## 1 Introduction  
Currently, the number of people with hearing difficulties is estimated to be 1.5 billion worldwide, equivalent to approximately one in five people. Such people often experience reduced quality of life and encounter lifelong difficulties, including delayed language development and academic failure in childhood, limited employment opportunities in adulthood, and accelerated cognitive decline in old age. Hard-of-hearing disability has economic repercussions, and the associated global annual macroeconomic losses are estimated at more than 980 billion dollars [1]. Hearing aids are devices used to compensate for difficulties in hearing, such as age-related hearing loss, or when comorbidities interfere with the treatment. Air-conduction hearing aids are often used to treat sensorineural hearing loss. However, air conduction hearing aids, such as external auditory canal atresia, may not provide effective hearing compensation. In such cases, bone conduction hearing aids are used [2]. These aids require a vibrator to vibrate the head bones, and the mastoid process presses against the vibrator with a force of 2-3 N from a headband, which causes painful skin aches and other problems. In a device called the bone-anchored hearing aid (BAHA), a titanium bolt is implanted in the head bones, and a vibrator is attached to it; consequently, the surgical procedure is burdensome for the patient. In collaboration with Nara Medical University, we developed cartilage conduction hearing aids (CCHAs) that transmit sound through vibrations by attaching a small vibrator to the ear cartilage [3, 4]. CCHAs have been developed for patients suffering from external auditory canal atresia and have demonstrated effectiveness and advantages in clinical studies [5, 6, 7]. In Japan, the product has been commercially available since 2017 and several medical institutionshave published various reports on it [8; 9; 10; 11; 12; 13]. Furthermore, in recent years, the applicability of CCHAs to patients diagnosed with various hearing impairments has also been under consideration [14]. Output performance is an important criterion in hearing aid evaluation methods, such as the IEC (International Electrotechnical Commission) 60118-0. The method for evaluating the output characteristics of bone conduction hearing aids is specified in the IEC (International Electrotechnical Commission) 60118-9. The evaluation method used a mechanical coupler specified in the IEC (International Electrotechnical Commission) 60318-6, which was used to measure the force level of bone conduction vibrators in audiometers. In the case of bone conduction, the mastoid or forehead of the human head vibrates to transmit vibrations to the inner ear through the head bones. The mechanical coupler simulated the mechanical impedance of a human mastoid with a circular contact area of 175 mm\({}^{2}\)[15]. A mechanical coupler is also used in the output evaluation of bone conduction hearing aids with the smaller contact area. This allows performance values from different manufacturers and models to be evaluated on the same basis. The presentation of mechanical impedance in papers and conference reports contributes to product diversification because it can be used by hearing device engineers to simulate output characteristics when designing vibrators. The mechanical impedance of the human head has been studied for bone conduction hearing aids such as BAHA [16; 17]. However, little is known about the mechanical impedance of the ear cartilage to evaluate the output of the CCHAs. There are three transmission pathways for cartilaginous conduction: direct air, cartilage-air, and cartilage-bone [18; 19]. When the vibrator of the CCHAs is worn in the concha auriculae (Figure 1), the sound pressure on the eardrum of a normal ear with a sealed ear canal entrance is highly dependent on the sealing condition. In air conduction hearing aids, the sound pressure is evaluated using a sound pressure object that simulates the eardrum in a sealed ear canal.