Mathematical models and numerical schemes for the simulation of human phonation

Current Bioinformatics

Volumn 6, Issue 3, 2011, Pages 323-343

  Alipour, Fariborz ^a   Brücker, Christoph ^b   Cook, Douglas D ^c   Gömmel, Andreas ^d   Kaltenbacher, Manfred ^e   Mattheus, Willy ^b   Mongeau, Luc ^f   Nauman, Eric ^g   Schwarze, Rüdiger ^b   Tokuda, Isao ^h   Zörner, Stefan ^e  

^a University of Arizona   (United States)

^b TU BERGAKADEMIE FREIBERG   (Germany)

^c NEW YORK UNIVERSITY ABU DHABI   (United Arab Emirates)

^d RWTH AACHEN UNIVERSITY   (Germany)

^e UNIVERSITY OF KLAGENFURT   (Austria)

^f Macdonald Engineering Bui   (Canada)

^g PURDUE UNIVERSITY   (United States)

^h JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Human phonation; Models based on partial differential equations; Multi mass models

Indexed keywords

BOUNDARY CONDITIONS; COMPUTERIZED TOMOGRAPHY; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; FLOW OF FLUIDS; MAGNETIC RESONANCE IMAGING; SURFACE WAVES; VIBRATIONS (MECHANICAL);

ACOUSTIC DATA; ACOUSTIC SIGNALS; HUMAN PHONATION; MASS MODELS; MODEL BASED ON PARTIAL DIFFERENTIAL EQUATION; MODEL-BASED OPC; MODELING AND NUMERICAL SCHEME; MULTI-MASS MODEL; STRUCTURAL SURFACES; VIBRATION FLOW;

PARTIAL DIFFERENTIAL EQUATIONS;

ACCURACY; ACOUSTICS; AIRFLOW; ARTICLE; COMPARATIVE STUDY; FLOW RATE; FLUID FLOW; GEOMETRY; HUMAN; MATHEMATICAL MODEL; MUCOSAL WAVE MODEL; ONE MASS MODEL; OSCILLATION; PARTIAL DIFFERENTIAL EQUATION BASED MODEL; PHONATION; PHYSICAL PARAMETERS; PRIORITY JOURNAL; REPRODUCIBILITY; SIMULATION; SOUND PRESSURE; THREE MASS MODEL; TWO MASS MODEL; VOCAL CORD;

EID: 80052237929     PISSN: 15748936     EISSN: None     Source Type: Journal    
DOI: 10.2174/157489311796904655     Document Type: Article

References (90)

1. Flanagan J, Landgraf L. Self-oscillating source for vocal-tract synthesizers. Audio Electroacoust IEEE Trans 1968; 16(1): 57-64.
2. Titze IR. The Human Vocal Cords: A Mathematical Model, Part I. Phonetica 1973; 28: 129-70.
3. Koizumi T, Taniguchi S, Hiromitsu S. Two-mass models of the vocal cords for natural sounding of voice synthesis. J Acoust Soc Am 1987; 82: 1179-92.
4. Kob M. Physical modeling of the singing voice. University of Technology Aachen, PhD thesis, 2002.
5. Alipour F, Berry DA, Titze IR. A finite-element model of vocalfold vibration. J Acoust Soc Am 2000; 108: 3003-12.
6. Tao C, Jiang J, Zhang Y. Simulation of vocal fold impact pressures with a self-oscillating finite element model. J Acoust Soc Am 2006; 119: 3987-94.
7. Rosa MO, Pereira JC, Grellet M, Alwan A. A contribution to simulating a three-dimensional larynx model using the finiteelement method. J Acoust Soc Am 2003; 114(5): 2893-905.
8. Zhao W, Frankel SH, Mongeau L. Numerical simulation of sound from confined pulsating axisymmetric jets. AIAA J 2001; 39: 1869-74.
9. Bae Y, Moon Y. Computation of Phonation aeroacoustics by an INS/PCE splitting method. Computers & Fluids 2008; 37: 1332-43.
10. Link G, Kaltenbacher M, Breuer M, Döllinger M. A 2D finiteelement scheme for fluid-solid-acoustic interactions and its application to human phonation. Comp Methods Appl Mech Eng 2009; 198: 3321-34.
11. Ishizaka K, Flanagan JL. Synthesis of voiced sounds from a twomass model of the vocal cords. BLTJ 1972; 51: 1233-68.
12. Stevens K. Physics of laryngeal behavior and larynx mode. Phonetica 1977; 34: 264-79.
13. Titze I. The physics of small-amplitude oscillation of the vocal folds. J Acoust Soc Am 1988; 83: 1536-52.
14. Ishizaka K, Isshiki N. Computer simulation of pathological vocalcord vibration. J Acoust Soc Am 1976; 60: 1193-98.
15. Steinecke I, Herzel H. Bifurcations in an asymmetric vocal fold model. J Acoust Soc Am 1995; 97: 1571-8.
16. Döllinger M, Hoppe U, Hettlich F, Lohscheller J, Schuberth S, Eysholdt U. Vibration parameter extraction from endoscopic image series of the vocal fold. IEEE Trans Biomed Eng 2002; 49: 773-81.
17. Story B, Titze I. Voice simulation with a body-cover model of the vocal folds. J Acoust Soc Am 1995; 97: 1249-60.
18. Hirano M. Morphological structure of the vocal cord as a vibrator and its variations. Folia Phonatrica 1974; 26: 89-94.
19. Hirano M, Kakita Y. Cover-body theory of vocal cord vibration. In Daniloff RG. (Ed.) Speech Science, College Hill Press, San Diego. 1985; p. 1-46.
20. Titze I, Story B. Rules for controlling low-dimensional vocal fold models with muscle activation. J Acoust Soc Am 2002; 112: 1064-76.
21. Adachi S, Yu J. Two-dimensional model of vocal fold vibration for sound synthesis of voice and soprano singing. J Acoust Soc Am 2005; 117: 3213-24.
22. Childers D, Hicks D, Moore G, Alsaka Y. A model for vocal fold vibratory motion, contact area, and electroglottogr. Am J Acoust Soc Am 1986; 80: 1309320.
23. Lous N, Hofmans G, Veldhuis R, Hirschberg A. A symmetrical two mass vocal fold model coupled to vocal tract and trachea, with application to prothesis design. Acta Acustica 1998; 84: 1135-50.
24. Lucero JC. The minimum lung pressure to sustain vocal fold oscillation. J Acoust Soc Am 1995; 98: 779-84.
25. Lucero JC. A theoretical study of the hysteresis phenomenon at vocal fold oscillation onset-offset. J Acoust Soc Am 1999; 105(1): 423-31.
26. Lucero JC, Koenig LL. On the relation between the phonation threshold lung pressure and the oscillation frequency of the vocal folds (L) [Article]. J Acoust Soc Am 2007; 121(6): 3280-3.
27. Laje R, Gardner T, Mindlin GB. Continuous model for vocal fold oscillations to study the effect of feedback. Phys Rev E 2001; 64(5): 056201.
28. Avanzini F. Simulation of vocal fold oscillation with a pseudo-onemass physical model. Speech Commun 2008; 50: 95-108.
29. Drioli C. A flow waveform-matched low-dimensional glottal model based on physical knowledge. J Acoust Soc Am 2005; 117(5): 3184-95.
30. Titze I. The human vocal cords: A mathematical model, part II. Phonetica 1974; 29: 1-21.
31. Wong D, Ito M, Cox N, Titze I. Observation of perturbation in a lumped-element model of the vocal folds with application to some pathological cases. J Acoust Soc Am 1991; 89: 383-94.
32. Titze I. Myoelastic Arodynamic Theory of Phonation. Iowa City, IA: National Center for Voice and Speech. 2006.
33. Berge P, Pomeau Y, Vidal C. Order within Chaos: Towards a deterministic approach to turbulence. New York: Wile. 1984.
