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Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

The fluid-structure energy exchange process for normal speech has been studied extensively, but it is not well understood for pathological conditions. ...

Clarkson University

Pulsatile flow through a one-sided diffuser and static divergent vocal-fold models is investigated to ascertain the relevance of viscous-driven flow asymmetries in the larynx. The models were 7.5 times real size, and the flow was scaled to match Reynolds and Strouhal numbers, as well as the translaryngeal pressure drop. The Reynolds number varied from 0-2000, for flow oscillation frequencies corresponding to 100 and 150 Hz life-size. Of particular interest was the development of glottal flow skewing by attachment to the bounding walls, or Coanda effect, in a pulsatile flow field, and its impact on speech. The vocal folds form a divergent passage during phases of the phonation cycle when viscous effects such as flow separation are important. It was found that for divergence angles of less than 20 degrees, the attachment of the flow to the vocal-fold walls occurred when the acceleration of the forcing function was zero, and the flow had reached maximum velocity. For a divergence angle of 40 degrees, the fully separated central jet never attached to the vocal-fold walls. Inferences are made regarding the impact of the Coanda effect on the sound source contribution in speech.

The occurrence of the Coanda effect in pulsatile flow through static models of the human vocal folds.

Supraglottal jet variability was investigated in a scaled-up flow facility incorporating driven vocal fold models with and without wall rotation. Principle component analysis was performed on the experimental supraglottal flow fields to ascertain the roll of glottal wall motion on the development of the supraglottal jet. It is shown that intraglottal flow asymmetries that develop due to wall rotation are not the primary mechanism for generating large-scale cycle-to-cycle deflection of the supraglottal jet. However, wall rotation does decrease the energy content of the first mode, redistributing it to the higher modes through an increase in unstructured flow variability.

Impact of wall rotation on supraglottal jet stability in voiced speech.

A theoretical flow solution is presented for predicting the pressure distribution along the vocal fold walls arising from asymmetric flow that forms during the closing phases of speech. The resultant wall jet was analyzed using boundary layer methods in a non-inertial reference frame attached to the moving wall. A solution for the near-wall velocity profiles on the flow wall was developed based on a Falkner-Skan similarity solution and it was demonstrated that the pressure distribution along the flow wall is imposed by the velocity in the inviscid core of the wall jet. The method was validated with experimental velocity data from 7.5 times life-size vocal fold models, acquired for varying flow rates and glottal divergence angles. The solution for the asymmetric pressures was incorporated into a widely used two-mass model of vocal fold oscillation with a coupled acoustical model of sound propagation. Asymmetric pressure loading was found to facilitate glottal closure, which yielded only slightly higher values of maximum flow declination rate and radiated sound, and a small decrease in the slope of the spectral tilt. While the impact on symmetrically tensioned vocal folds was small, results indicate the effect becomes more significant for asymmetrically tensioned vocal folds.

A theoretical model of the pressure field arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds.

Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < p(s) < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech.

The simplified two-mass model of human vocal folds, proposed by Steinecke and Herzel [J. Acoust. Soc. Am. 97(3), 1874-1884 (1995)], has seen widespread use throughout the speech community. Herein, an error is corrected in the contact loadings on colliding vocal folds with asymmetric tissue properties, as arises clinically in cases of unilateral paralysis. A revised contact model is proposed that remediates the erroneous asymmetric contact forces. The vibration regime map presented in Steinecke and Herzel illustrating the dynamical behavior of the system is revised using the corrected collision model.

Corrected contact dynamics for the Steinecke and Herzel asymmetric two-mass model of the vocal folds.

Block-type lumped-element models of the vocal folds are widely used for speech investigations due in part to the rich dynamics exhibited over a range of input parameters, particularly for asymmetric tissue properties. While self-consistent in derivation and application, block-type models of the vocal fold masses are inherently susceptible to non-physical aerodynamic loading conditions when vocal fold motion is highly asymmetric. A standard block-type model is compared against two modified models that disallow the non-physiological loading condition. These minor modifications toward a more physiologically relevant aerodynamic model alter the specific vibration regimes and prevalence of chaos, though bifurcations still exist.

The impact of glottal area discontinuities on block-type vocal fold models with asymmetric tissue properties.

Hirschberg [J. Acoust. Soc. Am. 134, 9-12 (2013)] presents a commentary and criticisms of the viscous flow model presented by Erath et al. [J. Acoust. Soc. Am. 130, 389-403 (2011)] that solves for the asymmetric pressure loading on the vocal fold walls. This pressure loading arises from asymmetric flow attachment to one vocal fold wall when the glottal channel forms a divergent configuration. Hirschberg proposes an alternative model for the asymmetric loading based upon inviscid flow curvature at the glottal inlet. In this manuscript further evidence is provided in support of the model of Erath et al. and the underlying assumptions, and demonstrates that the primary criticisms presented by Hirschberg are unwarranted. The model presented by Hirschberg is compared with the model from the original paper by Erath et al., and it is shown that each model describes different and complementary aspects of divergent glottal flows.

Response to "Comments on 'A theoretical model of the pressure distributions arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds'" [J. Acoust. Soc. Am. 130, 389-403 (2011)].

Byron D. Erath

Department of Mechanical and Aeronautical Engineering

Clarkson University

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp