Research Papers

Effect of Longitudinal Variation of Vocal Fold Inner Layer Thickness on Fluid-Structure Interaction During Voice Production

[+] Author and Article Information
Weili Jiang

Mechanical Engineering Department,
University of Maine,
Orono, ME 04469
e-mail: weili.jiang@maine.edu

Qian Xue

Mechanical Engineering Department,
University of Maine,
Orono, ME 04469
e-mail: qian.xue@maine.edu

Xudong Zheng

Mechanical Engineering Department,
University of Maine,
Orono, ME 04469
e-mail: xudong.zheng@maine.edu

1Corresponding author.

Manuscript received January 24, 2018; final manuscript received July 24, 2018; published online September 25, 2018. Assoc. Editor: Ching-Long Lin.

J Biomech Eng 140(12), 121008 (Sep 25, 2018) (9 pages) Paper No: BIO-18-1049; doi: 10.1115/1.4041045 History: Received January 24, 2018; Revised July 24, 2018

A three-dimensional fluid-structure interaction computational model was used to investigate the effect of the longitudinal variation of vocal fold inner layer thickness on voice production. The computational model coupled a finite element method based continuum vocal fold model and a Navier–Stokes equation based incompressible flow model. Four vocal fold models, one with constant layer thickness and the others with different degrees of layer thickness variation in the longitudinal direction, were studied. It was found that the varied thickness resulted in up to 24% stiffness reduction at the middle and up to 47% stiffness increase near the anterior and posterior ends of the vocal fold; however, the average stiffness was not affected. The fluid-structure interaction simulations on the four models showed that the thickness variation did not affect vibration amplitude, glottal flow rate, and the waveform related parameters. However, it increased glottal angles at the middle of the vocal fold, suggesting that vocal fold vibration amplitude was determined by the average stiffness of the vocal fold, while the glottal angle was determined by the local stiffness. The models with longitudinal variation of layer thickness consumed less energy during the vibrations compared with the constant layer thickness one.

