Evaluating surface microphone output prediction accuracy: interaction between forehead volume velocity and skin impact

The surface microphone (SM) is a promising sensor for predicting the output of bone conduction hearing aids (BCHAs), providing a non-invasive approach for device fitting and verification. Previous studies have demonstrated reliability in both experimental and clinical settings by comparing measured sound pressure levels with invasive reference measurements and aided hearing thresholds, particularly at low and mid frequencies. However, at higher frequencies, these studies reported inconsistencies regarding the reliability of SM-based output assessment. The present study aimed to investigate the relationship between forehead volume velocity and the resulting sound pressure measured by the SM, with a specific focus on the frequency-dependent influence of skin dynamics on the output reliability. Different BCHAs were mounted on five fresh-frozen human cadaver heads and temporal bone samples. Skin motion beneath and adjacent to the surface microphone (SM), as well as motion of the SM housing itself, was measured on one cadaver head using a laser Doppler vibrometer to obtain one-dimensional velocity and calculated volume velocity data. Custom-built SM units of varying sizes were positioned on the forehead, and measurements were conducted under controlled variations of contact force to evaluate their effect on SM output. Finally, a lumped-element model driven by the measured volume velocity was used to predict the expected cavity pressure and was compared with ear-canal sound pressure measurements obtained on four cadaver heads. The study demonstrated a measurable interaction between forehead volume velocity, average surface motion, and the sound pressure levels recorded by the SM. Skin motion exhibited a significant rigid body component that directly influenced SM output. However, the observed decrease in volume velocity at higher frequencies suggests a damping effect caused by modal motion of the skin relative to the underlying bone. The findings further indicate that reducing SM size may mitigate modal motion and thereby increase volume velocity in the higher frequency range. The findings underline the critical role of skin properties in determining surface microphone accuracy and its implications for BCHA fitting. However, its accuracy is affected and limited by the complex interaction at higher frequencies between the motion of the skin, the device and the underlying bone.

Bone conduction (BC) hearing aids (BCHA) deliver sound to the inner ear via skull vibrations, largely unaffected by the outer and middle ear. These devices can be coupled to the head either via the skin or by direct anchoring to the skull bone. The presence of soft tissue, however, introduces frequency-dependent effects (e.g., attenuation) that can significantly influence device performance and the resultant hearing sensation. It is well known that skin and subcutaneous tissue attenuate high-frequency vibrations, reducing BC transmission by approximately 10–20 dB at frequencies above 2 kHz based on experimental findings (Stenfelt and Goode, 2005; Beros et al., 2022). Finite-element models have demonstrated that skin-drive BC attachments yield cochlear responses that are similar or even slightly enhanced at low frequencies (< 1 kHz), but can even be up to 30 dB lower at higher frequencies compared to direct bone attachment (Chang and Stenfelt, 2019).

The underlying mechanism of these findings can be described as a damping spring: at low frequencies, soft tissue may provide a compliance boost (Surendran and Stenfelt, 2025), but at higher frequencies, its mass and damping properties limit vibration transmission (Reinfeldt et al., 2007). As a result, BC stimulators coupled via soft band or transcutaneous attachments lose efficiency in the upper end of speech-relevant mid-frequency range, compared to direct bone-anchored coupling. The device performance could be optimized if the expected stimulus at a specific patient was known, based on calibration procedures. While transducer characteristics can be controlled by the manufacturers, the final performance in each patient depends on individual skin properties, which have shown large inter-individual differences (Beros et al., 2022; Stenfelt, 2011), hindering the fitting process.

To explore the vibration properties of skin, non-contact measurements of skin vibration under BC stimulation have been performed, using laser Doppler vibrometry (LDV). For example, McLeod et al. (2018), based on their in-vivo data of the skin motion on one subject and previous skull bone vibration data, hypothesized that at low frequencies, the scalp moves in a rigid-body fashion with the skull, while around 1,000 Hz, the skin begins to move relative to the underlying bone, revealing a mass-spring transition and, at higher frequencies, more complex wave propagation. In addition, Dobrev et al. (2017) had done 3D LDV at 10–25 points across the skin and bone in the superior sections of the cadaver head, which indicated similar spatial distribution of the observed vibration pattern. Thus, while there was the expected increase in attenuation with higher frequencies, this behavior did not vary spatially across the superior sections of the skin-covered skull. In other words, the relative motion between the skin and skull, does not vary spatially, at least across the parietal plates.

