Using the relaxation oscillations principle for simple phonation modeling.

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, F0 decreased from 297.5 to 42.5 Hz and vibrational amplitude increased from 1.26 to 3.25 mm (for stiffness k=10Nm(-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.