## 4 Results
### Silicone Model Validation  
The silicone model experiments allow for a separate validation using a completely different model conception, which is desirable to eliminate any possible bias from our prior numerical validation. However, a separate challenge occurs in this scenario. State-of-the-art silicone VF model designs are multi-layered, with material properties that closely resemble human tissue properties. Thus, the estimation of the \"equivalent\" Young modulus for the purpose of the Hertz contact model is not straightforward. Studies in silicone VF models and human largynes have demonstrated that the estimation of the Young modulus is a function of the indentation method [45] and that it is  
Figure 8: Numerical validations for both complete (top row; TEST1) and incomplete (bottom row; TEST2) glottal closure scenarios. Apparent penetration (left column) and normalized pressure (right column) are presented for the reference model MBCM, the idealized HERTZ contact accounting for the superior and inferior tissue, and the proposed CPA scheme using the superior view only. Note that subglottal pressures below 1000 Pa were not sufficient to cause VF contact under incomplete glottal closure scenarios. likely to be affected by boundary conditions. Furthermore, the colliding portion of the VFs is a function of the vibrating tissue, which can involve different layers under different conditions, thus changing the equivalent elastic modulus involved during contact. To address this issue, we propose estimating the equivalent elastic modulus of the silicone model using the dynamic structure of the proposed Hertz and available measured pressure data and leaving some cases out for cross-validation. In particular, the recordings obtained with the modulus of elasticity with more data points, namely \(E_{cover}=1.65\) kPa, are used to estimate the equivalent Young modulus, as shown in Table 3. For this purpose, the peak contact pressure measured from the intraglottal Millar pressure probe is contrasted with the dimensionless term from Equation (20) to estimate the equivalent Young modulus. Note that we also use the correction factor \(\alpha=1.679\) obtained in the prior numerical validation. The resulting modulus of elasticity from Table 3 has a mean value of 15.1 Pa and a standard deviation of 7.2 Pa. The relatively large variability in the estimated values is due to various factors, including the hemilarynx configuration, errant shadowing, bright light reflections, etc. These effects were more or less critical in some cases, up to the point where it was not possible to accurately analyze the video (e.g., for the case of subglottal pressure equal to 3 kPa in Table 3). Efforts will be devoted to minimize these imaging problems in subsequent studies. As a first-order approximation, we assume that there is a linear relation between the equivalent elasticity and the cover elasticity, and if we normalize the former with the latter, we obtain a dimensionless elastic term that can be used to predict the equivalent elastic moduli for other conditions. Using this idea, we estimate that the silicone model with a cover stiffness of 0.95 kPa has an equivalent elasticity of 8.7 \(\pm\) 4.1 kPa (mean and standard deviation) and that the silicone model with a cover stiffness of 2.45 kPa has an equivalent elasticity of 22.4 \(\pm\) 10.7 kPa (mean and standard deviation). We then use these values to contrast the predicted and measured contact pressures, as shown in Table 4. It is interesting to note that there is almost a factor of 10 between the cover stiffness and the equivalent elastic module needed for Equation (20). Table 4 shows that there is an excellent agreement between the mean peak contact pressure predicted with the proposed approach and the one measured using an intraglottal pressure probe. However, there is a considerable variability in the estimates due to aforementioned image processing difficulties in our silicone experiments. Thus, further experiments with more controlled lighting