Simulation of soft tissue stimulation–Indication of a skull bone vibration mechanism in bone conduction hearing

Soft tissue conduction has been proposed as an alternative to bone conduction (BC) for hearing vibrations applied at soft tissue positions at the human head. Arguments for soft tissue conduction originate primarily from experimental studies with stimulation applied to different positions such as the neck, the eye, and directly to the dura. To investigate the mechanism for hearing when stimulations are at soft tissue positions, experimental studies were replicated using the ﬁnite element model for BC research, the LiU-Head. The vibrations at the cochlear promontory and the sound pressure in the cerebrospinal ﬂuid (CSF) close to the inner ear were extracted from simulations in the LiUHead. The LiUHead simulations were able to replicate data in the literature of cochlear promontory vibration levels and CSF sound pressures with stimulation applied at the soft tissue positions and at the skin covered mastoid. It was shown that the mechanical point impedance of the soft tissue positions affected the output of the BC transducer at frequencies below 1 kHz. The LiUHead simulated cochlear promontory velocities predicted the soft tissue position’s hearing thresholds reported in the literature within the inter-study range. This indicates that the hearing mechanism for stimulation at soft tissue positions equals the hearing mechanism for conventional BC hearing, and that soft tissue conduction is not an alternative hearing mechanism. Moreover, the simulations indicated that the CSF sound pressure is not an important pathway for BC hearing and that the CSF pressure is generated by the local skull bone vibrations. © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http


Introduction
Hearing by bone conduction (BC) stimulation is often considered as a sound transmitted in the skull bone that influences the inner ear directly by the skull bone vibrations ( Stenfelt, 2011 ;Stenfelt and Goode, 2005 ;Tonndorf, 1972 ).In addition, BC sound transmission has also been suggested to involve sound radiated into the ear canal ( Stenfelt et al., 2003 ;Surendran and Stenfelt, 2021 ) and motions of the middle ear ossicles driven by inertia ( Röösli et al., 2012 ;Stenfelt, 2006 ;Stenfelt et al., 2002 ).A BC transducer is often placed on the skin covered skull bone, such as on the mastoid or forehead, or directly coupled to the skull bone as in cases of BC hearing aids like the Cochlear BAHA system, Oticon medical Ponto system, or MedEl Bonebridge system ( Chang and Stenfelt, 2019 ;Reinfeldt et al., 2015 ).The consensus that BC sound is primarily caused by skull bone vibrations is based on experimental work evaluating sound transmission pathways for BC sound, clinical assessment of hearing by BC, and mathemati-cal simulations of mechanisms for BC hearing ( Dobrev et al., 2017 ;Eeg-Olofsson et al., 2013 ;Stenfelt, 2016 ;Stenfelt, 2020 ;Zhao et al., 2021 ).According to this, BC hearing is often described as the sum of the contributing components: 1) sound radiated into the ear canal, 2) inertial effects of the middle ear ossicles, 3) inertial effects of the fluid in the inner ear, and 4) space alteration of the inner ear due to the vibrations of the bone surrounding the inner ear ( Stenfelt, 2011( Stenfelt, , 2016 ; ;Stenfelt, 2020 ;Stenfelt and Goode, 2005 ).
In addition to these possible contributors to BC sound, it has been suggested that the sound can reach the inner ear by vibrations applied to non-osseous positions (soft tissue, fluid, etc) and that the vibrations are transmitted to the inner ear without involvement of the skull bone, or, at least, the vibration of the skull bone is not the dominant contributor to the perceived sound ( Sohmer, 2014 ;Sohmer et al., 20 0 0 ;Stump et al., 2018 ).One such phenomenon is when the vibration is applied to the outer parts of the ear, the pinna, concha, or just in front of the ear canal.For such positions, the sound is primarily radiated in the ear canal due to the vibrations of the cartilages of the outer ear ( Nishimura et al., 2015 ).The vibrations of the skull bone beneath the cartilages become a less significant contributor for the perceived sound in this condition.Other claims for the theory of non-osseous transmis-sion of BC sound are based on experiments where BC transducers have been positioned directly at the dura of the brain through craniotomies ( Sohmer et al., 20 0 0 ;Stump et al., 2018 ), or with the BC transducer applied to the eye or at a soft tissue position, typically at the neck ( Adelman et al., 2015 ;Chordekar et al., 2018 ;Ito et al., 2011 ;Watanabe et al., 2008 ).In these cases, a hearing perception have been reported with stimulation levels relatively close to those used for the stimulations of the skin covered skull, like the mastoid.The prevailing explanation for this hearing sensation is that the vibration is transmitted to the fluids in the head, for example the cerebrospinal fluid (CSF), and that this sound pressure in the fluid is transmitted to the inner ear fluid via the so called third window, a patent transmission pathway between the inner ear and the CSF fluid ( Sohmer, 2017 ).Those pathways may consist of the cochlear or vestibular aqueducts, or other pathways that can transmit a sound pressure like veins or neural tissue entering the inner ear ( Stenfelt, 2020 ).
Several arguments have been presented to support the hypothesis of a soft tissue BC transmission pathway not involving the skull bone.One such argument is that skull vibrations measured during BC stimulation was either practically zero, or at a level that was too low to suggest a significant skull bone vibration ( Adelman et al., 2012 ;Ito et al., 2011 ;Sohmer et al., 20 0 0 ).Another argument is that the impedance difference between soft tissue and skull bone is great and that, due to the impedance mismatch between the two structures, most of the vibration in the soft tissue is reflected and too little vibration is transmitted in the skull bone to enable BC hearing by skull bone vibration.However, based on impedance values of bone and soft tissues, the impedance mismatch would lead to an attenuation of the BC sound of approximately 7 dB going from the soft tissue to the bone ( Sohmer, 2017 ).This is in line with differences in BC sensitivity for bone applied and skin applied BC stimulation that is 0 to 15 dB at frequencies below 10 kHz ( Prodanovic and Stenfelt, 2021 ;Stenfelt, 2006 ;Stenfelt and Håkansson, 1999 ).
Another issue with the different studies of fluid and soft tissue stimulation and transmission is that most such studies have used the electrical voltage to a Radioear B71 transducer as the reference.This means that the actual output of the BC transducer can differ between the stimulation positions since the output of a Radioear B71 transducer depends on the load impedance it is applied to ( Chang and Stenfelt, 2019 ;Surendran and Stenfelt, 2021 ).Consequently, part of the difference seen between stimulation at different positions can be caused by the difference in output from the BC transducer.However, it is also possible that the difference in BC sensitivity between the different positions are greater than reported due to the different outputs from the Radioear B71 transducer at the different stimulation positions.Such an effect is most likely frequency dependent.
Investigating the sound pathways with BC stimulation experimentally is challenging.Another possibility is to evaluate the sound pressure and structure vibrations in computational models.One such model developed for BC research is the LiUHead, a finite element model that comprise 8 different structures including soft tissues, skull bone, CSF, eyes, brain tissue, and inner ears ( Chang et al., 2016 ).Analyzing the skull bone vibrations at the inner ear and the sound pressure in the CSF close to the inner ear in the LiUHead during conditions similar to experiments can reveal the sound pathways for BC sound in those studies.
The aim of the current study is to replicate experimental studies with BC stimulation at the neck, eye, and directly to the dura through a craniotomy in the finite element computational model LiUHead, and to compare the resulting vibrational motion at the cochlear promontory and the sound pressure in the CSF with stimulation at the skin covered mastoid.The hypothesis is that if the cochlear promontory vibration magnitude difference between the soft tissue stimulation and the mastoid stimulation is similar to the experimental hearing threshold shifts, the origin of the BC sound perception with soft tissue stimulation is similar to that of BC mastoid stimulation.However, a significant difference between the threshold shifts and difference in cochlear promontory vibration magnitude will indicate a BC pathway with soft tissue stimulation different from that with mastoid stimulation.