Those observations become relevant not just for stimulation, but also for objective quantification of skull motion and hearing sensation via surface mounted sensors in-vivo, as demonstrated by the surface microphone (SM) concept previously discussed in literature (Hodgetts et al., 2018; Persson et al., 2023). Thus, the motion of the skin could be used to objectively assess the output of BCHA. When the bone and skin move under BC excitation, the skin surface generates acoustic pressure in any adjacent air cavity, as demonstrated by Reinfeldt et al. (2013) in the ear canal. A SM device could detect this air pressure, providing a pressure waveform that reflects the local skin motion. In addition to the skin motion, the motion of the microphone's housing relative to the skin, could also be a source of pressure within the enclosed area cavity between the microphone and the skin.

Previous studies (Persson et al., 2023; Hodgetts et al., 2018; Mair et al., 2026) showed that forehead-mounted SMs can track aided BC output, but the reported reliable bandwidth varies across datasets. In particular, clinical measurements by Persson and Hodgetts indicate reliable output assessment up to at least 4 kHz, whereas a more recent experimental investigation on cadaver heads by Mair et al. reports reliable tracking up to 2.7 kHz. Differences in the reported range may be attributable to limitations of the specific SM prototypes, the output characteristics of the BCHAs, and intra-sample variability. Overall, SMs provide an objective measure of BC stimulation; however, their frequency-dependent accuracy, defined by the agreement between SM readout and skull/skin motion, is critical for clinical implementation and warrants further investigation.

In the present study, we adopt a mechanism-oriented perspective and consider the SM concept independently of prototype-specific performance differences. The aim is to identify the physical mechanism that govern SM signal generation during BC stimulation and to assess the frequency-dependent limitations that can be expected from this approach. We focus on the skin motion, how coupling a forehead-mounted sensor affects that motion, and how the enclosed air cavity converts the resulting motion into the pressure signal measured by the SM. By clarifying these mechanisms, the study provides a framework for interpreting discrepancies in reported SM bandwidth and offers insight into the underlying physics that ultimately constrains SM performance.

Overview

Measurements were performed on 5 adult human cadaver heads and on one temporal bone sample (age 62–82) obtained from the Anatomic Gift Foundation (Anatomy Gifts Registry, Hanover, Maryland, USA). The heads was stored at −20 °C and thawed for 48 h prior to preparation. The nasopharyngeal temperature was monitored to ensure it exceeded 20 °C before measurements began. All procedures were approved by the local ethics committee (No. 2023-02204). To assess the different research questions of our project, two different measurement setups have been investigated, with corresponding measurements summarized in Table 1. Detailed forehead skin velocity measurements were performed in a single cadaver head.

Temporal bone investigations

To estimate the relationship between the rigid, soft attached sensors and the skin inside the SM, the following measurements have been conducted on a temporal bone sample: 1D skin velocity of the skin on a temporal bone sample (Figure 1a)

1D skin velocity of the device (SM)

Cadaver head investigations

To assess the effect of size and contact pressure of the custom-made SM on the skin motion (described in Section 2.3), and to the estimated sound pressure on the forehead, the following measurements haven been conducted on one cadaver head sample: 1D velocity on the forehead without any device attached (Figure 1b)

1D velocity of the skin inside the custom-made SM without any device attached (Figure 1c)

Sound pressure inside the ear canal of across 4 human cadaver heads

Stimulation

For the whole head experiments, transcutaneous active BCHA were used (BONEBRIDGE, MED-EL, Austria), implanted behind the sigmoid sinus, 5–6 cm posterior to the external ear canal. For the temporal bone investigations, a percutaneous BCHA (BAHA Superpower 5, Cochlear, Ltd, Australia) on an implant screw (type BI300, Cochlear Ltd., Australia) was used for stimulation. Both actuators were driven directly by the National Instruments DAQ system, bypassing audio processors, to ensure direct control of the driving signal to the internal electromagnetic actuators. The stepped-sine excitation covered 0.3–8 kHz with logarithmic frequency spacing, and the drive voltage was maintained at 0.6 Vrms across all frequencies.

Costum surface microphone

An open custom-made SM was designed and manufactured, using a polylactide (PLA) 3D-printed body with internal diameters of 3.3 cm with two lateral wings for attachment with elastic soft bands (see Figures 1a, c, 2). In contrast to commercial prototypes SM, no silicone ring or other soft material was used at the skin interface for sealing purposes, for reasons of simplicity. The custom-made SM were placed centrally on the forehead, with the wings aligned horizontally. The elastic bands were adjusted to apply three distinct fixation forces −1 N, 3 N, and 5 N—to assess systematically the effect of contact force on the simultaneous measurement motion of the skin and the devices with the SLDV.

