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Summary Well-known multimass models of vocal folds are useful to describe main behavior observed in human voicing but their principle of functioning, based on harmonic oscillation, may appear complex. This work is designed to show that a simple one-mass model ruled by laws of relaxation oscillation can also depict main behavior of glottis dynamic. Theory of relaxation oscillation is detailed. A relaxation oscillation model is assessed through a numerical simulation using conventional values for tissue characteristics and subglottal pressure. As expected, raising the mass decreases the fundamental frequency and increases the amplitude of vocal fold vibration: for a mass ranging from 0.01 to 0.4 g, F 0 decreased from 297.5 to 42.5 Hz and vibrational amplitude increased from 1.26 to 3.25 mm (for stiffness k = 10 N m −1 , damping r = 0.015 N s m −1 , and subglottal pressure = 1 kPa). Stiffness value has the opposite effect. The subglottal pressure controls the fundamental frequency with a rate ranging from 20 to 50 Hz/kPa. The vibrational amplitude is also controlled linearly by subglottal pressure from 0.22 to 0.26 mm/kPa. The range of phonation threshold pressure (PTP) is close to the values currently proposed, that is, 0.1 to 1 kPa and varies with the fundamental frequency. The relaxation oscillator is a simple and useful tool for modeling vocal fold vibration.

Summary Numerous clinical findings indicate that viscosity of laryngeal mucosa is a crucial factor in glottal perfomance. Experience using experimental test benches has shown the importance of humidifying air stream used to induce vibration in excised larynges. Nevertheless, there is a lack of knowledge particularly regarding the physicochemical properties of laryngeal mucus. The purpose of this study was to research vocal fold vibration in excised larynges using artificial mucus of precisely known viscosity. Eight freshly harvested porcine larynges were examined. Parameters measured were Fo and vocal fold contact time. Measurements were performed under three conditions: basal (no fluid application on vocal cord surface), after application of a fluid of 60cP viscosity (Visc60), and after application of a fluid of 100cP viscosity (Visc 100). Electroglottographic measurements were performed at two different times for each condition: 1 s after airflow onset (T1) and 6 seconds after airflow onset (T2). Statistical analysis consisted of comparing data obtained under each condition at T1 and T2. The results showed a significant decrease in Fo after application of Visc60 and Visc100 fluids and a decrease in Fo at T2. Closure time was significantly higher under Visc60 conditions and under Visc100 conditions than under basal conditions. Application of artificial mucus to the mucosa of the vocal folds lowered vibratory frequency and prolonged the contact phase. Our interpretation of this data is that the presence of mucus on the surface of the vocal folds generated superficial tension and caused adhesion, which is a source of nonlinearity in vocal vibration.

Summary It has been shown that voice signal abnormalities, particularly in unilateral laryngeal paralysis (ULP), are not always randomly distributed and that "statistical" indexes of regularity, such as jitter and shimmer, may be unreliable in these cases. The techniques of nonlinear dynamics, particularly phase portraits, have been used to demonstrate that some of the abnormalities observed were the consequence of nonlinearity of glottic function. From a theoretical point of view, determination of Lyapunov exponents allows quantification of the complexity of the phase portraits. The authors studied vocal signals recorded in 12 normal subjects and 26 patients with ULP and calculated the largest Lyapunov exponent (LLE). In normal subjects, LLE mean value was 0.380 (SD = 0.182). In patients with ULP, LLE mean value was 0.570 (SD = 0.337). The difference is significant at P = 0.031. Determination of LLE was compared to more "classical" indexes such as jitter and oral airflow during phonation. A principal component analysis showed that information contained in LLE was not redundant but complementary to the other parameters.