Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 3, pp 777–792 | Cite as

Physical parameter estimation from porcine ex vivo vocal fold dynamics in an inverse problem framework

  • Pablo GómezEmail author
  • Anne Schützenberger
  • Stefan Kniesburges
  • Christopher Bohr
  • Michael Döllinger
Original Paper


This study presents a framework for a direct comparison of experimental vocal fold dynamics data to a numerical two-mass-model (2MM) by solving the corresponding inverse problem of which parameters lead to similar model behavior. The introduced 2MM features improvements such as a variable stiffness and a modified collision force. A set of physiologically sensible degrees of freedom is presented, and three optimization algorithms are compared on synthetic vocal fold trajectories. Finally, a total of 288 high-speed video recordings of six excised porcine larynges were optimized to validate the proposed framework. Particular focus lay on the subglottal pressure, as the experimental subglottal pressure is directly comparable to the model subglottal pressure. Fundamental frequency, amplitude and objective function values were also investigated. The employed 2MM is able to replicate the behavior of the porcine vocal folds very well. The model trajectories’ fundamental frequency matches the one of the experimental trajectories in \(98.6\%\) of the recordings. The relative error of the model trajectory amplitudes is on average \(9.5\%\). The experiments feature a mean subglottal pressure of 10.16 (SD \(= 2.31\)) \({\text {cmH}}_2{\text {O}}\); in the model, it was on average 7.61 (SD \(= 2.40\)) \({\text {cmH}}_2{\text {O}}\). A tendency of the model to underestimate the subglottal pressure is found, but the model is capable of inferring trends in the subglottal pressure. The average absolute error between the subglottal pressure in the model and the experiment is 2.90 (SD \(= 1.80\)) \({\text {cmH}}_2{\text {O}}\) or \(27.5\%\). A detailed analysis of the factors affecting the accuracy in matching the subglottal pressure is presented.


Inverse problem High-speed videoendoscopy Vocal fold oscillation Two-mass model 



This work was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—323308998 under Grant Nos. DO1247/8-1 and BO4399/2-1.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Ali MM, Törn A (2004) Population set-based global optimization algorithms: some modifications and numerical studies. Comput Oper Res 31(10):1703–1725MathSciNetCrossRefzbMATHGoogle Scholar
  2. Alipour F, Jaiswal S (2009) Glottal airflow resistance in excised pig, sheep, and cow larynges. J Voice 23(1):40–50CrossRefGoogle Scholar
  3. Alipour F, Brucker D, Cook DD, Gommel A, Kaltenbacher M, Mattheus W, Mongeau L, Nauman E, Schwarze R, Tokuda I et al (2011) Mathematical models and numerical schemes for the simulation of human phonation. Curr Bioinform 6(3):323–343CrossRefGoogle Scholar
  4. Ayache S, Ouaknine M, Dejonkere P, Prindere P, Giovanni A (2004) Experimental study of the effects of surface mucus viscosity on the glottic cycle. J Voice 18(1):107–115CrossRefGoogle Scholar
  5. Becker S, Kniesburges S, Müller S, Delgado A, Link G, Kaltenbacher M, Döllinger M (2009) Flow-structure-acoustic interaction in a human voice model. J Acoust Soc Am 125(3):1351–1361CrossRefGoogle Scholar
  6. Bhattacharya P, Siegmund T (2015) The role of glottal surface adhesion on vocal folds biomechanics. Biomech Model Mechanobiol 14(2):283–295CrossRefGoogle Scholar
  7. Birk V, Döllinger M, Sutor A, Berry DA, Gedeon D, Traxdorf M, Wendler O, Bohr C, Kniesburges S (2017) Automated setup for ex vivo larynx experiments. J Acoust Soc Am 141(3):1349–1359CrossRefGoogle Scholar
  8. Birkholz P, Kröger BJ, Neuschaefer-Rube C (2011) Synthesis of breathy, normal, and pressed phonation using a two-mass model with a triangular glottis. Interspeech 2011:2681–2684Google Scholar
  9. Chan RW, Tayama N (2002) Biomechanical effects of hydration in vocal fold tissues. Otolaryngol Head Neck Surg 126(5):528–537CrossRefGoogle Scholar
  10. Chan RW, Titze IR, Titze MR (1997) Further studies of phonation threshold pressure in a physical model of the vocal fold mucosa. J Acoust Soc Am 101(6):3722–3727CrossRefGoogle Scholar
  11. Chen J, Gutmark E (2014) Numerical investigation of airflow in an idealized human extra-thoracic airway: a comparison study. Biomech Model Mechanobiol 13(1):205–214CrossRefGoogle Scholar
  12. De Vries M, Schutte H, Veldman A, Verkerke G (2002) Glottal flow through a two-mass model: comparison of navier-stokes solutions with simplified models. J Acoust Soc Am 111(4):1847–1853CrossRefGoogle Scholar
  13. Decker GZ, Thomson SL (2007) Computational simulations of vocal fold vibration: Bernoulli versus navier-stokes. J Voice 21(3):273–284CrossRefGoogle Scholar
  14. Döllinger M, Hoppe U, Hettlich F, Lohscheller J, Schuberth S, Eysholdt U (2002) Vibration parameter extraction from endoscopic image series of the vocal folds. IEEE Trans Biomed Eng 49(8):773–781CrossRefGoogle Scholar
  15. Döllinger M, Braunschweig T, Lohscheller J, Eysholdt U, Hoppe U et al (2003) Normal voice production: computation of driving parameters from endoscopic digital high speed images. Method Inform Med 42(3):271–276CrossRefGoogle Scholar
  16. Döllinger M, Berry D, Hüttner B, Bohr C (2011) Assessment of local vocal fold deformation characteristics in an in vitro static tensile test. J Acoust Soc Am 130(2):977–985CrossRefGoogle Scholar
  17. Döllinger M, Dubrovskiy D, Patel R (2012) Spatiotemporal analysis of vocal fold vibrations between children and adults. Laryngoscope 122(11):2511–2518CrossRefGoogle Scholar
  18. Döllinger M, Gröhn F, Berry DA, Eysholdt U, Luegmair G (2014) Preliminary results on the influence of engineered artificial mucus layer on phonation. J Speech Lang Hear R 57(2):S637–S647CrossRefGoogle Scholar
  19. Döllinger M, Dubrovskiy D, Beck E, Patel R (2015) Model based comparison of vocal fold dynamics between children and adults. J Acoust Soc Am 138(3):1779CrossRefGoogle Scholar
  20. Erath BD, Zañartu M, Stewart KC, Plesniak MW, Sommer DE, Peterson SD (2013) A review of lumped-element models of voiced speech. Speech Commun 55(5):667–690CrossRefGoogle Scholar
  21. Erath BD, Zañartu M, Peterson SD (2017) Modeling viscous dissipation during vocal fold contact: the influence of tissue viscosity and thickness with implications for hydration. Biomech Model Mechanobiol 16(3):947–960CrossRefGoogle Scholar
  22. Forero LA, Kohler M, Vellasco MM, Cataldo E (2016) Analysis and classification of voice pathologies using glottal signal parameters. J Voice 30(5):549–556CrossRefGoogle Scholar
  23. Fulcher LP, Scherer RC, Melnykov A, Gateva V, Limes ME (2006) Negative coulomb damping, limit cycles, and self-oscillation of the vocal folds. Am J Phys 74(5):386–393CrossRefGoogle Scholar
  24. Gómez P, Kniesburges S, Schützenberger A, Bohr C, Döllinger M (2017) Degrees of freedom in a vocal fold inverse problem. In: International conference on bioinformatics and biomedical engineering, Springer, Berlin, pp 475–484Google Scholar
  25. Gray SD, Alipour F, Titze IR, Hammond TH (2000) Biomechanical and histologic observations of vocal fold fibrous proteins. Ann Otol Rhinol Laryngol 109(1):77–85CrossRefGoogle Scholar
  26. Hadwin PJ, Galindo GE, Daun KJ, Zañartu M, Erath BD, Cataldo E, Peterson SD (2016) Non-stationary bayesian estimation of parameters from a body cover model of the vocal folds. J Acoust Soc Am 139(5):2683–2696CrossRefGoogle Scholar
  27. Hirano M, Kurita S, Sakaguchi S (1989) Ageing of the vibratory tissue of human vocal folds. Acta Otolaryngol 107(5–6):428–433CrossRefGoogle Scholar
  28. Ishizaka K, Flanagan JL (1972) Synthesis of voiced sounds from a two-mass model of the vocal cords. Bell Syst Tech J 51(6):1233–1268CrossRefGoogle Scholar
  29. Jiang JJ, Zhang Y (2002) Chaotic vibration induced by turbulent noise in a two-mass model of vocal folds. J Acoust Soc Am 112(5):2127–2133CrossRefGoogle Scholar
