## 4 Discussion  
In this study, in vivo phonation tests and subject-specific computation modeling were used to investigate the changes in vibratory frequency in three experimental conditions. We found a difference in vibratory patterns between HP, as simulated by bilateral suture cricothyroid approximation, and sUVFP, as simulated by unilateral suture cricothyroid approximation. HP demonstrated symmetrical vibration while the sUVFP condition demonstrated asymmetry in left-right frequency. From this investigation, we concluded that the cricothyroid suture approximation approach implemented to generate the different laryngeal conditions in this experiment was valid to simulate both normal phonation and UVFP. The subjects demonstrated a wide range of vibration frequencies (~600-900 Hz), as shown in Table 1; however, this variability is consistent with previous frequencies observed in non-stimulated and electrically stimulated phonation in rabbits [29; 30; 39] and is likely attributable to inter-individual differences in tissue properties and laryngeal geometries. Given the high level of variability observed within species, one set of tissue properties will not adequately represent all subjects, illustrating a real need for subject-specific modeling to improve accuracy in surgical planning. In the current sUVFP condition, the unsutured side's frequency was only around 10% lower than the sutured side, while both sides were much higher than the NA condition. This implies that the unsutured side in the sVUFP condition still experienced significant stretching and stiffening as a consequence of the contralateral suture. Further examination of the cartilage position in Figure 5 shows that both sides of the vocal fold were stretched even after one side's suture was released, and this was due to residual downward and lateral tilting of the released thyroid cartilage toward the contralateral suture. While the thyroid cartilage is flexible, it is a single piece of cartilage spanning the full breadth of the larynx, thus manipulation of one side cannot be achieved with total independence from the other. This type of asymmetric approximation is different than that observed in clinical  
Figure 8: Eigenmodes of the vocal fold under different conditions. (**a**) HP condition with bilateral sutures (**b**) sUVFP condition with unilateral left-sided suture. Animations are included in the supplemental material. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Right(Hz)** & **Left (Hz)** & **Difference** \\ \hline \multirow{3}{*}{Sample 1} & NA & 334 & 333 & \textless{1}\% \\  & HP & 605 & 597 & 1\% \\  & sUVFP & 560 & 610 & 9\% \\  & NA & 302 & 300 & \textless{1}\% \\ Sample 2 & HP & 533 & 531 & \textless{1}\% \\  & sUVFP & 499 & 535 & 7\% \\  & NA & 329 & 330 & \textless{1}\% \\ Sample 3 & HP & 609 & 608 & \textless{1}\% \\  & sUVFP & 506 & 550 & 9\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Left and right vocal fold eigenfrequencies under experimental conditions. UVFP; however, this technique successfully achieves significant differences between the left and right vocal fold and therefore creates a useful in vivo phonation paradigm that will allow us to perform future combined experimental/computational investigation into the surgical restoration of symmetric vibration. The novel surgical and computational methods proposed in this study have several major benefits when compared to traditional techniques for modeling phonation and UVFP. Future approximation is reversible and minimizes risks of airway patency, aspiration, and long-term survival associated with RLN/SLN resection in animal models [60]. Additionally, suture approximation allows for imaging of the vocal folds at rest, during bilateral phonation, and in sUVFP in a fast and minimally invasive process that can easily be replicated in vivo and ex vivo allowing for maximum translatability between the two. Using MRI scan and 3D reconstruction provides precise information about the cartilage movement during vocal fold adduction.