Bone conduction devices are used in audiometric tests, hearing rehabilitation, and communication systems. The mechanical impedance of the stimulated skull location affects the performance of the bone conduction devices. In the present study, the mechanical impedances of the mastoid and condyle were measured in 100 Chinese subjects aged from 22 to 67 years. The results show that the mastoid and condyle impedances within the same subject differ significantly and the impedance differences between subjects at the same stimulation position are mainly below the resonance frequency. The mechanical impedance of the mastoid is significantly influenced by age, and not related to gender or body mass index (BMI). While the mechanical impedance of the condyle is significantly affected by BMI, followed by gender, and not related to age. There are some differences in mastoid impedance between the Chinese and Western subjects. An analogy model predicts that the difference in mechanical impedance between the mastoid and condyle leads to a significant difference in the output force of the bone conduction devices. The results can be used to develop improved condyle and mastoid stimulators for the Chinese.

## I. INTRODUCTION

Hearing is an important human sense to perceive and judge the surrounding environment, and it is essential for communication. People perceive sounds in two ways, where one is air conduction (AC) and the other is bone conduction (BC). The former is the process by which sound waves travel through the outer ear and middle ear and arrive at the cochlea, the latter is the process by which sound waves vibrate the bones of the skull to stimulate the cochlea (Bekesy, 1954; Stenfelt and Goode, 2005). Nowadays, bone conduction devices (BCDs) are widely used in audiometric tests, hearing rehabilitation, and communication systems (Reinfeldt *et al.*, 2015; Watabe *et al.*, 2006). In all BC systems, the transfer of energy from the BCD depends on the impedance match between the device and the load (Weecea and Allen, 2010). In all, the output properties of BCDs are affected by the mechanical impedance of the load.

There are three types of hearing loss, including conductive hearing loss, sensorineural hearing loss, and mixed hearing loss. Bone conduction audiometry is used to distinguish conductive hearing loss and sensorineural hearing loss (Stenfelt, 2011). The most commonly used BCD for audiometry is the Radioear B71 (Radioear, Middelfart, Denmark). The primary locations of the BC vibrators used in clinical audiology are the mastoid and the forehead. It is necessary to design a mechanical coupler that can be used to calibrate the vibrator applied to the mastoid as well as to the forehead. Corliss (1955) and Dadson *et al.* (1954) measured the mechanical impedance of these two positions. Based on the above measurement results, the mechanical impedance of a 1.75 cm^{2} circular surface of the average human mastoid is standardized in 1971 for the calibration of BC transducers used in audiometry (IEC, 1971). However, it is difficult to design mechanical couplers that meet this impedance, and the mechanical impedance of the B&K 4930 (Brüel & Kjær, Nærum, Denmark) artificial mastoid is used as the standard of the mechanical impedance for calibrating BC transducers (IEC, 1990). The mastoid impedance was thoroughly investigated by Flottorp and Solberg (1976), they measured the mastoid and the forehead mechanical impedance in 60 subjects (aged from 9 to 70 years) and analyzed the effects of age and gender on the mechanical impedance. They found that the mastoid impedance was lower in older people than in younger people. Zhang (1994) measured the mechanical impedance of the mastoid and forehead in 444 Chinese subjects using internationally standardized equipment and methods. The results from Zhang's study showed that there is a correlation between the impedance and average age for 5 ∼ 65 years in the frequency range of 100–1000 Hz, the impedance magnitude (100–1000 Hz) decreases with age. In addition, they found that the resonance frequency also decreases with age. In the two studies mentioned above, the subjects were asked to lie down on an operating table during the measurements, the vibration characteristics of the body and operating table may introduce some effect, which does not conform to the listening state of subjects sitting up right. Therefore, it may be more accurate to measure the impedance of a subject while sitting in a chair. Cortés (2002) measured the mechanical impedance at the mastoid in 30 subjects with a static force of about 5.9 N. They also measured the mechanical impedance of the skin in one subject with different static forces, the results suggest that the static force has an effect on the mechanical impedance. The stiffness of the mechanical impedance increases with the static force, so the resonance frequency increases with the static force. In addition, Mackey *et al.* (2016) investigated the mechanical impedance of the skin-covered skull at different skull positions and for different static forces for groups of infants, young children, and adults. Impedance increased with increasing contact force for low frequencies for each age group, this trend observed in the study is consistent with the previous study (Cortés, 2002). No previous research has studied whether obesity is correlated with mechanical impedance. Body mass index (BMI) is usually taken as an indicator to judge obesity. BMI can be calculated as a factor to test whether obesity affects mechanical impedance of the skin and skull.

The most important application of BCDs is hearing rehabilitation (Chang *et al.*, 2016). H*å*kansson (1986) measured the mechanical impedance of the mastoid on the human head with and without skin penetration, and the results indicated that the impedance magnitude with skin penetration is 10–30 dB higher than the impedance of intact skin over the skull. Recently, H*å*kansson *et al.* (2020) measured the mechanical skull impedance in 45 patients who were using percutaneous bone conduction implants. No significant differences related to gender or skull abnormalities are seen, just a slight dependence on age and major ear surgeries.

