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The role of glottal surface adhesion on vocal folds biomechanics

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Abstract

The airway surface liquid (ASL) is a very thin mucus layer and covers the vocal fold (VF) surface. Adhesion mediated by the ASL occurs during phonation as the VFs separate after collision. Such adhesion is hypothesized to determine voice quality and health. However, biomechanical insights into the adhesive processes during VF oscillation are lacking. Here, a computational study is reported on self-sustained VF vibration involving contact and adhesion. The VF structural model and the glottal airflow are considered fully three-dimensional. The mechanical behavior of the ASL is described through a constitutive traction–separation law where mucosal cohesive strength, cohesive energy, and rupture length enter. Cohesive energy values considered are bound below by the cohesive energy of water at standard temperature and pressure. Cohesive strength values considered are bound above by prior reported data on the adhesive strength of mucosal surface of rat small intestine. This model introduces a mechanical length scale into the analysis. The sensitivity of various aspects of VF dynamics such as flow-declination rate, VF separation under adhesive condition, and formation of multiple local fluid bridges is determined in relation to specific ASL adhesive properties. It is found that for the ASL considered here, the characteristics of the VF separation process are of debond type. Instabilities lead to the breakup of the bond area into several smaller bond patches. Such finding is consistent with in vivo observations.

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Abbreviations

\(AB\) :

Line oriented in anterior–posterior direction and situated on medial plane

\(C_L,C_R\) :

Collision-prone parts of \(S_L\) and \(S_R\)

\(c_R\) :

Rayleigh wave speed in VF tissue

\(d_g\) :

Initial distance between VFs

\(d_p\) :

Fixed separation between planes \(P_L\) and \(P_R\)

\(D\) :

VF medial–lateral extent (depth)

\(\delta {\varvec{D}}_v\) :

Virtual strain tensor associated with \(\delta {\varvec{u}}_v\)

\(\epsilon \) :

Volumetric strain

\({\varvec{e}}\) :

Deviatoric strain tensor

\(E\) :

Elastic modulus of VF tissue

\(f\) :

Vibration frequency

\(g_1\) :

Viscoelastic shear-modulus relaxation factor

\(G\) :

VF tissue shear modulus

\({\varvec{I}}\) :

Second-order identity tensor

\(k_1\) :

Viscoelastic bulk-modulus relaxation factor

\(K\) :

VF tissue bulk modulus

\(l_c\) :

Total length of all interaction line segments

\(l_{c,\mathrm{max}}\) :

Maximum value of \(l_c\) over a cycle

\(L\) :

VF anterior–posterior extent (length)

\(\hat{n}\) :

Unit vector directed normal to surface

\(p\) :

Flow pressure

\(p_\mathrm{in}\) :

Time-dependent flow pressure at glottal air tract inlet

\(p_\mathrm{max}\) :

Maximum flow pressure at glottal air tract inlet

\(P_L,P_R\) :

Rigid planes

\(\hat{r}\) :

Arbitrary unit vector parallel to surface

\(S_L,S_R\) :

Glottal surfaces; flow–structure interaction surfaces

\(t\) :

Time

\(\varDelta t\) :

Time increment

\(t_c, t_o, t_e, t_f\) :

Dimensional times denoting local events related to ASL

\(t_{c,\mathrm{min}}\) :

Time instant corresponding to the initiation of contact along line \(AB\)

\(t_{\mathrm{cycle}}\) :

Time instant corresponding to the end of collision cycle

\(t_{\mathrm{ramp}}\) :

Time duration for inlet pressure ramp

\(\hat{t}, \hat{t}_o, \hat{t}_d, \hat{t}_f\) :

Non-dimensional times denoting global events related to ASL

\(T\) :

VF inferior–superior extent (thickness)

\(T_\mathrm{entry}\) :

Subglottal channel length

\(T_\mathrm{exit}\) :

Supraglottal channel length

\(\delta {\varvec{u}}_v\) :

Arbitrary virtual displacement

\(\varvec{u}\) :

VF displacement

\(\varvec{v}\) :

Airflow velocity

\({\varvec{v}}_g\) :

Airflow domain grid velocity

\(v_c\) :

Average speed at which interaction line segment recedes

\(V^f\) :

Glottal air tract volume

\(V^s\) :

Volume of space occupied by VF pair

\(\partial (V^f)\) :

Glottal air tract boundary

\(\partial (V^s)\) :

Bounding surfaces of VF pair

\(W\) :

Glottal air tract width

\(x_\mathrm{is},x_\mathrm{ml},x_\mathrm{ap}\) :