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Mittal, R. , Zheng, X. , Bhardwaj, R. , Seo, J. H. , Xue, Q. , and Bielamowicz, S. , 2011, “ Toward a Simulation-Based Tool for the Treatment of Vocal Fold Paralysis,” Front. Physiol., 2(19).
Weiss, S. , Sutor, A. , Ilg, J. , Rupitsch, S. J. , and Lerch, R. , 2016, “ Measurement and Analysis of the Material Properties and Oscillation Characteristics of Synthetic Vocal Folds,” Acta Acust. Acust., 102(2), pp. 214–229. [CrossRef]
Murray, P. R. , Thomson, S. L. , and Smith, M. E. , 2014, “ A Synthetic, Self-Oscillating Vocal Fold Model Platform for Studying Augmentation Injection,” J. Voice, 28(2), pp. 133–143. [CrossRef] [PubMed]
Hirano, M. , Kurita, S. , and Nakashima, T. , 1981, “ The Structure of the Vocal Folds,” Vocal Fold Physiology, K. Stevens and M. Hirano, eds., University of Tokyo, Tokyo, Japan, pp. 33–41.
Murray, P. R. , and Thomson, S. L. , 2011, “ Synthetic, Multi-Layer, Self-Oscillating Vocal Fold Model Fabrication,” J. Vis. Exp., 58, p. e3498.
Xuan, Y. , and Zhang, Z. , 2014, “ Influence of Embedded Fibers and an Epithelium Layer on the Glottal Closure Pattern in a Physical Vocal Fold Model,” J. Speech. Lang. Hear. Res., 57(2), pp. 416–425. [CrossRef] [PubMed]
Story, B. H. , and Titze, I. R. , 1995, “ Voice Simulation With a Body-Cover Model of the Vocal Folds,” J. Acoust. Soc. Am., 97(2), p. 1249. [CrossRef] [PubMed]
Tokuda, I. , Horáček, J. , Švec, J. G. , and Herzel, H. , 2007, “ Comparison of Biomechanical Modeling of Register Transitions and Voice Instabilities With Excised Larynx Experiments,” J. Acoust. Soc. Am., 122(1), pp. 519–531. [CrossRef] [PubMed]
Bhattacharya, P. , Kelleher, J. E. , and Siegmund, T. , 2015, “ Role of Gradients in Vocal Fold Elastic Modulus on Phonation,” J. Biomech., 48(12), pp. 3356–3363. [CrossRef] [PubMed]
Zhang, Z. , 2014, “ The Influence of Material Anisotropy on Vibration at Onset in a Three-Dimensional Vocal Fold Model,” J. Acoust. Soc. Am., 135(3), pp. 1480–1490. [CrossRef] [PubMed]
Titze, I. R. , and Talkin, D. T. , 1979, “ A Theoretical Study of the Effects of Various Laryngeal Configurations on the Acoustics of Phonation,” J. Acoust. Soc. Am., 66(1), pp. 60–74. [CrossRef] [PubMed]
Cook, D. D. , Nauman, E. , and Mongeau, L. , 2009, “ Ranking Vocal Fold Model Parameters by Their Influence on Modal Frequencies,” J. Acoust. Soc. Am., 126(4), pp. 2002–2010. [CrossRef] [PubMed]
Xue, Q. , Zheng, X. , Bielamowicz, S. , and Mittal, R. , 2011, “ Sensitivity of Vocal Fold Vibratory Modes to Their Three-Layer Structure: Implications for Computational Modeling of Phonation,” J. Acoust. Soc. Am., 130(2), pp. 965–976. [CrossRef] [PubMed]
Titze, I. R. , 2000, Principles of Voice Production, National Center for Voice and Speech, Iowa City, IA.
Berry, D. A. , Montequin, D. W. , and Tayama, N. , 2001, “ High-Speed Digital Imaging of the Medial Surface of the Vocal Folds,” J. Acoust. Soc. Am., 110(5), pp. 2539–2547. [CrossRef] [PubMed]
Cook, D. A. , Nauman, E. , and Mongeau, L. , 2008, “ Reducing the Number of Vocal Fold Mechanical Tissue Properties: Evaluation of the Incompressibility and Planar Displacement Assumptions,” J. Acoust. Soc. Am., 124(6), pp. 3888–3896. [CrossRef] [PubMed]
Mittal, R. , Dong, H. , Bozkurttas, M. , Najjar, F. M. , Vargas, A. , and von Loebbecke, A. , 2008, “ A Versatile Sharp Interface Immersed Boundary Method for Incompressible Flows With Complex Boundaries,” J. Comput. Phys., 227(10), pp. 4825–4852. [CrossRef] [PubMed]
Zheng, X. , 2009, Biomechanical Modeling of Glottal Aerodynamics and Vocal Fold Vibration During Phonation, George Washington University, Washington, DC.
Zheng, X. , Xue, Q. , Mittal, R. , and Beilamowicz, S. , 2010, “ A Coupled Sharp-Interface Immersed Boundary-Finite-Element Method for Flow-Structure Interaction With Application to Human Phonation,” ASME J. Biomech. Eng., 132(11), p. 111003. [CrossRef]