Scanning laser Doppler vibrometer measurements

A SLDV (SWIR Scan-Sense, Optomet, Germany) was used to measure the one-dimensional velocities of both the forehead-mounted devices and the skin inside the device. The SLDV was mounted on a 6 degrees-of-freedom robotic arm (R16, KUKA Robotics, Germany) and precisely aligned to provide a perpendicular view of the target surface, at a fixed working distance of 1.1–1.3 meters. The measurement area, centered on the forehead (8–10 cm in width) and, respectively, on the skin inside the surface microphone (SM; 3 cm), was scanned using a custom point grid comprising 30–160 measurement points with a spatial pitch of 3–4 mm. Prior to measurement, the skin was carefully cleaned of any residues or debris. For optical enhancement, a thin layer of retroreflective beads (Niermann et al., 2025) was applied to the forehead.

Volume velocity calculation, average point velocity and rigid body motion estimation

Surface velocity data

Surface velocity was measured using the SLDV across custom-defined grids as described in above in 2.4. Each grid point (i) was defined by its spatial coordinates, with the corresponding surface element area (ΔA i) calculated as the product of the grid pitch in the X and Y directions. The coordinate system was defined in the SLDV measurement frame, with the LDV beam aligned visual orthogonal to the forehead such that the measured line-of-sight component was defined as the Z-axis. The center of the coordinate system is approximately the center of the measurement points.

Data quality checks

To ensure robust and reliable analysis, all acquired velocity data underwent a multi-step filtering and quality control procedure, for each frequency bin, prior to further processing as described by Niermann et al. (2025). This included exclusion of points with low signal-to-noise ratio based on a coherence threshold (< 0.8), removal of points displaying abnormally high velocity magnitudes (above the 99.9 th percentile of the overall amplitude distribution at a given frequency), and filtering out points whose motion deviated by more than 50% different from their immediate neighbors, which have been defined by the grid to reject isolated local noise. In addition, any remaining points, identified as bad or noisy based on known artifacts, were detected visually and manually excluded. This sequential masking procedure was applied to each measurement dataset, yielding a refined spatial velocity data for subsequent calculations.

Volume velocity calculation

Volume Velocity Calculation (U): Volume velocity (U) was computed by multiplying the normal velocity at each valid scan point (vi) by the corresponding surface element area (ΔAi), and summing across the entire grid:

U = volume velocity

vi = normal velocity at scan point i

ΔAi = surface element area at scan point i

N = total number of accepted scan points

Average surface velocity based on the area-averaged volume velocity

Based on the volume velocity, the area-normalized average surface velocity was calculated by dividing the volume velocity by the total measurement area. The idea of this metrics is to provide an averaged surface volume velocity estimate that is representative of the parts of the motion which contribute to the resultant volume velocity. In other words, this is volume velocity-weighted average of the surface velocity.

Rigid body motion estimation

The surface velocity data were decomposed into rigid-body (common) and differential (non-rigid) components, following the approach described by Stenfelt (2015) and Sim et al. (2010). The common motion corresponds to the best-fit rigid-body motion (RBM) of the measured surface region as described below, whereas the differential motion represents the point-wise deviation between the measured velocity and the RBM-predicted velocity (Farahmandi et al., 2022; Dobrev et al., 2020).

The RBM fit provides a quantification of the translational and rotational components of surface motion. For each measurement, the position of each point on the surface was defined in the measurement plane (x, y coordinates), and the normal velocity was obtained from the SLDV data.

Only scan points with valid velocity data, as determined by a data quality checks, were included in the RBM calculation. A minimum number of valid points (minimum 20% total) was required. The RBM model assumes that the measured normal velocity at each point (v i) can be expressed as the sum of a global translational velocity in the direction of the laser beam (V { RBM, Z }), plus rotational components (ω { RBM, x }, ω { RBM, y }) around the orthogonal axes in the measurement plane:

v i = measured normal velocity at point i

V { RBM, Z } = rigid-body translational velocity along the z-axis (measurement/laser direction)

ω { RBM, x }, ω { RBM, y } = rigid-body angular velocities about the x- and y-axes, respectively

x i, y i = planar coordinates of scan point i

The rigid-body motion parameters were estimated by fitting the RBM model to all valid scan points using a standard linear least-squares method. To ensure the fit was numerically stable, the condition number of the design matrix was checked, and solutions with excessively high values (e.g., 10 5) were discarded. After fitting, the predicted common velocity at each scan point was calculated using the estimated translation and rotation of the whole point cloud. This common motion was then subtracted from the measured motion at each point to formulate the difference (residual) between measured and RBM fit, which corresponds to the deformation within the point cloud. This allowed quantification of both the rigid-body and differential (deformational) components of surface motion. All computations were implemented in MATLAB (MathWorks, Natick, MA, USA), and custom scripts were used for calculations and visualization.