Coordinate axes in inferior–superior, medial–lateral, and anterior–posterior directions, respectively

\({\mathbf X}_\mathrm{MC}\) :

Reference location on mid-coronal plane prone to collision

:

Time derivative

\(\mathrm{d}\) :

Differential operator

\(\nabla \) :

Spatial gradient

\({()}^T\) :

Transpose

\(\langle \cdot \rangle \) :

Average taken over cycle time period

\(:\) :

Double contraction between two tensors

\(\delta _0\) :

Linear-elastic length limit of VF mucus layer

\(\delta _f\) :

Rupture length limit of VF mucus layer

\(\Delta \) :

Length of mucus layer

\(\phi \) :

Cohesive energy or surface tension

\(\phi _\mathrm{aq}\) :

Surface tension of water

\(\phi ^*_\mathrm{aq}\) :

Cohesive energy of an equivalent one-sided aqueous ASL

\(\eta \) :

Non-dimensional ratio of VF bulk and ASL adhesive properties

\(\lambda \) :

Normalized interaction line segment length

\(\mu \) :

Dynamic viscosity of air

\(\nu \) :

Poisson’s ratio of VF tissue

\(\rho _f\) :

Density of air

\(\rho _s\) :

Density of VF tissue

\(\varvec{\sigma }\) :

Cauchy stress tensor in VF volume

\(\sigma _0\) :

Cohesive strength of mucus layer

\(\hat{\sigma }_0\) :

Cohesive strength of rat intestinal mucosal surface

\(\tau _1\) :

Viscoelastic relaxation rate

\(\varvec{\tau }_f\) :

Stress tensor within air flow domain

\(\varvec{\tau }_s\) :

Traction on VF surface

\(\chi \) :

Collision state variable

References

  • 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):107–115

    Article  Google Scholar 

  • Bhattacharya P, Siegmund T (2012) A canonical biomechanical vocal fold model. J Voice 26(5):535–547

    Article  Google Scholar 

  • Bhattacharya P, Siegmund T (2014) A computational study of systemic hydration in vocal fold collision. Comput Meth Biomech Biomed Eng. doi:10.1080/10255842.2013.772591

  • Bonilha H, White L, Kuckhahn K, Gerlach T, Deliyski D (2012) Vocal fold mucus aggregation in persons with voice disorders. J Commun Disord 45:304–311

    Article  Google Scholar 

  • Bonilha HS, Aikman A, Hines K, Deliyski DD (2008) Vocal fold mucus aggregation in vocally normal speakers. Logoped Phoniatr Vocol 33(3):136–142

    Article  Google Scholar 

  • Chodara AM, Krausert CR, Jiang JJ (2012) Kymographic characterization of vibration in human vocal folds with nodules and polyps. Laryngoscope 122(1):58–65

    Article  Google Scholar 

  • Davidovich-Pinhas M, Bianco-Peled H (2010) Mucoadhesion: a review of characterization techniques. Expert Opin Drug Deliv 7(2):259–271

    Article  Google Scholar 

  • Dean JA (1999) Lange’s handbook of chemistry, 15th edn. McGraw-Hill, New York

    Google Scholar 

  • Decker GZ (2006) Modeling the mechanical effects of liquid mediated adhesion between the human vocal folds. Master’s thesis, Brigham Young University

  • Epstein M (1999) A comparison of linguistic and pathological breathiness using the LF model. Master’s thesis, University of California, Los Angeles

  • Freund L (1990) Dynamic fracture mechanics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Ghatak A, Chaudhury MK (2003) Adhesion-induced instability patterns in thin confined elastic film. Langmuir 19:2621–2631

    Article  Google Scholar 

  • Gunter HE, Howe RD, Zeitels SM, Kobler JB, Hillman RE (2005) Measurement of vocal fold collision during phonation: methods and preliminary data. J Speech Lang Hear Res 48(3):567–576

    Article  Google Scholar 

  • Hsiao TY, Liu CM, Lin KN (2002) Videostrobolaryngoscopy of mucus layer during vocal fold vibration in patients with laryngeal tension-fatigue syndrome. Ann Oto Rhinol Laryn 111(6):537

    Article  Google Scholar 

  • Hsiung MW (2004) Videolaryngostroboscopic observation of mucus layer during vocal cord vibration in patients with vocal nodules before and after surgery. Acta Oto-laryngol 124(2):186–191

    Article  Google Scholar 

  • Jiang JJ, Titze IR (1994) Measurement of vocal fold intraglottal pressure and impact stress. J Voice 8(2):132–144