Model overview
All simulations were conducted with the LiUHead, a whole head finite element model developed for BC sound transmission investigations ( Chang et al., 2016 ).Fig. 1 show the eight domains of the model: 1) soft tissue, 2) cartilage, 3) cortical bone, 4) soft bone (diploë), 5) CSF, 6) brain and nervous tissue, 7) eyes, and 8) inner ears.The model consists of 480,0 0 0 tetrahedral elements and comprises 87,100 nodes.A detailed description of the LiUHead is found in Chang et al. (2016) .

Experimental studies
The simulations in the LiUHead were compared to experimental findings with vibration stimulations on the eye, neck, and directly to the dura in living humans and cadaver heads.Only studies that report frequency specific hearing thresholds and/or vibration measurements that are repeatable were included in the comparisons.The details for each dataset are given below and an overview of the included studies is given in Table 1 .

Stimulation on the eye
Ito et al. ( 2011) measured hearing thresholds and vibration of the teeth when the stimulation was provided by a Radioear B72 BC transducer in 10 participants with normal hearing and 5 participants with unilateral deafness.The data used in the present study are the outcomes during vibration stimulation with 5 N static force at the mastoid and vibration stimulation with 2 N static force on the closed eye.An insert earphone was present during the testing that may have introduced an occlusion effect.Vibration data at the teeth were obtained from the participants biting on an accelerometer.
Sohmer et al. (20 0 0) present hearing thresholds with a Radioear B71 transducer applied to the mastoid and to the eye in

Table 1
An overview of the studies included in the analysis.10 female participants with normal hearing.The testing was done with an earplug that may have introduced an occlusion effect.Watanabe et al. (2008) tested 12 young adults (18-30 years) with hearing thresholds better than 20 dB HL using a Radioear B71 BC transducer at the eye and at the mastoid.The BC transducer was held by hand by the participants, the opposite ear was masked by noise, and the ipsilateral ear had a foam earplug inducing an occlusion effect.Adelman et al. (2015) measured on 10 young adults (20-30 years) with hearing thresholds of 15 dB HL or better using a Radioear B71 BC transducer at the mastoid and the submandibular triangle (below the earlobe and posterior to the body of the mandible).On the mastoid, the BC transducer was applied by a static force of 5 N provided by a headband while the participant held the transducer on the neck by hand providing a static force of 5 N controlled by a spring.Chordekar et al. (2018) evaluated stimulation on the mastoid and on the neck (5 cm below the ear-lobe over the sternocleidomastoid muscle) with a Radioear B71 BC transducer in two groups.One group consisted of 10 participants with hearing thresholds of 15 dB HL or better and one group consisted of 5 participants with conductive or mixed hearing losses that had been implanted with fixtures for BC hearing aids.In the current study, data from the group with normal hearing are used.The static force of the BC transducer was 5 N for both test positions and they had earplugs causing occlusion effects.

Stimulation on the dura
Sohmer et al. (20 0 0) measured the BC thresholds in two children (10 and 13 years old) with craniotomies.The BC stimulation was applied by a Radioear B71 transducer on the dura in the craniotomy and on the skin covered skull bone.Neither the craniotomies' nor the skull bone stimulations' exact positions were provided and it was here assumed that the craniotomy was at the center of the vertex and the stimulation on the skull bone was adjacent to that.The BC transducer was held by hand with equal static force on both positions, but the exact force was not provided.Dobrev et al. (2019) measured the cochlear promontory vibration in three spatial dimensions and the intracranial sound pressure while the stimulation was at the skin-covered mastoid, the neck, and the eye in five severed and Thiel embalmed human cadaver heads.The stimulation was applied by a Cordelle II transducer (Cochlear BAS, Mölnlycke, Sweden) coupled to a plastic plate on a steel band providing approximately 5 N.In some of the cadaver heads the eye was deflated and was replaced by an artificial 3 cm diameter eyeball of water encapsulated in a latex glove.Sim et al. (2016) report on cochlear promontory vibration and intracranial sound pressure from four Thiel embalmed human cadaver heads when the stimulation was provided by a Bonebridge BC transducer (Med-El, Australia) at either the mastoid (screwed to the bone) or at the dura through a craniotomy.No data on the transducer output were provided.Röösli et al. (2016) measured the cochlear promontory vibration and intracranial sound pressure in four Thiel embalmed cadaver heads when the stimulation was applied to the skin covered mastoid, the skin covered forehead, the eye, and the neck.The stimulation was a 10 V electric signal to a Cordelle II BC transducer attached to a steel headband with a plastic circular interface of approximately 15 mm in diameter.

LiUHead simulations
All parameter values of the LiUHead are those previously published and analyzed.The one exception is the addition of the dura for the craniotomy simulations ( Fig. 2 C).The dura is here modelled as an 18 mm diameter 0.7 mm thick layer.Consequently, there is a 1.5 mm space between the stimulation plate (Ø 15mm) and the skull bone.The Youngs modulus of the dura was set as 70 MPa ( Zwirner et al., 2019 ), the density was 1133 kg/m 3 ( Barber et al., 1970 ), the Poisson's ratio assumed to be 0.45, and no damping.The outer radius of the dura is attached to the cortical skull bone and the inner part of the dura is attached to the CSF.
The excitation in the human studies of soft tissue stimulation described above was done with a Radioear B71 or B72 transducer.To replicate this in the simulations, the stimulation was provided as a dynamic force equally distributed over a 15 mm in diameter stiff circular plate (area of 175 mm 2 ).In total, the excitation was provided at five different positions: 1) the mastoid behind the ear normally used for audiometry ( Fig. 2 a), 2) the neck below the skull bone ( Fig. 2 a), 3) the eye ( Fig. 2 b), 4) a duracovered craniotomy opening into the CSF ( Fig. 2 c), and 5) a position in front of the craniotomy (termed off-craniotomy) on the skin-covered skull.For the simulations, a dynamic force of 1 N was applied on these positions at frequencies between 0.1 kHz and 10 kHz.
The outcomes of the human experimental studies were hearing thresholds.It is not possible to obtain a hearing threshold in the LiUHead, so the simulations were analyzed using two different outcomes, the three-dimensional vibration of the cochlear promontory and the sound pressure in the CSF close to the cochlea.The positions where these two outcomes were obtained in the LiUHead are shown in Fig. 3 where a cross section image of the LiUHead is displayed.The position for the cochlear promontory vibration is indicated by a red cross in the enlarged part of the skull base ( Fig. 3 ), a position similar to several cadaver head studies on BC sound transmission ( Dobrev et al., 2019 ;Dobrev et al., 2016 ;Eeg-Olofsson et al., 2011 ;Eeg-Olofsson et al., 2008 ;Ghoncheh et al., 2021 ;Håkansson et al., 2008 ) as well as in live human studies obtaining the cochlear promontory vibration ( Eeg-Olofsson et al., 2013 ).The CSF pressure is obtained as the average pressure over a cylindrical-like volume of 75 mm 3 in the CSF close to the cochlea, indicated in Fig. 3 .The rationale for this is that the exact way the CSF sound pressure would influence hearing is currently unknown, but the transmission of a CSF sound pressure to the cochlea is most likely in the cranial area close to the cochlea.
The stimulation in the LiUHead is accomplished by applying a dynamic force of 1 N on a stiff circular area corresponding to the area of a Radioear B71 or B72 BC transducer, and like the cadaver head experiments with a 15 mm circular interface.However, the experimental studies used the reading of an audiometer dial to estimate the stimulation level.It is here assumed that the reading on the audiometer directly relates to the voltage delivered to the BC transducers.However, the mechanical point impedances at the different stimulation positions differ, and are different from an artificial mastoid on which the BC transducers are calibrated ( Flottorp and Solberg, 1976 ;Surendran and Stenfelt, 2021 ).Therefore, the dynamic output force from a B71 transducer is computed based on a lumped element model of a B71 transducer ( Chang and Stenfelt, 2019 ;Surendran and Stenfelt, 2021 ) and the mechanical point impedance of the different stimulation positions based on the simulations in the LiUHead.