Estimation of the pressure from surface velocity measurements

To relate the measured surface motion to an equivalent acoustic pressure, a lumped acoustic model was applied. The total volume velocity U (f) was obtained by summing the complex surface-normal velocities across the skin of the forehead enclosed by the custom-made SM, under 5 N tension. This preserves the phase relationships between individual points, ensuring that in-phase motion contributes constructively and out-of-phase motion leads to partial cancellation. The volume velocity was used as the input to a model representing a small air cavity with rigid sidewalls and one vibrating end, namely the skin surface, while any acoustic emission from motion of the custom made SM are ignored. The air cavity was assumed to have a diameter of 33 mm, based on the current SM body size. The thickness of the air volume enclosed by the SM body was chosen so that the resultant volume is the same as the median adult ear canal volume of approximately 1.5 mL (Katz et al., 2015) resulting in a thickness of 1.8 mm. Under these conditions, the cavity behaves as a lumped acoustic compliance for frequencies below approximately 1–1.5 kHz, ensuring that the acoustic pressure remains spatially uniform. The acoustic pressure (in complex frequency dependent form) within the air cavity was estimated as:

where ρ 0 = 1. 2 k g / m 3 is the air density, c = 343 m / s is the speed of sound in air, and C = V / (ρ 0 c 2) is the acoustic compliance of the enclosed air volume. The resulting pressure magnitude was expressed as sound pressure level (SPL).

Ear canal sound pressure

For comparison with the estimated surface sound pressure on the forehead, ear canal sound pressure (ECSP) was measured on four human cadaver heads using an ER-7C Series B probe microphone (Etymotic Research). The microphone was inserted into the ear canal through a rigid metal tube placed at the junction between the cartilaginous and bony canal, with the tip positioned approximately 5 mm from the tympanic membrane. All recordings were performed with an open, ear canal and intact tympanic membrane. The probe-microphone output voltage was converted to dB SPL using its sensitivity factor, which was verified prior to the experiments using the ER-7C built-in calibration stimulus.

Relative motion between soft attached custom-made SM and skin on a temporal bone sample

Figure 3 shows the magnitude of the average point velocity for the costume-made SM and the skin inside SM on a temporal bone sample, in dB re to 1 m/s/V, across the frequency range of 300 Hz and 8 kHz. The measured velocities (black) are decomposed in common motion (red) and differential motion (blue), and area-normalized average skin surface velocity (volume velocity divided by total measured area) as described in Table 2. Overall, the common and measured motion align well with each other, showing a decrease in average magnitude from a maximum velocity of approximately −115 dB re 1 m/s/V for the skin and −110 dB for the device around 400 Hz. Above this maximum, the average point velocity of the device declines by 30 dB per decade, whereas the skin shows a decrease of approximately 15 dB. Overall, the skin exhibited greater differential motion than the SM across the entire measured frequency range, indicating more pronounced local deformation-driven motion of the skin. For both, the skin and the device, however, the magnitude differences between the common motion and the differential motion start to decrease at higher frequencies. This indicates that, at higher frequencies, deformation-driven motion becomes more pronounced.

The subplot on the right shows the average velocity of the device relative to the skin. From 400 Hz to 4 kHz, the relative motion exhibits an average decline from approximately −5 to −20 dB, indicating an increase in skin motion relative to the device of about 15–20 dB. Above 1.5 kHz, the relation exhibits a sequence of narrow peaks and dips. At the same time, the differential motion between the device and skin increases, indicating a more complex pattern of relative motion and local deformations at higher frequencies.