34. JC L. Optimal glottal configuration for ease of phonation. J Voice 1998; 12: 151-8.
35. Pelorson X, Hirschberg A, van Hassel R, Wijnands A, Auregan Y. Theoretical and experimental study of quasi-steady flow separation within the glottis during phonation. J Acoust Soc Am 1994; 96: 3416-31.
36. Sciamarella D, d'Alessandro C. On the acoustic sensitivity of a symmetrical two-mass model of the vocal folds to the variation of control parameters. Acta Acustica 2004; 90: 746-61.
37. Tao C, Zhang Y, Hottinger DG, Jiang JJ. Asymmetric airflow and vibration induced by the Coanda effect in a symmetric model of the vocal folds. J Acoust Soc Am 2007; 122(4): 2270-8.
38. de Vries MP, Schutte HK, Veldman AEP, Verkerke GJ. Glottal flow through a two-mass model: Comparison of Navier-Stokes solutions with simplified models. J Acoust Soc Am 2002; 111(4): 1847-5.
39. Alipour F, Scherer RC. Flow separation in a computational oscillating vocal fold model. J Acoust Soc Am 2004; 116: 1710-9.
40. Decker G, Thomson S. Computational Simulations of Vocal Fold Vibration: Bernoulli Versus Navier-Stokes. J Voice 2007; 21: 273-84.
41. Sciamarella D, Quere PL. Solving for unsteady airflow in a glottal model with immersed moving boundaries. Eur J Mech B/Fluids 2008; 27: 42-53.
42. Thomson SL, Mongeau L, Frankel SH. Physical and numerical flow-excited vocal fold models. In: 3rd International Workshop MAVEBA. Firenze University Press 2003; p. 147-50. ISBN 88-8453-154-3.
43. Luo H, Mittal R, Zheng X, Bielamowicz SA, Walsh RJ, Hahn JK. An immersed-boundary method for flow-structure interaction in biological systems with application to phonation. J Comput Phys 2008; 227: 9303-32.
44. Coanda H. Device for deflecting a stream of elastic fluid projected into an elastic fluid. US-patent 1935; 2.052.869.
45. Erath BD, Plesniak MW. The occurrence of the Coanda effect in pulsatile flow through static models of the human vocal folds. J Acoust Soc Am 2006; 120(2): 1000-11.
46. Zhao W, Zhang C, Frankel SH, Mongeau L. Computational aeroacoustics of phonation, Part I: Computational methods and sound generation mechanisms. J Acoust Soc Am 2002; 112: 2134-46.
47. Zhang Z, Mongeau L, Franke SH, Thomson SL. Sound generation by steady flow through glottisshaped orifices. J Acoust Soc Am 2004; 116: 1720-8.
48. Williams JEF, Hawkings DL. Sound generation by turbulence and surface in arbitrary motion. Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical. Sciences. 1969; 264: 321-42.
49. Suh J, Frankel SH. Numerical simulation of turbulence transition and sound radiation for flow through a rigid glottal model. J Acoust Soc Am 2007; 121(6): 3728-39.
50. Krane MH. Aeroacoustic production of low-frequency unvoiced speech sounds. J Acoust Soc Am 2005; 118: 410-27.
51. Gloerfelt X, Lafon P. Direct Computation of the noise induced by a turbulent flow through a diaphragm in a duct at low Mach number. Computers & Fluids 2008; 37: 388-401.
52. Horáček J, Šidlof P, Švec JG. Numerical simulation of selfoscillations of human vocal folds with Hertz model of impact forces. J Fluid Struct 2005; 20: 853-69.
53. Horáček J, Laukkanen AM, Šidlof P. Estimation of impact stress using an aeroelastic model of voice production. Logop Phoniatr Vocol 2007; 32: 185-92.
54. Decker GZ, Thomson SL. Computational simulations of vocal fold vibration: Bernoulli Versus Navier-Stokes. J Voice 2007; 21: 273-84.
55. Zheng X, Xue Q, Mittal R, Beilamowicz S. A coupled sharpinterface immersed boundary-finite-element method for flowstructure interaction with application to human phonation. J Biomech Eng 2010; 132(11): 111003.
56. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Chichester: J. Wiley & Sons Ltd; 2000.
57. Seo JH, Mittal R. A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries. J Comput Phys 2011; 230: 1000-19.
58. Tokuda I, Horáček J, Švec J, Herzel H. Comparison of biomechanical modeling of register transitions and voice instabilities with excised larynx experiments. J Acoust Soc Am 2007; 122: 519-31.
59. van den Berg J, Tan T. Results of experiments with human larynxes. Pract Otorhinolaryngol (Basel) 1959; 21: 425-50.
60. van den Berg J. Sound productions in isolated human larynges. Annals of New York Academy of Sciences 1968; 155: 18-27.
61. Horáček J, Švec J, Veselý J, Vilkman E. Bifurcations in excised larynges caused by vocal fold elongation. In Giovanni A, Dejonckere P, Ouaknine M, (Eds.). Proc Int Conf Voice Physiol Biomech 2004; p. 87-89.
62. OpenCFD Ltd. OpenFOAM1.5 documentation; http://www.opencfd.co.uk/openfoam/doc/index.html.
