## 3 Results
### Validation of the Two Model-Based Estimates of Vocal Fold Collision Pressure  
Figure 5 shows the results of the contact pressure analysis method that incorporated a Hertzian model of collision [45]. Plotted are the input measured variables to the model from the high-speed videoendoscopy imaging data (calibrated glottal area and vocal fold displacement) and output estimated parameters from the model (vocal fold deformation at contact and vocal fold collision pressure). See Video S4 (Supplementary Materials) showing a movie of Figure 5 that plots over time the input and output variables overlaid on the high-speed videoendoscopy frames. Direct comparison between the estimates of collision pressure from the model and the measured intraglottal pressure sensor signal  
Figure 4: Calibrated signals recorded during a phonatory segment when the intraglottal pressure sensor was determined to be in the strike zone. Shown as circles are the peak collision pressures in the intraglottal sensor signal during each phonatory cycle.  
is illustrated in Figure 5 as well. The impact stress component matches the first peak of the measured intraglottal signal well. The root mean square error between the estimated collision pressure peaks and the measured peak collision pressures across all cycles in this 100 ms phonatory segment was 1.04 cm H\({}_{2}\)O, corresponding to a mean absolute error of 0.81 cm H\({}_{2}\)O and mean absolute percentage error of 9.1%. The resulting contact pressure component is in good agreement with prior numerical studies [18].  
Figure 6 shows the results of the second model that applied Bayesian estimation to a subject-specific, lumped-mass vocal fold model [46]. Plotted on the left panels of Figure 6 are the input measured variables to the model from the high-speed videoendoscopy imaging data: calibrated glottal area, vocal fold displacement, and vocal fold velocity of the medial edge. On the right panels of Figure 6 are the output estimated parameters from the model: normalized muscle activation levels of the cricothyroid and thyroarytenoid muscles (\(a_{CT}\) and \(a_{TA}\), respectively), subglottal pressure, and the vocal fold collision pressure signal. In addition to the parameter estimates, Bayesian estimation also provides the confidence intervals associated with each output parameter waveform. The large initial model uncertainty within the first 10 ms was expected due to the initial conditions applied; following that transient period, the confidence interval of the model outputs rapidly decreased and reached steady-state values, illustrating good model convergence with tight confidence intervals. As found in direct measurement, an approximate 1:1 relation between the model-based peak collision pressure and subglottal pressure values was observed using the Bayesian estimation method. The root mean square error between the estimated vocal fold collision pressure peaks and the measured peak collision pressures was 1.82 cm H\({}_{2}\)O,  
Figure 5: Results of the Hertzian contact pressure analysis method of [PERSON] et al. [45]. Shown are the **(a)** first high-speed videoendoscopic frame with vocal fold edge tracking, **(b)** measured glottal area waveform, **(c)** vocal fold displacement at the middle digital kymogram of the left (\(x_{\text{I}}\)) and right (\(x_{\text{I}}\)) folds using a Kalman filter, **(d)** vocal fold deformation during contact (model output), and **(e)** vocal fold collision pressure as estimated by the model (Est.) and directly measured by the ISP probe’s intraglottal sensor.  
corresponding to a mean absolute error of 1.58 cm H\({}_{2}\)O and mean absolute percentage error of 17.9%.