    Article  Google Scholar 

  • Kutta H, Steven P, Kohla G, Tillmann B, Paulsen F (2002) The human false vocal folds—An analysis of antimicrobial defense mechanisms. Anat Embryol 205:315–323

  • Leite F, Bueno C, Da Róz A, Ziemath E, Oliveira O Jr (2012) Theoretical models for surface forces and adhesion and their measurement using atomic force microscopy. Int J Mol Sci 13:12773–12856

    Article  Google Scholar 

  • Leydon C, Sivasankar M, Falciglia DL, Atkins C, Fisher KV (2009) Vocal fold surface hydration: a review. J Voice 23(6):658–665

    Article  Google Scholar 

  • Lin D, Dimitriadis E, Horkay F (2007) Elasticity of rubber-like materials measured by AFM nanoindentation. Express Polym Lett 1(9): 576–584

  • Lin D, Dimitriadis E, Horkay F (2007b) Robust strategies for automated AFM force curve analysis- II: adhesion-influenced indentation of soft, elastic materials. J Biomech Eng 129(6):904–912

    Article  Google Scholar 

  • Mihaescu M, Khosla SM, Murugappan S, Gutmark EJ (2010) Unsteady laryngeal airflow simulations of the intra-glottal vortical structures. J Acoust Soc Am 127(1):435–444

    Article  Google Scholar 

  • Mortazavi SA, Smart JD (1994) An in-vitro method for assessing the duration of mucoadhesion. J Control Release 31(2):207–212

    Article  Google Scholar 

  • 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): 183–194

  • Needleman A (1990) An analysis of tensile decohesion along an interface. J Mech Phys Solids 38(3):289–324

    Article  Google Scholar 

  • das Neves J, Bahia MF, Amiji MM, Sarmento B (2011) Mucoadhesive nanomedicines: characterization and modulation of mucoadhesion at the nanoscale. Expert Opin Drug Deliv 8(8):1085–1104

    Article  Google Scholar 

  • Peterson-Falzone S, Caldarelli D, Landahl K (1981) Abnormal laryngeal vocal quality in ectodermal dysplasia. Arch Otolaryngol 107(5):300–304

    Article  Google Scholar 

  • Pickup BA, Thomson SL (2011) Identification of geometric parameters influencing the flow-induced vibration of a two-layer self-oscillating computational vocal fold model. J Acoust Soc Am 129(4): 2121–2132

  • Plumpe MD, Quatieri TF, Reynolds DA (1999) Modeling of the glottal flow derivative waveform with application to speaker identification. IEEE Trans Speech Audio Process 7(5):569–586. doi:10.1109/89.784109

    Article  Google Scholar 

  • Scherer RC, Shinwari D, DeWitt 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):1616–1630

    Article  Google Scholar 

  • Spencer M, Siegmund T, Mongeau L (2006) Determination of superior-surface strains and stresses, and vocal fold contact pressure in a synthetic larynx model using digital image correlation. J Acoust Soc Am 123(2):1089–1103

    Article  Google Scholar 

  • Suh J, Frankel SH (2007) Numerical simulation of turbulence transition and sound radiation for flow through a rigid glottal model. J Acoust Soc Am 121(6):3728–3739

    Article  Google Scholar 

  • Thomson SL, Mongeau L, Frankel SH (2005) Aerodynamic transfer of energy to the vocal folds. J Acoust Soc Am 118(3):1689–1700

    Article  Google Scholar 

  • Verdolini K, Hess MM, Titze IR, Bierhals W, Gross M (1999) Investigation of vocal fold impact stress in human subjects. J Voice 13(2):184–202

    Article  Google Scholar 

  • Vilmin T, Ziebert F, Raphaël E (2009) Simple view on fingering instability of debonding soft elastic adhesives. Langmuir 26(5):3257–3260

    Article  Google Scholar 

  • Zhang Z, Neubauer J, Berry DA (2006) The influence of subglottal acoustics on laboratory models of phonation. J Acoust Soc Am 120(3):1558–1569

    Article  Google Scholar 

  • Zheng X, Bielamowicz S, Luo H, 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):625–642

    Article  Google Scholar 

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Acknowledgments

This work was supported by NIDCD Grant 5R01DC008290-04.

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Authors and Affiliations

  1. School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA

    Pinaki Bhattacharya & Thomas Siegmund

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  1. Pinaki Bhattacharya
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  2. Thomas Siegmund
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Correspondence to Pinaki Bhattacharya.

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Bhattacharya, P., Siegmund, T. The role of glottal surface adhesion on vocal folds biomechanics. Biomech Model Mechanobiol 14, 283–295 (2015). https://doi.org/10.1007/s10237-014-0603-7

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