## 5 Results and Discussion
### Distinguishing between Model Configurations  
As the eventual goal of this research is patient-specific modeling, we wish to investigate whether the FE model is sufficiently sensitive and if HSV data provide enough information to distinguish between similar experimental configurations. As a first order exploration we consider varying subglottal pressures for silicone VFs with medial compression. As discussed in Section 2.1, the pressures considered range from 0.91 to 1.18 kPa. The fits to each GAW are shown in Figure 6 and the resulting estimates of the degree of medial compression, along with the other material properties, are shown in Table 5. Similar to Figure 5, the fits are again reasonable given the simplified model being used. As the subglottal pressure increases, so too does the maximum glottal area, as expected; this increase is captured by the FE model. As with the previous comparison, the open quotient and speed quotient are both lower for the FE model, though the difference decreases with increasing subglottal pressure. Figure 5: The glottal area waveform extracted from HSV of self-oscillating silicone vocal folds at \(p_{\text{sub}}=1.00\) kPa (**a**) without medial compression and (**b**) with medial compression. Blue dashed line: HSV; red solid line: FE model; orange solid lines: uncertainty bounds from the FE estimate. As shown in Table 5, all experimental values fall within two standard deviations of the estimated values; furthermore, the viscosity is estimated to be approximately 3 Poise, which is consistent with the previous results. The estimated medial compression, \(x_{0}\), varies somewhat from case to case, but all values are within two standard deviations of one another, indicating statistical consistency. Overall, comparing the estimates in Tables 3-5, we find that the estimated material properties are quite consistent across all cases studied, engendering confidence in the method. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathbf{p_{\text{sub}}}\) & \(\mathbf{E_{\text{bdy}}}\) & \(\mathbf{E_{\text{cvr}}}\) & \(\mathbf{E_{\text{lig}}}\) & \(\mathbf{p_{\text{sub}}}\) & \(\rho\) & \(\eta\) & \(\mathbf{x_{0}}\) \\ (**kPa**) & (**kPa**) & (**Pa**) & (**kPa**) & (**Pa**) & (**kg/m\({}^{3}\)**) & (**Poise**) & (**mm**) \\ \hline
0.91 & 12.38 & 643.0 & 2.375 & 901.2 & 1048 & 2.98 & 8.29 \\  & (4.31\%) & (6.22\%) & (12.67\%) & (6.16\%) & (0.28\%) & (6.28\%) & (0.37\%) \\ \hline
1.00 & 12.28 & 629.8 & 1.842 & 991.9 & 1051 & 3.11 & 8.27 \\  & (4.3\%) & (4.1\%) & (12.16\%) & (4.53\%) & (0.26\%) & (4.66\%) & (0.30\%) \\ \hline
1.09 & 12.15 & 635.1 & 1.858 & 1062 & 1047 & 3.01 & 8.33 \\  & (2.27\%) & (3.01\%) & (10.39\%) & (2.89\%) & (0.16\%) & (4.45\%) & (0.28\%) \\ \hline
1.18 & 12.25 & 639.6 & 2.098 & 1164 & 1049 & 3.03 & 8.32 \\  & (2.07\%) & (2.74\%) & (8.1\%) & (2.43\%) & (0.15\%) & (3.86\%) & (0.22\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Material properties estimates for varying subglottal pressures with medial compression. The associated estimate uncertainties as a percentage of the estimate values are in brackets. Figure 6: Comparison on the glottal area waveforms extracted from HSV and the FE predictions from the fitted material properties for (**a**) \(p_{\text{sub}}=0.91\), kPa (**b**) \(p_{\text{sub}}=1.00\) kPa, (**c**) \(p_{\text{sub}}=1.09\) kPa, and (**d**) \(p_{\text{sub}}=1.18\) kPa. Blue dashed line: HSV; red solid line: FE model; orange solid lines: uncertainty bounds from the FE estimate. Considering the uncertainty in the estimates, we see that as the subglottal pressure increases its uncertainty decreases. As the variance of the measurement noise is treated as fixed at \(1\,\mathrm{mm}^{2}\) in all estimates, this decrease in uncertainty is not due to a decrease in measurement uncertainty. Furthermore, the same prior distributions are used in all cases.