Analysis
The outcome measure in the human experimental studies is hearing thresholds with the BC transducer applied to the mastoid, the neck, the eye, or the dura.At current, hearing thresholds cannot be obtained in the LiUHead.However, the aim of the study is to investigate mechanisms involved in hearing with vibration stimulation at the above-mentioned positions.Our hypothesis is that the vibrations are transmitted to the skull bone and that the mechanisms leading to hearing perception are the same as in ordinary BC stimulation.According to such hypothesis, the change in hearing thresholds between stimulation positions should equal the change in vibration levels of the bone encapsulating the inner ear.This vibration analysis is done by computing the threedimensional root mean squared (RMS) velocity level from the vibration obtained at the cochlear promontory, illustrated in Fig. 3 .According to Zhao et al. (2021) , the 3D RMS vibration of the bone at the cochlea estimates the thresholds with a mean absolute error of less than 7 dB.
A second hypothesis investigated in the current study is that the intracranial sound pressure is caused by the skull bone vibration independent of stimulation position.According to that hypothesis, the ratio of CSF sound pressure and cochlear promontory vibration should be equal for all stimulation positions.Therefore, the ratio of CSF sound pressure and cochlear promontory vibration, as shown in Fig. 3 , are computed and compared for all stimulation positions ( Fig. 2 ).If this ratio differs among positions or the cochlear promontory vibration level difference deviates from threshold differences, the mechanisms responsible for the hearing perception is other than that hypothesized here.Therefore, the CSF sound pressure level is computed for each stimulation position and related to the experimental hearing thresholds.Such analysis could reveal the importance of the intracranial sound pressure for hearing BC sound.
The results from the cadaver head measurements with BC stimulations on the mastoid, neck, eye, and dura are used for validation of the LiUHead simulations.

Statistics
Differences between model predictions of hearing threshold shifts and the reported threshold shifts in the experimental studies were analyzed by independent samples t-test.No adjustment for multiple testing was incorporated.

Mechanical point impedance
The mechanical point impedances at the five stimulation positions in the LiUHead are shown in Fig. 4 .In addition, the typical impedance of an artificial mastoid is included for comparison ( Surendran and Stenfelt, 2021 ).In the frequency range 0.1 to 10 kHz, the mechanical point impedances are all stiffnessdominated at the low frequencies (negative magnitude slope and negative phase, close to -π /2 radians) but transitions to massdominated at higher frequencies (positive magnitude slope and positive phase, close to π /2 radians).The resonance frequency at the eye is the lowest among the different stimulation position with a resonance frequency of 0.225 kHz while the highest resonance frequency is found for the dura stimulation with 3.0 kHz.These two positions are different from the other stimulation positions which are on the skin-covered skull bone.For the skincovered skull bone stimulation positions (Mastoid, Neck, and Offcraniotomy) the thickness of the skin and subcutaneous tissues (soft tissues) determines the stiffness and resonance frequency.
Since the stimulation area is the same for all positions, the mass of the soft tissues that moves with the circular stimulation plate is the same for all, and this mass determines the impedance at high frequencies.This is apparent in Fig. 4 a where the impedance magnitude of the three skin-covered skull positions come together at the highest frequencies.The same reasoning explains the similarity of the impedance magnitudes for the stimulation of the eye and dura at the highest frequencies where the stimulation is primarily on fluid.
There is a large variety in the impedance magnitudes at lower frequencies with the impedance magnitude of the dura the highest and of the eye the lowest at 100 Hz with a ratio of 270 (49 dB).Here, the dura connected to the skull bone results in a high impedance level while the stimulation on the eye is like vibrating a ball of fluid which has high compliance.There are also differences between the skin-covered stimulation positions where the off-craniotomy has the highest impedance magnitudes, and the neck has the lowest impedance magnitudes.These are a result of the soft tissue thickness.The neck has the most soft tissue inbetween the stimulation position and the skull bone and thereby the highest compliance (less stiffness).The impedance at low frequencies is stiffness controlled, and a lower stiffness leads to a lower impedance magnitude.
The impedance magnitude of the artificial mastoid is in Fig. 4 higher than that of the skin covered mastoid by 2 to 3 times.This means that the artificial mastoid does not mimic the impedance of the skin-covered mastoid.It should be noted that the impedance magnitude of the mastoid in the LiUHead is slightly lower than in an average human (e.g Flottorp and Solberg (1976) ), but the impedance magnitude of the artificial mastoid is up to 6 dB higher than that of an average human ( Surendran and Stenfelt, 2021 ).

Transducer stimulation levels
The estimated output force levels from a Radioear B71 transducer with 1 volt excitation when applied to the six stimulation positions are shown in Fig. 5 a.These results indicate significant differences in output levels at frequencies below 1 kHz where the low-impedance positions (eye and neck) also result in low force output from the B71 transducer.This is even more apparent when the force level output from the B71 transducer is related to the force output on the mastoid position ( Fig. 5 b).At frequencies between 200 Hz and 400 Hz, the output level at the eye is around 40 dB below the output force level at the mastoid with the same electrical input to the B71 transducer.The other stimulation positions deviate by up to 20 dB from that at the mastoid at low frequencies but are mainly within 10 dB.The deviations reduce at higher frequencies and at frequencies above 1 kHz, the output force levels from the B71 transducer are within a couple of dBs of the mastoid stimulation.The exceptions are the dura and the artificial mastoid.The artificial mastoid results in 12 dB higher force levels at frequencies between 1.5 and 2 kHz compared to the mastoid.The dura stimulation result in approximately 10 dB higher output at frequencies between 1.4 and 1.8 kHz, while producing 8 dB lower levels at frequencies between 3.0 and 3.5 kHz compared to mastoid stimulation.
The results in Fig. 5 correlate well with the results of the impedance in Fig. 4 where there are large impedance magnitude differences at lower frequencies but at higher frequencies, the impedance becomes mass-dominated and the impedance primarily depends on the stimulation area that is the same for all positions.In general, a larger impedance magnitude leads to a higher output force level from the B71 transducer.Moreover, the B71 transducer output fall drastically at frequencies above 4 kHz due to a reso-  nance in the casing of the transducer, which limits is usability at higher frequencies.
Another metric that can be important to consider is the stimulation velocity.This is computed as the stimulation force ( Fig. 5 ) divided by the mechanical point impedance ( Fig. 4 ).Fig. 6 show the simulated stimulation velocity levels for a B71 transducer applied at the stimulation positions in relation to the velocity level when applied at the mastoid.The largest variation in the velocity output is seen at the lowest frequencies where the soft tissue stimulation result in 20 to 25 dB higher velocities than at the mastoid.However, compared with the simulated force levels at the stimulation positions ( Fig. 5 ) the velocity levels vary less between the stimulation positions.

