Following the outlined methodology, we computed the motion raw data and estimated the components vo, ωo, and \({\text{C}}_{\text{p}}\) for both human and guinea pig cochleae. To facilitate a comparative analysis, these results are depicted in Figs. 4 and 5, and 6.Fig. 4Central point velocity of human and guinea pig cochlea vibration.Fig. 5Angular velocity of human and guinea pig cochlea vibration.Fig. 6Compress velocity of human and guinea pig cochlea vibration.Figure 4 illustrates the central point velocities (vo) between human and guinea pig cochleae. Notably, the human cochlear velocity is significantly lower than that of the guinea pig in general, which is attributable to the greater mass of the human head relative to that of the guinea pig, despite identical 1 N force application in both cases. Furthermore, the figure elucidates the relative velocity distribution across the x, y, and z directions. At lower frequencies, the x directional velocity predominates in both models, with y and z directional velocities exhibiting comparable levels. However, at higher frequencies (approximately 3 kHz to 5 kHz for humans and 6 kHz to 12 kHz for guinea pigs), the x-directional velocity decreases sharply, supplanted by the y-directional velocity. Additionally, there was a notable peak around 400 Hz in the x directional velocity for the guinea pig model.Figure 5 compares the angular velocities (ωo) between the two species, with human values again being lower for the same reason as the velocities of the central point. At the first data point, 100 Hz, there is a scientifically high peak. The reason may be that, when the simulation begins, the system transitions from a state of an initial condition to a state of vibration. This sudden transition can cause transient effects, where the system has not yet reached a steady-state vibrational mode. The first data point might capture these initial transient behaviors, which can be unrepresentative or abnormal for the first data point. Therefore, we will not consider the data result at 100 Hz. After this, at low frequencies, both human and guinea pig data show a peak around 300–400 Hz. After this peak, the values decrease with some fluctuations. However, at high frequencies, both velocities increase significantly and reach a second peak. Moreover, at higher frequencies, the wavelength of the sound wave is shorter, because the shell of the cochlea is a stiff structure, moreover, the shape of the cochlea is a cone which the distance between the outer wall of the cochlea decreases as the cochlea moves toward the apex. This makes the cochlea vibrate more quickly to respond to the sound, especially as the frequency increases. This makes the apex of the cochlea vibrate more quickly than the bottom, resulting in the cochlea twisting and the angular velocity growing up as the frequency increases. These findings are in accordance with our angular velocity simulation results. Additionally, at high frequencies in guinea pig, our simulation shows there are two peaks approximately 7 and 16 kHz. These peaks were found in our previous studies7,8, in which we measured the velocity of guinea pig cochlear vibration and found two distinct peaks at approximately 8 kHz and 16 kHz, respectively, accompanied by a notable trough at approximately 10 kHz. Because in the previous experiment, we only measure 2, 4, 8, 12, 16, and 20 kHz frequencies, they are not continuous and make the comparisons slightly different7,8. However, the trend and amplitude change in the vibration velocity are in accordance with our simulation. These consistent findings show that angular velocity contributes to both low and high frequencies in BC hearing and plays a more important role in high frequencies. Moreover, at low frequencies, the angular velocity in the y direction is the highest, while that in z direction is the highest at high frequencies. These situations occur in both the human and guinea pig.In Fig. 6, the compression velocities (\({\text{C}}_{\text{p}}\)) of the human cochlea are again lower than those of the guinea pig for the same reason as the velocities of the central point. When plotted on a logarithmic scale, both species exhibit a similar trend of increasing compression velocities with frequency, with some fluctuations, among the three directions, they follow nearly the same trend. A further comparison of the resultant velocity of compression between the human and guinea pig yielded a correlation coefficient of 0.89. This correlation coefficient is high, indicating that the human and guinea pig have a similar trend in compression velocities according to frequency. Additionally, in detail, we also found a small peak at approximately 400 Hz in the guinea pig results. The reason we observed a peak at approximately 400 Hz in all 3 types of responses was that the guinea pig responded to this frequency as an integral. This is probably a result of the vibration of the entire guinea pig’s head, likely resulting from a rotational response. At high frequencies, from 2 kHz in the human and 3 kHz in the guinea pig also exhibited a similar trend that they both drastically increased. Moreover, there are two noteworthy peaks at approximately 7 and 16 kHz and one trough at approximately 10 kHz. These results are in accordance with the experimental results obtained for angular velocities and indicate that the compression velocity also contributes slightly to approximately 400 Hz and more to high frequencies. However, in the human cochlea, the y and z directions are the higher than the x direction in high frequencies, while the x direction is the highest in the guinea pig. And both have a valley for 3 directions at high frequencies.