With the advantage and development of BC, BCDs are gradually used in communication systems (MacDonald *et al.*, 2006). For ease of wear, the transducers of such BCDs for communication are located on the bone in front of the ear canal, of which the position is named condyle. McBride *et al.* (2008) used an Oticon A20 (Oticon, Copenhagen, Denmark) bone vibrator to compare the perceived performance of the different locations of the human head, such as the mastoid, the forehead, the condyle, the vertex, and the other positions. The results demonstrated that the condyle has the lowest mean hearing threshold and the condyle is the most effective location for the vibrators used in the BC communication interfaces. Dobrev *et al.* (2016) measured the cochlear promontory in cadaver heads with the laser Doppler vibrometry, while seven different positions around the pinna were stimulated by a bone-anchored hearing aid, and they also measured the hearing thresholds in twenty subjects with the bone vibrator B71 attached to the same seven stimulation positions. They suggested that stimulation on a position superior-anterior to the pinna generates higher cochlear responses and lower BC thresholds than does stimulation on the mastoid. The study by Qin *et al.* (2019) showed that the hearing threshold on the condyle is lower than that on the mastoid. In addition, the study by Stanley and Walker (2009) indicated that the mastoid position shows lower performance in intelligibility than the condyle position, approaching statistical significance. Therefore, many BCDs used in consumer electronics have transducers placed on the condyle. The mechanical impedance of the condyle affects the BCDs' output performance. However, the mechanical impedance of the condyle has not been investigated by measurements and analysis. There is no suitable calibrator like the artificial mastoid or the skull simulator to simulate the condyle impedance and predict the BCDs' output force in the communication system.

The main aim of this study is to measure the mechanical impedance of the mastoid and condyle on a large number of Chinese subjects. Experimental results were analyzed to explore the effects of age, gender, and BMI on mechanical impedance. A secondary aim is to explore whether the difference in mechanical impedance affects the output performance of BCD. In addition, the difference in output force of the BCD between the artificial mastoid and the human condyle was studied. Finally, the difference in output velocity of the BCD between the mastoid and condyle was analyzed.

## II. METHODS

### A. Subjects

One hundred subjects (50 males, 50 females) participated in the experiments, and their ages ranged from 22 to 67. The subjects were divided into three groups by age and subdivided by gender (see Table I). All subjects had no history of major ear surgery or craniofacial abnormalities, with no skin penetration of temporal bone. Most subjects have hearing thresholds at or below 20 dB Hearing Level (HL) from 250 Hz to 8 kHz (measured by standard pure tone audiometry tests). None of the subjects have ever used hearing aids or cochlear implants. Body mass index (BMI) is a person's weight in kilograms divided by the square of height in meters. A high BMI can be an indicator of obesity. According to the obesity criteria promulgated by the Chinese Ministry of Health, the subjects were divided into the over-weight group (BMI ≥ 24) and the normal-weight group (BMI < 24).

### B. Mechanical impedance

Mechanical point impedance can be defined as the resistance of an object to being set in motion. A dynamic force $F(j\omega )$ applied to an object will result in a certain velocity $v(j\omega )$, which is

where $\omega =2\pi f$ is the excitation angular frequency and $Z(j\omega )$ is a frequency-dependent complex quantity that has magnitude as well as phase. The higher the magnitude of the impedance, the lower the vibration for a given force. Moreover, BC devices can typically provide a greater output force when applied to high mechanical impedance loads than low mechanical impedance loads. The impedance of a mass-controlled mechanical system is a straight line in double logarithmic coordinates that rises 6 dB per octave with frequency. Similarly, when the system is purely stiffness controlled, the impedance is a straight line that decreases 6 dB per octave with frequency. In the case of a purely damped system, the impedance will be constant with frequency (Zhang, 1994). H*å*kansson (1986) defined two relevant impedances: the “skull impedance” is related to moving the boney skull and its contents, while “skin impedance” included the skull plus the overlying skin and subcutaneous soft tissues. In the present study, skin impedance was measured for both the condyle and the mastoid.

### C. Measurement setup

A setup for the measurement of mechanical impedance is shown in Fig. 1. A signal analyzer ($B&K$-3560-C) was used for signal acquisition and analysis. The analyzer's generator section drove a power amplifier, which drove the mini-shaker $B&K$ 4810. This applied a vibratory force to the measured load through the impedance head $B&K$ 8000, which consists of an accelerometer and a force gauge built together in a standard titanium housing. The impedance head was rigidly attached to the mini-shaker by a brass stud. Then the force and acceleration outputs from the impedance head were amplified by two charge preamplifiers $B&K$ 2647-A, respectively. The velocity level was kept constant by integrating the acceleration output and using the velocity signal to control the generator. The output signal from the force gauge was now proportional to the mechanical impedance. The complex impedance was recorded in terms of magnitude and phase.

Before starting the measurement, a calibration process was performed on the impedance head $B&K$ 8000. First, the sensitivity of the accelerometer was calibrated using a calibration exciter $B&K$ 4294, which generated a constant acceleration of 10 $m/s2$ at 159.15 $Hz$. The second step of calibration measurement was performed with masses of 10 and 15 g, respectively. Adjust the force gauge's sensitivity so that the output from the analyzer agreed with the theoretical impedance values of the two masses at 159.15 Hz. During the calibration process, the masses were affixed to the driving platform with a thin double-stick tape. The impedance measurements were performed at a velocity of 1 $m/s$, which can avoid causing discomfort to the subjects and ensure the signal-to-noise ratio is good.

