## 3 Results and Discussion
### Glottal Flow and Implications for Phonation  
Phonation is essentially an energy-transfer process, transforming aerodynamic energy into acoustic energy. Because the glottal flow is the main determinant of voice production, further studying its properties can help us learn the effect of muscle activation on  
Figure 4: Glottal volume flow velocity \(U\) for a unilateral polyp vocal fold model with different \(a_{\text{TA}}\). In each case, \(a_{\text{CT}}\) was fixed at 0.25 and \(a_{\text{LC}}\) was fixed at 0.5. Figure 5: Glottal volume flow velocity \(U\) for a unilateral polyp vocal fold model with different \(a_{\text{LC}}\). In each case, \(a_{\text{CT}}\) was fixed at 0.25 and \(a_{\text{TA}}\) was fixed at 0.25.  
onset, effort, and quality. Following the experimental method in III.A and referring to the experimental design from [PERSON] [12], we plotted the variation of four airflow parameters affecting sound quality with respect to different levels of muscle activation (Figure 6). Figure 6 shows the root-mean-square fluctuation of the airflow velocity (\(U_{\text{A}}\)). We defined the intensity of fluctuation in glottal flow rate as \(U_{\text{A}}\). The effect of increasing \(a_{\text{CT}}\) was to obtain an initial increase in \(U_{\text{A}}\), followed by a decrease. \(U_{\text{A}}\) reaches a maximum when \(a_{\text{CT}}\) ranges from 0.4 to 0.5. In contrast to \(a_{\text{CT}}\), glottal flow fluctuation decreases monotonically with \(a_{\text{TA}}\) and \(a_{\text{LC}}\). For small values of \(a_{\text{LC}}\), however, \(U_{\text{A}}\) is always at a high level. Likewise, we plotted the time rate of glottal flow-rate change, \(U_{\text{B}}\), in Figure 6, which is related to the sound strength of human [12]. This plot shows several important factors that have direct impact on the onset and intensity of vocal fold vibration in phonation (\(U_{\text{B}}\)). Compared with \(U_{\text{A}}\), the behavior of \(U_{\text{B}}\) is similar, which means that the variation in glottal flow velocity with different muscle activation is approximately the same as the variation in acceleration of change of the airflow. \(U_{\text{B}}\) also provides an understanding of efforts to improve intensity of voice production. Changes in laryngeal muscle activities, such as increased CT muscle activities and decreased TA and LC muscle activities, will result in an increase in the amplitude of vocal fold vibration, thus increasing intensity of the voice. The cricothyroid muscle plays the primary role in controlling \(F_{0}\). However, in the pathological vocal fold, the process of changing cricothyroid muscle activity to make \(F_{0}\) reach the medium-high frequency is accompanied by irregular glottal airflow (large airflow velocity fluctuations and large airflow acceleration fluctuations). This suggests that stable voice production cannot be obtained in the vocal fold with a unilateral polyp. Thus, humans usually increase subglottal pressure to match the muscle activation to reduce laryngeal muscle fatigue and increase sound intensity. When the value of \(a_{\text{CT}}\) is large enough to create a high frequency, \(U_{\text{A}}\) and \(U_{\text{B}}\) decrease significantly. According to Section 3.1, this is because the stiffness of the vocal fold is high at this point, making it almost impossible for the vocal folds to vibrate effectively. Hence, it is difficult for a patient with a polyp to phonate even with small fluctuations in the amplitude of \(U_{\text{A}}\) and \(U_{\text{B}}\). Similarly, for the throarytenoid and lateral cricoarytenoid muscles, low activity leads to unstable sound intensity. The values of \(U_{\text{A}}\) and \(U_{\text{B}}\) decrease monotonically with \(a_{\text{TA}}\) and \(a_{\text{LC}}\). Two figures related to glottal flow rate are shown here that evaluate the effect of muscle activation on sound quality. Figure 6 shows the mean value of volume glottal flow rate (\(U_{\text{C}}\)) which is indicative of flow impedance.