Surface volume velocity of the skin-covered forehead motion under BC

Figure 4 shows the spatial phase and magnitude distributions (panel A) of the total, common and differential motion of surface velocities of the skin on the forehead of a fresh frozen cadaver head sample at five representative frequencies (500, 1,000, 2,000, 4,000, and 6,000 Hz). Each column corresponds to a measurement frequency, and each row represents a component of the motion, the upper subplot shows the motion magnitude, while the lower subplot the phase. In addition, estimates of the averaged surface motion and the surface volume velocity are included in panels C-D, as described in Table 2. The aim of this figure is to visualize the spatial and frequency complexity of the dynamic response of the skin surface of the forehead in a fresh intact cadaver head sample, and specifically the contribution of the common and differential motion components. The magnitude maps are accompanied by a color bar with corresponding velocity values (in dB re 1 m/s/V), and the color scale are adjusted individually for each frequency to enhance the visibility of the spatial variations. The color scale in the phase plots indicates the phase of the complex surface velocity relative to the stimulus signal, ranging from –π/2 rad (blue) to +π/2 rad (red), with green representing zero phase. For the measured velocity maps, distinct magnitude and phase gradients were observed across the surface at all frequencies, with increasing spatial complexity at higher frequencies. At 500 Hz, the phase pattern appeared largely homogeneous with almost no phase delay, as indicated by the uniform blue color in the plot, showing that the measurement points within the ROI moved in phase. At this frequency, and similarly at 1,000 Hz and 2,000 Hz, the measured points can be predominantly described by the common motion component. Above 2,000 Hz, increasing localized variations are represented by the common motion (based on the RBM fit), which therefore leads to larger differences between the measured and common-motion phase plots. The differential motion maps (Figure 4A, bottom row) highlighted the difference between the measured and the common motion component, not explained by rigid-body-motion behavior. These maps showed relatively small and spatially confined phase deviations at lower frequencies, while at higher frequencies (≥2,000 Hz), more pronounced local phase variations were visible. Overall, differential motion remained substantially smaller in magnitude, as shown in Figures 4B, C, than the measured or common motion, confirming that the majority of the measured response was represented by the rigid-body component.

While the magnitude of the differential motion was with a contribution within −15 to −5 dB of the total motion, the resultant volume velocity (Figure 4D) is primarily composed of rigid body motion. The differential motion generates almost zero net volume velocity, more than 100 dB lower than the common motion volume velocity. This was due to complex spatial modes canceling its contribution.

Forehead skin motion with SM contact

Figure 5 provides insight into the average surface motion of the skin, enclosed by the SM prototype under 5 N tension, using several metrics described in Table 2. The aim of this figure is to compare the skin motion, when restricted by the SM prototype, relative to the free skin motion, shown in Figures 4B, C. The left subplots show the spatially averaged surface velocity based on the measured, common and differential motion, as well as the volume velocity divided by the measurement area, in an equivalent way to Figure 4B. The right subplot displays the relative contributions of the different motion metrics from the left plot, normalized to the averaged measured motion. The analysis showed that the magnitude of the differential motion was comparable to both the common and the measured motion, with contributions between −20 and −5 dB. This indicated an overall decrease in the contribution of the differential motion, relative to the intact skin response (Figure 4C). In contrast the average skin motion was similar between the free skin and under contact with the SM, with 1–3 dB lower response below 1–2 kHz, and 2–10 dB higher response at higher frequencies, with the SM placed on the skin.

Impact on contact pressure on the volume velocity

Figure 6 provides insight into the volume velocity of the forehead skin measured without the SM and the volume velocity derived from the skin area enclosed by the SM prototype under different attachment forces (1 N, 3 N, and 5 N). The aim of this figure is to assess the influence of SM attachment force on the measured skin vibration, by comparing restricted skin motion under the SM to the free skin motion condition, addressing a potential source of test–retest variability. Figure 6A show the absolute volume velocity, subplot Figure 6B shows the surface-area–normalized volume velocity of the forehead skin and the skin area enclosed by the SM, and the Figure 6C displays the relative volume velocity of the enclosed skin area normalized to the intact (unloaded) skin condition. The majority of the differences in surface velocity magnitude between the forehead skin and the skin enclosed by the device can be attributed to differences in the ROI size, as shown in Figure 6A. When normalized by surface area, as shown in Figure 6B, only a small decrease in volume velocity is observed with increasing attachment force, with a maximum difference of ≤ 5 dB for attachment forces of 3 N and 5 N, in the low frequency range. This indicates that the presence of the device has only a minor effect on the underlying skin motion. Above 1.5, the volume velocity of the skin without attachment begins to diverge from that measured with the SM. Above 2.5 kHz, all conditions exhibited a decline of approximately 25–35 dB, with the largest reduction observed for the skin on the forehead without any attachment, as shown in Figure 6C.

