3D-FV-FE Aeroacoustic Larynx Model for Investigation of Functional Based Voice Disorders

Abstract

For the clinical analysis of underlying mechanisms of voice disorders, we developed a numerical aeroacoustic larynx model, called simVoice, that mimics commonly observed functional laryngeal disorders as glottal insufficiency and vibrational left-right asymmetries. The model is a combination of the Finite Volume (FV) CFD solver Star-CCM+ and the Finite Element (FE) aeroacoustic solver CFS++. simVoice models turbulence using Large Eddy Simulations (LES) and the acoustic wave propagation with the perturbed convective wave equation (PCWE). Its geometry corresponds to a simplified larynx and a vocal tract model representing the vowel /a/. The oscillations of the vocal folds are externally driven. In total, 10 configurations with different degrees of functional-based disorders were simulated and analyzed. The energy transfer between the glottal airflow and the vocal folds decreases with an increasing glottal insufficiency and potentially reflects the higher effort during speech for patients being concerned. This loss of energy transfer may also have an essential influence on the quality of the sound signal as expressed by decreasing sound pressure level (SPL), Cepstral Peak Prominence (CPP), and Vocal Efficiency (VE). Asymmetry in the vocal fold oscillations also reduces the quality of the sound signal. However, simVoice confirmed previous clinical and experimental observations that a high level of glottal insufficiency worsens the acoustic signal quality more than oscillatory left-right asymmetry. Both symptoms in combination will further reduce the quality of the sound signal. In summary, simVoice allows for detailed analysis of the origins of disordered voice production and hence fosters the further understanding of laryngeal physiology, including occurring dependencies. A current walltime of 10 h/cycle is, with a prospective increase in computing power, auspicious for a future clinical use of simVoice.

Keywords: computational aero acoustics; computational fluid dynamics; glottal insufficiency; left-right asymmetry; posterior gap; simVoice (numerical larynx model).

Figure 1

2D view of a human head (left) with an enlargement of the larynx (right) and its embedded structures that are important for the phonatory process. The vocal folds (VF) and the above arranged ventricular folds (VeF) are indicated.

Figure 2

(A) 3D representation of simVoice, including a velocity field in the mid-coronal plane, the vocal folds (VF), the ventricular folds (VeF), and the vowel /a/-vocal tract. Points P1, and P2 are located 6 mm, and 20 mm in distance to the vocal folds. (B) Geometry and domain of the CAA model of simVoice as introduced by Schoder et al. (2020). Mic.1 and Mic.2 are located 5 and 8 cm in distance of the vocal tract exit (mouth).

Figure 3

Workflow of vocal folds modeling. Upper left part: four GC types of ex vivo experiments based on high-speed videos (Birk et al., 2017b) and the corresponding schematic numeric GC geometries (superior view). Lower left part: phases of the vocal fold motion of the synthetic vocal fold model (view on the coronal plane) during one oscillation cycle (Lodermeyer et al., 2015) and the GAW was taken from high-speed videos (Sadeghi et al., 2018). Right part: Four plus one additional GC types with the adapted GAWs.

Figure 4

Exemplary vocal fold motion of GC1 for the symmetric and asymmetric case along the y-axis (medial-lateral direction) for a point on the medial plane of the VF surface, see the red mark at GC1 in Figure 3. The solid red line represents the motion on the y-axis of the upper vocal fold for the symmetric and the dashed line for the asymmetric motion. The blue line represents the motion on the y-axis of the lower vocal fold.

Figure 5

(A) Volume flow rate through the glottis for one oscillation cycle for different mesh resolutions MB-M3. (B) Instantaneous pressure evolution for mesh resolutions MB-M3 for one oscillation cycle at point P1, see Figure 2. The pressure evolutions were smoothed by a low-pass filter (Butterworth), with a cut-off frequency of 2,000 Hz, to reduce the numerical noise.

Figure 6

Volume flow through the glottis for the five GC types with (A) a symmetric and (B) an asymmetric vocal fold motion. For both motion types the volume flows are rising with an increasing glottal insufficiency, whereas the corresponding volume flows of the asymmetric motion are collectively smaller than those of the symmetric motion.

Figure 7

Net rate energy transfer (Ė_net) of the five GC types with (A) a symmetric and (B) an asymmetric vocal fold motion. A positive Ė_net means an energy flux from the glottal flow toward the vocal folds and a negative Ė_net an energy flux from the vocal folds toward the airflow. For both motion types Ė_net is positive at the beginning and the end of the oscillation cycle. In these intervals Ė_net decreases with an increasing glottal insufficiency, whereas the corresponding values of the asymmetric motion are collectively smaller than those of the symmetric motion.

Figure 8

(A) Symmetric vocal fold motion: velocity magnitude in the midcoronal (xy-plane) and the sagittal (xz-plane) plane for the five GC types at two instances (t₁ = 0 and t₂ = 0.56T) of an oscillation cycle. While GC1 fully interrupts the glottal jet at the end of the cycle, GC2 and GC3 only partly, and GC4 and GC5 do not interrupt the laryngeal fluid flow. (B) Asymmetric vocal fold motion: Velocity magnitude in the midcoronal (xy-plane) and the sagittal (xz-plane) plane for the five GC types at two instances (t₁ = 0 and t₂ = 0.56T) of an oscillation cycle. The upper vocal fold moves with the 50% amplitude and the glottal jet impinges mainly the lower VeF and subsequently, just a vortex in the lower ventricle occurs.

Figure 9

Amplitude Spectral Density (ASD) for the GC1 type for the symmetric and asymmetric vocal fold motion. The spectra of both motions show similar slope and only slight deviations in the amplitudes at the fundamental frequency, whereas more significant differences occur at higher harmonics.

Figure 10

Formant chart as proposed by Peterson and Barney (1952), shows the formant frequencies of the first two formants found in this study and that of Probst et al. (2019). In contrast to Probst et al. (2019), F1 = 1, 020Hz and F2 = 1, 350Hz simulated by simVoice are well-positioned within the region of the /a/ vowel.

Figure 11

SPL (A) and VE (B) vs. the GC types with a symmetric (red dots) and an asymmetric (green dots) vocal fold motion. The SPL and the VE significantly decrease with an increasing glottal insufficiency. The comparison between both motion types shows significant differences for GC1 and GC4 and only minor differences for GC2, GC3, andGC5.

Figure 12

CPP vs. the GC types with a symmetric (red points) and an asymmetric (green points) vocal fold motion. The CPP for the symmetric vocal fold motion almost remains at the same level for GC1 to GC3 followed by a decrease. The CPP for the asymmetric vocal fold motion decreases for an increasing glottal insufficiency. The CPP for the asymmetric motion is collectively smaller than those for the symmetric motion.