Mathematical Modelling of Fluid-Structure Interaction in Human Vocal Folds

A new lumped-parameter model of human vocal folds with smooth shape derived from measurements on excised human larynges is presented. The mechanical equations of motion are based on previous studies, while the aerodynamic equations are solved by a new finite difference scheme. The model deals with 1-D Navier-Stokes equations, fully coupled with a 2 degrees of freedom rigid body vibrating in the channel wall. To mimic the motion of real elastic vocal folds and to avoid discontinuities in the channel, the model employs smooth spline interpolation on both edges of the rigid body. The finite difference scheme allows to take into account variable flow separation point in terms of a moving boundary condition. With the help of the model it is possible to investigate subcritical vocal fold vibrations and to determine stability thresholds for various configurations. The model is also able to perform numerical simulations of supercritical vocal fold movement including impacts. A physical model of vocal folds with the same geometry as the computational one was fabricated and measured. With the flow rate given by means of a digital mass flow controller, the vibration was observed by videostroboscopy and the acoustic output measured by a sound level meter.