MRI-Based Vocal Tract Representations for the Three-Dimensional Finite Element Synthesis of Diphthongs

The synthesis of diphthongs in three-dimensions (3D) involves the simulation of acoustic waves propagating through a complex 3D vocal tract geometry that deforms over time. Accurate 3D vocal tract geometries can be extracted from Magnetic Resonance Imaging (MRI), but due to long acquisition times, only static sounds can be currently studied with an adequate spatial resolution. In this work, 3D dynamic vocal tract representations are built to generate diphthongs, based on a set of cross-sections extracted from MRI-based vocal tract geometries of static vowel sounds. A diphthong can then be easily generated by interpolating the location, orientation and shape of these cross-sections, thus avoiding the interpolation of full 3D geometries. Two options are explored to extract the cross-sections. The first one is based on an adaptive grid (AG), which extracts the cross-sections perpendicular to the vocal tract midline, whereas the second one resorts to a semi-polar grid (SPG) strategy, which fixes the cross-section orientations. The finite element method (FEM) has been used to solve the mixed wave equation and synthesize diphthongs [${\alpha i}$] and [${\alpha u}$] in the dynamic 3D vocal tracts. The outputs from a 1D acoustic model based on the Transfer Matrix Method have also been included for comparison. The results show that the SPG and AG provide very close solutions in 3D, whereas significant differences are observed when using them in 1D. The SPG dynamic vocal tract representation is recommended for 3D simulations because it helps to prevent the collision of adjacent cross-sections.