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Compensatory Vocal Folds for Source Voice Generation: Computational Modeling of Vocal Folds Function
Matug, Michal ; Vampola, Tomáš (referee) ; Horáček, Jaromír (referee) ; Švancara, Pavel (advisor)
This doctoral thesis focuses on computational modelling of human vocal folds and vocal tract functions using finite element method (FEM). Human voice is crucial in human communication. Therefore one of the main targets of current medicine is creation of artificial vocal folds, which would substitute the original vocal folds. The computational modelling can be used to understand principles of voice production, determination of parameters that the artificial vocal folds have to meet and verification of their functionality. First part of this thesis focuses on modelling of human voice creation by whisper. Influence of intraglottal gap on eigenvalues distribution for individual vowels was analysed using FEM vocal tract and trachea model. Further there is presented two-dimensional (2D) finite element model of the flow-induced self-oscillation of the human vocal folds in interaction with acoustic spaces of the vocal tract. The 2D vocal tract model was created on the basis of converting the data from magnetic resonance images (MRI). Explicit coupling scheme with separated solvers for structure and fluid domain was used for modelling of the fluid-structure interaction. Created computational model comprises: large deformations of the vocal folds tissue, contact between vocal folds, fluid-structure interaction, morphing the fluid mesh according to the vocal-fold motion (Arbitrary Lagrangian-Eulerian approach), unsteady viscous compressible or incompressible airflow described by the Navier-Stokes equations and airflow separation during glottis closure. This model is used to analyse the influence of stiffness and damping changes in individual vocal fold tissue layers (in particular in superficial lamina propria). Part of this computational analysis is also comparison of vocal folds behaviour for compressible and incompressible flow model. Videokymograms (VKG) are subsequently created from obtained results of FEM calculations which enable to compare individual variants between themselves and with motion of real human vocal folds. In next part of this thesis is presented three-dimensional (3D) finite element model of the flow-induced self-oscillation of the human vocal folds. This 3D model was created from a previous 2D model by extrude to the third direction. Using this model was again compared influence of compressible and incompressible flow model on vocal folds motion and generated sound by using videokymograms and acoustic spectra. The last part of this thesis focuses on the possibility to replace missing natural source voice in form reed-based element. Behaviour of reed-based element was analysed using computational modelling and using measurements on experimental physical model. The physical model enables changes in setting gap between reed and reed stop and performing acoustical and optical measurements.
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Finite element modal analysis of a silicone vocal fold filled with fluid
Hájek, P. ; Radolf, Vojtěch ; Horáček, Jaromír ; Švec, J. G.
A three dimensional (3D) finite element (FE) model of a silicone vocal fold (VF) filled with fluid is presented here. The silicone part of the model is based on partial differential equations of the continuum mechanics and consider large deformations. The fluid domain encapsulated in the silicone VF is defined semianalytically as a lumped-element model describing the fluid in hydrostatic conditions. The elongated and pressurized silicone VF was subjected to perturbed modal analysis. Results showed that the choice of the fluid inside the VF substantially influences the natural frequencies. Namely, the water-filling lowers the natural frequencies approximately by half over the air-filling. Besides, the procedure of reverse engineering for obtaining the geometry of the VF from already 3D-printed mold is introduced.
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Damping of human vocal folds vibration
Radolf, Vojtěch ; Horáček, Jaromír ; Bula, Vítězslav ; Geneid, A. ; Laukkanen, A. M.
This study investigates the biomechanics of the end-part of phonation, i.e. the so-called phonation offset, experimentally. This information of vocal fold damping is important for testing and further development of mathematical modelling of phonation. The measurements of the damping ratio, based on high-speed videolaryngoscopic registrations, were realized on a male subject phonating on the vowel [o:]. The results show during the phonation offset a remarkable decrease of vibration frequency of the vocal folds and an increased damping ratio limiting to the value D≈ 0.2. The results for vocal folds’ damping are in agreement with previous measurements performed on humans using different methods.
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Estimation of damping in human vocal folds vibration: measurements in vivo and on model
Horáček, Jaromír ; Radolf, Vojtěch ; Bula, Vítězslav ; Košina, Jan ; Geneid, A. ; Laukkanen, A. M.