  30. Jiang JJ, Raviv JR, Hanson DG (2001) Comparison of the phonation-related structures among pig, dog, white-tailed deer, and human larynges. Ann Otol Rhinol Laryngol 110(12):1120–1125CrossRefGoogle Scholar
  31. Kelleher JE, Siegmund T, Chan RW, Henslee EA (2011) Optical measurements of vocal fold tensile properties: Implications for phonatory mechanics. J Biomech 44(9):1729–1734CrossRefGoogle Scholar
  32. Khosla S, Oren L, Ying J, Gutmark E (2014) Direct simultaneous measurement of intraglottal geometry and velocity fields in excised larynges. Laryngoscope 124(S2):S1–S13CrossRefGoogle Scholar
  33. Kucinschi BR, Afjeh AA, Scherer RC (2008) On the application of the lattice Boltzmann method to the investigation of glottal flow. J Acoust Soc Am 124(1):523–534CrossRefGoogle Scholar
  34. Leydon C, Sivasankar M, Falciglia DL, Atkins C, Fisher KV (2009) Vocal fold surface hydration: a review. J Voice 23(6):658–665CrossRefGoogle Scholar
  35. Lohscheller J, Toy H, Rosanowski F, Eysholdt U, Döllinger M (2007) Clinically evaluated procedure for the reconstruction of vocal fold vibrations from endoscopic digital high-speed videos. Med Image Anal 11(4):400–413CrossRefGoogle Scholar
  36. Lucero JC (1993) Dynamics of the two-mass model of the vocal folds: equilibria, bifurcations, and oscillation region. J Acoust Soc Am 94(6):3104–3111CrossRefGoogle Scholar
  37. Mauprivez J, Cataldo E, Sampaio R (2012) Artificial neural networks applied to the estimation of random variables associated to a two-mass model for the vocal folds. Inverse Prob Sci Eng 20(2):209–225MathSciNetCrossRefzbMATHGoogle Scholar
  38. Min YB, Titze IR, Alipour-Haghighi F (1995) Stress-strain response of the human vocal ligament. Ann Otol Rhinol Laryngol 104(7):563–569CrossRefGoogle Scholar
  39. Mongeau L, Franchek N, Coker CH, Kubli RA (1997) Characteristics of a pulsating jet through a small modulated orifice, with application to voice production. J Acoust Soc Am 102(2):1121–1133CrossRefGoogle Scholar
  40. Nakagawa H, Fukuda H, Kawaida M, Shiotani A, Kanzaki J (1998) Lubrication mechanism of the larynx during phonation: an experiment in excised canine larynges. Folia Phoniatr Logop 50(4):183–194CrossRefGoogle Scholar
  41. Patel RR, Dixon A, Richmond A, Donohue KD (2012) Pediatric high speed digital imaging of vocal fold vibration: a normative pilot study of glottal closure and phase closure characteristics. Int J Pediatr Otorhinolaryngol 76(7):954–959CrossRefGoogle Scholar
  42. Pelorson X, Hirschberg A, Van Hassel R, Wijnands A, Auregan Y (1994) Theoretical and experimental study of quasisteady-flow separation within the glottis during phonation. Application to a modified two-mass model. J Acoust Soc Am 96(6):3416–3431CrossRefGoogle Scholar
  43. Qin X, Wang S, Wan M (2009) Improving reliability and accuracy of vibration parameters of vocal folds based on high-speed video and electroglottography. IEEE T Bio-Med Eng 56(6):1744–1754CrossRefGoogle Scholar
  44. Rothenberg M (1977) Measurement of airflow in speech. J Speech Lang Hear R 20(1):155–176CrossRefGoogle Scholar
  45. Roy N, Merrill RM, Gray SD, Smith EM (2005) Voice disorders in the general population: prevalence, risk factors, and occupational impact. Laryngoscope 115(11):1988–1995CrossRefGoogle Scholar
  46. Ruben RJ (2000) Redefining the survival of the fittest: communication disorders in the 21st century. Laryngoscope 110(2):241–241CrossRefGoogle Scholar
  47. Scherer RC, Shinwari D, De Witt KJ, Zhang C, Kucinschi BR, Afjeh AA (2001) Intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees. J Acoust Soc Am 109(4):1616–1630CrossRefGoogle Scholar
  48. Schwarz H, Kröckler N (2013) Numerische mathematik. Springer, BerlinGoogle Scholar
  49. Schwarz R, Hoppe U, Schuster M, Wurzbacher T, Eysholdt U, Lohscheller J (2006) Classification of unilateral vocal fold paralysis by endoscopic digital high-speed recordings and inversion of a biomechanical model. IEEE Trans Biomed Eng 53(6):1099–1108CrossRefGoogle Scholar