Cochlear promontory vibration
The simulated ipsilateral cochlear promontory velocities in the LiUHead when the stimulation is a dynamic force of 1 N are shown in Fig. 7 a for the five stimulation positions.The data are rearranged in Fig. 7 b to show the relative cochlear promontory velocity in relation to the cochlear promontory velocity with stimulation at the mastoid.At low frequencies, the low-impedance positions produce 10 to 30 dB higher promontory velocity compared to the mastoid position with the same force stimulation.Stimulation at the dura and off-craniotomy positions result in nearly the same cochlear promontory velocity as stimulation at the mastoid position at frequencies up to 500 Hz, above which the mastoid position gives 10 to 15 dB higher cochlear promontory velocity levels compared to the other two up to 2 kHz.Above 2 kHz, stimulation at the dura and the off-craniotomy positions gives 0 to 10 dB worse cochlear promontory vibration compared to mastoid stimulation,  with around 5 dB lower velocities for the off-craniotomy stimulation than for the dura stimulation at frequencies above 5 kHz.The eye and neck stimulation positions goes from positive to negative relative cochlear promontory vibration levels compared to mastoid stimulation at frequencies between 600 and 800 Hz and becomes close to -22 dB at 3 kHz.Above this frequency, the eye stimulation recovers slightly compared to mastoid stimulation and falls at around -15 dB for most of the higher frequencies.The neck stimulation cochlear promontory vibrations continue to fall compared to mastoid stimulation at higher frequencies and end at -34 dB at 10 kHz.Fig. 7 show the cochlear promontory vibration levels for a 1 N dynamic force at the stimulation positions.However, as indicated in Fig. 5 , the predicted output force from the B71 transducer model differed between the stimulation positions.Fig. 8 a show the predicted ipsilateral cochlear promontory velocity in the LiU-Head when an electrical excitation of 1 volt is provided to the B71 transducer model.This is the same as combining the B71 transducer transfer function (electric input to force output, Fig. 5 ) and stimulation force to cochlear promontory velocity function ( Fig. 7 ).The velocities vary between the stimulation positions with approximately one order of magnitude and the velocities fall mainly between 3 and 300 μm/s at frequencies below 4 kHz.At frequencies above 4 kHz, the velocities diminish rapidly with frequency at a rate of 40 to 50 dB/octave.

Stimulation at the eye
Based on the cochlear promontory vibration, the model prediction of positioning the B71 transducer at the eye compared to at the mastoid is shown in Fig. 9 .The model prediction indicates that the eye is 5 to 25 dB less sensitive compared to the mastoid for BC stimulation by the B71 transducer in the frequency range 250 Hz to 4 kHz, for which human data exist.Also included If an average is computed for the result in the three studies, the model estimate is 10 dB below the studies' average at 500 Hz, 3 dB below at 1 kHz, 11 dB below at 2 kHz, and 2 dB above at 4 kHz.These deviations are of the same size as the differences between the results in the three studies.Moreover, there are no clear trends in the thresholds as a function of frequency, but most thresholds and model predictions fall in the 5 to 20 dB range.

Stimulation at the neck
The results in Fig. 10 show the predicted sensitivity difference between stimulation at the neck and at the mastoid using a B71 transducer.There is a clear trend of increasing predicted thresholds with frequency where the predicted threshold is -20 to -15 dB at frequencies below 200 Hz, above which it increases rapidly to 2 dB at 500 Hz, to become 34 dB at 10 kHz.The two datasets for neck stimulation thresholds are computed as the difference between the thresholds at the neck and at the mastoid.The thresholds for both datasets show nearly identical slopes but the thresholds in Chordekar et al. (2018) are around 9 dB higher than in Adelman et al. (2015) .Here, the model predictions are nearly identical with the Adelman et al. (2015) results.

Stimulation at the dura
Fig. 11 shows the cochlear-promontory-vibration-based threshold prediction for stimulation at the dura compared to stimulation at the off-craniotomy position.This is different from the two other threshold comparisons ( Figs. 9 and 10 ) that used the mastoid position as the reference.The reason for this difference is that the experimental data from Sohmer et al. (20 0 0) presented thresholds for stimulation at the skin-covered dura and at a position off the craniotomy.The thresholds difference at the craniotomy (dura) and

Analysis of model predicted thresholds
For all three types of soft tissue stimulation, the threshold shifts in the 0.5 to 4 kHz frequency range are between -12 dB and 28 dB.This limited spread may mean that any simulated prediction would fit any of the soft tissue stimulation equally well.This was explored by comparing the average absolute differences between the model predictions and the threshold data for the frequencies 0.5, 1, 2, and 4 kHz.This average absolute difference between the model prediction and threshold data for eye stimulation ( Fig. 9 ) is 7.6 dB, but when the model prediction for the eye is compared with the thresholds for the dura and neck stimulation, the average absolute difference becomes 14.3 dB which was statistically significant ( p = 0.025).For the neck stimulation ( Fig. 10 ) the same computation showed a statistically significantly different ( p = 0.030) average absolute difference of 5.0 dB for the predicted thresholds and 10.9 dB for the dura and eye thresholds.The dura stimulation gave also a statistically significant different ( p = 0.033) average absolute difference of 6.4 dB for the simulated predictions and 13.8 dB for the eye and neck thresholds.To summarize, cochlear promontory vibrations were significantly better at estimating the threshold shifts for the specific soft tissue stimulation position compared to predicting the threshold shifts for the two other conditions.

