# Effect of Subglottic Stenosis on Expiratory Sound Using Direct Noise Calculation
## 1 Introduction  
### Subglottic Stenosis and Respiratory Sounds  
Subglottic stenosis (SGS) refers to a pathological narrowing of the trachea near the larynx. SGS can be of idiopathic, congenital, or acquired origin (e.g., as a result of prolonged intubation) [1]. Apart from common symptoms like hoarse voice, shortness of breath, and dysphonia, SGS can also lead to adventitious tonal sound during respiration, which is sometimes referred to as stiridor [1; 2; 3; 4]. For example, [PERSON] et al. [4] reported that in infants and children with congenital SGS, 43% presented stridor. On the other hand, stridor is only one of the many possible types of adventitious respiratory sounds, and it arises from other airway obstructions more regularly than from SGS (see, e.g., references [5; 6]). Due to the subjective nature of human perception [7] and the variability in the characteristics of stridor and other respiratory sounds, patients with SGS and stridor are sometimes misdiagnosed with other conditions like asthma and pneumonia. Such a misdiagnosis can be life-threatening [1; 8; 9]. Respiratory sounds are recognized as an integral part in the evaluation of patients with complaints related to the respiratory system and may provide valuable clues about their pathological conditions [10]. Establishing the relationship between the sound, the severity, and the location of the airway obstruction could reduce the use of invasive procedures for diagnosis. Therefore, it is important to both quantify the characteristics of the sounds and to understand the underlying sound generation mechanisms. Research efforts have been made to differentiate respiratory sounds due to upper airway obstruction from othersources, to quantify the acoustic characteristics of the respiratory sounds of obstructed airways, and to study the tonal sound generation by airflow in an obstructed bronchial airway. [PERSON] & [PERSON] [11] compared the sound signals of patients with stridor and asthma and found that while the spectrum content was similar, the signal was more intense over the neck than the chest. In patients with stridor, musical sounds occurred during inspiration, while in patients with asthma, they mostly occurred during expiration. [PERSON] & [PERSON] [12] used a model consisting of an orifice plate in a variable length tube to study the acoustic effects of airway obstruction. They showed that the noise level increased with stenosis severity and flowrate and suggested that the spacing of peaks in the sound spectrum indicated the location of the stenosis. [PERSON] et al. [13] hypothesized and then experimentally showed that tonal sound is produced by nozzle-jet-obstacle structures in obstructed bronchial airways, explained by the hole tone mechanism [14]. Most recently, there are research efforts using the machine learning approach to address the challenges in identifying airway obstructions based on respiratory sounds [15; 16]. A few recent studies on SGS have focused on its influence on voice production [17; 18; 19]. A common finding was that SGS had no significant effect on the glottal flow until high severity (where the area blockage was 80%-90%). In their experimental study, [PERSON] & [PERSON] [18] observed that high-frequency noise became significant by 80% obstruction. However, these studies were performed under the phonation condition where the glottis was closed and the vocal folds vibrated during interaction with the air flow. Thus, the dominant sound source was the pulsatile flow, which was regulated by the vocal fold vibration. This is essentially different from the respiratory condition where the vocal folds are abducted and do not vibrate. Studies that specifically focus on the respiratory sound due to SGS are very limited. [PERSON] et al. [20] used numerical simulation to study the sound generated by SGS in a patient-derived realistic geometric airway model, finding that the stridor generated by SGS produced a 15-20 dB higher broadband turbulent noise at higher frequencies compared to the healthy model.