Fig 1.
(A) Sketch of the sagittal section of the head and neck, indicating the vocal folds and the rigid endoscope. (B) Glottis (dark) and on the left and right sides the two vocal folds as seen through the HSV. (C) Larynx with highlighted acoustic sound sources (arrows) resulting from the vocal fold vibrations.
Fig 2.
(A) Two-mass model as used in this work with indicated subglottal pressure Ps. (B) Six-mass model allowing the simulation of the vocal fold trajectories along three positions, i.e. at posterior, medial and anterior positions of the vocal folds. (C) Three-dimensional multi-mass model that additionally allows the simulation of vertical dynamics and the vocal fold medial surface at 25 positions along each vocal fold.
Fig 3.
Performed steps for image processing yielding the experimental vocal fold trajectories.
Fig 4.
HSE image with indicated glottal axis (vertical blue line) and medial positions (~50% position between anterior and posterior) on left (blue dot) and right (red dot) vocal folds where the trajectories were extracted (left figure).
The 2MM used (middle figure). Extracted trajectories for left (blue) and right (red) vocal folds (right figure).
Table 1.
Standard parameters of the 2MM.
In this study, the chosen vocal fold lengths l were 10 mm for women and 16 mm for men. The rest positions x01, x02 for the 2MM optimization were computed based on the mean amplitudes of the HSV trajectories yielding also individual rest areas a0i [26]. During the 2MM optimization, the mi, ki and Ps values are varied.
Fig 5.
Flow diagram of the optimization procedure.
Fig 6.
Examples for a young female (unmatched glottis closure and left amplitude), young male (unmatched amplitude), elderly female (unmatched glottis closure and amplitude) and elderly male (unmatched amplitudes and glottis closure) that illustrate the extracted trajectories and the incorrectly optimized trajectories of the 2MM for the left and vocal fold right side.
Table 2.
Overview of how often each optimization algorithm (Nelder Mead–NM, Particle Swarm Optimization–PSO, Simulated Bee Colony—SBC) and cost function Γ1, Γ2, and Γ3 yielded the best optimization result; i.e., smallest Γ value–see Eq (4).
Table 3.
Mean values, standard deviations and range (minimum–maximum) of Γ, the optimized parameters Ps [cmH2O], Ql, Qr and the symmetry quotient Qlr for the four subject groups are given.
Fig 7.
Fundamental frequencies (fEl, fEr) of the experimental HSE-recorded trajectories versus the frequencies (fMl, fMr) of the optimized model trajectories shown separately for left and right vocal folds.
Fig 8.
Examples for a young female, young male, elderly female and elderly male that illustrate the extracted trajectories and the correctly optimized trajectories of the 2MM for the left and vocal fold right side.
The values for the cost function Γ are given.
Table 4.
Overview on subglottal pressure vales (cmH20) as reported for healthy subjects during normal and loud phonation in the literature.
Fig 9.
Scatterplots for the distribution of the four groups relating (A) Ql vs. Qr (B) the fundamental frequencies f0 vs. Ps, (C) f0 vs. (Ql, Qr) and (D) (Ql, Qr) vs. Ps.