63. Kaltenbacher M, Escobar M, Ali I, Becker S. Numerical simulation of flow-induced noise using LES/SAS and Lighthill's Acoustics Analogy. Intl J Numerical Methods Fluids 2010; 63(9): 1103-22.
64. Kaltenbacher M. Advanced simulation tool for the design of sensors and actuators. In: Proceedings of Eurosensors XXIV. Linz, Austria, 2010; CD-ROM.
65. Triep M, Brücker C, Schröder W. High-speed PIV measurements of the flow downstream of a dynamic mechanical model of the human vocal folds. Experiments Fluids 2005; 39(2): 232-45.
66. Mattheus W, Zörner S, Kaltenbacher M, Schwarze R, Brücker C. Vortex induced sound in a pulsating flow through an elliptic glottal shaped constriction. Eur J Mech B/Fluids (In review).
67. Schwarze R, Mattheus W, Klostermann J, Brücker C. Starting jet flows in a three-imensional channel with larynx-shaped constriction. Computers & Fluids (submitted).
68. Zheng X, Bielamowicz S, Luo H, Mittal R. A computational study of the effect of false vocal folds on glottal flow and vocal fold vibration during phonation. J Biomed Eng Soc 2009; 37: 625-42.
69. Simo JC, Laursen TA. An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 1992; 42: 97-116.
70. Thomson SL, Mongeau L, Frankel SH. Aerodynamic transfer of energy to the vocal folds. J Acoust Soc Am 2005; 118(3): 1689-100.
71. Titze IR, Strong WJ. Normal modes in vocal cord tissues. J Acoust Soc Am 1975; 57(3): 736-44.
72. Hunter EJ, Titze IR, Alipour F. A three-dimensional model of vocal fold abduction/adduction. J Acoust Soc Am 2004; 115: 1747-59.
73. Cook DD, Mongeau L. Sensitivity of a continuum vocal fold model to geometric parameters, constraints, and boundary conditions. J Acoust Soc Am 2007; 121(4): 2247-53.
74. Berry DA, Titze IR. Normal modes in a continuum model of vocal fold tissues. J Acoust Soc Am 1996; 100(5): 3345-54.
75. Cook DD, Nauman E, Mongeau L. Reducing the number of vocal fold mechanical tissue properties: Evaluation of the incompressibility and planar displacement assumptions. J Acoust Soc Am 2008; 124(6): 3888-96.
76. Cook DD, Nauman E, Mongeau L. Ranking vocal fold model parameters by their influence on modal frequencies. J Acoust Soc Am 2009; 126(4): 2002-10.
77. Alipour F, Titze IR. Combined simulation of airflow and vocal fold vibrations, in Vocal Fold Physiology, Controlling Complexity and Chaos. Singular Publishing Group, San Diego. 1996; p. 17-29.
78. Alipour F, Scherer R. Vocal fold bulging effects on phonation using a biophysical computer model. J Voice 2000; 4(14): 470-83.
79. Ruty N, Pelorson X, Hirtum AV, Lopez-Arteaga I, Hirschberg A. An in vitro setup to test the relevance and the accuracy of loworder vocal folds models. J Acoust Soc Am 2007; 121(1): 479-90.
80. Cisonni J, Hirtum AV, Luo X, Pelorson X. Experimental validation of quasi-one-dimensional and two-dimensional steady glottal flow models. Med Biol Eng Comput 2010; 48: 903-10. 10.1007/s11517-010-0645-7.
81. Scherer RC, Titze IR, Curtis JF. Pressure-flow relationships in two models of the larynx having rectangular glottal shapes. J Acoust Soc Am 1983; 73(2): 668-76.
82. Fulcher LP, Scherer RC, Witt KJD, Thapa P, Bo Y, Kucinschi BR. Pressure distributions in a static physical model of the hemilarynx: Measurements and computations. J Voice 2010; 24(1): 2-20.
83. Gomes JP, Lienhart H. Experimental study on a fluid-structure interaction reference test case. In Fluid-Structure Interaction - Modelling, Simulation, Optimization. 2006.
84. Kakita Y, Hirano M, Ohmaru K. Physical properties of the vocal fold tissue. In: Vocal Fold Physiology; 1981.
85. Min YB, Titze IR, Alipour-Haghighi F. Stress-strain response of the human vocal ligament. Ann Otol Rhinol Laryngol 1995; 104: 563-9.
86. Chan RW, Titze IR. Viscoelastic shear properties of human vocal fold mucosa: Measurement methodology and empirical results. J Acoust Soc Am 1999; 106: 2008-21.
87. Hirano M. Clinical Examination of Voice: Disord Human Commun 1981; p. 100.
88. Holmberg EB, Hillman RE, Perkell JS. Glottal airflow and transglottal air pressure measurements for male and female speakers in soft, normal, and loud voice. J Acoust Soc Am 1988; 84(2): 511-29.
89. Alipour F, Scherer RC. Effects of oscillation of a mechanical hemilarynx model on mean transglottal pressures and flows. J Acoust Soc Am 2001; 110(3): 1562-9.
90. Tao C, Zhang Y, Hottinger DG, Jiang JJ. Asymmetric airflow and vibration induced by the Coanda effect in a symmetric model of the vocal folds. J Acoust Soc Am 2007; 122: 2270-8.