The subject was sitting in a height-adjustable chair with the impedance head pressed against the right side of the head with a static force $F$ generated by weight as shown in Fig. 2. The weight generated downward gravity $G=mg$, then the tension on the rope acted on the side of the rotation axis so that the impedance head produced an equal static force ($F=G$) pressing on the right side of the head. A lever will balance when the product of the force and the force arm equals the product of the resistance and the resistance arm. Because the force arm was equal to the resistance arm in the present study, so the force was equal to the resistance. During the measurement, the subject remained as still as possible to keep the whole system in a state of equilibrium. The weight was 500 $g$ during the measurement of the mechanical impedance of the mastoid, then the weight was changed to 300 $g$ during the measurement of the mechanical impedance of the condyle. The reason is that in the standardized test of clinical audiology, the bone vibrators should maintain a static force of 5.4 ± 0.5 N (ISO, 1994). However, when bone vibrators are applied in communication and entertainment devices, they provide less static force to improve comfort.

During the mastoid measurements, the impedance head was placed on the flattest part of the mastoid portion of the temporal bone to obtain optimum contact with the skin. During the condyle measurements, the impedance head was placed in the position where the bone conduction headphone was worn. The locations of the condyle and the mastoid are shown in Fig. 3. The mechanical impedance of the mastoid and condyle were measured three times for each subject, with at least one minute between measurements. All measurement signals were a logarithmic sweep of 161 single-frequency sinusoidal signals ranging from 100 Hz to 10 kHz. Each measurement took approximately 30 s. The total measurement time for each subject was approximately 10 min.

### D. Analysis

The complex impedance was recorded in terms of magnitude and phase. The magnitude and phase can be converted into the resistive and reactive components of the mechanical impedance. The impedance magnitude values were logarithmically scaled using a formula of $20\xd7log(X/1)$ and were expressed in dB re: 1 Ns/m. The mechanical impedance resonance frequency of mastoid and condyle were obtained for each subject. In this paper, the frequency where the absolute value of impedance is the lowest is defined as the resonance frequency.

The standard deviation of the three measurements was less than 3 dB for each subject, regardless of whether it was mastoid or condyle. The following analysis used the average of three repeated measurements as the impedance for each subject. Impedance magnitude below the resonance frequency of the mastoid and condyle was analyzed using the analysis of variance (ANOVA) with gender, age, and BMI as fixed factors. The resonance frequency and the minimum impedance magnitude were analyzed with the same fixed factors. Before applying ANOVA, the data's normal distribution and homogeneity of variance were tested. An alpha criterion of 0.05 was used for statistical significance. Conservative Bonferonni multiple comparison *post hoc* analyses were conducted on significant main effects and interactions.

## III. RESULTS

### A. All subjects

Figure 4 shows the magnitude and phase of the measured mechanical impedance of the mastoid for all 100 subjects, meanwhile, the average values are shown by the black solid lines and the median values are shown by the red dashed lines. Figure 5 shows the magnitude and phase of the measured mechanical impedance of the condyle for all 100 subjects, meanwhile, the average values are shown by the black solid lines and the median values are shown by the red dashed lines. It can be seen that the median and average values are very close to each other at all measured frequencies. Combining the magnitude with the phase, it can be discovered that below the resonance frequency, the mechanical impedance is mainly controlled by the stiffness, while above the resonance frequency, it transforms to be controlled by the mass. The resonance frequency of the mechanical impedance is equal to $(1/2\pi )\xd7(K/M)1/2$, where $K$ is the stiffness, and $M$ is the mass. H*å*kansson (1986) measured impedance of the skin-covered skull and impedance of the skull through the BAHA abutment in adults. They found that the impedance of the skull was much higher than the impedance of the skin at approximately the same spot and the same frequency, and therefore the impedance of the skin-covered skull is determined by the properties of the skin and subcutaneous soft tissue. In the present study, the mechanical impedance of the mastoid and condyle were measured on the skin surface, thus the mechanical impedances of the mastoid and the condyle are mainly determined by the properties of the skin and subcutaneous soft tissues where they are located. According to the results in Figs. 4 and 5, it can be observed that the impedance magnitude difference between individuals is larger below the resonance frequency than that above it. It can be derived that the inter-individual differences in stiffness $K$ are more pronounced than that in mass $M$.