Averaged forehead relative to three-dimensional promontory motion

Figure 7 illustrates the frequency-dependent magnitude of the 3-D one point velocity of the promontory and the skull surface near the actuator, and the one-dimensional surface-averaged velocity of the skin on the forehead derived from the corresponding SLDV data in m/s. Only the skin enclosed within the custom SM (under 5 N tension) was included from the forehead response. All data was recorded in the same cadaver head in a single measurement session. All quantities are plotted on a logarithmic frequency scale between 300 Hz and 8 kHz. The velocity of skull surface near the actuator exhibited the highest magnitudes around 1 kHz, at approximately 20 dB higher response than the one observed below 500 Hz. After a plateau at 1.5–7 kHz, a 10 dB decrease occurred above 8 kHz. Similar vibrational response have been assessed at the promontory with 5–10 dB less than the skull surface above 2 kHz. The surface-averaged velocity at the skin-covered forehead showed similar motion to the promontory, below 700 Hz, but 5–15 dB lower magnitudes at 0.7–2.5 kHz, and a 20–30 dB drop at higher frequencies. Both curves exhibited several local fluctuations, indicating frequency-dependent structural vibration behavior.

Estimated pressure of the surface microphone

Figure 8 shows the estimated SPL of the air volume within the SM prototype (under 5 N tension), as a function of frequency (300–8,000 Hz), based on the measured enclosed skin surface volume velocity, and air volume size considerations outlined in Section 2.6. The data is compared to the average, and 95% confidence interval, ear canal sound pressure level measured in 4 intact cadaver heads, under BONEBRIDGE stimulation. The estimated pressure increased from approximately 75–90 dB SPL at low frequencies to a maximum of 100 dB SPL around 0.8 kHz, during BONEBRIDGE stimulation behind the sigmoid sinus. Above 1 kHz, the pressure magnitude gradually decreased to 90 dB SPL at 3 kHz, and then steeply (20 dB/oct.) dropped to 30–40 dB SPL at 8 kHz.

The small spectral fluctuations visible in the curve correspond to spatial variations in the measured surface velocity and do not represent standing-wave phenomena, as the cavity was modeled under lumped, non-propagating acoustic conditions.

The estimated pressure profile from the skin surface of the forehead, enclosed by the SM prototype, was compared to directly measured open ear-canal sound pressure levels obtained from four human cadaver heads. The ear-canal measurements exhibited a similar overall spectral shape, with a broad maximum around 1 kHz and a comparable high-frequency roll-off. Overall, the ear canal pressure was decreasing slower than the estimated within the SM prototype, resulting in an increasing difference (Figure 8B) at 20–30 dB/decade.

Relative motion between SM body and skin

Data in Figure 3 indicates a relative motion between the SM body and skin, due to the device lagging the motion of the skin. In other words, the device moves slower than the skin, and this effect increases with frequency. Since the primary source of the motion is the bone, and the device is driven by this motion through the skin, this situation is effectively the inverse of a transcutaneous BHCA driving the skull bone through the skin. This is supported by the observed attenuation patterns being comparable to previously oversized skin attenuation in literature from transcutaneous BHCA devices on cadaver heads and patients (Ellsperman et al., 2021; Kurz et al., 2014; Beros et al., 2022). It should be noted that the amount of motion of the SM body is 10–20 dB lower (see Figure 3C) than the skin, within the 0.5–3 kHz bands, indicating that the SM body is kinetically decoupled from the skin. Thus, the volume velocity contribution from the motion of the SM body is ignored in air pressure predictions in Section 2.6. However, this this effect should be comprehensively investigated when designing an SM-based device for clinical diagnostic purposes.

Common and differential motion of the skin at the forehead

As shown in Figure 4 the common motion component reproduced the main spatial phase gradients of the measured volume velocity, indicating that the surface motion at low frequencies can predominantly be attributed to bulk translation and rotation of the underlying bone described by Dobrev et al. (2017). The differential motion maps revealed only small and spatially confined deviations, confirming the low contribution in the overall measured motion, below 5–6 kHz, consistent with minor local deformation or skin–skull relative motion. Between 1 and 2 kHz, even though local deformation and wave propagation across the skull start to occurred (Stenfelt, 2011), the skin volume velocity, within the measured forehead ROI, still follows the bulk translation and rotation of the underlying bone, due to the relatively long wavelengths (McKnight et al., 2013; Dobrev et al., 2020; Farahmandi et al., 2022). At higher frequencies (> 2 kHz), the spatial complexity of the measured phase increased, and the differential motion maps showed more pronounced local phase irregularities. Simultaneously, Figure 4B shows a decrease in averaged surface velocity, especially from the measured and common estimation. This behavior suggests a transition from quasi-rigid motion toward more complex surface vibration, likely caused by the viscoelastic properties of the skin and soft tissue. Previous investigations reported an increasingly complex motion pattern on the skull bone surface in cadaver heads (Farahmandi et al., 2022; Dobrev et al., 2017; McKnight et al., 2013), shown by the onset of detectable waveforms and mode shapes in the mid-frequency range, and increasing local deformation at higher frequencies. In our dataset, this transition occurs between 2 and 4 kHz on the skin surface. This is higher than that observed on the sides of the skull (1–2 kHz), or near the stimulation device (0.5 kHz), however, it is consistent with the transition to predominantly wave motion across the upper sections of the skull in cadaver heads (Farahmandi et al., 2022). In addition, there might be differences in the observed trends on the skin surface relative to the underlying bone due to the mechanical impedance mismatch between the soft tissue and the underlying skull (Surendran and Stenfelt, 2025).

