Estimation of vocal-tract length based on distribution of sound pressure.

The purpose of this study was to estimate the vocal-tract length based on the distribution of sound pressure in the three-dimensional vocal tract during production of the vowels /a/ and /i/. The distribution of sound pressure was estimated in the three-dimensional vocal tract using the Finite Element Method (FEM).The three-dimensional shapes of a vocal tract and a dental crown were measured using Magnetic Resonance Imaging (MRI). A male subject was asked to produce the vowels /a/ and /i/ while wearing a dental crown plate that contained a contrast medium for MRI processing. Three-dimensional MR images of the vocal tract for each sound were obtained while the subject’s tongue was kept still.The vocal tract shapes were obtained from profiles of their sagittal sections. First, sagittal MR images (4-mm interval) were estimated from coronal MR images using grey-level interpolation. Second, air-tissue boundaries of the sagittal sections were obtained from each MR image using a threshold operation in which the threshold value is the average of grey levels at the air-tissue border points. Adjacent air-tissue boundaries are connected by spline interpolation, since the vocal tract shapes are constructed by a cascade connection of the air-tissue boundaries.The three-dimensional vocal tract shapes during vowel production were divided with a tetrahedral element (/a/: 11, 179 elements, 3, 185 nodes; /i/: 12, 763 elements, 3, 558 nodes). At the glottis, the whole area of the cross-section was driven, and at the radiational surface, the radiational impedance was assumed to be that of a circular piston in a rigid sphere. The boundary condition of the wall was defined as the wall impedance.The distribution of sound pressure shows that a sound wave propagates in the vocal tract as a non-plane wave in the high-frequency region.In this study, the vocal tract model with cascading circular tubes was called the VT model. The vocal tract transfer characteristics for both the VT model and the three-dimensional FEM model were determined. A comparison of the VT model and FEM model showed that they share almost the same characteristics in the low-frequency region, but express a difference at high frequencies.The vocal-tract length was estimated based on the distribution of sound pressure in the three-dimensional vocal tract. As a result, in the case of /a/, the vocal-tract length is 188 mm for a driving frequency of 1000 Hz, and 226 mm for a driving frequency of 3000 Hz. In the case of /i/, the vocal-tract length is 163 mm for a driving frequency of 1000 Hz, and 173 mm for a driving frequency of 3000 Hz. These results suggest that the vocal-tract is long in the high-frequency region.