Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 6662625, 11 pages https://doi.org/10.1155/2021/6662625 Research Article Effects of Sulcus Vocalis Depth on Phonation in Three- Dimensional Fluid-Structure Interaction Laryngeal Models Changwei Zhou , Lili Zhang , Yuanbo Wu , Xiaojun Zhang ,DiWu , and Zhi Tao School of Optoelectronic Science and Engineering, Soochow University, Suzhou 215000, China Correspondence should be addressed to Di Wu; firstname.lastname@example.org and Zhi Tao; email@example.com Received 20 November 2020; Revised 19 March 2021; Accepted 29 March 2021; Published 9 April 2021 Academic Editor: Fahd Abd Algalil Copyright © 2021 Changwei Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Sulcus vocalis is an indentation parallel to the edge of vocal fold, which may extend into the cover and ligament layer of the vocal fold or deeper. The eﬀects of sulcus vocalis depth d on phonation and the vocal cord vibrations are investigated in this study. The three-dimensional laryngeal models were established for healthy vocal folds (0 mm) and diﬀerent types of sulcus vocalis with the typical depth of 1 mm, 2 mm, and 3 mm. These models with ﬂuid-structure interaction (FSI) are computed numerically by sequential coupling method, which includes an immersed boundary method (IBM) for modelling the glottal airﬂow, a ﬁnite- element method (FEM) for modelling vocal fold tissue. The results show that a deeper sulcus vocalis in the cover layer decreases the vibrating frequency of vocal folds and expands the prephonatory glottal half-width which increases the phonation threshold pressure. The larger sulcus vocalis depth makes vocal folds diﬃcult to vibrate and phonate. The eﬀects of sulcus vocalis depth suggest that the feature such as phonation threshold pressure could assist in the detection of healthy vocal folds and diﬀerent types of sulcus vocalis. 1. Introduction the voice. However, considering the aerodynamic theory of phonation, these methods ignore the eﬀects of airﬂow Sulcus vocalis is related to the inhomogeneous damage of viscosity. the cover and ligament with structural malformation of The features of vocal cord vibration and glottal jet the vocal fold. This disease often leads to concomitant dynamics are diﬃcult to characterize with physical models vocal fold disorders and has a signiﬁcant inﬂuence on and reduced-order vocal models. On the contrary, computa- vocal fold vibratory function [1, 2]. According to clinical tional models do well in that. The distribution of pressure and histopathologic analysis, Ford et al.  have classiﬁed and airﬂow was obtained from studies of steady ﬂow in laryn- geal models . For exploring the more complex biomechan- sulcus vocalis into three types: type I is a physiologic var- iant in cover of the vocal folds; type II and III are charac- ical modelling of phonation, Alipour et al.  modelled an terized by destruction of the intermediate and deep lamina oscillating glottis to study pulsatile ﬂow with a ﬁnite volume propria, respectively. Diﬀerent types of sulcus vocalis have method. However, the forced oscillation model only charac- diﬀerent sulcus depth ranges. terized glottis dynamics, which ignored vortex dynamics To explore the pathophysiology, clinical characteristics of and temporal ﬂow variation, especially, signiﬁcant asymmet- sulcus vocalis, open and endoscopic procedures were applied ric ﬂow due to jet deﬂection. Thus, based on the combination by Seth et al. . Welham et al.  used the Voice Handicap of the two-mass vocal fold model and the Navier-Stokes Index (VHI) for characterizing the psychosocial eﬀect of dis- equation, Xue et al.  focused on capturing asymmetric orders on patients with sulcus vocalis. Combining subjective glottal jet deﬂection in an asymmetric larynx. In the past and objective methods, Soares et al.  investigated the vocal few decades, most of the scholars employed a two- characteristics of individuals with sulcus