**4. Discussion**

Since the human ear is a complicated biological system with tiny structures and complex geometry, systematic experimental investigation on it is tough to conduct. Considering the finite element method has the advantage of simulating this complicated biological system, many researchers built a human ear FE model, and used it to study the sound transmission properties of the ear [32–35] and facilitate the design of IMEHDs [14,36,37]. In our human ear FE model, the cochlea was constructed as two fluid-filled channels. This modelling method of the cochlea is widely used in the field of cochlear mechanics [16]. Different individual human ears have similar vibration properties, and to confirm our model's validity, we compared our model-predicted results with the mean value of the experimental

results, which were measured on many human ears, to prove that our model can predict the general response of the human ear. This kind of validation has been widely used by scholars in this fields [20,23].

According to the vibrational energy transmission pathway, the implantable middle ear hearing device can be classified as forward stimulation and reverse stimulation [38]. Stimulating the eardrum, the incus body, the incus long process, and the stapes belong to forward stimulation, since their vibration energy are transmitted to the cochlea through the cochlear oval window, which is the same as the normal hearing process. Whereas, stimulating the round window membrane is called reverse stimulation as its vibration energy is transmitted to the cochlea though the cochlear round window, the other opening window of the cochlea. For the forward driving, our results demonstrate that the piezoelectric transducer provides better performance when stimulating the stapes than stimulating the eardrum's umbo or the incus long process. The performance of stimulating the incus long process is superior to that of stimulating the eardrum's umbo. This result can be easily predicted for forward stimulation since the stapes is close to the cochlea and therefore more e fficient to transmit vibrational energy into the cochlea. Besides, we found that the superiority of the stapes stimulation is significant at high frequencies. To further analyze this phenomenon, we plot the z direction's (along the longitudinal axis of the stapes) displacement contour plot (Figure 13) of the ossicular chain since the stapes transmits its vibration mainly through its piston motion [39]. Figure 13 shows that the stapes can be e fficiently stimulated at a low frequency for all these three stimulating sites, especially for stimulating the stapes and stimulating the incus long process. With an increase in the stimulation's frequency, the vibration cannot be e ffectively transmitted to the stapes for stimulating the incus long process and the umbo, especially for stimulating the umbo. This may attribute to the incudomallear joint and the incudostapedial joint, whose viscous behavior become significant at a higher frequency and weaken the vibrational energy transmission from the stimulating point to the stapes.

**Figure 13.** The z-direction (along the longitudinal axis of the stapes) displacement contour plot of the ossicular chain.

For the forward stimulation, the incus body is the worst stimulating site for the transducer. This result is consistent with Bornitz et al.'s report [18] based on stapes displacement. This owing to the fact that the rotation nod of the ossicular chain is close to the incus body [40]; therefore, the incus body is the least e fficient point for stimulating the ossicular chain. Figure 13 also shows that most of the stimulated response are restrained around the incus body; the vibration cannot be e fficiently transmitted to the stapes footplate under the incus-body stimulation, especially at a high frequency. Thus, compared with other forward stimulation, the high-frequency output should be enhanced for the incus-body simulating-type piezoelectric transducer.

Compared with forward stimulation, it is di fficult to estimate the performance of the round window's stimulation, i.e., the reverse stimulation, since its vibration energy transmission pathway is di fferent from that of forward driving. Although comparison of the forward stimulation with the round window's stimulation were reported [16,22], these studies only focus on the electromagnetic transducer, which is a force-driven transducer. Bornitz et al.'s study [18] demonstrates that the stimulating site's influence for the electromagnetic transducer is di fferent from that for the piezoelectric transducer. For the piezoelectric transducer, our study finds that stimulating the round window membrane can produce a similar ESPL as when stimulating the stapes. Regardless of which site is stimulated, the piezoelectric transducer can generate high ESPL at a high frequency. Since most sensorineural hearing loss is severe at a high frequency [41], this characteristic is a crucial advantage for the piezoelectric transducer to compensate for the hearing loss. This better high-frequency performance of the piezoelectric transducer was reported in many experimental studies [6,10,42].

The performance of the RW membrane stimulation, as well as that of the stapes stimulation are susceptible to the change of the excitation's direction. This result for the RW membrane stimulation conforms to Arnold et al.'s temporal bone's study [43], which found that the transducer's direction significantly a ffects the energy transferred to the cochlea of up to 35 dB. The clinical result also shows that the postoperative performance of the RW stimulation has a high variability [44], which may attribute to the change of the transducer's direction. Meanwhile, this sensitivity for RW membrane stimulation and stapes stimulation to the excitation direction is prominent at a high frequency. Considering the main type of sensorineural hearing loss is the "high-frequency" hearing loss [41], the piezoelectric transducer's orientation for RW stimulation or stapes stimulation should be guaranteed during the surgery. For the design of these two types of transducers, it is recommended to design a fixing part to ensure its orientation after implantation.

The main purpose of this paper is to investigate the stimulating site's influence on the piezoelectric transducer. To facilitate this study, the real structure of the piezoelectric transducer was not considered in this paper; instead, we simplified it as an ideal displacement driven transducer, i.e., a transducer generates a certain displacement without limitations in force. Under this simplification, the retroaction of the human ear system onto the piezoelectric transducer was neglected. This simplification for the IMEHD's piezoelectric transducer is based on the fact that the blocking force of the transducer is much larger than its working force. For instance, the piezoelectric transducer (Model PL-033, Physik Instrumente, Waldbronne, Germany) used in Wang et al.'s study [41] for IMEHD has a blocking force of 300 N, which is much larger than the force (89 μN [45]) required to drive the vibration of ossicles to the equivalent of 100 dB SPL. Thus, the resistant force of the human ear cannot change the piezoelectric displacement output significantly. Based on a coupled FE model of the middle ear and a piezoelectric transducer, which is a 20-layer stack of 3 mm diameter and 4 mm thickness made of PZN-4.5PT, Bornitz et al. [18] also found that there is no retroaction of the human ear onto the piezoelectric transducer. Thus, simplifying the piezoelectric transducer in IMEHD as a displacement-driven transducer is acceptable.

It should be noted that our FE model is constructed only based on one human ear specimen. Based on a numerical study, Daniel et al. [46] found that the human ear's geometrical variation can lead to di fferences of 4 dB in the lower frequencies and up to 6 dB around 2 kHz, but similar shapes in the calculated response curves. Thus, the patients' individual geometrical di fferences may alter our results quantitatively at lower frequencies and frequencies around 2 kHz. Nevertheless, the overall trend of our results still holds under di fferent individual human ear geometries.