After obtaining vo, ωo, and \({\text{C}}_{\text{p}}\) results for both species, we applied Eq. (6) to estimate the motion of the cochlea. By comparing the mean amplitude and phase values between the estimated and original data using the Pearson Correlation Coefficient, we observed near-perfect correlations, all greater than 0.9999, indicating the accuracy of our simulations. Furthermore, the relative error velocities, presented in dB scale (20*lg((Vestimated-Voriginal)/Voriginal)), generally increase from approximately − 80 dB to -20 dB with frequency, such as x direction of the human and guinea pig shown in Figs. 7 and 8. These findings confirm that the amplitudes of the estimated and original data are consistent, especially at lower frequencies. Phase shifts (PHestimated-PHoriginal) across frequencies and differences between estimated and original phase are shown in Figs. 7 and 8. These differences are minimal and the Pearson Correlation Coefficient between the estimated and original phases are all greater than 0.9758. These high correlation coefficients further validate the alignment between the estimated results and original data, barring minor fluctuations at very high frequencies.Fig. 7Mean relative velocity and phase shift with std of human cochlea vibration.Fig. 8Mean relative velocity and phase shift with std of guinea pig cochlea vibration.Upon completing individual analyses, to intuitively contrast the resultant vibration patterns of human and guinea pig cochleae, we normalized their resultant velocities (\({\mathbf{v}}_{\mathbf{p}}=\sqrt{{{\varvec{v}}_{\varvec{px}}^{2}}+{{\varvec{v}}_{\varvec{py}}^{2}}+{{\varvec{v}}_{\varvec{pz}}^{2}}}\)) and previous guinea pig experimental data for comparison by \({\mathbf{v}}_{\mathbf{p}}/{\mathbf{v}}_{\mathbf{p}\mathbf{m}\mathbf{a}\mathbf{x}}\), as shown in Fig. 9. These findings are consistent with prior human and guinea pig experimental outcomes7,8,19,21. In previous studies7,8, the focus was on frequencies between 0.1 and 10 kHz for humans and between 2 and 20 kHz for guinea pigs. In our simulations, human cochlear responses exhibit a decrease starting from 0.1 kHz, reaching a trough at approximately 0.4 kHz, followed by an increase to a peak near 2 kHz, before tapering off at higher frequencies. This pattern aligns with earlier findings19,21. In guinea pigs, from 2 kHz, both our simulation and previous experimental data decrease until 4 kHz, and then increase to a peak at approximately 7 kHz; after this, they decrease to a trough at approximately 10 kHz, climb again and reach the second peak at approximately 16 kHz, and finally decline again. Because in the previous experiment7,8, we only measured 2, 4, 8, 12, 16, and 20 kHz frequencies, there is no data available for 100–400 Hz, where the highest peaks appear in the other three datasets. I could only select the highest value within the measured frequencies and then normalize the velocity by \({\mathbf{v}}_{\mathbf{p}}/{\mathbf{v}}_{\mathbf{p}\mathbf{m}\mathbf{a}\mathbf{x}}\)​​. This makes the previous guinea pig experiment data appear much higher than the others. Additionally, since the experimental data is discontinuous, the curve is not smooth enough. These all make the comparisons slightly different. However, the trend and amplitude change are in accordance with the guinea pig FEM simulation result. Our simulations of the cochlear resultant velocity for the human and guinea pig match well with the previous research, they both have a similar trend and amplitude changes according to frequencies, and at certain frequencies, they have similar peaks and troughs. These findings further prove the accuracy of our guinea pig FEM and our method for estimating the cochlear vibration. They can accurately describe and anticipate the details of cochlear motion in both humans and guinea pigs.Fig. 9Normalized relative mean estimated resultant velocity between human and guinea pig.By comparing the resultant velocities between the human and guinea pig, this analysis revealed commonalities and differences in their cochlear responses. Both species demonstrate fluctuating vibration velocities across frequencies, indicating a complex cochlear response. Generally, vibration velocities fluctuate with increasing frequency in both species. However, the specific frequencies of the peaks and troughs differ. For example, humans exhibit a pronounced peak at approximately 2 kHz, while guinea pigs exhibit significant peaks at approximately 300–400 Hz, and smaller ones at approximately 7 and 16 kHz. Above 5 kHz, guinea pigs consistently exhibit higher vibration velocities than humans. These distinctions may be the pure mechanics resulting from the differences in geometry.We further investigated the contributions of vo, ωo, and \({\text{C}}_{\text{p}}\) to the resultant velocities in humans and guinea pigs, as illustrated in Fig. 10. Based on this figure, particularly at frequencies below 7 kHz in humans and 8 kHz in guinea pigs, the vo component plays a predominant role in both human and guinea pig models. Beyond these frequencies, the influence of vo diminishes. In humans, its effect nearly vanishes at certain high frequencies, whereas in guinea pigs, it retains some presence. The difference likely stems from the disparity in cochlear mass between the species. When the mass is heavier, by the same force, it is difficult to vibrate quickly as an integral, especially it cannot respond well to high frequencies. That is why at the very high frequencies, the vo of guinea pig cochlea still retains some presence. For the same species, the reason is similar, with the same mass, as the frequency increases, the common vibration (vo) becomes weaker. This makes \({\mathbf{v}}_{\mathbf{o}}\) take more proportion at low frequencies for both the human and guinea pig. For ωo, in both humans and guinea pigs, below 4 kHz and 3 kHz respectively, the role of the ωo component is minimal. However, beyond