Zheng, X. , Mittal, R. , Xue, Q. , and Bielamowicz, S. , 2011, “ Direct-Numerical Simulation of the Glottal Jet and Vocal-Fold Dynamics in a Three-Dimensional Laryngeal Model,” J. Acoust. Soc. Am., 130(1), pp. 404–415. [CrossRef] [PubMed]
Tao, C. , and Jiang, J. J. , 2008, “ A Self-Oscillating Biophysical Computer Model of the Elongated Vocal Fold,” Comput. Biol. Med., 38(11–12), pp. 1211–1217. [CrossRef] [PubMed]
Gunter, H. E. , 2004, “ Modeling Mechanical Stresses as a Factor in the Etiology of Benign Vocal Fold Lesions,” J. Biomech., 37(7), pp. 1119–1124. [CrossRef] [PubMed]
Gunter, H. E. , 2003, “ A Mechanical Model of Vocal-Fold Collision With High Spatial and Temporal Resolution,” J. Acoust. Soc. Am., 113(2), pp. 994–1000. [CrossRef] [PubMed]
Alipour, F. , and Scherer, R. C. , 2000, “ Vocal Fold Bulging Effects on Phonation Using a Biophysical Computer Model,” J. Voice, 14(4), pp. 470–483. [CrossRef] [PubMed]
Story, B. H. , 2005, “ A Parametric Model of the Vocal Tract Area Function for Vowel and Consonant Simulation,” J. Acoust. Soc. Am., 117(5), p. 3231. [CrossRef] [PubMed]
Story, B. H. , Titze, I. R. , and Hoffman, E. A. , 1996, “ Vocal Tract Area Functions From Magnetic Resonance Imaging,” J. Acoust. Soc. Am., 100(1), pp. 537–554. [CrossRef] [PubMed]
Zheng, X. , Bielamowicz, S. , Luo, H. , and Mittal, R. , 2009, “ A Computational Study of the Effect of False Vocal Folds on Glottal Flow and Vocal Fold Vibration During Phonation,” Ann. Biomed. Eng., 37(3), pp. 625–642. [CrossRef] [PubMed]
Zhang, Z. , 2016, “ Cause-Effect Relationship Between Vocal Fold Physiology and Voice Production in a Three-Dimensional Phonation Model,” J. Acoust. Soc. Am., 139(4), pp. 1493–1507. [CrossRef] [PubMed]
Alipour, F. , Berry, D. A. , and Titze, I. R. , 2000, “ A Finite-Element Model of Vocal-Fold Vibration,” J. Acoust. Soc. Am., 108(6), pp. 3003–3012. [CrossRef] [PubMed]
Xue, Q. , Mittal, R. , Zheng, X. , and Bielamowicz, S. , 2012, “ Computational Modeling of Phonatory Dynamics in a Tubular Three-Dimensional Model of the Human Larynx,” J. Acoust. Soc. Am., 132(3), pp. 1602–1613. [CrossRef] [PubMed]
Xue, Q. , Zheng, X. , Mittal, R. , and Bielamowicz, S. , 2014, “ Subject-Specific Computational Modeling of Human Phonation,” J. Acoust. Soc. Am., 135(3), pp. 1445–1456. [CrossRef] [PubMed]
Zheng, X. , Mittal, R. , and Bielamowicz, S. , 2011, “ A Computational Study of Asymmetric Glottal Jet Deflection During Phonation,” J. Acoust. Soc. Am., 129(4), pp. 2133–2143. [CrossRef] [PubMed]
Xue, Q. , and Zheng, X. , 2017, “ The Effect of False Vocal Folds on Laryngeal Flow Resistance in a Tubular Three-Dimensional Computational Laryngeal Model,” J. Voice, 31(3), pp. 275–281. [CrossRef] [PubMed]
Geng, B. , Xue, Q. , and Zheng, X. , 2017, “ A Finite Element Study on the Cause of Vocal Fold Vertical Stiffness Variation,” J. Acoust. Soc. Am., 141(4), pp. EL351–EL356. [CrossRef] [PubMed]
Berry, D. , Herzel, H. , Titze, I. R. , and Krischer, K. , 1994, “ Interpretation of Biomechanical Simulations of Normal and Chaotic Vocal Fold Oscillations With Empirical Eigenfunctions,” J. Acoust. Soc. Am., 95(6), pp. 3595–3604. [CrossRef] [PubMed]
Thomson, S. L. , Mongeau, L. , and Frankel, S. H. , 2005, “ Aerodynamic Transfer of Energy to the Vocal Folds,” J. Acoust. Soc. Am., 118(3), p. 1689. [CrossRef] [PubMed]
Dion, G. R. , Jeswani, S. , Roof, S. , Fritz, M. , Coelho, P. G. , Sobieraj, M. , Amin, M. R. , and Branski, R. C. , 2016, “ Functional Assessment of the Ex Vivo Vocal Folds Through Biomechanical Testing: A Review,” Mater. Sci. Eng. C, 64, pp. 444–453. [CrossRef]
Dembinski, D. , Oren, L. , Gutmark, E. , and Khosla, S. M. , 2014, “ Biomechanical Measurements of Vocal Fold Elasticity,” OA Tissue Eng., 2(1), pp. 1–5. http://www.oapublishinglondon.com/article/1483
Miri, A. K. , 2014, “ Mechanical Characterization of Vocal Fold Tissue: A Review Study,” J. Voice, 28(6), pp. 657–667. [CrossRef] [PubMed]
Oren, L. , Dembinski, D. , Gutmark, E. , and Khosla, S. , 2014, “ Characterization of the Vocal Fold Vertical Stiffness in a Canine Model,” J. Voice, 28(3), pp. 297–304. [CrossRef] [PubMed]