Vibration measurements
The cochlear promontory vibration results from the LiUHead are compared to other vibration measurements with stimulation at the mastoid, neck, eye, and dura.The analysis here is done by comparing the cochlear promontory vibration in the LiUHead with stimulation at the soft tissue positions (dura, eye, and neck) with stimulation at the mastoid, with the same analysis of the experimental studies.Some difficulties in the comparisons with the experimental studies are that the exact conditions for the experiments are seldom given and the methods used are not always applicable to manipulations in the LiUHead.
Skull-bone vibration measurements with stimulation at the dura are rare.One dataset comes from Sim et al. (2016) where cochlear promontory velocity was measured in one dimension when stimulation was provided by a Bonebridge BC transducer, either rigidly attached at the mastoid bone or pressed against the dura in an opening at the forehead.This is different from the mastoid and dura stimulation simulated in the LiUHead in the current study.To enable comparison between the datasets, the simulated cochlear promontory vibration with stimulation at the dura and mastoid with 1 N dynamic force was used ( Fig. 7 B) and presented in Fig. 12 .The output force of the Bonebridge BC transducer is not provided in the Sim et al. (2016) study, and an estimation is used based on the mechanical impedance of the dura in Fig. 4 and the simulated output force of a Bonebridge BC transducer in Chang and Stenfelt (2019) .According to the transducer model and the impedances at the dura and rigidly attached in the mastoid, the output force from the Bonebridge BC transducer Fig. 13.The relative cochlear promontory vibration level between stimulation at the neck and at the mastoid from LiUHead simulations (blue line) and cadaver heads (red and magenta lines).Also included are relative vibration data from an implant in the parietal bone when the stimulation was at the neck and mastoid ( Chordekar et al., 2018 ). is equal at the two positions at frequencies up to 500 Hz, and 5 dB higher at the mastoid than at the dura for frequencies above 500 Hz.Another difference is that the Bonebridge BC transducer was applied directly to the skull bone in ( Sim et al., 2016 ) while the stimulation is applied at the skin in the simulations.This was compensated by using the skin-to-bone difference provided in Prodanovic and Stenfelt (2021) ( Fig. 9 in that study).Based on these corrections, the data from Sim et al. (2016) were adjusted and presented in Fig. 12 .
In general, the results from Sim et al. ( 2016) are below the estimated difference of cochlear promontory vibration between stimulation at the dura and at the mastoid.One reason for the differences can be that the vibration is only obtained in one direction in the experiments while it is measured in three dimensions in the simulation.Another possible reason is that the dura stimulation is nearly orthogonal to the vibration measurement direction while the mastoid stimulation is in line with the measurement direction in Sim et al. (2016) .Such misalignment would enhance the mastoid stimulation and diminish the dura stimulation, in line with the results in Fig. 12 .Another unknown is the size of the opening to the dura.In the simulations this was 18 mm in diameter, while it is likely to be larger in the experiments.A larger opening would reduce the cochlear promontory vibration with dura stimulation.Moreover, the corrections made for different types of transducers in the simulation and experiment and skin versus bone stimulation introduce uncertainty in the comparison.With that in mind, the comparison in Fig. 12 does not reject the validity of the simulations.
The comparison between simulations of neck and mastoid stimulation with experimental vibration data is shown in Fig. 13 2018) was on a titanium implant in the pari-Fig.14.The relative cochlear promontory vibration level between stimulation at the eye and at the mastoid from LiUHead simulations (blue line) and cadaver heads (red and magenta lines).Also included are relative vibration data from an accelerometer placed between the teeth when the stimulation was at the eye and mastoid ( Ito et al., 2011 ).
etal bone in live humans, and not at the cochlear promontory in isolated heads as in the simulations and the other experimental studies.
There is general agreement between the simulations and experimental studies in Fig. 13 at frequencies between 0.3 and 4 kHz where most of the experimental data are within 10 dB of the simulation.The Chordekar et al. (2018) data are 5 to 10 dB below the simulation throughout the entire frequency range.A possible explanation for this is that the vibration measurement in that study was obtained at a position close to the mastoid stimulation and in line with the stimulation direction of the mastoid.That would likely enhance the vibration measurement for the mastoid stimulation and diminish it for the neck stimulation in relation to a 3D vibration measurement on the cochlear promontory, as in the simulation, leading to the outcome in Fig. 13 .The Dobrev et al. (2019) and Röösli et al. (2016) data hovers in the -20 to -10 dB range at frequencies above 4 kHz while the simulation falls from -20 dB at 4 kHz to -34 dB at 10 kHz.However, when inspecting the promontory vibration data with neck stimulation in the two experimental studies, the measured vibration levels are close to the noise floor (SNRs between 0 and 10 dB) and the neck-stimulated promontory vibration could be lower than that measured and affected by noise.Such noise problem prevents the relative vibration levels of the experimental studies to fall at the higher frequencies in Fig. 13 .
The last comparison of promontory vibration is for eye stimulation and is shown in Fig. 14 .The experimental data are obtained from Dobrev et al. (2019) and Röösli et al. (2016) with the same corrections as done for Fig. 13 with neck stimulation.Also included are data from Ito et al. (2011) where the vibration was measured on the teeth in live humans.The results from the cadaver head studies and the simulations are similar with differences mainly in the 5 to 15 dB range.In Fig. 14 , the difference between the model simulations and the experimental studies is the same as the difference among the cadaver head studies.One apparent difference is in the 0.2 to 0.7 kHz range where the simulation shows a dip at 0.3 kHz and the cadaver head studies shows a dip at 0.4 kHz.This dip is caused by the resonance shift in the BC transducer with stimulation at the soft tissues and at the mastoid (see Fig. 5 ).
The experimental studies used a different transducer (Cordelle II), and its resonance frequency is different from the modelled transducer's.Consequently, the corrections made for the use of the different transducers did not fully compensate for the differences between experimental and simulation data.A similar finding is visible in the neck-mastoid data in Fig. 13 where a dip at 0.4-0.5 kHz appears in the cadaver head data while the simulation data has its dip at a lower frequency.The same reasoning can explain the difference in the threshold data in Fig. 9 where the results from Watanabe et al. (2008) has a dip at 0.5 kHz and the model simulations predict it to appear at 0.3 kHz.
The live human data from Ito et al. (2011) are similar to the simulations and the other experimental data in the 0.25 to 1 kHz region, but deviates significantly at 3 and 4 kHz.The vibrations were obtained at a different position (the teeth) compared to the other data, but it is not clear why that would affect the result in such way.

CSF pressure simulations
The sound pressure in the CSF was computed by averaging the fluid sound pressure in the CSF close to the ipsilateral cochlea ( Fig. 3 ).The sound pressure level in the CSF close to the cochlea, either in relation to a 1 N stimulation or a 1 V excitation of the BC transducer model is shown in Fig. 15 for stimulation at the five positions.At frequencies below 5 kHz, the variability of CSF sound pressure among the stimulation positions is between 20 and 40 dB for force stimulation and 10 to 30 dB for electric stimulation to the transducer model.At frequencies above 5 kHz, the results with neck stimulation fall more rapidly than for the other stimulation positions and become 30 to 50 dB below the other stimulations at 10 kHz for both stimulation modalities.
When the CSF sound pressure results are compared with the results obtained at the cochlear promontory in Figs.7 and 8 , there are several similarities.For force stimulation, the low-frequency results are dominated by the eye stimulation while mastoid and dura show the lowest outcome levels.At mid-frequencies the mastoid stimulation dominates the outcomes and stimulation at both the mastoid and dura gives the highest outcome levels at the highest frequencies.The neck stimulation gives the lowest outcome levels for both cochlear promontory vibration and CSF pressure.The results with transducer stimulation ( Figs. 8 A and 15 B) are in line with the outcomes by force stimulation.These results suggest that the cochlear promontory vibrations and CSF sound pressures are affected in a similar way by changing the stimulation positions The validity of the CSF sound pressure estimate in Fig. 15 was explored by comparing the model estimations with the CSF sound pressure reported in Dobrev et al. (2019) .This comparison is shown in Fig. 16 for stimulation at the mastoid ( Fig. 16 A), for stimulation at the neck ( Fig. 16 B), and for stimulation at the eye ( Fig. 16 C).The results are based on the sound pressure in relation to the voltage to a BC transducer.Since the BC transducer in Dobrev et al. (2019) is different from the model of a B71 BC transducer that is used for the LiUHead simulations, the results in the cadaver head studies were adjusted for different transducers in a similar way as done in Figs. 13 and 14 .Fig. 16 A shows that the experimental data are around 10 dB higher than the LiUHead simulations at frequencies below 1.5 kHz.In the frequency range 1.5 to 4 kHz, they are within a few dBs of each other while the simulations are 5 to 10 dB higher than the experimental data at frequencies of 4 kHz and up to 8 kHz.With stimulation at the neck ( Fig. 16 B), the model predictions are approximately 10 dB higher at frequencies below 0.3 kHz.At frequencies between 0.3 and 3 kHz, the model predictions and experimental data are primarily within 5 dB while the model predictions fall off faster at high frequencies compared to the experimental sound pressures resulting in a difference of around 40 dB at 10 kHz.With stimulation at the eye  ( Fig 16 C), the experimental sound pressures are 5 to 20 dB higher than that predicted by the LiUHead model for the entire frequency range.
It should be noted that even if the values differ between the model predictions and the experimental data from the cadaver heads, the curves have the same morphology for each stimulation position.The caveat is that the model simulations is based on the sound pressure in the CSF between the skull bone and the brain tissue close to the ipsilateral cochlea while the experimental data are obtained in the center of the skull in cadaver heads where the brain tissue has been replaced by fluid.

