Effect of Subglottic Stenosis on Vocal Fold Vibration and Voice Production Using Fluid-Structure-Acoustics Interaction Simulation  
[PERSON]  
1  
[PERSON]  
1  
[PERSON]  
1  
[PERSON]  
2 Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA;  
1  
Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
Footnote 2: [[https://www.mdpi.com/journals/pdf/10/](https://www.mdpi.com/journals/pdf/10/)]([https://www.mdpi.com/journals/pdf/10/](https://www.mdpi.com/journals/pdf/10/))  
of SGS on voice was not correlated with its severity, because some patients with a higher grade SGS retained normal voice quality. However, no detailed qualitative or quantitative data were available for a systematic understanding of the underlying reason.  
Voice production is driven by a fluid-structure interaction process in which the air forced from the lungs interacts with the vocal folds, to generate self-sustained vibration of the vocal folds. Vocal fold vibration, in turn, modulates the airflow into a pulsatile flow, to form the sound source. Voice quality is indirectly related to the dynamics of the glottal flow and vocal fold vibrations. To understand how SGS affects voice production, it is necessary to understand how SGS affects the dynamics of the glottal flow and vocal fold vibration.  
Several studies used computational fluid dynamics models to evaluate the effect of the severity of SGS on airway pressure drop [12; 13; 14; 15] and flow resistance [16; 17] (defined as \(\Delta P/Q\) or \(\Delta P/Q^{2}\), in which \(\Delta P\) is the pressure drop and \(Q\) is the mean flow rate) during respiration; however, the effect of SGS on vocal fold vibration was not studied. To the best of the authors' knowledge, the only work focusing on the effect of SGS on vocal fold vibration was a study by [PERSON] and [PERSON] [18]. In this work, an idealized SGS was incorporated into a two-dimensional airway and fluid-structure interaction simulations were performed, to examine the effect of SGS on vocal fold vibration. The severity of SGS was measured as the percentage of the width reduction of the airway and varied from 0% to 99%, to cover the possible pathological range. The study found no change in vocal fold vibration and glottal flow rate up to 60% of SGS severity. By increasing the SGS severity to 90%, a decrease in vocal fold vibration was observed. By further increasing the SGS severities, both vocal fold vibration and the flow rate amplitude were decreased. However, the decrease in the maximum flow declination rate (MFDR, defined as the maximum negative slope of the glottal flow rate waveform [19]) and fundamental frequency (\(f_{0}\)) was observed only when the SGS severity was above 95%. The study also suggested that these effects were primarily related to the effect of SGS on flow resistance.  
While the study provides quantitative measurements of the effect of SGS on vocal fold vibration, it is limited by the underlying two-dimensional (2D) assumption. It is unclear if the effects remain the same in three-dimensional (3D) geometries, and more importantly, how the effects are related to the 3D properties of SGS. In the current study, we used an in-house 3D fluid-structure-acoustic interaction numerical solver to quantify the effect of SGS on the dynamics of glottal flow and vocal fold vibration in an idealized 3D vocal tract model. Two SGS properties, the percentage of area occlusion and the location of the SGS, were varied to investigate the effect of these two properties on the glottal flow rate and its waveform; vocal fold vibration amplitude, primary vibratory modes, and voice acoustics were quantified. In the context below, the modeling method, including the numerical algorithms of the computational solver, geometric models, and simulation setup, is presented in Section 2; the results and discussions are presented in Section 3, and the conclusion is presented in Section 4.