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Fig. 1

The averaged thickness of the cover and ligament layers of five male vocal fold samples measured by [4]. The square and diamond symbols represent the original measurement of ligament layer and cover layer, respectively. Fourth-order polynomial curves are applied to fit the data: y = 5.92x4−12.16x3+11.16x2−4.84x + 1.51 for the ligament and y = 5.10x4−9.29x3+3.60x2+0.62x + 0.15 for the cover, where x is the nondimensioned longitudinal position and y is the layer thickness (mm). 1.11 mm and 0.33 mm are the averaged layer thicknesses for the ligament and cover, respectively.

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Fig. 2

(a) The geometry and boundary conditions of the vocal fold. T denotes the height of the medial surface. Points A and B locate at Y = 3.86 cm and Y = 3.66 cm, respectively, which were used in the calculation of the glottal angles. (b) The varied thickness along the longitudinal direction of the cover and ligament layers in the four cases. (c) and (d) The three-dimensional configurations of the cover and ligament layers of the vocal fold in the baseline case and extreme variation case, respectively. The shapes of the cross section in the vertical direction in the medial surface of the cover and ligament layers were plotted beside the vocal fold with the color of red and black, respectively. (e) The computational domain, geometry of the larynx, vocal fold and vocal tract, and the boundary conditions of the vocal tract; (f) the location and geometry of the ventricle and false vocal folds.

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Fig. 3

The stiffness distributions along the longitudinal direction at the medial surface of the four vocal fold models. The subfigure illustrates the sections used in the numerical indentation.

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Fig. 4

(a) The time history of the glottal flow rate and glottal opening of the baseline case, and (b) the phase-averaged flow rate and glottal opening for the four cases

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Fig. 5

The midcoronal profiles of the vocal folds at four time instants during one vibration cycle in the baseline and extreme variation cases. The corresponding time instant is indicated as a black dot on the flow rate plot shown at the right-bottom of each subfigure.

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Fig. 6

The two most energetic modes of the baseline case: (a) Mode 1 and (b) Mode 2. In each subfigure, the left side is the three-dimensional shape and the right side is the midcoronal profile of the vocal fold.

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Fig. 7

The phase-averaged glottal angle variation at the three coronal planes for the four cases. The position of each coronal plane is denoted at the top-right corner of each figure.

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Fig. 8

The phase-averaged maximum glottal angle distribution in the longitudinal direction: (a) convergent angle and (b) divergent angle

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Fig. 9

(a) The phase-averaged time history of the power transferred from the air flow to one vocal fold in the four cases and (b) the phase-averaged glottal opening size. The time instants of MFDR are represented by black dots.

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Fig. 10

The phase-averaged intraglottal pressure along the centerline at the time instants of the positive power peak observed in Fig. 9 for the four cases



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