  50. Semmler M, Kniesburges S, Birk V, Ziethe A, Patel R, Döllinger M (2016) 3d reconstruction of human laryngeal dynamics based on endoscopic high-speed recordings. IEEE Trans Med Imaging 35(7):1615–1624CrossRefGoogle Scholar
  51. Šidlof P, Zörner S, Hüppe A (2015) A hybrid approach to the computational aeroacoustics of human voice production. Biomech Model Mechanobiol 14(3):473–488CrossRefGoogle Scholar
  52. Smith SW et al (1997) The scientist and engineer’s guide to digital signal processing. California Technical Pub, San DiegoGoogle Scholar
  53. Sommer DE, Erath BD, Zanartu M, Peterson SD (2012) Corrected contact dynamics for the steinecke and herzel asymmetric two-mass model of the vocal folds. J Acoust Soc Am 132(4):EL271–EL276CrossRefGoogle Scholar
  54. Steinecke I, Herzel H (1995) Bifurcations in an asymmetric vocal-fold model. J Acoust Soc Am 97(3):1874–1884CrossRefGoogle Scholar
  55. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  56. Story BH, Titze IR (1995) Voice simulation with a body-cover model of the vocal folds. J Acoust Soc Am 97(2):1249–1260CrossRefGoogle Scholar
  57. Sundberg J, Scherer R, Hess M, Müller F, Granqvist S (2013) Subglottal pressure oscillations accompanying phonation. J Voice 27(4):411–421CrossRefGoogle Scholar
  58. Tao C, Zhang Y, Jiang JJ (2007) Extracting physiologically relevant parameters of vocal folds from high-speed video image series. IEEE Trans Biomed Eng 54(5):794–801CrossRefGoogle Scholar
  59. Titze IR (1988) The physics of small-amplitude oscillation of the vocal folds. J Acoust Soc Am 83(4):1536–1552CrossRefGoogle Scholar
  60. Titze IR (1989) On the relation between subglottal pressure and fundamental frequency in phonation. J Acoust Soc Am 85(2):901–906CrossRefGoogle Scholar
  61. Titze IR (1994) Mechanical stress in phonation. J Voice 8(2):99–105CrossRefGoogle Scholar
  62. Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Congress on evolutionary computation, CEC2004, IEEE, vol 2, pp 1980–1987Google Scholar
  63. Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):65–85CrossRefGoogle Scholar
  64. Wilson JA, Deary IJ, Millar A, Mackenzie K (2002) The quality of life impact of dysphonia. Clin Otolaryngol Allied Sci 27(3):179–182CrossRefGoogle Scholar
  65. Wittenberg T, Moser M, Tigges M, Eysholdt U (1995) Recording, processing, and analysis of digital high-speed sequences in glottography. Mach Vis Appl 8(6):399–404CrossRefGoogle Scholar
  66. Wurzbacher T, Schwarz R, Döllinger M, Hoppe U, Eysholdt U, Lohscheller J (2006) Model-based classification of nonstationary vocal fold vibrations. J Acoust Soc Am 120(2):1012–1027CrossRefGoogle Scholar
  67. Yang A, Stingl M, Berry DA, Lohscheller J, Voigt D, Eysholdt U, Döllinger M (2011) Computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model. J Acoust Soc Am 130(2):948–964CrossRefGoogle Scholar
  68. Yang A, Berry DA, Kaltenbacher M, Döllinger M (2012) Three-dimensional biomechanical properties of human vocal folds: parameter optimization of a numerical model to match in vitro dynamics. J Acoust Soc Am 131(2):1378–1390CrossRefGoogle Scholar
  69. Zambrano-Bigiarini M, Clerc M, Rojas R (2013) Standard particle swarm optimisation 2011 at CEC-2013: a baseline for future PSO improvements. In: 2013 IEEE congress on evolutionary computation, IEEE, pp 2337–2344Google Scholar
  70. Zhang K, Siegmund T, Chan RW (2006) A constitutive model of the human vocal fold cover for fundamental frequency regulation. J Acoust Soc Am 119(2):1050–1062CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Division of Phoniatrics and Pediatric Audiology, Department of Otorhinolaryngology, Head and Neck Surgery, University Hospital ErlangenFriedrich-Alexander University Erlangen-NürnbergErlangenGermany
  2. 2.ENT Department, University Hospital RegensburgUniversity RegensburgErlangenGermany

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