Physical mechanisms of phonation onset as revealed by a linear stability analysis of an aeroelastic, continuum model of phonation

David A. Berry, Zhaoyan Zhang, Juergen Neubauer

In an investigation of phonation onset, a linear stability analysis was performed on a two-dimensional, aeroelastic, continuum model of phonation. Although a similar stability analysis was completed previously by Ishizaka for the two-mass model (1981, 1989), such an analysis has not been performed previously on a continuum model, with physiologically relevant parameters. While several investigators have performed eigen-analyses of an idealized three-dimensional vocal fold continuum (Berry & Titze, 1996; Cook & Mongeau, 2007), such studies have focused on the in vacuo eigenmodes. That is, the eigenmodes and eigenfrequencies were computed intentionally in the absence of aerodynamic pressures. While Titze (1988) accounted for the aerodynamic component, the latter study assumed a priori both the spatial shape and the temporal phase relationship of the two eigenmodes. Thus, the impact of glottal aerodynamics on the eigenmodes and the coupling of the eigenmodes related to phonation onset were not fully disclosed. The motivation of the present study was to investigate physical mechanisms of phonation onset in an aeroelastic, continuum model of the vocal folds, using methods similar to those utilized by Ishizaka (1981, 1989) in his study of the two mass model. The continuum model consisted of a vocal fold-shaped constriction situated in a rigid pipe coupled to a potential flow. The vocal-fold constriction was modeled as a plane-strain linear elastic layer. Linear stability analysis was conducted on the fluid-structure-interaction system. The critical eigenvalues and eigenmodes at onset (corresponding to the fundamental frequency and composite vibrations of the folds at onset, respectively) were investigated over a range of glottal channel widths, vocal fold geometries, and viscoelastic properties of the folds. Through such analyses, physical mechanisms of phonation onset were elucidated, including: (1) the matching of the intraglottal airflow pressure, or flow stiffness, with the elastic stiffness of the vocal fold tissues, and (2) the entrainment of two structural eigenmodes, facilitating energy transfer from the airflow to the tissue to overcome structural dissipation.

David A. Berry, Zhaoyan Zhang, Juergen Neubauer

Affiliation and Contact Information:
The Laryngeal Dynamics Laboratory
Division of Head and Neck Surgery
David Geffen School of Medicine at UCLA
31-24 Rehabilitation Center
1000 Veteran Ave.
Los Angeles, CA 90095-1794
phone: 310-206-5043
fax: 310-825-0969
daberry@ucla.edu