**3. Results**

#### *3.1. Validation of the Human Ear Finite Element Model*

To confirm the validity of the established human ear finite element model, three sets of comparisons with the published experimental data were conducted. Since the stapes response is the input of the cochlea, we firstly selected the stapes' footplate displacement to verify our model. Figure 4 shows the mean value of experimental measurements on five temporal bones reported by Gan et al. [27]. In this experiment, a set of pure tone sounds of 90 dB SPL were applied to the eardrum, and the displacement of the stapes footplate was measured using a laser vibrometer. For comparison, we carried out a harmonic analysis across the frequency range of 250–8000 Hz under the same sound pressure applied to the lateral side of the eardrum of our FE model. The model-predicted result was also plotted in Figure 4. It demonstrates that our model-derived displacement of the stapes footplate agrees well with the experimental curve.

**Figure 4.** Comparison of the stapes' footplate displacement under 90 dB SPL sound pressure applied at the eardrum.

The BM's response was also selected for our model's validation as it responsible for sensing the cochlear input vibration. Figure 5 displays the experimental curves of the ratio of the BM's velocity at 12 mm from the stapes to the stapes' velocity. The experimental tests were conducted by Gundersen et al. [26] and Stenfelt et al. [28] with a 90 dB SPL input sound pressure applied to the eardrum. Similarly, with a uniform sound pressure applied at the lateral side of the eardrum in our model, a harmonic analysis was conducted across the frequency range of 250–8000 Hz. The model-calculated result was plotted with the experimental curves in Figure 5. It shows that the maximum peak appears at 3500 Hz, which conforms to the experimental data of Gundersen et al. [26]. Besides, our model-predicted result has the same trend as Stenfelt et al.'s [28] data.

**Figure 5.** Comparison of the ratio of the basilar membrane's (BM) velocity at 12 mm from the stapes to the stapes' velocity.

Finally, we compared the model-derived cochlear input impedance, which is a measure to represent the cochlear resistance of transmitted vibration from the middle ear, with the experimental data measured by Aibara et al. [29], Puria et al. [30], and Merchant et al. [31], as shown in Figure 6. The cochlear input impedance was calculated from the ratio of the pressure in the SV to the stapes volume velocity (product of the stapes' footplate velocity and the stapes' footplate area). It shows that our predicted result is in the range of these experimental data, and has the same trend with these experimental data, especially the data of Puria et al. [30]. These above comparisons prove that our model can be utilized to predict the sound transmission properties of the human ear.

**Figure 6.** Comparison of the cochlear input impedance.

#### *3.2. The Stimulating Site's Influence on the Piezoelectric Transducer's Performance*

Figure 7 shows the influence of the piezoelectric transducer's stimulating sites on its hearing compensation performance. It demonstrates that the piezoelectric transducer can produce high ESPL at high frequency no matter which sites is stimulated. Stimulating the RW membrane as well as stimulating the stapes can produce a more equivalent sound pressure level than stimulating the other sites, especially at a high frequency. Besides, the ESPL under the stimulation applied at the incus-long-process is superior to that generated by the umbo stimulation. The incus body is the worst stimulating site for the piezoelectric transducer.

**Figure 7.** The influence of a piezoelectric transducer's stimulating sites on its hearing compensation performance. (**a**) Equivalent sound pressure level of the piezoelectric transducers stimulating at different sites; (**b**) ratio of equivalent sound pressure of the piezoelectric transducer stimulating at different sites (the reference is the stimulation applied at the stapes along the stapes longitudinal axis).

#### *3.3. The Sensitivities of Each Stimulating Site to the Changes of Excitation's Direction*

For stimulating the eardrum's umbo, the influence of a piezoelectric transducer's excitation direction on its hearing compensation performance is shown in Figure 8. It indicates that the transducer's stimulated ESPL decreases with the increase of the angle of the excitation's inclination, especially at the middle frequency. The maximum decrease is found at 1 kHz for 60◦ to CP, with a reduction of 13 dB.

**Figure 8.** The sensitivity of umbo stimulation due to the change of its excitation's direction. (**a**) Equivalent sound pressure level of the piezoelectric transducer's stimulation; (**b**) change of equivalent sound pressure level.

While the stimulating site is the incus body, the stimulation direction's influence is shown in Figure 9. It demonstrates that the change of the stimulation direction's influence on the transducer's stimulated ESPL is complex in this case. Increasing the angle of the stimulation's inclination decreases the transducer-stimulated ESPL at a lower frequency, but increases the ESPL slightly at a higher frequency. The maximum decrease is at 250 Hz for 45◦ to CP, with a reduction of 17 dB.

**Figure 9.** The sensitivity of incus-body stimulation due to the change of its excitation's direction. (**a**) Equivalent sound pressure level of the piezoelectric transducer's stimulation; (**b**) change of equivalent sound pressure level.

As for stimulating the incus long process, the excitation direction's influence is shown in Figure 10. Similar to the influence in stimulating the eardrum's umbo, the boost of the angle of the excitation's inclination reduces the transducer-stimulated ESPL, especially at the middle frequency. The maximum decrease is also at 1 kHz for 60◦ to CP, with a reduction of 16 dB.

**Figure 10.** The sensitivity of incus-long-process stimulation due to the change of its excitation's direction. (**a**) Equivalent sound pressure level of the piezoelectric transducer's stimulation; (**b**) change of equivalent sound pressure level.

In terms of stimulating the stapes, the effect of the transducer's stimulation direction is shown in Figure 11. It indicates that the transducer-stimulated ESPL also decreases with the increase of inclination angle. Unlike previous stimulating sites, the ESPL at a high frequency decreases significantly in this case. The maximum decrease is at 400 Hz for 60◦ to CP, with a reduction of 40 dB. For a high frequency region, the maximum reduction is 36 dB at 4 kHz for 60◦ off the reference direction.

**Figure 11.** The sensitivity of stapes stimulation due to the change of its excitation's direction. (**a**) Equivalent sound pressure level of the piezoelectric transducer's stimulation; (**b**) change of equivalent sound pressure level.

For stimulating the RW membrane, the influence of the transducer's stimulation direction is shown in Figure 12. It demonstrates that the increase of the inclination angle mainly reduces the transducer's high frequency ESPL. The maximum decrease is at 6 kHz for 60◦ off the reference direction, with a reduction of 31 dB.

**Figure 12.** The sensitivity of RW membrane stimulation due to the change of its excitation's direction. (**a**) Equivalent sound pressure level of the piezoelectric transducer's stimulation; (**b**) change of equivalent sound pressure level.