### B. The mechanical impedance of the mastoid

Figure 6 displays the mean mastoid mechanical impedance of the three age groups. It appears from the curves that the mean impedance magnitude of the mastoid in the three age groups differ. The resonance frequency of the mastoid mechanical impedance decreases with age. It is also found that the impedance magnitude below the resonance frequency decreases with age. A comparison of the mastoid's mean mechanical impedance between the males and the females is shown in Fig. 7. There is no clear difference in the mean mastoid mechanical impedance magnitude between the males and the females. Figure 8 displays the mean mastoid mechanical impedance of the normal-weight group subjects and the over-weight group subjects, respectively. As can be seen in Fig. 8, the resonance frequency of the mean mastoid mechanical impedance in the normal-weight group subjects is higher than that in the over-weight group subjects. The mean mastoid impedance magnitude of the normal-weight group subjects is slightly higher than that of the over-weight group subjects below 2 kHz. A three-way ANOVA was conducted, treating age, gender, and BMI as the three fixed factors and the impedance magnitude below the resonance frequency of the mastoid as the dependent variable. The results indicate a significant effect of age $[F(2,88)=6.432,p<0.05(p=0.002)]$. The results of *post hoc* Bonferroni adjusted pairwise comparisons confirm that the impedance magnitude below the resonance frequency is significantly higher for Group I compared with the other age groups (Group I vs Group II, *p *<* *0.05; Group I vs Group III, *p *<* *0.001), the remaining pairwise comparison is not significant (Group II vs Group III, *p *>* *0.05). There is no significant effect of BMI $[F(1,88)=2.113,p=0.150]$ or gender $[F(1,88)=4.394,p=0.088]$. There is a significant interaction between age and gender $[F(2,88)=4.204,p<0.05(p=0.018)]$. The results of the *post hoc* analyses show that only Group II ($p<0.05(p=0.001)$) of the males have significantly higher impedance magnitude below resonance frequency than the females, and there is no significant difference between the males and the females in both Group I and Group III. None of the interactions involving BMI reached statistical significance $[F(2,88)=0.29,p=0.749$ for age × BMI; $F(1,88)=1.872,p=0.175$ for gender × BMI; $F(2,88)=0.04,p=0.961$ for age × gender × BMI $]$.

A second three-way ANOVA was conducted, treating age, gender and BMI as the three fixed factors, and resonance frequency of the mastoid impedance as the dependent variable. There is a significant effect of age $[F(2,88)=6.399,p<0.05(p=0.003)]$. The results of *post hoc* Bonferroni adjusted pairwise comparisons confirm that the resonance frequency of the mastoid impedance is significantly higher for Group I compared with the other age groups (Group I vs Group II, *p *<* *0.01; Group I vs Group III, *p *<* *0.001). Between Group II and Group III, there is no statistically significant difference (*p *>* *0.05). There is no significant effect of gender $[F(1,88)=0.898,p=0.346]$ or BMI $[F(1,88)=3.45,p=0.067]$. None of the interactions reached statistical significance $[F(2,88)=2.391,p=0.097$ for age × gender; $F(2,88)=0.026,p=0.975$ for age × BMI; $F(1,88)=1.487,p=0.226$ for gender × BMI; $F(2,88)=0.595,p=0.553$ for age × gender × BMI $]$.

Finally, a third three-way ANOVA was performed, treating age, gender and BMI as the three fixed factors, and the minimum impedance magnitude of the mastoid impedance as the dependent variable. There is no significant effect of age $[F(2,88)=0.438,p=0.647]$ or gender $[F(1,88)=0.702,p=0.404]$ or BMI $[F(1,88)=1.607,p=0.208]$. None of interactions reached statistical significance $[F(2,88)=0.303,p=0.740$ for age × gender; $F(2,88)=0.48,p=0.620$ for age × BMI; $F(1,88)=1.166,p=0.283$ for gender × BMI; $F(2,88)=0.288,p=0.750$ for age × gender × BMI $]$. The above analysis suggests that the mechanical impedance of the mastoid is influenced by age.

### C. The mechanical impedance of the condyle

The magnitude and phase of the mean condyle mechanical impedance of the three age groups are shown in Fig. 9. The mean mechanical impedance magnitude of the condyle in Group II and Group III is equal. There are some slight differences between Group I and the other groups in the frequency range of 0.1–1 kHz. Figure 10 plots the comparison of the mean mechanical impedance of the condyle between the males and the females. There is a difference in the condyle's mean impedance magnitude between the males and the females at resonance frequency. It can be seen from Fig. 11 that the normal-weight group's mean condyle impedance magnitude below the resonance frequency is higher than that of the over-weight group and the resonance frequency of the mean condyle mechanical impedance of the normal-weight group is higher than that of the over-weight group. A three-way ANOVA, treating age, gender, and BMI as the three fixed factors and the impedance magnitude below the resonance frequency of the condyle as the dependent variable, shows there is a significant effect of BMI $[F(1,88)=12.799,p<0.05(p=0.001)]$. There is no significant effect of gender $[F(1,88)=0.067,p=0.796]$ or age $[F(2,88)=0.451,p=0.639]$. None of the interactions reached statistical significance $[F(2,88)=0.843,p=0.434$ for age × gender; $F(2,88)=0.047,p=0.954$ for age × BMI; $F(1,88)=0.000,p=0.992$ for gender × BMI; $F(2,88)=0.485,p=0.617$ for age × gender × BMI $]$.

A second three-way ANOVA was conducted, treating age, gender and BMI as the three fixed factors, and resonance frequency of the condyle impedance as the dependent variable. There is a significant effect of BMI $[F(1,88)=8.569,p<0.05(p=0.004)]$. There is no significant effect of gender $[F(1,88)=0.002,p=0.969]$ or age $[F(2,88)=0.022,p=0.978]$. None of the interactions reached statistical significance $[F(2,88)=0.843,p=0.434$ for age × gender; $F(2,88)=0.047,p=0.954$ for age × BMI; $F(1,88)=0.00,p=0.992$ for gender × BMI; $F(2,88)=0.485,p=0.617$ for age × gender × BMI $]$.

