# Acoustic and Aerodynamic Coupling during
## 2 Materials and Methods  
### Vocal Tract Replicas  
In this study, the VT MRI data of six professional tenors as published in a previous study by [PERSON] et al. [34] were used. The acquisition of the MRI data and the analysis of the acoustic properties were performed at the Institute Musicians' Medicine of the University Hospital Freiburg by [PERSON] et al. [17; 34]. The images were acquired with a _3.0-tesla TIM TRIO_ (Siemens, Munich, Germany) MRI device in sagittal planes in the center of the head. Further information regarding the MRI acquisition can be found in [34]. The professional tenors sustained the vowel /a/ on a pitch of F4 (349 Hz) in falsetto register for 20 s in a stable manner. In two subjects, the velopharyngeal area was not entirely closed; hence, the aerated nasopharyngeal cavity was removed at the upper uvula. Additionally to the MRI imaging, the sound was recorded in a separate session. The formants for each subject were determined based on inverse filtering [34].  
The VTs were segmented manually using the open-source software _3D-Slicer_[36; 37]. Since the teeth are not resolved in standard MRI procedures, they were neglected in this study. This is a limitation of the presented model; however, according to [PERSON] [38], the change of the cross-sectional area due to the teeth is not sufficient to yield a statistically significant change of the formant frequency for the vowel /a/. The lips were also neglected in the model, as their influence on the first resonance frequencies is not perceptually relevant according to [PERSON] et al. [21]. The VT replicas that directly rely on the segmentation of the MRI data represent the most realistic VT shape used in this study. They are depicted in Figure 1.  
The influence of the VT is often investigated in numerical and analytical models using simplified VT geometries. Thus, the segmented VT shapes have been further processed to analyze the effects of this simplification in an experimental setup with self-oscillating vocal folds. The resulting simplified VTs represent straight replicas with circular cross section that varies along the centerline, similar to the work by [PERSON] et al. [13]. They are based on the area functions that were determined by [PERSON] et al. [34].  
A simplified, averaged model of the VT was developed for the application with larynx replicas to understand the basic mechanisms of the VT filtering and the contribution of the aerodynamics. We determined a mean VT geometry based on the area functions of the simplified models. As Figure 2 shows, we averaged the six area functions of the tenors' VTs to achieve a mean VT. Therefore, the length of each simplified VT was normalized to their mean length and the cross section area was averaged at each axial position to yield the mean VT replica, as depicted in Figure 2.  
Figure 1: Segmented VTs of the six subjects.  
The generation of standing waves in a tube like the VT depends on the gradient of the reflection coefficient. Hence, the reflection coefficients along the VT have been determined to evaluate the resonance properties of the VT replicas. Based on the corresponding area function \(A_{i}\), the reflection coefficient \(r=(A_{i}-A_{i+1})/(A_{i}+A_{i+1})\) was calculated at each cross sectional jump along the centerline.