## 3 Methods
### Silicone Model Experiments for Validation  
Contact dynamics in silicone, self-oscillating vocal fold models are used for validation of the Hertzian contact approach. The silicone models utilize the same material and follow previously developed approaches for a multi-layer fabrication of silicone vocal fold surrogates [40; 41; 42; 43]. Details of the geometry utilized for the models are shown in Figure 5, and the corresponding modulus of elasticity for each layer are presented in Table 1. The models are inserted into a hemi-laryngeal flow facility, which is driven by regulated, compressed air. Details of the flow facility are presented in Figure 6. Airflow passes through an in-line Dwyer RMC 103-SSV flow meter before entering the flow facility. The flow facility consists of a lung plenum with a 0.03 m\({}^{3}\) volume, that has acoustically treated interior walls to minimize acoustic reflections. The plenum exits into a 2.50 cm wide by a 0.75 cm high subglottal channel. The synthetic vocal folds are mounted at the exit of the subglottal tract. A static pressure tap measuring 1.25 mm in diameter is placed upstream of the exit and is connected to a Kulite ET-3 DC pressure transducer that monitors the unsteady subglottal pressure. Details of the vocal fold geometry and the stiffness of each corresponding layer are detailed in Figure 5.  
During oscillation, the medial vocal fold surface contacts the lower wall of the subgtlottal tract, which has a movable contact plate insert to enable a direct measurement of the contact pressure and location. The contact pressure is measured by a Millar Mikro-Cath pressure transducer that is flush mounted in the wall of the contact plate and is embedded in silicone such that the upper surface of the tongue remains flat. The pressure transducer is recalibrated while embedded in the silicone via static weight tests that measure the contact force and area of silicone discs resting on the surface of the tongue. In addition, the frequency response of the embedded transducer was measured to be greater than 3.8 kHz. To measure the precise location of contact, the procedure first proposed by Reference [44] is followed. A 1.50 mm wide (anterior-posterior direction) by 3.00 mm long (inferior-superior direction) \begin{table}
\begin{tabular}{c c} \hline \hline
**Layer** & **Modulus of Elasticity kPa** \\ \hline Adipose tissue & 6.8 \\ Body & 17.3 \\ Cover & 0.95–2.45 \\ Epithelium & 101.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of the synthetic vocal fold models. Figure 5: Geometry and dimensions of the synthetic vocal fold model. All reported dimensions have units of cm. Figure 6: A schematic of the experimental flow facility. All dimensions shown are in mm. copper strip is mounted flush to the surface of the tongue and is positioned precisely 3.00 mm inferior to the pressure transducer. The vocal folds models are covered in graphite powder and, together with the copper strip, are wired into one leg of a Wheatstone bridge. Each of the other three legs of the Wheatstone bridge are comprised of a 330 k\(\Omega\) resistor. In this manner, when the vocal folds contact the copper strip, the resistance through the VF leg of the circuit, which is determined by monitoring the output voltage from the circuit via LabView(r) PICe-6321 data acquisition card, decreases, and contact is identified. The movable contact plate extends beyond the exit plane of the vocal folds and is attached to a micropositioner (Thor Labs PT1) so that it can be precisely positioned in the inferior-superior position to determine the contact location. Once the precise position of contact is identified, the plate is adjusted inferiorally/superiorally by 3.0 mm, which corresponds to the offset distance between the copper contact strip and the pressure transducer, thereby ensuring that the contact pressure sensor is centered within the region of contact, where the contact measurements are performed.