3. OVERVIEW OF VOCAL FOLD MODELS The kinematic patterns of tissue motion discussed in the previous section are initiated,and sustained over time, by the steady air flow and pressure supplied by the lower respiratory system. Once in vibration,the vocal folds effectively convert the steady air flow from the lungs into a series of flow pulses by periodically opening and closing the air space between the vocal folds. This airspace is called the glottis; hence,the stream of flow pulses is referred to as the glottal flow and provides the sound source for the excitation of the vocal tract resonances in vowels. That the vocal folds are capable of converting a steady, flowing stream of air into vibratory motion puts them into a category of physical systems known as self-oscillating systems. Understanding the precise mechanisms responsible for self-sustained vocal fold oscillation has occupied researchers for several decades. The first formal introduction of a theory on the subject was Van den Berg’s [11] ‘‘Myoelastic-aerodynamic theory of voice production’’ which empirically explored the interaction of vocal fold tissue elasticity and aerodynamic forces. This paper described the oscillatory mechanisms of vocal fold vibration in terms of tissue elasticity and the so-called Bernoulli effect. That is,high air velocity through a narrow glottis would create a negative pressure that would ‘‘suck’’ the vocal folds together,afterwhich a build-up of subglottal pressure would blow the vocal folds apart and start the process again. However,subsequent theoretical studies have assigned a secondary role to the Bernoulli effect and have formed the current view that the vocal folds may oscillate whenever an asymmetry exists between the aerodynamic driving forces produced within the glottis and the opening and closing phases of the vocal folds [9,12–14]. This asymmetry is facilitated by (1) the mucosal wave,which creates a time delay with respect to the upper and lower portions of the vocal folds,and (2) the inertial acoustic loading presented by the vocal tract which creates a time delay between the build up and release of supraglottal pressure and glottal opening/closing. Both of these factors will have the effect of decreasing the aerodynamic driving forces during the glottal closing phase and increasing them during the opening phase. The effect of inertial loading by the vocal tract was demonstrated in an early model [15] in which the vocal fold tissue (of either the right or left side) was lumped into a single mass (Fig. 6) and allowed to have only lateral displacement. The mass was connected to a ‘‘rigid’’ lateral boundary with spring and damping elements intended to account for tissue elasticity and energy losses,respectively. With its single-degree of freedom this one-mass model cannot represent the mucosal wave (unless it is allowed a rotational degree of freedom [16]). As a result,coupling to the acoustic inertance of the vocal tract is essential to create a condition where the tissue velocity and the intraglottal pressure are in phase and hence initiate and sustain oscillation. While the one-mass model is generally not sufficient for research purposes,it is a useful instructive tool for learning some of the fundamental principles of self-sustained oscillation [3]. Shortly after the introduction of the one-mass model [15] a slightly more complex version was proposed that represented a single vocal fold by two-masses in the coronal (vertical) dimension [12,17] (Fig. 7). Again,each mass was allowed only lateral displacement and was connected to a rigid boundary with a spring and damper system. In addition,the two masses were directly coupled to each other through another spring element to account for shear forces. The two degrees of freedom afforded by the two-mass model allows for the mucosal wave to be represented as well as overall lateral tissue displacement. While it is admittedly a crude discretization of the real tissue structure it provides appropriate conditions for oscillation to occur with or without a coupled vocal tract inertance. Because of its simplicity and reasonable agreement with physiologic data,the two-mass model has been widely used in simulation/synthesis studies of vocal fold vibration. A limitation of both the one-mass and two-mass models is that their discretization of tissue in the coronal plane does not capture the known layered structure of the vocal folds