Finally, a third three-way ANOVA was conducted, treating age, gender and BMI as the three fixed factors, and the minimum impedance magnitude of the condyle impedance as the dependent variable. There is a significant effect of gender $[F(1,88)=4.449,p<0.05(p=0.038)]$. There is no significant effect of age $[F(2,88)=0.295,p=0.731]$ or BMI $[F(1,88)=1.889,p=0.173]$. None of the interactions reached statistical significance $[F(2,88)=0.693,p=0.503$ for age × gender; $F(2,88)=0.256,p=0.775$ for age × BMI; $F(1,88)=0.008,p=0.869$ for gender × BMI; $F(2,88)=1.371,p=0.259$ for age × gender × BMI $]$. The above analysis suggests that the mechanical impedance of the condyle is influenced by BMI, and the minimum impedance magnitude of condyle is influenced by gender.

## IV. DISCUSSION

### A. Difference between mastoid and condyle

A comparison between the mean mechanical impedance magnitude of the mastoid and the condyle in 100 subjects is shown in Fig. 12. It can be found that the resonance frequencies of the mean condyle and mean mastoid are 0.9 and 2 kHz, respectively. The average impedance magnitude difference between the mastoid and condyle is 12 dB below 1 kHz. Figure 13 illustrates the resistances and reactances of the mechanical impedances at the mastoid and condyle. It can be observed that the difference in reactance between the mastoid and the condyle is noticeable below 1 kHz, and the difference decreases with frequency. At low frequencies, the reactance is mainly determined by the stiffness K, and the greater the K, the higher the reactance, where $K\u2009=\u20091/C$. At higher frequencies, the reactance is mainly determined by the mass M, and the larger the M, the higher the reactance. Comparing the reactance of the mastoid with condyle, it can be derived that the difference in the stiffness $K$ between the mastoid and the condyle is large and the difference in mass $M$ between the mastoid and the condyle is small. The thickness of the skin and subcutaneous soft tissue affects its stiffness, which decreases with thickness (Delalleau *et al.*, 2008; Liu, 2017). The stiffness $K$ of the mastoid is greater than that of the condyle because the thickness of the skin and subcutaneous soft tissue of the mastoid is less than that of the condyle. This is consistent with our experimental and analysis results. The mass $M$ is due to the mass in the outer layer of the soft tissue, which should be related to the measured area (H*å*kansson, 1986). In the present study, the measured area of both the mastoid and condyle was 1.75 cm^{2}, so the difference in mass $M$ between the mastoid and the condyle is small and could be negligible. The resistance $R$ of the mastoid is greater than that of the condyle (see Fig. 13), which results in a higher minimum impedance magnitude of the mastoid than that of the condyle (see Fig. 12).

### B. Comparison with previous measurements

The results in the present study are compared with similar measurements from some previous studies (see Fig. 14). Flottorp and Solberg (1976) measured the mechanical impedance at the forehead and mastoid region in 60 human volunteers, the solid blue line shows the mean impedance magnitude of the mastoid in 30 subjects (aged from 16.6 to 37.5 years). The chain-dotted line shows the mean impedance magnitude of the mastoid of 30 subjects (aged from 22 to 51 years) in the study of Cortés (2002). The dotted line represents the actual measured impedance magnitude of the B&K artificial mastoid 4930. Zhang (1994) measured the mastoid impedance in 444 Chinese subjects (aged from 5 to 80 years) using the same measurement equipment, the dashed line shows the mean mastoid impedance magnitude of all subjects. The solid green line shows the mean impedance magnitude of the mastoid measured in 100 subjects in the present study. It can be observed that below 3 kHz, the mean impedance magnitude of mastoid measured in the present study is more close to that measured by Zhang (1994), while the results of the present study and Zhang (1994) have apparently lower mean impedance magnitude below 2 kHz than the other three measurements. In addition, it can be found that the resonance frequencies of the results from Flottorp and Solberg (1976), Cortés (2002), and B&K 4930 are all closer to about 3 kHz. However, the resonant frequencies of the results from both the present study and Zhang (1994) are at 2 kHz. In the studies of Flottorp and Solberg (1976) and Cortés (2002), the subjects were all Western, while the subjects in the present study and Zhang (1994) were all Chinese. The difference in mean mastoid impedance between different measurement results may be because the presence of subjects over 50 years old in the present study and Zhang (1994) will reduce the mean mastoid impedance. However, differences in the age of the subjects cannot explain all of the differences observed between the measurements reported here and by Zhang (1994) and the measurements of Cortés (2002) and Flottorp and Solberg (1976).

Concerning variation with age, the results of Flottorp and Solberg (1976) showed that mean mastoid impedance of Group IV (aged from 48.8 to 71.3 years) has a lower impedance magnitude than that of Group III (aged from 20.3 to 37.5 years). Zhang (1994) showed that in the range of 100–1000 Hz, the impedance magnitude of the mastoid from 5 to 65 years is correlated with age, the impedance magnitude decreases with age. They also found that the resonance frequency of the mastoid shifts to lower frequency with age. In addition, they obtained a relationship between resonance frequency *f*_{0} and the age *Y*, which is $f0=3.1\u22120.17*Y1/2$. In the present study, the resonance frequency of mastoid impedance was calculated for each subject. Then the square root of age was taken as the independent variable, and the resonance frequency of mastoid was taken as the dependent variable. The results of linear regression analysis show that there is a correlation between them $(R2=0.258,p<0.001)$, and the linear regression model is $f0=2.9\u22120.17*Y1/2$. The correlation coefficient, however, suggests that only 26% of the variance in our results can be explained by age.