Average velocity as a proxy for volume velocity

The volume velocity closely followed the spatially averaged velocity, with negligible contributions from deformation across the forehead region. This behavior was unaffected by the measured area, as shown in Figures 4, 5. This indicates that the magnitude of average velocity and volume velocity of the skin on the forehead, under bone-conduction stimulation, is largely dominated by common motion rather than localized deformation. As a result, fewer single-point LDV measurements on the forehead are likely sufficient to represent the entire area covered by the surface microphone, magnitude wise, suggesting that future studies may not require full-area scanning to obtain comparable information.

However, it should be noted that this apparent spatial uniformity may be influenced by the relatively large distance between the transducer and the surface microphone. At shorter distances, for example, when measuring on the skin over the mastoid while simultaneously stimulating on the mastoid, the contribution of differential motion is likely higher because local deformation becomes more pronounced. With increasing distance from the transducer, local deformation decreases and the head behaves more like a rigid body (Farahmandi et al., 2022). Therefore, point velocities further away from stimulation location might be more reliable to assess the general head motion.

It should be noted that the deformation across the SM eclosed skin (Figure 5, blue line), as overall lower than the deformation across the intact skin (Figure 4C, blue line). This is intuitively expected as the SM body would provide support for the skin, and the headband tension will increase the skin's stiffness (Surendran and Stenfelt, 2025).

Influence of coupling stiffness on the volume velocity of the skin

The comparison of surface-averaged velocity magnitudes for different attachment forces showed that the mechanical coupling between a surface-mounted microphone and the skin has a limited effect on the skin's motion. Increasing the static preload from 1 N to 5 N resulted in a limited increase (1–3 dB) surface velocities at mid-frequencies (1–3 kHz), indicating a stiffer skin due pretension induced by SM. In contrast, the skin without any attachment exhibited (1–3dB) larger amplitudes at low frequencies but stronger attenuation above 3 kHz. This behavior suggests that freely vibrating skin—unconstrained by a device housing—undergoes greater motion at low frequencies but experiences stronger damping at higher frequencies, consistent with the skin acting as a compliant interface whose stiffness and damping depend on contact pressure. However, up to approximately 4 kHz, the magnitude differences between conditions remained within about 5 dB, indicating that the contact the static preload of softly attached sensors have only a minor effect on the underlying skin motion and therefore on the measured sound pressure in this frequency range.

Relation between surface motion and cochlear bone response

When comparing the surface-averaged forehead velocity of the skin with the 3-D velocity measured at the promontory and the 3-D velocity on the skull surface (measured in the same head), the surface motion on the skin exhibited consistently lower magnitudes across the entire frequency range above 1 kHz. Several factors may contribute to this discrepancy. First, the forehead measurement was obtained using a single-axis laser vibrometer, which captures only one component of the local three-dimensional motion. As a result, the measured velocity represents a projection of the true 3-D motion vector, inherently underestimating the total magnitude (Bustos et al., 2025). Second, the surface-averaging procedure further reduces peak amplitudes by smoothing spatially heterogeneous motion patterns. In addition, at higher frequencies, the soft-tissue layers between the skull and the skin introduce substantial mechanical attenuation due to their viscoelastic properties and the impedance mismatch at the tissue–bone interface. This damping effect becomes increasingly dominant above approximately 2.5–3 kHz, consistent with the observations reported by (Surendran and Stenfelt, 2025). The prominent magnitude peak, observed around 1 kHz at the stimulation area (Figure 7), could be attributed to local deformations in the vicinity of the stimulation location, as indicated described by Fahramadi et al. (2022). These localized deformations are affecting nearby (2–4 cm distance) skull bone, including the promontory, but not the forehead (>10 cm away). In contrast, skull bone at the forehead, is experiencing primarily rigid body motion, up to 4 kHz, above which the whole skull bone is affected by wave motion (Fahramadi et al., 2022, Dobrev et al., 2020). This is consistent with the current observations of the motion across the forehead skin (blue line in Figure 4C), where the differential component is less than 8–10 dB of the total motion, below 4 kHz.