Importance of CSF pressure for BC hearing
The final analysis is an estimation of the likelihood for the CSF sound pressure to be an alternative way of exciting the inner ear during BC stimulation of the soft tissues.This analysis is conducted by computing the CSF sound pressure in relation to the cochlear promontory vibration.If the CSF sound pressure pathway is more important for some of the stimulation positions, the sound pressure in relation to the cochlear promontory vibration should be higher for that or those stimulation positions compared to the other stimulation position.
Fig. 17 A show the computed CSF sound pressure relative to cochlear promontory velocity for the five different stimulation positions in the LiUHead.There is no clear dominant or inferior stimulation position but all fall within 20 dB of each other in an irregular fashion.In addition, experimentally obtained CSF sound pressure in relation to the cochlear promontory velocity with stimulation at the mastoid from Sim et al. ( 2016) and Dobrev et al. (2019) are also included in Fig. 17 A. Here, no ad-ditional corrections were done for the stimulation type where Dobrev et al. (2019) stimulated on the skin covered mastoid as in the simulations, while Sim et al. (2016) provided the stimulation directly to the mastoid bone.The experimentally obtained results are within the range of the simulated results, and mainly within 10 dB of the simulated result with mastoid stimulation except at frequencies at 5 kHz and above, where the experimentally data are 10 to 20 dB below the simulated data with mastoid stimulation.
To further assess the results, the mean simulated CSF sound pressure in relation to cochlear promontory velocity was computed (mean of all simulated curves in Fig. 17 A).Then the differences between this mean and the simulated CSF sound pressure for all stimulation positions were computed and shown in Fig. 17 B.In addition, the average absolute difference for the CSF from the five stimulation positions in relation to the calculated CSF mean from all positions is added to Fig. 17 B.According to this computation, the mean absolute difference is around 5 dB for the entire frequency range.Also, most differences are in the -5 dB to 5 dB range.This implies that among the stimulation positions investigated here, none excite the CSF pressure significantly more than it vibrates the skull bone.One interesting observation is that the simulated direct dura stimulation shows the overall least CSF sound pressure in relation to skull bone velocity (red line in Fig. 17 B).This was unexpected since the stimulation of the dura is the most direct stimulation of the CSF among the stimulation positions investigated.

Discussion
The aim of the current study was to investigate the mechanism underlying the so-called soft tissue sound transmission in the hu- man.Specifically, the hypothesis was that hearing with stimulation at these soft tissue positions is the same as with stimulation at the skin covered mastoid where the vibration of the skull bone is ultimately responsible for the hearing perception ( Stenfelt, 2011 ;Stenfelt, 2020 ;Stenfelt and Goode, 2005 ).This hypothesis was supported by hearing threshold alterations in human studies when the stimulation was at the eye, neck, or directly at the dura ( Figs. 9-11 ).Consequently, based on the simulation predictions in the LiU-Head, BC stimulation at soft tissue positions causes a hearing perception in the same way as when applied at the skin covered mastoid or directly to the skull bone.

BC transducer output
One factor that was ignored in most of the studies in Table 1 is that the output of a BC transducer depends on the mechanical load which it is applied to.For example, according to the simulations in Fig. 6 , the dynamic force out from a B71 BC transducer can differ more than 40 dB when it is applied to the eye compared to when it is applied at the mastoid.This huge deviation is related to the low impedance magnitude at the eye compared to at the mastoid ( Fig. 4 ), and the B71 transducer is unable to provide the same output force at both stimulation positions.However, at the same time the stimulation velocity is significantly higher when the stimulation is applied to the low-impedance magnitude sites (eye and neck) compared to the mastoid ( Fig. 6 ).This deviation in output from a BC transducer appears primarily at low frequencies and at frequencies above 1 kHz, variation in output force or velocity is mostly limited to 5 dB even if deviations up to 10 dB is visible for some of the positions at limited frequency ranges.
The dependence of the output from a BC transducer as a function of the mechanical impedance at the stimulation position has been shown previously Flottorp and Solberg (1976) .analyzed the output from a model of a BC transducer based on the variability of the mechanical impedance of the skin covered mastoid, and reported that the output varies by ±6 dB among the normal population Chang and Stenfelt (2019) .investigated the output from a general model of a BC transducer on different positions and interfaces on the LiUHead, and reported the dynamic output force to be higher at high-impedance positions compared to positions with lower impedance magnitudes Surendran and Stenfelt (2021) .showed that the difference between the impedances of the artificial mastoid used for calibration of BC transducers and the skin covered mastoid leads to output differences, and Prodanovic and Stenfelt (2021) showed that such calibration deviations result in erroneous comparison between skin and skull-bone applied BC stimulation.Application directly to the skull bone also shows variation in mechanical impedance leading to output differences of around 3 dB at frequencies above 5 kHz ( Håkansson et al., 2020 ).

Model predictions
The LiUHead simulations were setup to mimic the experimental conditions as much as possible.Even so, the exact conditions for each experiment are difficult to know based on the information in the publications.One such example is the study of Sohmer et al. (20 0 0) that did not disclose the exact position and size of the craniotomy.Those parameters influence the vibrational response of the head and the comparison in Fig. 11 is uncertain.Another difference between the model simulations and the measurements in Sohmer et al. (20 0 0) is that the measurements were obtained in children (age 10 and 13 years) while the model is based on a female adult.In the threshold experiments with neck stimulation ( Fig. 10 ), the stimulation position was given as "5 cm below the earlobe, over the sternocleidomastoid muscle" ( Chordekar et al., 2018 ) and as "submandibular triangle (below the earlobe and posterior to the body of the mandible)" ( Adelman et al., 2015 ).If these are exactly the same positions and if they correspond exactly to the neck position in the simulation ( Fig. 2 ) is unclear.Moreover, the LiUHead lacks part of the neck and vertebrae, so it is likely that the positions between the simulations and experiments differ to some extent.
Another caveat is that several of the studies occluded the ear during the measurements ( Table 1 ).It is well documented that an occlusion improves BC hearing thresholds at frequencies below 2 kHz ( Stenfelt and Reinfeldt, 2007 ).Since the alteration of BC thresholds with occlusion also depends on the stimulation position ( Reinfeldt et al., 2013 ), part of the threshold shifts between the soft tissue positions and mastoid positions in Figs. 9 and 10 could have originated in the occlusion effect.The cochlear promontory vibration in the LiUHead was not affected by an occlusion effect.Also, several of the studies applied the BC transducer to the soft tissue position by hand.The Radioear B71 and B72 transducer has the motor unit attached to the backside of the housing.This means that the housing itself is part of the transmission pathway and holding it by hand can affect its mechanics and thereby the vibration transmission.Moreover, the LiUHead model assumes a single domain for the soft tissues that also comprise muscles.In a living human, the tension of the muscle can influence the mechanical parameters and thereby the impedance.Consequently, the stiffness of the mechanical impedance for the neck in Fig. 4 can be higher in a live human compared to the simulations from the LiUHead.
It should also be remembered when comparing the simulation predictions and threshold alterations in Figs.9-11 that all studies have small sample sizes with 2 to 12 participants.Such small number of participants makes the threshold differences uncertain with reported standard deviations in the 5 to 15 dB range.This is also noticeable in Figs. 9 and 10 where the inter-experimental results differ by up to 15 dB.Consequently, if the model predictions based on cochlear promontory vibration are within 5 to 10 dB of the experimental results, they are in a good agreement with the experiments.Also, the statistical analysis showed that the model predictions were significantly better at estimating the threshold shifts of the same soft tissue stimulation position compared to stimulation at the other two positions.
The simulated relative cochlear promontory velocity between mastoid and soft tissue stimulation was compared to experimental data obtained in cadaver heads and live humans in Figs.12-14 .These data were primarily included to validate the LiUHead model's ability to predict promontory vibration from the different soft tissue positions, as it has only been validated for mastoid and forehead stimulations ( Chang et al., 2016 ;Lim et al., 2021 ;Prodanovic and Stenfelt, 2021 ).The results with dura stimulation ( Fig. 12 ) show large deviations (up to 25 dB) at some frequencies compared to the data from Sim et al. (2016) .These data were the only dataset found that reported dura stimulation and cochlear promontory vibration.However, as already stated in the Results section, the conditions in Sim et al. (2016) experimental study differed from the simulations of dura stimulation that was designed to mimic the conditions in Sohmer et al. (20 0 0) .The compensations done to facilitate comparison between the LiUHead simulations and the results from Sim et al. (2016) (different transducers, different stimulation positions, effect of skin) are unlikely to fully compensate for the differences between the experimental data and the simulations.With this in mind, the results in Fig. 12 do not disprove the validity of the simulations of dura stimulation in the LiUHead.
The comparison between neck and mastoid stimulation in Fig. 13 and between eye and mastoid stimulation in Fig. 14 shows overall similar results between experimental studies and the simulations.The greatest deviation between the cadaver head studies and LiUHead simulations was at frequencies above 4 kHz in Fig. 13 where the simulations show a general decline of -20 dB/decade while the cadaver head data indicate a nearly flat response.The cadaver head data are unexpected as the bulk of soft tissue at the neck is expected to increase the vibration attenuation as a function of frequency.One explanation for this finding can be the low SNR for the eye and neck stimulations at frequencies of 4 kHz and above in Dobrev et al. (2019) leading to an overestimation of the cadaver head functions in Fig. 13 due to the noise.The results from Chordekar et al. (2018) are more in-line with the simulations showing a decrease as a function of frequency.In Fig. 14 , the results from Ito et al. (2011) deviates from the others at frequencies above 2 kHz.The reason for this deviation is unknown, but the vibration measurements were done with an accelerometer between the participants teeth, which is different from measuring the vibrations at the cochlear promontory, and this can be one reason for the discrepancy.
To summarize, the results of vibration measurements in humans and cadaver heads for the different stimulation positions presented in Figs 12 -14 support the validity of the cochlear promontory vibration simulations for the same stimulation positions in the LiUHead.