### C. Influence of gender, age, and BMI

In the study by Flottorp and Solberg (1976), the mechanical impedance of the human head bones (mastoid and forehead) is modeled by a three-parameter model consisting of mass, compliance, and damping (see Fig. 15). In this model, the compliance is derived from the reactance at 125 Hz, and the mass is calculated from the resonance frequency and the compliance; the damping is simply taken from the minimum impedance magnitude. However, with such modeling method, there are some non-negligible differences between the calculated and the measured impedance magnitude in the present study. In order to make the three-parameter model fit the measured impedance magnitude better, the following improvements are made. First, the damping is still taken from the minimum impedance magnitude, the initial compliance is derived from the reactance at 100 Hz, and the initial mass is calculated from the resonance frequency and the initial compliance. Then the parameters $C$ and $M$ are varied until the maximum difference between the three-parameter model impedance magnitude and the measured impedance magnitude is minimized, and then the optimal values of the compliance and the mass are stored. Following the above method, the three-parameter model of the mastoid and the condyle impedance can be obtained for each subject separately. Figure 16 displays the measured impedance magnitude and the corresponding model magnitude for the mastoid and the condyle of the same subject. The difference between the measured impedance magnitude and the model magnitude is small.

In the section with the mechanical impedance of the mastoid and the mechanical impedance of the condyle, the analysis results show that the mechanical impedance of the mastoid may be influenced by age, and the mechanical impedance of the condyle may be influenced by BMI. It is interesting to explore the reasons why age has an effect on mastoid impedance and why BMI has an effect on condyle impedance. Six three-way ANOVAs were conducted, with age, gender, and BMI as the three fixed factors, with $Rm,\u2009Cm,\u2009Mm,\u2009Rc,\u2009Cc$, and $Mc$ as dependent variables, respectively. The subscript “m” indicates the mastoid, and the subscript “c” indicates the condyle. Table II summarizes the statistical findings for $Rm,\u2009Cm$, and $Mm$, the significant effects (*p* < 0.05) are given in boldface. It can be found that there are significant differences in the $Cm$ in the three age groups. *Post hoc*, Bonferroni adjusted pairwise comparisons identified the $Cm$ of the Group I $(5.735\u2009\xb1\u20090.583)$ is lower than both Group II $(7.347\u2009\xb1\u20090.502,p<0.05)$ and Group III $(8.445\u2009\xb1\u20090.048,p<0.001)$, there is no significant difference in $Cm$ between Group II and Group III (*p *=* *0.349). In addition, there is a significant interaction between age and gender in $Cm$. *Post hoc* testing revealed that the $Cm$ is significantly higher for the females than for the males in Group II (*p *<* *0.05), and there are no significant differences between the males and the females in both Group I (*p *=* *0.237) and Group III (*p *=* *0.112). The impedance magnitude at low frequencies is mainly determined by the compliance $C$, the greater the compliance $C$, the lower the impedance magnitude at low frequencies. In addition, when the difference in mass M is small, the greater the C, and the smaller the resonance frequency of the impedance, in agreement with the results in Fig. 6. The analysis results demonstrate that mastoid impedance is affected by age because the stiffness of the skin is affected by age and decreases with age. Table III summarizes the statistical findings for $Rc,\u2009Cc$, and $Mc$. The significant effects (*p* < 0.05) are given in boldface. The results show that the R_{m} of the males is significantly higher than that of the females (*p *<* *0.05). The minimum impedance magnitude is determined by the damping *R*, the greater the damping *R*, the greater the minimum impedance magnitude. In addition, the results show that there is a significant difference in the $Cc$ of the normal-weight group and the over-weight group. The $Cc$ of the over-weight group is higher than that of the normal-weight group (*p *<* *0.05). Therefore, the mean impedance magnitude below the resonance frequency and the resonance frequency of the normal-weight group are significantly higher than those of the over-weight group. This is consistent with the results in Fig. 11. The results show that the condyle impedance is influenced by BMI, which might influence the thickness of the skin and subcutaneous soft tissue and thus the stiffness of the condyle tissue.

To verify that the thickness of the skin and subcutaneous soft tissue at the condyle is influenced by BMI and the stiffness of skin and subcutaneous tissue at the condyle is influenced by its thickness, measurements of the thickness of the skin and subcutaneous soft tissue at the mastoid and condyle were conducted. Computerized tomography (CT) scan was used to measure the thickness of the skin and subcutaneous soft tissue at the condyle and mastoid. It was not feasible to ask all the 100 subjects to hospitals to conduct this measurement with CT. Thus, only ten subjects were recruited to participate in the CT measurement, aged from 22 to 27 years, five subjects from the normal-weight group ($BMI<24$), five subjects from the over-weight group ($BMI\u226524$). Pearson correlation coefficient between the BMI and the thickness of the skin and subcutaneous soft tissue at the condyle was calculated, the results show that there is a strong correlation between them $[r(10)=0.853,p<0.05(p=0.002)]$. It can be confirmed that the thickness of the skin and subcutaneous soft tissue at the condyle in the over-weight group subjects is higher than that in the normal-weight group. The Pearson correlation coefficient between the thickness of the skin and subcutaneous soft tissue at the condyle and the compliance $Cc$ was also calculated, the results show that there is a strong correlation between them $[r(10)=0.864,p<0.05(p=0.001)]$. The compliance $Cc$ increases with the thickness of the skin and subcutaneous soft tissue, which is consistent with our analysis results. There is no correlation between the BMI and the thickness of the skin and subcutaneous soft tissue at the mastoid $[r(10)=0.404,p=0.246]$, and there is also no correlation between the thickness of the skin and subcutaneous soft tissue at the mastoid and the compliance $Cm[r(10)=0.356,p=0.313]$, which is consistent with our analysis results.

