The use of whole human cadaver heads for these experiments was approved by the ethics committee of the Hannover Medical School (8151_BO_K_2018). This study intends to investigate the possible relationship between the sound pressure recorded from the skin on the forehead and the one-dimensional promontory vibration velocity when the skull is excited by a bone vibrator. In case of a linear relationship, the sound pressure recorded would be:

where P is the sound pressure, f is the frequency, a(f) is a frequency-dependent factor, and v(f) is the velocity measured on the promontory at each frequency on the promontory. As the promontory vibration and sound pressure are evoked by the vibratory excitation, a possible constant in Eq. 1 must be zero at all frequencies. In logarithmic domain and in terms of decibel related to m/s (dB re. m/s) for the cochlear promontory velocity \(CP_\) and decibel sound pressure level measured with the surface microphone \(SM_\) [dB SPL] follows:

$$SM_ (f)[dB\;SPL] = A_ (f) + CP_ (f)[dB\;re\;m/s]$$

(2)

where \(A_ (f) = a(f) + const\) is a frequency-dependent constant. Hence, in the linear case, the measured sound pressure level is related to the measured promontory velocity in dB with a slope of one and a frequency-dependent constant.

Five fresh frozen human cadaver full heads (four males/one female) were deployed for measurements of cochlear promontory (CP) vibrations and forehead sound radiation in response to vibration stimulation with the percutaneous bone anchored hearing system (BAHS) Ponto 3 (Oticon Medical, Askim, Sweden). Specimens were the same described in a previous publication on output performance of a novel transcutaneous bone conduction implant [16]. The cohort comprised one female and four male head specimens. There was no information on medical or injury history. All heads were scanned with flat-panel cone-beam computed tomography (CT) prior to experiments. Two experienced surgeons (RS, NP) examined the CTs to exclude fractured skulls before experiments. Defrosting of heads took place in a cooling room at + 4 °C at least 24 h before the experiment. The cochlear promontory of both ears was made accessible via a > 2 × 2 mm opening in the tympanic membrane above the promontory. The CP vibration (ipsi- and contralateral) responses and sound pressure measurements on the forehead were simultaneously performed, and experiments were conducted sequentially on both ears during two consecutive days in the five heads, resulting in datasets for ten ears. In between measurements on day 1 and day 2, heads were stored at + 4 °C.

For the determination of linearity of the relationship between CP vibration and SM recording, the attenuation of ambient airborne sound by the surface microphone, an additional human cadaver full head was stimulated with a percutaneous device (Ponto SP, Oticon Medical, Sweden) and a loudspeaker in the sound field (Mackie, HR824mk2, USA) in an anechoic chamber.

A Ponto system (Wide Ponto implant, Oticon Medical, Askim, Sweden) was implanted at the intended percutaneous BAHS implant position approximately 55 mm posterior-superior to the ear channel entrance. An incision was made, and skin was retracted for exposing the skull bone. A 4-mm-long and 4.5-mm-diameter wide implant was placed into the skull bone using the standard guide drill and a 4-mm countersink drill (Oticon Medical, Askim, Sweden). A 9-mm-long abutment was attached to the implant of the Ponto BAHS system (Oticon Medical, Askim, Sweden).

A modified Ponto 3 sound processor (Oticon Medical, Askim, Sweden) was used for stimulation. Modifications enabled direct electrical stimulation via one microphone port, turning off the other microphone and setting the gain to linear. Before and after each experiment, the sound processor’s performance was verified with a skull-simulator (SKS-10, Interacoustics, Middelfart, Denmark) to ensure its functionality according to specifications.

Stimulation signal synthesis was the same as described in a previous publication [16]. In short, the signal injected to the sound processor was a stepped sine consisting of 77 logarithmically spaced sinusoids from 87.5 Hz to 10 kHz. The signal was generated by a multi-channel data acquisition system (NI-4431 BNC, National Instruments, Austin, TX, USA) with a 24-bit analogue-to-digital converter. The acquisition system was controlled with custom-made control software using LabVIEW (National Instruments, Austin, TX, USA). For providing the required current, a power amplifier (SA1, Tucker Davis Technologies, USA) was connected between the signal generator and the modified sound processor.

