concerns of THD at lower input drive levels do not influence threshold measurements for normal hearing subjects. At maximum drive levels using the KH70, Hallmo was unable to detect BC thresholds above 13kHz for many individuals in his 30–39 age group while the upper limits of the Tascam dynamic range in EHF was able to determine thresholds at every frequency in every subject up to 45 years of age. For reference the maximum linear output of the Tascam is shown in Fig 11, demonstrating the 20–30dB increased dynamic range over the KH70.

We also note a wide range of threshold values in our cohort despite inclusion criteria that required ≤ 20dB HL thresholds at standard frequencies. Difference in thresholds could be from a number of sources. First, we did not have EHF AC threshold exclusion criteria and there was a wide variability in EHF AC thresholds within our subjects as shown in Table 3. Second, our cohort had a wider age range than the individual groups described by Hallmo; however, in the 30–39-year-old cohort of Hallmo, the range of threshold values was similar to our cohort. Third, our cohort was relatively small making segregation by age a challenge. In comparison, Hallmo had 40–50 subjects in each group, and he was able to demonstrate a clear association of EHF BC thresholds and increased age.

Several other studies have evaluated EHF BC thresholds using the KH70 transducer with similar force threshold values. Richter and Frank (1985) report on BC thresholds in EHF range for 16 normal hearing individuals aged 18–23 using the KH70. The reported thresholds are similar to Hallmo et al (1994) in their 18–24yo range. However, their reported thresholds at 8 and 10kHz are 10dB lower (35dB re 1rms μN). Across subject thresholds, standard deviations at tested frequencies are 8.4 to 12.4dB and increase with increasing frequency in a fashion very similar to our data. In their study, testing was done unmasked and without the ear canal occluded. They found no difference in thresholds between occluded and unoccluded ear canal. This lack of noted occlusion effect at EHF could permit use of modified BC transducers with higher levels of acoustic radiation.

Frank and Ragland (1987) evaluated 30 ‘normal hearing’ (AC thresholds 0.25–8k of <=15dB, normal tympanograms) subjects ages 19 to 27 years old with KH70 with ear canal plugged and with no masking. Their primary goal was to evaluate test-retest variability within subjects. They find that thresholds within subjects (same day and across days) differ by 0.5 to 3.0dB. They did not find a statistically significant difference between trials, indicating that repeat placement of the BC transducer does not appear to affect thresholds and that repeatability is similar to low frequency BC thresholds. In comparing EHF BC thresholds by Frank and Ragland (1987) to the study by Richter and Frank (1985), they find high levels of agreement with 8–16kHz thresholds. Specifically, their threshold values are 1–1.5dB different with standard deviation of similar magnitude (7.3 to 11.5dB – again moving higher with increased frequency).

Although the Tascam has a superior dynamic range in EHF, it does still harbor several limitations. A resonance in force output around 10kHz (Fig 9) can introduce variability in output with positioning, although we have shown that these differences are small, especially when compared to differences in inter-subject EHF BC thresholds. Second, the Tascam is not produced to meet the same standards as clinical BC transducers, and certain devices (such as Tascam 3L) may behave quite differently from others (Fig 9B). Calibration and output assessment are needed prior to attempting clinical use. Third, higher overall levels of THD break the 5% rule with lower stimulus levels at several frequencies and could complicate threshold testing at low levels, although we see no clear signs of this issues in our subject cohort and report EHF BC thresholds that are similar to historical studies with the KH70 BC transducer. Nonetheless the superior Tascam output makes it a viable BC transducer that can extend the measurable BC range into the EHF and improve diagnostic options for normal subjects as well as those with impaired EHF thresholds.

When the KH70 was being employed for EHF BC threshold testing, authors Frank and Ragland (1987) state: “An innovative BC transducer, possibly made of a piezoelectric material, having a relatively flat low-and high-frequency response and capable of producing a very high output with minimal distortion would be desirable for both low- and high frequency BC audiometry.” We find that the Tascam can produce such a flat EHF response with a wide dynamic range prior to nonlinear behavior, and we find it permits EHF threshold testing in normal subjects. In the future, the Tascam low frequency response merits further evaluation.

5. CONCLUSIONS

Through assessment of linearity, harmonic distortion, and acoustic artifact, we define a nominal maximum linear drive input limit for four BC transducers at EHF. The maximal linear output force and dynamic range of the Tascam^® HP-F200 demonstrates a relatively flat and superior maximum output force, which supports its use as a clinical EHF BC transducer. Acoustic artifact was comparatively low for the Tascam. Tascam measured EHF BC thresholds in normal hearing subjects demonstrated the potential to record a wider range of thresholds than previously reported. Median EHF BC thresholds reported in dB re 1µN were comparable to prior studies using an alternate BC transducer. Although some limitations were found, the Tascam is useful for the measurement of BC thresholds in the EHF range.

Supplementary Material

1

Supplemental Figure 1. Photograph with labeling of experimental setup for the measurement of BC transducer acceleration with computation of BC transducer output force. Static force is applied with a 500g weight over the positioning arm of the B&K 4930 Artificial Mastoid. The BC transducer is placed under the positioning arm but over the B&K 4393 accelerometer, which is in contact with the Artificial Mastoid diaphragm.

Highlights:

• A new bone conduction calibration scheme is used at extended high frequencies

• At 4–20kHz, force output is determined for 4 different bone conduction transducers

• Non-linearity, distortion and acoustic radiation limit BC transducer output

• Tascam HP-F200 shows superior force output by 25–40dB above 8kHz

• In 15 normal hearing subjects, we report BC thresholds in dB re 1 rms μN