### D. Influence of variations in mechanical impedance on the output performance of the BCD

The influence of variations in the mechanical load on the output of a bone conduction device is studied here. Source calibration measurements using the artificial mastoid will be in error if there are significant differences between the mechanical impedance of the subject's mastoid and the artificial mastoid. We need to simulate how the output force of the BCD is influenced. The BCD can be modeled by an electro-mechanical analogy, as shown in Fig. 17. The values of the parameters in the network of BC are taken from Lundgren (2010), and their values are shown in Table IV. The BCD used in the model is Radioear B71, a standard BC transducer used for audiometric testing. On the right side of the model in Fig. 17 is a model of the mastoid impedance or the condyle impedance, or the artificial mastoid B&K 4930 impedance.

On the electrical side, *U _{g}* represents an input voltage source, while the transducer's coil ohmic resistance, coil inductance, and magnetic losses are represented by

*R*

_{0},

*L*

_{0}, and $R\omega $, respectively. The gyrator

*g*converts the current

*i*on the electrical side into the velocity

*v*on the mechanical side. The resistance

*R*

_{1}and the compliance

*C*

_{1}are the damping and compliance of the transducer suspension, while the total mass of the armature, bobbins, and wire is represented by

*m*

_{1}. The mass of the B71's housing is divided into two parts, represented by

*m*

_{2}and

*m*

_{3}, respectively. The resistance

*R*

_{2}and the compliance

*C*

_{2}are the damping and compliance of the B71's housing, respectively.

As shown in Fig. 18(A), in the range of 0.125–2.2 kHz, the mechanical impedance of the artificial mastoid B&K 4930 differs significantly from the mean mastoid measured in the present study. The difference is most remarkable at 2 kHz, which can be up to 10 dB. Figure 18(B) shows the output force of the BCD when the input voltage is 1 V, with different mechanical impedance as loads. The output force of the BCD with the measured mean mastoid impedance as a load differs significantly from that with the artificial mastoid B&K 4930 as a load by as much as 11 dB at 0.3–3 kHz. The variation of impedance has little influence on the output force of the BCD below 0.3 kHz because the internal impedance of BCD is smaller than the load impedance, and the B71 acts as a constant force source. The results indicate that there is a bias in using the IEC-valued replication device $B&K$ 4930 as an audiometric calibration device for Chinese subjects in some frequencies. As can be seen in Fig. 18(B), the output force of the BCD on the artificial mastoid B&K 4930 differs significantly from that on the subject's condyle, with a maximum difference of 24 dB, and the average deviation is 8.2 dB. Therefore, the artificial mastoid is not suitable for calibrating bone conduction headphones, which are placed on the condyle.

In addition, it is also interesting to investigate how the impedance variation of the subject affects the output performance of the BCDs. Section Influence of gender, age, and BMI of this study shows that the mechanical impedance of both the mastoid and condyle in each individual can be expressed in terms of three parameters: compliance $C$, mass $M$ and damping $R$. Inter-individual differences in compliance $C$ are greatest for the mastoid and the condyle, followed by damping $R$, inter-individual differences in mass $M$ are minimal. Therefore, the three parameters of the subjects' mean mastoid impedance can be taken as a nominal value ($C=6.50\xb710\u22126\u2009m/N,\u2009M=1.1\xb710\u22123\u2009Ns2/m,\u2009R\u2009=\u20098.50\u2009Ns/m$). Then the mass $M$ and the damping $R$ are kept constant, and the compliance $C$ is set to $4.06\xb710\u22126\u2009m/N,6.50\xb710\u22126\u2009m/N,\u20098.94\xb710\u22126\u2009m/N$, respectively. Three relevant combinations can be obtained. Figure 19(A) displays three different mechanical impedance of the mastoid with the internal impedance of BCD. Figure 19(B) displays the output force of the BCD loaded with the mechanical impedance in Fig. 19(A). Figure 19(C) displays the output velocity of the BCD loaded with the mechanical impedance in Fig. 19(A). It can be inferred from Fig. 19(A) that the compliance $C$ mainly affects the resonance frequency and impedance magnitude below the resonance frequency. The larger the compliance $C$, the smaller the resonance frequency and the impedance magnitude below the resonance frequency. Figure 19(B) shows that the variation of the compliance $C$ affects not only the output force level but also the first and second resonance frequencies of the output force. However, the third resonance frequency is largely independent of the impedance of load. The larger the $C$, the lower the first and second resonance frequencies. The smaller the compliance $C$, the higher the impedance magnitude, and the greater the output force of the BCD. Comparing the BCD's output force between the mean mastoid mechanical impedance (dashed line) and the maximum mastoid impedance (dotted line), it can be observed that the difference is more pronounced around the first and second resonance frequencies, the maximum difference can be up to 15.5 dB, and the average difference is 2.6 dB in the whole range of frequency. From Fig. 19(A), it can be seen that the difference in impedance magnitude between the maximum mastoid mechanical impedance and the minimum mastoid impedance is about 7 dB below 250 Hz. However, the difference in output force below 250 Hz is tiny. The reason is that the load impedance magnitude is much larger than the internal impedance of the B71 below 250 Hz, resulting in the B71's behavior close to an ideal force source. Therefore, below 250 Hz, the variation in load has little effect on the output force of the B71. It can be observed from Fig. 19(C) that as the frequency increases, the B71 transitions to an ideal velocity source at 0.5 kHz because the internal impedance of the B71 is much greater than the load impedance. Then it can be seen from Fig. 19(B) that the B71 is again converted to an ideal force source near 1.2 kHz. Finally, the B71 is fixed as an ideal velocity source after 1.3 kHz.