This study investigates the biomechanics of the end-part of phonation, i.e. the so-called phonation offset, experimentally. This information of vocal folds damping is important for testing and further development of mathematical modelling of phonation. The measurements of the damping ratio, based on high-speed videolaryngoscopic registrations, were realized in vivo on a male subject and in vitro using an originally developed silicon replica of the human vocal folds. In both cases the results show remarkable decrease of vibration frequency of the vocal folds and increase of damping ratio D in the phonation offset limiting to the values D=0.12 in vivo measurement and D=0.11 in vitro measurement. The results for vocal folds’ damping are in good agreement with previous measurements performed in humans using different methods.
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Three-dimensional numerical analysis of Czech vowel production
Hájek, P. ; Švancara, P. ; Horáček, Jaromír ; Švec, J. G.
Spatial air pressures generated in human vocal tract by vibrating vocal folds present sound sources of vowel production. This paper simulates phonation phenomena by using fluid-structure-acoustic scheme in a three-dimensional (3D) finite element model of a Czech vowel [o:]. The computational model was composed of four-layered M5-shaped vocal folds together with an idealized trachea and vocal tract. Spatial fluid flow in the trachea and in the vocal tract was obtained by unsteady viscous compressible Navier-Stokes equations. The oscillating vocal folds were modelled by a momentum equation. Large deformations were allowed. Transient analysis was performed based on separate structure and fluid solvers, which were exchanging loads acting on the vocal folds boundaries in each time iteration. The deformation of the fluid mesh during the vocal fold oscillation was realized by the arbitrary Lagrangian-Eulerian approach and by interpolation of fluid results on the deformed fluid mesh. Preliminary results show vibration characteristics of the vocal folds, which correspond to those obtained from human phonation at higher pitch. The vocal folds were self-oscillating at a reasonable frequency of 180 Hz. The vocal tract eigenfrequencies were in the ranges of the formant frequencies of Czech vowel [o:] measured on humans, during self-oscillations the formants shifted to lower frequencies.
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Experimental modelling of vibroacoustics of the human vocal tract with compliant walls
Radolf, Vojtěch ; Horáček, Jaromír ; Košina, Jan
Experimental model of human vocal tract cavities with hard walls has been modified to take into account the compliance of the soft tissue of the human vocal tract. The paper presents the studied acoustic-structural interaction of the vocal tract cavities with a dynamical system originated in vibration of the soft tissue. The experimental results are in qualitative agreement with the results of mathematical modelling. Compliant walls of acoustic cavities generate additional low frequency acoustical-mechanical resonances of the system and increase acoustic resonance frequencies.
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Human vocal tract models with yielding walls – preliminary experimental results
Radolf, Vojtěch ; Horáček, Jaromír ; Košina, Jan
Yielding walls of acoustic cavities cause an additional low frequency acoustical – mechanical resonance of the system. This resonance changes also the higher acoustic resonance frequencies. Experimental model of human vocal tract cavities with hard walls has been modified to take into account the compliance of the soft tissue of human vocal tract. The unique experimental set-up has been assembled to study in detail acoustic-structural interaction of the vocal tract cavities with a dynamical system originated in vibration of the soft tissue. The experimental results are in qualitative agreement with the results of mathematical modelling.
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Influence of tissue changes in superficial lamina propria on production of Czech vowels
Hájek, P. ; Švancara, P. ; Horáček, Jaromír ; Švec, J.
Superficial lamina propria (SLP) is a water-like vocal fold (VF) layer located directly under overlying epithelium. Its material properties affect VF motion and thus resulting spectrum of produced sound. Influence of stiffness and damping of the SLP on sound spectrum of Czech vowels is examined using a two-dimensional (2D) finite element (FE) model of a human phonation system. The model consists of the VF (structure model) connected with an idealized trachea and vocal tract (VT) (fluid models). Five VTs for all Czech vowels [a:], [e:], [i:], [o:] and [u:] were used and their geometry were based on MRI data. Fluid flow in the trachea and VT was modelled by unsteady viscous compressible Navier-Stokes equations. Such a formulation enabled numerical simulation of a fluid-structure-acoustic interaction (FSAI). Self-sustained oscillations of the VF were described by a momentum equation including large deformations and a homogeneous linear elastic model of material was used. Fluid and structure solvers exchange displacements and boundary forces in each iteration. During closed phase VFs are in contact and fluid flow is separated. We can observe that both the damping and the stiffness of the SLP substantially influence the amplitude and frequency of VFs vibration as well as the open time of the glottis.\n
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