**1. Introduction**

Hearing loss, affecting around 466 million people worldwide, is one of the six leading causes of disease burden in our society [1]. Up to now, there is still no effective medical treatment to sensorineural hearing loss (SNHL), which is the main type of hearing loss taking up approximately 90% of reported hearing loss [2]. The patients with SNHL mainly turn to hearing aids for restoring audibility [3]. Although sophisticated hearing aids have been developed, hearing aids still have a number of inherent shortcomings, such as a limited high-frequency amplification gain, ear canal occlusion, and feedback annoyance [4]. To overcome these problems, many researchers proposed and designed the implantable middle ear hearing devices (IMEHDs), which restores audibility by the mechanical vibration of their implanted transducers [5].

IMEHD primarily comprises four components: the microphone, the sound processor, the transducer, and the battery. A typical schematic illustration of the IMEHD is shown in Figure 1 [6]. Briefly, the microphone, which is implanted closer to the ear canal, receives the outside sound and transmits to the sound processor. Then, the sound processor processes the input signal according to patients' hearing loss and outputs a driving signal to the piezoelectric transducer. The piezoelectric transducer mainly consists of three parts: the piezoelectric stack, the rod, and the support sleeve. One side of the piezoelectric stack is stuck to the rod, which is attached to the incus body. While the other side of the piezoelectric stack is held to the support sleeve, which is fixed to the skull. Under the electrical driving signal's stimulation, the piezoelectric stack, which is a monolithic ceramic construction of many thin piezoelectric ceramic layers, expands and contracts. Finally, the vibration of the piezoelectric stack is transmitted to the incus body by the rod and compensates for hearing loss. All these parts are powered by the battery. Among these IMEHD parts, the transducer is a key component as it is responsible for stimulating the human ear. Based on actuation mechanisms, the IMEHDs' transducers are divided into two types: the electromagnetic transducer and the piezoelectric transducer [5]. Compared with the electromagnetic transducer, the piezoelectric transducer has the advantages of a lower power consumption, compatibility with external magnetic field, and ease of fabrication [4]. Owing to these advantages, piezoelectric transducer have been widely used in IMEHDs, especially the totally implanted type IMEHDs [7]. In terms of the stimulating sites, the transducer can be further classified into five categories: the eardrum driving [8,9], the incus body driving [6], the incus long process driving [10], the stapes driving [11,12], and the round window (RW) membrane driving [13,14].

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**Figure 1.** Schematic view of an implantable middle ear hearing device with a piezoelectric transducer attached on the incus body.

Clinical study shows that the stimulating site influence the transducer's hearing compensation performance [15]. To uncover this influence and optimize the transducer's design, some preliminary studies have been carried out. Based on numerical analysis, Zhang et al. found that stimulating the round window membrane is more e fficient than stimulating the incus long process [16]. The human temporal bone experiment conducted by Deveze et al. demonstrates that stimulating the stapes is superior to stimulating the incus body and incus long process [17]. However, the above researches only focus on the electromagnetic transducer. A numerical study shows that the stimulating site's influence on the electromagnetic transducer is di fferent from that on the piezoelectric transducer [18]. To investigate the stimulating site's e ffect on the piezoelectric transducer's performance, Bornitz et al. constructed a human ear finite element (FE) model and compared the stapes displacements under di fferent piezoelectric transducers' stimulation [18]. Their result demonstrates that the incus body is the least e ffective stimulating site for the piezoelectric transducer. However, auditory response

measurements show that the stapes response is unreliable for evaluating round window stimulation [19]. Besides this, stimulating the incus long process, which is widely utilized clinically, was not investigated.

Accordingly, in the present study, we carried out a systematic study on the influence of piezoelectric transducer's stimulating sites. To facilitate this study, we built a human ear FE model and confirmed its validity. Then, the stimulating site's e ffect was analyzed based on the basilar membrane's displacement, which is reliable for evaluating IMEHD performance. The result could help the surgeon choose a piezoelectric transducer and aid the designer to optimize the piezoelectric transducer.

#### **2. Materials and Methods**

#### *2.1. Constructions of the Human Ear FE Model*

A 3D FE model of the human ear was built using CT scanning and reverse modelling techniques based on a fresh human temporal bone specimen. Figure 2 shows the constructed model, consisting of the external ear canal, the middle ear (middle ear cavity, ossicular chain, and supporting ligaments and tendons), and the cochlea. The middle ear was separated from the external ear canal by the eardrum. The ossicular chain (malleus, incus, stapes and the joints) was connected to the wall of the middle ear cavity by the ligaments and tendons. The air in the middle ear cavity and the ear canal was meshed by acoustic tetrahedral elements, with a total of 277,863 elements. The eardrum was divided into the eardrum pars tensa and the eardrum pars flaccida. The eardrum pars tensa was established as a three-layer structure [20]. The inner layer and outer layer of the pars tensa was assumed to be isotropic, while the middle layer of the pars tensa was assumed to be orthotropic, with fibers in circumferential and radial directions. The eardrum pars tensa's inner layer, middle layer, and the outer layer had a thickness of 0.017 mm, 0.016 mm, and 0.017 mm, respectively. The thickness of the eardrum annulus ligament and the eardrum pars flaccida were 0.2 mm and 0.1 mm, respectively. A total of 1939 three-noded shell elements were created to mesh the eardrum. The other middle ear structures were meshed by 45,609 four-noded tetrahedral elements.

**Figure 2.** The constructed human ear finite element model.

The middle ear connects to the spiral cochlea with the stapes footplate attached to the oval window. The model's cochlea consists of two fluid-filled chambers: the scala vestibuli (SV) and the scala tympani (ST). These chambers were separated by the basilar membrane (BM) and the bony spiral plate. A total of 361,589 four-noded acoustic tetrahedral elements were created to mesh the fluid in the cochlea. The BM and the bony spiral plate were meshed by 7666 shell elements. The BM thickness and width vary approximately linearly from the base of the cochlea to the apex of the cochlea. The BM length is

34 mm. The thickness of the BM varies from 5.2 μm to 0.6 μm, and the width varies from 0.1 mm to 0.5 mm. The round window membrane was meshed by 851 three-noded tetrahedral elements. The RW membrane has a thickness of 0.1 mm and an area of 2 mm2, which is close to the size of 2.08 mm<sup>2</sup> reported by Atturo et al. [21].

Considering the ligaments and tendons connect to the bony wall of middle ear cavity, we fixed the end nodes of these components in our FE model. The surfaces of the acoustic elements, which attached to the bony wall in the ear canal, the middle ear cavity, and the cochlea, were defined as rigid walls. The outer edges of the round window membrane and the cochlear spiral plate were set as fixed constraints since they are anchored to the bony wall of the cochlea. Fluid structure interfaces were defined for the surfaces of the acoustic elements attached to the movable structures, i.e., the eardrum, the ossicles, the ligaments, the tendons, the oval window, the BM, and the round window membrane.
