## 5 Discussion  
The fundamental tenet of CPA is that sufficient information regarding the collision mechanics is embedded in the vocal fold kinematics, which is accessible through high-speed videos to obtain reasonable first-order estimates of contact pressure. That is, CPA is founded on the principle that impact velocity and contact time are sufficient to assess collision pressure magnitudes. Our validation using silicone vocal fold models illustrated that there is an excellent agreement between the mean predicted contact pressure, although with some nonnegligible variability due to image processing difficulties. Agreements with prior numerical studies [20; 21; 22; 46; 47], experimental measurements in  
Figure 10: Validation of the proposed Hertz contact model (red lines) against published data (blue lines). For ease of comparison, the time axis was normalized to maintain a contact duration of 1 ms. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subjective Loudness** & \begin{tabular}{c} **Sound Pressure Level** \\ **dB ref: 20**\(\mu\)**Pa** \\ \end{tabular} & \
\begin{tabular}{c} **Contact Pressure** \\ **(Estimated) kPa** \\ \end{tabular} &
\begin{tabular}{c} **Ratio with Respect to** \\ _Normal Loudness_ \\ \end{tabular} \\ \hline _Soft_ & 72.9 & 1.03 & 0.58 \\ _Normal_ & 81.8 & 1.77 & 1.00 \\ _Loud_ & 93.3 & 3.76 & 2.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CPA results for in vivo HSV case of study. The CPA estimates include the absolute pressure and the relative pressure with respect to the normal loudness case. humans [6; 7; 8], and excised hemilarynx studies [16] also have been found. This supports that the Hertz contact framework is appropriate for the goal of estimating contact pressure directly from the kinematic information, as described in the CPA framework. There are clinical arguments that suggest that aerodynamic parameters, such as _Maximum Flow Declination Rate_ (MFDR), are related to collision pressure and stress [1; 5]. Similar relative changes in aerodynamic-based assessment parameters with loudness for normal subjects have been observed in prior studies [47] as found with the contact pressure estimates in this study. Numerical models support this relation between MFDR and collision pressure [5; 37], but the conjecture is still not proven and only theoretical studies that evaluate this are known. That said, our case study supports the idea that CPA is capable of discriminating the increasing effect of collision pressure with loudness in actual in vivo scenarios despite the lack of aerodynamic or other additional information in the recordings. The proposed Hertz contact model, which, by virtue of employing cylinders, implicitly assumes uniform and simultaneous contact along the thickness of the VFs, has the advantage of not requiring additional subject-specific information in order to estimate the normalized contact pressure. Geometric variations in the inferior-superior direction, however, do influence the contact pressure, as evidenced by the estimated value of \(\alpha\) in Equation (20) differing from one. The value employed in this study was obtained from the numerical validation phase through a comparison with the reduced order model performance. It remains unclear how universal this geometric correction factor may be and requires additional data sets. It is unlikely that the value of \(\alpha\), even if it is not relatively constant between individuals, will change dramatically, however. Similarly, to obtain absolute measures of contact pressure from CPA, one requires additional patient-specific information, namely tissue elasticity. This value can change significantly between subjects or even between vocal gestures. However, even though there could be a bias in the exact magnitude of the collision pressure due to either \(\alpha\) or elastic modulus, the relative changes within the same subject are expected to be well-represented.