For many years, the vocal tract shape has been approximated by one-dimensional (1D) area functions to study the production of voice. More recently, 3D approaches allow one to deal with the complex 3D vocal tract, although area-based 3D geometries of circular cross-section are still in use. However, little is known about the influence of performing such a simplification, and some alternatives may exist between these two extreme options. To this aim, several vocal tract geometry simplifications for vowels [A], [i], and [u] are investigated in this work. Six cases are considered, consisting of realistic, elliptical, and circular cross-sections interpolated through a bent or straight midline. For frequencies below 4-5 kHz, the influence of bending and cross-sectional shape has been found weak, while above these values simplified bent vocal tracts with realistic cross-sections are necessary to correctly emulate higher-order mode propagation. To perform this study, the finite element method (FEM) has been used. FEM results have also been compared to a 3D multimodal method and to a classical 1D frequency domain model.
Three-dimensional (3-D) numerical approaches for voice production are currently being investigated and developed. Radiation losses produced when sound waves emanate from the mouth aperture are one of the key aspects to be modeled. When doing so, the lips are usually removed from the vocal tract geometry in order to impose a radiation impedance on a closed cross-section, which speeds up the numerical simulations compared to free-field radiation solutions. However, lips may play a significant role. In this work, the lips' effects on vowel sounds are investigated by using 3-D vocal tract geometries generated from magnetic resonance imaging. To this aim, two configurations for the vocal tract exit are considered: with lips and without lips. The acoustic behavior of each is analyzed and compared by means of time-domain finite element simulations that allow free-field wave propagation and experiments performed using 3-D-printed mechanical replicas. The results show that the lips should be included in order to correctly model vocal tract acoustics not only at high frequencies, as commonly accepted, but also in the low frequency range below 4 kHz, where plane wave propagation occurs.
Medical imaging techniques are usually utilized to acquire the vocal tract geometry in 3D, which may then be used, eg, for acoustic/fluid simulation. As an alternative, such a geometry may also be acquired from a biomechanical simulation, which allows to alter the anatomy and/or articulation to study a variety of configurations. In a biomechanical model, each physical structure is described by its geometry and its properties (such as mass, stiffness, and muscles). In such a model, the vocal tract itself does not have an explicit representation, since it is a cavity rather than a physical structure. Instead, its geometry is defined implicitly by all the structures surrounding the cavity, and such an implicit representation may not be suitable for visualization or for acoustic/fluid simulation. In this work, we propose a method to reconstruct the vocal tract geometry at each time step during the biomechanical simulation. Complexity of the problem, which arises from model alignment artifacts, is addressed by the proposed method. In addition to the main cavity, other small cavities, including the piriform fossa, the sublingual cavity, and the interdental space, can be reconstructed. These cavities may appear or disappear by the position of the larynx, the mandible, and the tongue. To illustrate our method, various static and temporal geometries of the vocal tract are reconstructed and visualized. As a proof of concept, the reconstructed geometries of three cardinal vowels are further used in an acoustic simulation, and the corresponding transfer functions are derived.
We introduce a framework to study speech production using a biomechanical model of the human vocal tract, ArtiSynth. Electromagnetic articulography data was used as input to an inverse tracking simulation that estimates muscle activations to generate 3D jaw and tongue postures corresponding to the target articulator positions. For acoustic simulations, the vocal tract geometry is needed, but since the vocal tract is a cavity rather than a physical object, its geometry does not explicitly exist in a biomechanical model. A fully-automatic method to extract the 3D geometry (surface mesh) of the vocal tract by blending geometries of the relevant articulators has therefore been developed. This automatic extraction procedure is essential, since a method with manual intervention is not feasible for large numbers of simulations or for generation of dynamic sounds, such as diphthongs. We then simulated the vocal tract acoustics by using the Finite Element Method (FEM). This requires a high quality vocal tract mesh without irregular geometry or self-intersections. We demonstrate that the framework is applicable to acoustic FEM simulations of a wide range of vocal tract deformations. In particular we present results for cardinal vowel production, with muscle activations, vocal tract geometry, and acoustic simulations.
MRI-based vocal tract representations for the three-dimensional finite element synthesis of diphthongs
We propose a method to automatically generate deformable 3D vocal tract geometries from the surrounding structures in a biomechanical model. This allows us to couple 3D biomechanics and acoustics simulations. The basis of the simulations is muscle activation trajectories in the biomechanical model, which move the articulators to the desired articulatory positions. The muscle activation trajectories for a vowel-vowel utterance are here defined through interpolation between the determined activations of the start and end vowel. The resulting articulatory trajectories of flesh points on the tongue surface and jaw are similar to corresponding trajectories measured using Electromagnetic Articulography, hence corroborating the validity of interpolating muscle activation. At each time step in the articulatory transition, a 3D vocal tract tube is created through a cavity extraction method based on first slicing the geometry of the articulators with a semi-polar grid to extract the vocal tract contour in each plane and then reconstructing the vocal tract through a smoothed 3D mesh-generation using the extracted contours. A finite element method applied to these changing 3D geometries simulates the acoustic wave propagation. We present the resulting acoustic pressure changes on the vocal tract boundary and the formant transitions for the utterance [Ai].
Three-dimensional computational acoustic models need very detailed 3D vocal tract geometries to generate high quality sounds. Static geometries can be obtained from Magnetic Resonance Imaging (MRI), but it is not currently possible to capture dynamic MRI-based geometries with sufficient spatial and time resolution. One possible solution consists in interpolating between static geometries, but this is a complex task. We instead propose herein to use a semi-polar grid to extract 2D cross-sections from the static 3D geometries, and then interpolate them to obtain the vocal tract dynamics. Other approaches such as the adaptive grid have also been explored. In this method, cross-sections are defined perpendicular to the vocal tract midline, as typically done in 1D to obtain the vocal tract area functions. However, intersections between adjacent crosssections may occur during the interpolation process, especially when the vocal tract midline quickly changes its orientation. In contrast, the semi-polar grid prevents these intersections because the plane orientations are fixed over time. Finite element simulations of static vowels are first conducted, showing that 3D acoustic wave propagation is not significantly altered when the semi-polar grid is used instead of the adaptive grid. The vowel-vowel sequence [Ai] is finally simulated to demonstrate the method.
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