Velocity responses were measured on both ipsi- and contralateral cochlear promontories (CPs) for each stimulation side, but results and analyses shown in this publication originate from the ipsilateral cochlear promontory only. Measurement sites were visually accessed via the small incision in the tympanic membrane, and LDV measurements were obtained from a small reflector placed on the CP to improve signal-to-noise ratio. The laser beam was almost perpendicular to the CP surface.

For the velocity response measurements, a laser Doppler vibrometer (LDV) (OFV 534, Polytech, Germany) mounted on a surgical microscope (OPMI 1, Zeiss, Germany) was used. The LDV system’s sensitivity was set to 5 mm/s/V, and data were sampled at 51.2 kS/s and averaged between 30 and 500 times for ensuring a signal-to-noise ratio (SNR) of a minimum of 12 dB. For the noise floor estimation, the average of six adjacent bins to the stimulation frequency in the computed Fast Fourier transform (FFT) was employed. Data with a SNR below 12 dB were excluded from the data analysis.

The employed surface microphone was the next-generation prototype by Interacoustics A/S (Middelfart, Denmark) based on an earlier design by Hodgetts et al. [6]. In our setup, the surface microphone (SM) was attached to the middle of the forehead using an elastic band (Fig. 1) and connected via a preamplifier to the data acquisition input. The recording was performed simultaneously using the same data acquisition system and SNR criterion of ≥ 12 dB as described before for the LDV vibration measurements. The stimulation was done sequentially on both sides, and due to the symmetry with respect to measurement points, data from left and right ears was pooled for the analysis.

a Absolute output voltage of the SM and reference probe microphone ER7c in response to bone-conducted stimulation by the Ponto 3. b Difference in output of the SM to the reference sound pressure level as measured approximately 2 mm and 3 mm above the skin surface in the SM cavity. c The configuration of the ER7c reference microphone tube guided subcutaneously to the cavity below the SM. d The SM held by a headband on the middle of the forehead during the calibration measurement

The design of the surface microphone follows the principle of a stethoscope. In a conical cavity, structural vibrations of skull and skin tissue at the SM base emit sound into the void. At the apex, a microphone is placed sensing the acoustic sound field [6].

Calibration of the SM output was performed with a calibrated probe microphone (ER7c, Etymotic, IL, USA) placed in the cavity of the SM on the forehead of one cadaver head specimen. The silicone probe tube attached to the reference probe microphone was guided subcutaneously into the SM cavity, with the opening placed approximately 2 mm and 3 mm above the skin (Fig. 1c). Both microphones measured the sound pressure in the surface microphone cavity during BAHS stimulation simultaneously. Figure 1a shows the magnitude response of the surface microphone output and the reference microphone 2 and 3 mm above the skin; the difference between 2 and 3 mm was negligible; therefore, we used 2 mm as reference. The magnitudes’ difference between reference and surface microphone recordings was used to calibrate the output magnitude of the surface microphone (see Fig. 1b, Supplementary Table 1). All SM data in the following analysis are shown calibrated in dB SPL and shown as SMSPL.

The modified Ponto 3 sound processor (Oticon Medical, Askim, Sweden) was used to investigate the linearity between the measured sound pressure by the SM and the vibration of the cochlear promontory measured by the single-beam LDV in bone conduction stimulation mode. The input voltage for the actuator to test the linearity was between 0.1 mV and 2.43 V.

The performance of the SM in terms of attenuation of the ambient acoustic airborne sound was tested using a loudspeaker (Mackie, HR824mk2, USA) in an anechoic chamber. Therefore, in a single human head specimen, the sound pressure close to the housing of the surface microphone was measured using a probe microphone (ER7C, Etymotic, IL, USA) and compared to the synchronously measured SPLs by the SM at frequencies between 100 Hz and 10 kHz and sound field levels between 101 and 119 dB SPL outside the SM at a distance < 1 cm.

To determine the level of airborne sound emitted by the bone conduction device, the Ponto 3 was driven electrically with an input voltage of 1.0 V and the sound pressure level measured approximately 1 cm next to the SM.

Data visualization and analyses were performed with Matlab (Matlab R2021a, MathWorks) and SigmaPlot 15 (Inpixon, Düsseldorf, Germany). A Shapiro–Wilk test was used to check the normality of the dataset. In case of normally distributed data, a paired Student’s t–test was used; in case of non-normal distribution, a Mann–Whitney rank sum test was performed. Statistical tests were performed to investigate the differences (p < 0.05) between conditions at each frequency.