The compliance C of the mastoid impedance is affected by age, the compliance C increases with the age. The compliance C of the condyle impedance is affected by BMI, the compliance C increases with the BMI. When the internal impedance of B71 is smaller than the load impedance, the variation of the compliance C due to age or BMI has a small effect on the output force of the B71. Then when the internal impedance of the B71 is larger than the load impedance, the variation of the compliance C due to age or BMI has a larger effect on the output force of the B71.

### E. Influence of stimulation position on the sensitivity for bone conduction devices

The previous studies indicated that when the stimulation is applied on the condyle, the sensitivity of BC hearing is higher than that on the mastoid (McBride *et al.*, 2008; Qin *et al.*, 2019). McBride *et al.* (2008) measured the BC hearing thresholds on 11 different skull locations of 14 volunteers seated in a quiet environment. They demonstrated that the condyle has the lowest mean threshold, and the mean BC hearing thresholds on the condyle are 7.4, 1.8, 10, 4.1, and 6.4 dB lower than on the mastoid at 0.25, 0.5, 1, 2, and 4 kHz, respectively. Figure 20 displays the output velocity magnitude of the transducer model (Fig. 17) excited by 1 V and loaded with the measured mastoid impedance (dashed line) and condyle impedance (solid line). It can be observed that the velocities on the condyle are about 8, –1, 8, –1.5, and 0 dB higher than that on the mastoid at 0.25, 0.5, 1, 2, and 4 kHz, respectively. This implies that the variation of velocity magnitude is relevant to the variation of the BC hearing thresholds at different frequencies between condyle and mastoid. Dobrev *et al.* (2016) measured the cochlear promontory motion of the cadaver heads using a laser Doppler vibrometry, while stimulating seven different positions around the pinna using a bone-anchored hearing aid transducer. They also measured BC hearing thresholds in twenty participants, with the B71 attached to the same seven stimulation positions. The stimulation on a position superior-anterior to the pinna, which was defined by Dobrev *et al.* (2016) as the “condyle,” results in lower BC hearing thresholds and higher cochlear promontory vibrations than does stimulation on the mastoid. However, there might be discrepancies between their described “condyle” and the condyle in the present research. Stimulation on the position superior-anterior to the pinna induces vibrations on the parietal bone that maybe propagate to the cochlea in a more direct way because no joint capsule is between the site of stimulation and the cochlea. Sound propagation in bone conduction stimulation depends on the underlying structures, which needs further investigation.

## V. CONCLUSION

To investigate the mechanical impedance of the mastoid and condyle, measurements were conducted in 100 Chinese subjects. It is found that both the mechanical impedance of mastoid and condyle are mainly stiffness-controlled below the resonance frequency and transform to mass-controlled above the resonance frequency. The mastoid and condyle impedances of the same subject are significantly different in the stiffness-controlled region. The mechanical impedance modeling and factor analysis show that the stiffness of mastoid is significantly influenced by age, and the stiffness of condyle is significantly affected by BMI and the damping of the condyle is significantly affected by gender. The mean mastoid mechanical impedance in the stiffness-controlled region and the resonance frequency measured in the Chinese subjects differ significantly from that in the standard artificial mastoid.

Further analysis is performed to investigate the effect of impedance differences on the force output of the BCD, through the simulation of the electro-mechanical analogy of both the BCD and the load mechanical impedance. The results indicate that there are significant differences in the mechanical impedance of the mastoid and condyle, resulting in significant differences in the force output of the BCD, with a maximum difference of up to 20 dB.

The variability of the mechanical impedance among subjects at the same stimulation location has a slight effect on force output of the BCD. By simulation comparison of the velocity of the BCD at different stimulation positions, it is implied that the velocity of the BC vibrators might correspond to BC hearing sensitivity at different locations. The results of this study can be used to develop condyle simulators and mastoid simulators adapted to the Chinese subjects, which can evaluate, predict, and calibrate BCDs.

## ACKNOWLEDGMENTS

This work was supported by the Open Research Project of the State Key Laboratory of Media Convergence and Communication, Communication University of China, China (Nos. SKLMCC2020KF005 and SKLMCC2021KF014). This work was also supported by National Key Research and Development Project (2021YFB3201702), the National Science Fund of China (Grant Nos. 12074403 and 11974086), the Guangzhou Science and Technology Plan Project (No. 201904010468), Guangzhou University Science Research Project (No. YJ2021008), and Hainan Provincial Natural Science Foundation of China (Grant No. 619QN265).