Volume velocity in a canine larynx model using time‑resolved tomographic particle image velocimetry

Abstract

In the classic source-filter theory, the source of sound is flow modulation. "Flow" is the flow rate (Q) and flow modulation is dQ/dt. Other investigators have argued, using theoretical, computational, and mechanical models of the larynx, that there are additional sources of sound. To determine the acoustic role of dQ/dt in a tissue model, Q needs to be accurately measured within a few millimeters of the glottal exit; however, no direct measures of Q currently exist. The goal of this study is to obtain this waveform in an excised canine larynx model using time-resolved tomographic particle image velocimetry. The flow rate data are captured simultaneously with acoustic measurements to determine relations with vocal characteristics. The results show that glottal waveform characteristics such as maximum flow declination rate are proportional to the subglottal pressure, fundamental frequency, and acoustic intensity. These findings are important as they use direct measurements of the volume flow at the glottal exit to validate some of the assumptions used in the source-filter theory. In addition, future work will address the accuracy of indirect clinical measurement techniques, such as the Rothenberg mask.

Fig. 1

Details of the experimental setup: a larynx mounted on the aerodynamic nozzle (before applying fluorescent red dye). The folds are adducted by inserting prongs into the vocal processes. b Schematic of the tomo-PIV setup. The orientation of the setup with respect to the larynx is given by the anterior (A), posterior (P), left (L), and right (R) directions on each side of the focal plane

Fig. 2

Sample data from the microphone (blue line) and camera TTL (orange bars) signals for phonation at P_sg = 22.7 cmH₂O. Red circles show the reference points on the microphone signal where θ(modulo 360) = 0°. The TTL signal marks the acquisition of the frames by the PIV cameras

Fig. 3

Instantaneous flow field plotted as contours of velocity magnitude and velocity streamlines. Volume mesh is overlaid to appreciate the spatial resolution yielded by the tomographic reconstruction. a The plane z = 0 mm is in the mid-sagittal plane of the measurement volume and shows the posterior-anterior extents of the glottal jet. b The plane y = 0 mm is an axial plane located immediately above the glottal opening. Due to tissue obstruction at the level of the vocal folds, it is within 1–2 mm above the superior edge of the vocal folds. The orientation of the views is given by the anterior (A), posterior (P), left (L), and right (R) directions

Fig. 4

Representation of the 3D glottal jet for low and high sub-glottal pressures. a–f Low subglottal pressure (P_sg = 22.7 cmH₂O) and g–l high (P_sg = 32.2 cmH₂O) subglottal pressure. The figure displays only phases between 0° and 216°, since the 216°–360° range corresponds to the closed phase of the glottal cycle, and despite the small posterior opening leakage, the flow does not qualitatively change above the glottis

Fig. 5

Phase-averaged flow fields over one glottal flow cycle plotted as contours of velocity magnitude. (Left column) plane z = 0 mm is located in the mid-sagittal plane of the measurement volume and shows the extents of the glottal jet from x = 0 mm (posterior) to x = 16.4 mm (anterior). Added streamlines indicate the in-plane direction of the flow over the contours of velocity magnitude. (Center column) plane y = 0 mm is located immediately above the folds. It shows the cross section of the glottal jet. (Right column) Phase-ordered reconstructed glottal waveform $\overline{Q}(y=0mm)$. The dots show the θ-ordered instantaneous Q (y = 0 mm)

Fig. 6

Time-resolved glottal waveforms at a low (P_sg = 22.7 cmH₂O) and b high (P_sg = 32.2 cmH₂O) subglottal pressures for the larynx model. The blue dots represent the instantaneous flow rate integrated from the velocity fields, and a 4th order Fourier series is fitted to it (red line). Two-sigma dotted lines show the confidence bounds of the fit

Fig. 7

A single period of the glottal volume flow rate for a low (P_sg = 22.73 cmH₂O) and b high (P_sg = 32.23 cmH₂O) subglottal pressures. The top vignettes display the Q(t) fitted curve (red solid line) and its 2-sigma confidence interval. The bottom vignettes show their derivative dQ/dt, for which the minimum represents the maximum flow declination rate (MFDR). The time at which MFDR occurs is identified on all plots as a vertical dashed line (blue)

Fig. 8

a Maximum flow declination rate (MFDR) vs. subglottal pressure (P_sg). b MFDR vs. fundamental frequency (F₀). c MFDR vs. sound pressure level (SPL_a). The linear fit to the five experiments suggests there is a linear relationship between the subglottal pressure and MFDR. Moreover, it agrees with other quantities that have been known to increase with P_sg, such as F₀ and SPL_a