CSF sound pressure
The simulated CSF sound pressure was obtained by computing the average sound pressure in a volume of the CSF close to the inner ear.The rationale for this is based on the assumption that if the sound pressure in the CSF influences the hearing, the CSF sound pressure close to the inner ear would be most important.The CSF sound pressures as obtained in the LiUHead were compared to experimental data from intracranial sound pressures in Dobrev et al. (2019) that were measured in the cranial center of cadaver heads where the brain was replaced with fluid.Although different set-ups, the results in Fig. 16 show similar values where the deviation between the simulations and the experimentally obtained sound pressures are mostly in the 5 to 10 dB range, with overall similar shapes of the curves.One difference between the Dobrev et al. ( 2019) study and the current simulations is that a Cordelle BC transducer was used for stimulation in the cadaver heads while a BC transducer model of the BAHA was used for the simulation.The model parameters for the Cordelle are unknown and the model of the BAHA transducer presented in Chang and Stenfelt (2019) was used in the simulations.A Cordelle BC transducer is around 10 dB stronger than a BAHA transducer, and the CSF sound pressure is expected to be 10 dB higher in Dobrev et al. (2019) compared to the simulations ( Fig. 16 ).But according to Dobrev et al. (2019) , the intracranial sound pressure is around 10 dB higher at the ipsilateral side of the intracranial space compared to the skull center.Actually, all positions closer to the skull bone were reported to give higher sound pressures compared to the sound pressures at the center in Dobrev et al. (2019) .Consequently, the higher sound pressure expected from the Cordelle BC transducers compared to the BAHA BC transducer is somewhat compensated by the sound pressure difference between the cranial center and a position close to the skull bone.
When the intracranial sound pressures were related to the cochlear promontory velocity, all stimulations positions gave results that were within 10 to 20 dB without a dominant position.Also, the experimentally obtained intracranial sound pressure related to the cochlear promontory velocity was in the same range as the simulated ones, except at the higher frequencies where the experimentally obtained CSF sound pressure to cochlear promontory velocity was 10 to 20 dB below the simulated.One explanation for this difference is the different measurement positions where the experimental data are from the center of the head while the Li-UHead simulations' sound pressure was computed from the CSF close to the inner ear ( Fig. 3 ).Also, removal of brain tissue and drilling of the mastoid bone can influence the resulting cochlear promontory vibration ( Prodanovic andStenfelt, 2020 , 2021 ).The LiUHead cochlear promontory vibration was found 5 to 10 dB below average cochlear promontory vibration in cadaver heads at frequencies above 3 kHz when the stimulation was at the mastoid ( Prodanovic and Stenfelt, 2021 ), which can partly explain the highfrequency deviation between simulations and experimental data.

Does soft tissue conduction exist?
If this question refers to if sound is conducted in soft tissues, then the answer is yes.Sound is transmitted through the soft tissues when, for example, the BC transducer is applied to the skin covered mastoid as in ordinary audiometry.However, if soft tissue conduction is suggested as an alternative pathway to BC, then the results in the current study suggest that it is not the case.Even if the BC transducer is applied at soft tissue positions, the final excitation of the inner ear is through vibrations of the skull bone, i.e.BC.
The general concept of BC hearing is a summation of sound generated in the ear canal ( Stenfelt et al., 2003 ;Surendran and Stenfelt, 2021 ), inertial motion of the middle ear ossicles ( Homma et al., 2009 ;Stenfelt et al., 2002 ), and inertial and compressional effects in the inner ear fluid ( Kim et al., 2011 ;Stenfelt, 2015 ;Stenfelt, 2020 ).In addition to these, sound pressure that is transmitted from the CSF have been suggested as contributing to BC hearing ( Sohmer et al., 20 0 0 ;Stenfelt, 2016 ;Stenfelt, 2020 ).The importance of these different contributors has been estimated in Stenfelt (2016;2020) indicating that for a stimulation at the mastoid, the vibration around the inner ear is most important.
When the stimulation position is different, the im portance of the different contributors for BC changes.This is apparent when the stimulation position is close to the ear canal or at the auricle, where vibrations of the soft tissue and cartilage enhances the sound pressure in the ear canal ( Nishimura et al., 2015 ).This has been termed cartilage conduction ( Nishimura et al., 2015 ;Shimokura et al., 2014 ).However, it is not different from the classical BC hearing suggested by von Békésy (1932) or Tonndorf (1966) , but is a special case where the ear canal sound pressure part dominates the BC perception.This is in part similar to BC hearing with occluded ears, where the occlusion effect enhances the ear canal sound pressure at low frequencies and it becomes dominant for BC hearing at frequencies below 2 kHz ( Khanna et al., 1976 ;Reinfeldt et al., 2013 ;Stenfelt and Reinfeldt, 2007 ).In a normal open ear with the stimulation at the mastoid, the sound pressure in the ear canal is mainly generated by the soft tissues ( Stenfelt et al., 2002 ) but does not dominate the sound perception ( Stenfelt, 2007 ), even if it is close to other contributors at frequencies below 4 kHz ( Surendran and Stenfelt, 2021 ).Hence, the ear canal sound pressure during vibration stimulation, either to a soft tissue position or directly to the bone, is dominated by the vibration in the soft tissue part of the ear canal, but is still part of the classical definition of BC hearing.
The other possible sound transmission pathway not including vibration of the bone surrounding the inner ear is transmission of sound pressure from the CSF.This pathway was deemed insufficient to elicit the inner ear during BC stimulation in a normal ear when the vibration is applied at the mastoid ( Stenfelt, 2016 ;Stenfelt, 2020 ), but could possibly dominate the BC perception when the stimulation is applied at positions that induce higher CSF sound pressure than bony vibrations.This theory was disputed in the current study where all stimulation positions gave vibrations of the cochlear promontory bone that were similar in relation to the CSF sound pressure ( Fig. 17 ).Even stimulation directly to the dura did not induce a CSF pressure that were significantly higher than at other positions when related to the cochlear promontory vibration.Moreover, threshold alterations predicted from cochlear promontory vibrations in the LiUHead were generally within 5 to 10 dB of the experimentally obtained threshold alterations and in the same order as the inter-study variabilities .
The current findings suggest that the CSF sound pressure is induced by skull-bone vibrations.This is also supported by the results in Dobrev et al. (2019) where an intracranial sound pressure close to the bone had higher magnitude than at a position further away from the bone.The sound pressure at the center of the head was lower than at the contralateral side of the stimulation, even though the bone vibration is lower at the contralateral side compared to the ipsilateral side ( Stenfelt, 2012 ).Consequently, the sound pressure in the CSF at the contralateral side of the head is caused by the local bone vibration and not through intracranial cross-head sound transmission, as also suggested by Chang et al. (2018) .
An alternative interpretation of the data in Fig. 17 is that the cochlear promontory bone vibration is driven by the CSF sound pressure for all stimulation positions.Such interpretation is unlikely based on the finding that the intracranial sound pressure is lower at the center of the head than at the contralateral side, as discussed in the previous paragraph.Another finding supporting the skull bone and not the CSF as the dominant vibration pathway was presented in Prodanovic and Stenfelt (2021) where replacing the CSF and brain tissue with air did not change the cochlear promontory vibration.Consequently, the cochlear promontory vibration was independent of the status of the CSF and brain.
Based on the simulation results and their corroboration with experimental data, we conclude that neither stimulation at the neck, dura, nor at the eye leads to a vibration response of the bone surrounding the cochlea that is significantly different from stimulation at the mastoid.Moreover, the data also suggest that soft tissue conduction is not an alternative transmission pathway but is part of classical BC hearing resulting in skull bone vibration primarily responsible for the hearing perception.