Estimated cavity pressure and implications for surface microphones

The pressure estimates derived from forehead surface velocity measurements (with an SM attached) provide new insight into the mechanical–acoustic coupling between BC stimulation and the overlying soft tissue. The lumped model, based on volume velocity, predicts pressure magnitudes on the order of 80–100 dB SPL around the resonance frequency of the BONEBRIDGE around 1 kHz (Dobrev et al., 2019), which is consistent with the measured maximum magnitude recorded with our SM prototype. At low frequencies (< 1 kHz), the volume velocity of the skin, moving quasi-rigidly with the skull as described above, may represent the primary driving mechanism of the sound pressure recorded by softly attached sensors. With increasing frequency, as the complexity of skin motion begins to increase, the predicted pressure gradually decreases, with an steeper decrease above 2.5 kHz. This behavior likely reflects the combined effects of nonuniform vibration patterns, spatial phase variations across the ROI on the skin surface, skin attenuation, and limitations of the lumped-acoustic assumption.

As the cavity dimensions approach a significant fraction of the acoustic wavelength, spatial phase gradients and partial standing waves form within the cavity, leading to either under- or overestimation of pressure depending on the local pressure distribution. In addition, the air cavity thickness, which was defined as 1.8 mm, should be regarded as a conceptual approximation representing a cavity in direct contact with the skin, as a more anatomically detailed representation would substantially increase the complexity of the model.

Despite these limitations, the model provides valuable first-order predictions of the coupling efficiency between the vibrating skin and a small air-filled cavity representative for SM prototypes. The spectral trends, particularly the broad maximum near 0.8–1 kHz and the decline above ~2.5 kHz, suggest that most of the acoustic energy transmitted from the skin into a confined air volume lies within the low-kilohertz range. Although the lumped approximation is most accurate up to roughly 1–1.5 kHz, the ECSP serves as a useful reference for interpreting the model's trends above 1.5 kHz. In this higher-frequency range, the lumped-element model can be regarded as an order-of-magnitude estimator of the pressure spectrum, capturing the overall frequency dependence while not resolving higher-order modal contributions or standing-wave behavior.

In comparison with the ECSP, despite local differences due to the resonance of the bony ear canal between 2 and 3 kHz (Reinfeldt et al., 2013; Stenfelt et al., 2003), the estimated sound pressure level on the forehead for a closed cylindrical cavity follows a similar response profile. This indicates that both the ear canal sound pressure and the surface sound pressure are driven by vibrations of the bony skull and the overlying soft tissue. As the ECSP cannot be assessed in at least a subpopulation of patients with a BCHA (Hodgetts et al., 2010), the surface microphone may serve as an alternative measurement approach. Our estimated sound pressure levels can be interpreted as a sensitivity profile for future surface-microphone-based sensors, indicating a sensitivity comparable to that of ear-canal sound pressure assessments, but without the anatomical constraints associated with ECSP measurements, such as ear-canal atresia, ear canal stenosis or surgically closed ear canals. This expands the range of potential applications for this sensor type, particularly in the low- to mid-frequency range. In addition, as discussed in more detail in Section 4.2, the averaged surface velocity on the forehead shows negligible local differences. This indicates that the surface microphone can be positioned at different locations on the forehead while still providing a representative measure of the overall forehead surface velocity. To further validate this concept, detailed test–retest variability assessments and larger sample sizes, preferably in vivo, are required.

Together, the findings demonstrate that BC stimulation on the forehead primarily excites rigid-body motion of the skin and the underlying skull at low frequencies, with increasing skin–soft-tissue decoupling and local deformation at higher frequencies, based on a detailed forehead velocity examination in a single sample. This study provides a practical basis for optimizing skin-mounted sensing: within the investigated range, attaching a sensor to the skin and increasing preload did not substantially alter the measured skin motion, suggesting that coupling and sealing can be stabilized without markedly compromising the underlying vibration response. At the same time, the results indicate the inherent sensitivity profile across the measured frequency range for forehead mounted sensors, and the limitations at higher frequencies, where the impedance mismatch between skin and skull leads to increased damping. In this frequency regions, differential motion and local deformation begin to influence the skin's response and therefore reduce the generated sound pressure.