vocalis, especially dimensional laryngeal model [10, 11] for the sake of compu- including asymptomatic subjects, using suspension microlar- tational cost and complex laryngeal structure. However, yngoscopy, voice self-assessment, and acoustic evaluation of experimental studies mostly have shown that the glottal ﬂow 2 Applied Bionics and Biomechanics 3 mm, which are type II sulcus and type III sulcus, respec- is highly three-dimensional [12–14]. What is more, three- dimensional vibration could have inﬂuence on laryngeal tively. All types of sulcus vocalis have the same length with pathologies for anterior-posterior vibration in the three- 2 mm. The sulcus depth of the healthy vocal fold is consid- dimensional model, such as sulcus vocalis and vocal fold ered to be 0 mm in this study. paralysis [15–17]. The adduction of the vocal folds closes the glottis, thereby Recently, the ﬂuid-structure coupling method is widely creating a barrier for the expulsion of air from the lungs. As applied in numerical simulation of the larynx model [18, air is forced from the lungs, the adducted vocal folds are 19]. Valasek et al.  coupled linear elastic problem with pushed apart owing to air pressure, and the vocal folds are the incompressible Navier-Stokes equations in the arbitrary set into sustained ﬂow-induced vibrations. Thus, the bound- Lagrangian-Eulerian form in order to model ﬂuid-structure ary conditions of vocal folds’ surfaces are ﬂuid-structure interaction problem. Smith and Thomson  investigated interaction conditions. It is noted that the air pressure from the eﬀect of subglottic stenosis on vocal fold vibration by the lungs is between 0.5 kPa and 2.5 kPa. When the human establishing a fully coupled ﬁnite element model of the vocal speaks normally, the pressure of the lungs is often considered folds as well. Luo et al.  devised a coupled solver with the as 1 kPa. Therefore, the total pressure on the inlet boundary immersed boundary method to model the ﬂow-structure is set to 1 kPa. And the relative pressure of the outlet bound- interaction of phonation. Tian et al.  combined the ary is equal to 0 kPa. immersed boundary ﬂow solver with a nonlinear ﬁnite- element solid-mechanics solver, handling boundaries of large 3. Numerical Method displacements with simple mesh generation. Chang et al.  Four laryngeal models are established with the depth of studied the eﬀect of geometric nonlinearity on the vocal fold 0 mm, 1 mm, 2 mm, and 3 mm. The model with a depth of and the airﬂow, suggested that accurate simulations of vocal 0 mm corresponds to the healthy vocal folds, while the others fold dynamic needs the large-displacement formulation in a are diﬀerent types of sulcus vocalis. Numerical analysis of computational model. Although there are some numerical ﬂow ﬁelds in the larynx with sulcus vocalis needs to consider simulation studies of sulcus vocalis with respect to sulcus the highly complex interaction between vocal fold tissue and patients’ vocal fold vibration and hydrodynamic analysis, glottal airﬂow. In this research, a ﬂow-structure interaction the eﬀects of sulcus vocalis depth on phonation have not computational solver is applied, which includes an immersed yet been performed. Sulcus vocalis that the depth is less than boundary method (IBM) [27, 28] for modelling the glottal the cover of the vocal fold generally does not give rise to dys- airﬂow, a ﬁnite-element method (FEM) for modelling vocal function, which is classiﬁed as type I. As the depth gets larger fold tissue, and a sequential coupling method for ﬂuid- with sulcus extending into the intermediate and deep layers structure interaction during phonation. Each model with of vocal folds, these types of sulcus vocalis usually bring ﬂuid-structure interaction has the same computational about moderate to severe anomaly. domain. And sequential coupling method was applied to In current research, the three-dimensional laryngeal solve ﬂuid-structure