## 4 Discussion  
Consistent with previous findings [18], the cartilage-conduction peak (around 800 Hz) of the pinna simulator approached that of human aural cartilage when the hardness of the pinna simulator was A20 or A10 (Figure 3). Unlike the previous simulation study that used a polyurethane pipe [17], the resonance peak in the external auditory canal (around 2.5 kHz) in the present study was closer to that of a human ear because of the more precise pinna shape (see Figure 1b). The frequencies of the HATS at the maximum peak below 1 kHz were 1 kHz for A40, 841 Hz for A20, and 841 Hz for A10, while that for a human ear was 749 Hz. In a previous study [18], these frequencies were 1414 Hz for A40, 1 kHz for A20, and 561 Hz for A10. The previous [18] and current pinna simulators were made out of silicon rubber and polyurethane resin, respectively, so dissimilarities in the physical properties might have created the differences in peak frequencies. If the cartilage-conduction peak is shifted toward the lower-frequency range (Figure 3c), the outputs from the pinna simulators and real ears can be more closely approximated for sounds below this peak. The durometer value can be applied to [PERSON]'s modulus using the following equation:  
\[E=\frac{0.0981(56+7.62336S)}{0.137505(254-2.54S)} \tag{1}\]  
where \(E\) is [PERSON]'s modulus [Mpa] and \(S\) is a type A durometer hardness [19]. This equation is considered a good first-order approximation of [PERSON]'s modulus for type A  
Figure 3: Simulated cartilage-conduction sound obtained by the HATS with different pinna simulators: (**a**) A40, (**b**) A20, (**c**) A10, and (**d**) original silicon-rubber-based HATS pinna simulator (solid line). The dashed lines indicate the measured cartilage-conduction sound obtained from the participants. The spectral shapes of A10 and A20 became more similar to those obtained from the participants. hardness, especially from A20 to A80. Based on this equation, the [PERSON]'s moduli of the pinna simulators were 1.69 Mpa for A40, 0.73 Mpa for A20, 0.41 Mpa for A10, and 0.28 Mpa for the original HATS pinna. Although [PERSON]'s moduli are often measured in research on aurican reconstructions, the values differ according to the measurement equipment and procedure. For cadaveric aurican cartilage dissected from the skin and fascia, the measured [PERSON]'s moduli were 5.02 Mpa in [20] and 1.41 to 2.08 Mpa in [21]. To simulate sound transmission numerically through an ear-filling earplug, [PERSON] et al. assigned [PERSON]'s moduli to each type of tissue that makes up the pinna: 0.65 Mpa for skin, 0.001 Mpa for fat, 0.79 Mpa for muscle, 13.6 Mpa for bone, and 1.9 Mpa for cartilage [22]. According to this classification, the A20 and A10 correspond to the skin or muscle. In the previous study, the hardness of human aural cartilage was measured using a durometer (GS-719N; Teclock, Nagano, Japan) [18]. The pointed cylinder of the durometer was pressed against the ear tragus and was allowed to inflect the tragus during the measurement. In this case, the pointed cylinder directly contacted the skin over the cartilage, and so the measured hardness might be lower than the hardness of the singular aural cartilage. In hardness measurements that limited the displacement of the pinna, the hardness of the ear helix ranged from A25 to A55 according to individual differences [23]. The numerical simulations conducted by [PERSON] et al. revealed that the vibrations at the points of the pinna might be propagated via the surface of the skin [22]. However, stimulation at the ear lobe (adipose tissue) did not effectively propagate vibrations on the pinna, even though the ear lobe is also covered by skin [3]. Furthermore, vibrations were not propagated through the osseous part of the external auditory canal even though this bone is covered by skin [8]. According to these data, the layer construction of the skin and the aural cartilage appear to facilitate vibrational propagation.