Controlling chaotic vocal fold oscillations in the numerical production of vowel sounds

Lumped mass models have been studied in depth to unveil the complex nonlinear physics of phonation. Even in the case of simple symmetric models, slight changes in muscle restoring forces or excessive subglottal pressure can cause abnormal or even chaotic vocal fold oscillations. In a recent work, it was shown that it was possible to device a theoretical pacemaker for phonation that could render the chaotic motion regular again. This consisted of attaching an additional mass–spring–damper system to the vocal fold model, the damping of which could be adjusted according to an altering energy chaos control strategy. The chaos of phonation is low-dimensional and one may wonder whether it has a profound effect in voice production and, if so, whether the proposed phonation pacemaker could compensate for it. For this purpose, we compute the time evolution of the glottal volume velocity generated by normal, chaotic and controlled oscillations of the vocal folds and convolve it with the impulse response of magnetic resonance imaging (MRI) geometries of the human vocal tract, corresponding to the vowels /ɑ/, /i/ and /u/. The impulse response for each vowel is obtained from the solution of the wave equation by the finite element method, when a Gaussian pulse is prescribed as a boundary condition in the glottis of the vocal tract. It will be demonstrated that the chaotic vibration of the vocal folds severely distorts the vowel sounds and that the proposed control strategy is able to recover with high quality the vowels produced in normal phonation. Audiovisual files are provided to support the objective results of the phenomena in terms of spectral and time analysis of the train of glottal pulses generated by the vocal folds and the produced vowel sounds.