these frequencies, its significance increases rapidly, indicating a more prominent role of rotational motion at relatively higher frequencies. Notably, in guinea pigs, an exceptional peak at approximately 400 Hz may stem from a rotational component ωo of the entire guinea pig head. Additionally, at higher frequencies, particularly at approximately 8 and 16 kHz, we observe two minor peaks. These findings align with our previous guinea pig experimental results7,8, and further emphasize the increased contribution of rotational motion at these higher frequencies. This is quantitatively supported by the dramatic increase in the contribution percentage of ωo, which escalates from 3.8 to 34.7% in humans and from 1.7 to 40.1% in guinea pigs, beyond 2 kHz. For \({\text{C}}_{\text{p}}\), the situation is similar to that of ωo, before 2 kHz, its contribution is negligible in both humans and guinea pigs, and almost nonexistent. However, above 10 kHz, there is a dramatic increase. These findings highlight the significant role of \({\text{C}}_{\text{p}}\) at higher frequencies. Specifically, after 2 kHz, the contribution of \({\text{C}}_{\text{p}}\) increases from 3.8 to 55.8% in humans and from 0.8 to 17.7% in guinea pigs. Considering these velocity characteristics and the contributions of ωo and \({\text{C}}_{\text{p}}\), ωo and \({\text{C}}_{\text{p}}\) predominantly influence, and may even determine, all the observed peaks in the experimental data. Finally, to compare the contributions between the human and guinea pig, we calculated the Pearson Correlation Coefficient for \({\mathbf{v}}_{\mathbf{o}}\), ωo, and \({\text{C}}_{\text{p}}\) between the two species. The corresponding results are 0.9607, 0.9510 and 0.9779, respectively. These high Pearson Correlation Coefficients show that the \({\mathbf{v}}_{\mathbf{o}}\), ωo, and \({\text{C}}_{\text{p}}\) have similar contributions to the resultant velocities between humans and guinea pigs.Fig. 10\({\mathbf{v}}_{\mathbf{o}}\), \({{\varvec{\upomega}}}_{\mathbf{o}}\), \({\text{C}}_{\text{p}}\) percent in human and guinea pig cochlea vibration.In summary, our simulations revealed both similarities and differences in the cochlear vibration patterns of humans and guinea pigs.For the common points, for the relative velocities of the central point, the velocity in the x direction is the highest, that in the z direction is in the middle and that in the y direction is the lowest for most frequencies. At high frequencies, the x and y directions exchange positions, the y direction increases to the highest position while the x direction decreases to the lowest position. These situations happen in both the human and guinea pig results. The common velocity component of both humans and guinea pigs constitutes a significant majority of the resultant velocities at low frequencies. However, its impact starts to diminish beyond the 3–4 kHz range. Similar trends are observed in angular velocities for both humans and guinea pigs. At low frequencies, both have peaks at approximately 300–400 Hz, and at high frequencies, both increase substantially and have their second peaks. The compression velocities also follow a similar trend in which the compression velocities increase with some fluctuations, especially over 2 kHz, they drastically increase considerably, and both exhibit a trough at approximately 10 kHz at high frequencies. These similar patterns make the guinea pig a good model for human hearing research.For the different parts, although the total force of the stimulation in the two models is the same, 1 N, the place on which the transducer is applied is different. The difference in size and mass of the cochlea only affects the vibration results in terms of magnitude by the same force, but it does not impact the trends change and relative comparison. While the difference of the transducer location, in the human model, the stimulation is from the right mastoid, and it is almost in the x direction in the human model coordinate system, while the stimulation in the guinea pig model was applied on the top of the head. After transposing the human cochlear model to the guinea pig cochlear local coordinate system, and adjusting these two models, we found that the angle between the two stimulation directions was 52.78° and both were almost in the xy plane, perpendicular to the z direction, the central axis of the two cochleae, as shown in Fig. 1. Usually, the vibration velocity is the highest in the stimulation direction, but the computed results do not reveal that the z direction has much greater vibration velocity compared to the x and y directions. This discrepancy could be because the original stimulation was applied in the z direction within the guinea pig model’s coordinate system, not in the guinea pig cochlear local coordinate system. After transforming the data to the guinea pig cochlear local coordinate system, the stimulation direction no longer aligned with the z direction. Since cochlea is a snail-shaped which is a repetitive structure, it is almost round shape in the xy plane and the stimulations of the human and guinea pig are both applied in the xy plane, the radial direction in the round plane of the cochlea, this perhaps makes the two stimulations not too different for the cochlea. Based on these findings, we can recommend the chosen stimulation sites for bone conduction stimulation. These sites are convenient and comparable locations for experimental operations and ensure that the stimulation produces similar effects. Moreover, we also found peaks at approximately 300–400 Hz in the guinea pig central point velocity and compression velocity results. At high frequencies, these peaks and trends are in accordance with previous experimental result7,8,24. This finding again verified the accuracy of our guinea pig FEM.
Finite element analysis on the human and guinea pig cochlear vibration patterns under bone conduction stimulations
