Numerical study of laryngeal airflow dynamics and voiced phonation

Abstract

To build a proper numerical tool, this work takes into consideration of the fluid-structure interactions and the acoustics, and its acoustic behavior during the phonation process. The Immersed Finite Element Method, a fully coupled algorithm for fluid-structure interaction problems, is used as the backbone for the numerical aspect of this study, with a contact mechanics algorithm implemented to tackle the collision between the vocal folds and therefore to guarantee proper evaluation of interaction forces as the solid structure stays immersed in the fluid domain; moreover, the laryngeal airflow is modeled as compressible ideal gas under an isentropic process, combined with implementation of Perfectly Matched Layer technique, a non-reflective boundary condition, is used to accurately simulate the acoustic behavior of the airflow.

Upon the success of building numerical and analytical tools, numerical simulations of the phonation process are carried out with simplified two-dimensional vocal tract and vocal fold models. Two vocal tract models are examined, where the first one is a finite-length model that is commonly used in phonation simulations, and the other model has non-reflective boundary condition applied and therefore has no filter effect and behaves as an infinitely long vocal tract, where a clear evaluation of acoustic sources and the generated sound from the source can be clearly accounted. The control volume analysis using the derived analytical tools reveal that a combination of pressure drive and vocal fold vibration patterns ensures positive energy flow from the laryngeal airflow into the vocal fold structure, and therefore sustains vocal fold vibration. It is found that the differential lateral forcing is responsible for glottal jet asymmetry, but does not affect the vocal fold vibration as much; the glottal jet asymmetry leads to slight differences in the generated sound, notably pronounced aperiodicity and low-frequency modulation, while the mean glottal resistance is not found to be significantly affected by the jet asymmetry.

The analytical tools are necessary to a thorough understanding of laryngeal airflow and vocal fold vibration, here we present full derivation of a ``generalized'' Bernoulli equation, as well as control volume equations on conservation of mass, momentum, and energy from first principles of continuum mechanics. Each of these equations is divided into mathematical terms with mechanical and physical significance, recognizing various factors which attribute to flow characteristics and interaction across the control volume interface. This approach can be applied to any volume of interest for analysis of fluid-structure interaction problem.

The phonation process is responsible for generating voiced sounds, an essential and ubiquitous component of speech communication. Although it is long understood that the vocal tract geometry filters the sound to make different vowels, and that the ultimate sound source is attributed to the interaction between the laryngeal airflow and the vocal folds, quantitative studies are necessary for better understanding of the underlying physics of the phonation process and potentially better treatment of voicing pathologies. The goal of this study is to build an effective numerical tool and quantitative analytical tool to study the laryngeal airflow and the fundamental mechanism of sustained vocal fold vibration, in order to complement previous analytical and experimental studies, as well as make improvements to numerical simulation of the phonation process. Using these tools, vocal fold vibration induced by laryngeal airflow is simulated, with which the laryngeal flow dynamics are studied and the underlying physics of sustained vocal fold vibration is explained.