Conclusions
The LiUHead was used to replicate experiments of BC stimulation at soft tissue positions (eye, neck, dura).The results from the simulations were the cochlear promontory velocity and the sound pressure in the CSF.The simulated outcomes were in line with experimental data from cadaver heads.This indicates that the LiU-Head can be used for simulations of BC stimulations from multiple positions of the head and that it is able to predict sound pressure in the CSF in line with experimental data.
The simulations showed that the vibration level of the cochlear promontory was able to predict hearing thresholds reported in experimental studies with an error of the same size as the experimental inter-study variability.Consequently, the hypothesis that the hearing originated in skull bone vibrations irrespective of stimulation position was supported.The current simulations suggest that vibration stimulation at soft tissue positions on the human head result in hearing by conventional BC mechanisms and soft tissue conduction is not a general concept for hearing.Moreover, the simulations also indicate that BC sound is not transmitted through CSF sound pressure.

Fig. 2 .
Fig. 2. The stimulation positions used in the LiUHead.(A) The mastoid and neck positions.(B) The stimulation on the eye.(C) The stimulation position for the craniotomy (dura stimulation) and the off-craniotomy position.

Fig. 3 .
Fig. 3.A cross section image of the LiUHead showing the two measurement positions.In the enlarged image the red oval indicates the volume for the CSF sound pressure and the red cross indicates the position where the cochlear promontory vibration is obtained.

Fig. 4 .
Fig. 4. The mechanical point impedances as (A) magnitude and (B) phase for the 5 stimulation positions in the LiUHead and a model of the artificial mastoid.The impedances are obtained for a circular interface with a diameter of 15 mm.

Fig. 5 .
Fig. 5. (A) The estimated output force magnitude from a model of the Radioear B71 BC transducer when applied at the 5 stimulation positions and the artificial mastoid.(B) The output force level from the model of the Radioear B71 BC transducer at the four alternative stimulation positions and at the artificial mastoid in relation to the force at the mastoid.

Fig. 6 .
Fig. 6.The output velocity level from the model of the Radioear B71 BC transducer at the four alternative stimulation positions in relation to the velocity at the mastoid.

Fig. 7 .
Fig. 7. (A) The simulated cochlear promontory velocity when the stimulation is a force of 1 N at the five stimulation positions.(B) The simulated cochlear promontory velocity level with stimulation at the four alternative positions in relation to stimulation at the mastoid.

Fig. 8 .
Fig. 8. (A) The simulated cochlear promontory velocity magnitude when the excitation is 1 volt to a model of the Radioear B71 transducer applied at the five stimulation positions.(B) The simulated cochlear promontory velocity level with 1 volt B71 BC transducer model stimulation at the four alternative positions in relation to stimulation at the mastoid.
Shown in Fig. 8 b are the cochlear promontory velocities from Fig. 8 a normalized by the velocity produced by mastoid stimulation.This manipulation predicts the difference in perceptual thresholds between stimulation at the mastoid and at the other stimulation position investigated.Based on the simulation results in Fig. 8 b, changing the stimulation site from the mastoid to the neck (magenta line in Fig. 8 b) improves the audibility by approximately 15 dB at frequencies of 200 Hz and below, reduces the audibility by 10 dB at 1 kHz, and reduces the audibility by 20 dB at 4 kHz.For the eye (black line), the audibility is reduced 15 to 25 dB at frequencies between 150 and 350 Hz, by 5 dB at frequencies between 0.5 and 1.0 kHz, and by 20 dB at frequencies between 1.8 and 3.0 kHz.Consequently, the estimated BC stimulation of the cochlear promontory in Fig. 8 b is used to predict hearing threshold alterations with stimulation at the mastoid and the other positions.

Fig. 9 .
Fig.9.The estimated hearing thresholds with a Radioear B71 BC transducer at the eye based on simulations in the LiUHead (blue line) and reported average thresholds from three studies.

Fig. 10 .
Fig. 10.The estimated hearing thresholds with a Radioear B71 BC transducer at the neck based on simulations in the LiUHead (blue line) and reported average thresholds from two studies.

Fig. 11 .
Fig. 11.The estimated hearing thresholds with a Radioear B71 BC transducer at the dura in relation to stimulation adjacent to the craniotomy (off-craniotomy).Also included are averaged threshold shifts from two the children between stimulation at a craniotomy and adjacent to the craniotomy ( Sohmer et al., 20 0 0 ).

Fig. 12 .
Fig. 12.The relative cochlear promontory vibration level between stimulation at the dura and at the mastoid from LiUHead simulations (blue line) and cadaver heads (red line).
. The simulations are based on B71 transducer data ( Fig 8 .B) and the experimental studies using voltage-driven BC transducers.The BC transducer in the Dobrev et al. (2019) and Röösli et al. (2016) studies was a Cordelle II transducer on a plastic interface which is different from the B71 transducer model used for the simulation.This was here compensated by computing the force output on the neck and mastoid impedances shown in Fig. 4 with a model of a BAHA BC transducer presented in Chang and Stenfelt (2019) with the addition of a 1 g plastic interface.The vibration measurement in Chordekar et al. (

Fig. 15 .
Fig. 15.The simulated sound pressure in the CSF close to the ipsilateral inner ear when (A) the stimulation was a dynamic force of 1N at the stimulation positions and (B) when the stimulation was an electric signal of 1 volt to a model of a Radioear B71 transducer applied at the stimulation positions.

Fig. 16 .
Fig. 16.Sound pressure estimations in the CSF in the LiUHead (blue line) and measurements in cadaver heads (red line) when the stimulation was a 1 volt electric signal to a model of a BC transducer (LiUHead) or a Cordelle BC transducer (cadaver heads) at (A) the mastoid, (B) the neck, and (C) the eye.

Fig. 17 .
Fig. 17. (A)The CSF sound pressure level in relation to the cochlear promontory velocity from LiUHead simulations at five stimulation positions and from two cadaver head studies with stimulation at the mastoid.(B) The simulated data in (A) in relation to an average from all five stimulation positions.In addition, the mean absolute difference is included that is computed as the mean of the absolute value from the five curves.