interaction problem. models are developed to simulate and study vocal fold vibra- tions as well as the aerodynamics in the larynx model with 3.1. Fluid Mechanics. The Mach number of the ﬂow in the diﬀerent sulcus vocalis depth. glottis is generally assumed to be smaller than 0.3 , which could be considered that the airﬂow is incompressible. Based 2. Computational Model on the laws of momentum and mass conservation, the gov- erning set of airﬂow is as follows: We established a computational model of the larynx utilized by Zheng et al. . In fact, the human vocal folds have three layers, consisting of cover, ligament, and muscle, and can be ∂u =0, ð1Þ assumed to be made of a viscoelastic material which is trans- ∂x versally isotropic . For the reality of numerical simulation, the isotropic lin- ear elastic material was applied in all layers with the density of 1070 kg/m , and the Poisson ratio to be 0.4. The elastic ∂ u u ∂u 1 ∂P ∂ ∂u i i j i + = − + v , ð2Þ modulus of cover, ligament, and body was 10, 100, and ∂t ∂x ρ ∂x ∂x ∂x j i j j 40 kPa. In Figure 1, the larynx is assumed to be a rectangular duct. Based on the real size of the human larynx, the total length of the duct is 120 mm, and the length of supraglottal where i, j =1,2,3, u are the velocity components, P is the and false vocal folds is 63 mm and 23 mm, respectively, for pressure, and ρ and v are the ﬂuid density and kinematic the easy observation of glottal jet dynamics. The glottal gap viscosity. which is the distance between vocal folds is 1 mm primarily. Equation (2) is discretized in space using a cell-centre And the thickness T and depth of vocal folds are 10 mm collocated ﬁnite diﬀerence scheme. The description of the and 9 mm. For the diseased vocal folds, the sulcus vocalis is naming convention and location of variables used in the spa- modelled by shallow longitudinal furrow to cover, and the tial discretization is shown in Figure 2. depth d is 1 mm, which is type I sulcus. In addition, there Equation (2) is integrated in time using the fractional- are shallow longitudinal furrows with depth of 2 mm and step method , including three substeps. 23.14 mm 64 mm 20 mm 120 mm Applied Bionics and Biomechanics 3 (a) Body Body Body Cover Ligament Cover Ligament Cover Ligament 1 mm 2 mm 3 mm (b) (c) (d) Figure 1: (a) The geometry of computational domain with true and false vocal folds. (b) Type I sulcus vocalis (with depth of 1 mm). (c) Type II (2 mm). (d) Type III (3 mm). nent normal to the cell-face is computed and stored. The averaging procedure is as follows: 1 δP n ~ U = U + Δt , i i ρ δx cc b ~ U = γ u ~ +1 − γ u ~ , 1 ðÞ 1 v 1P v 1W P E W w ~ U = γ u ~ +1 − γ u ~ , ðÞ ð4Þ 2 s 2P s 2S U = γ u ~ +1 − γ u ~ , ðÞ 3 b 3P b 3B 1 δP U = U − Δt , i i ρ δx where γ , γ , and γ are linear interpolation weights for the w s b Figure 2: The description of the naming convention and location of west, south, and back face velocity components, respectively. variables used in the spatial discretization . cc and fc represent cell-centre and face-centre. (2) A pressure correction variable P is computed from (1) A modiﬁed momentum equation with a previously the pressure correction equation computed pressure ﬁeld is solved to calculate an intermediate velocity U . n+1 ∗ u − u 1 δP i i = − : ð5Þ Δt ρ δx ∗ n n U − u 1 1 δP 1 i i n n−1 ∗ n + 3N − N = − + D + D , ð3Þ ðÞ i i i i Δt 2 ρ δx 2 n+1 When the ﬁnal velocity u is divergence free, equation (5) is integrated the equation over the single cell, which where N = δðU u Þ/δx , D = vðδ/δx Þðδu /δx Þ are the con- i j i i i j i j results in the pressure Poisson equation as follows: vective and diﬀusion terms, respectively, and δ/δx denotes a second-order central diﬀerence. The intermediate face- 1 δ δP 1 δU = : ð6Þ centre velocity U is computed by averaging the neighboring ρ δx δx Δt δx ∗ i i i cell-centre velocities u , and only the face velocity compo- Inlet Outlet 15 mm 4 Applied Bionics and Biomechanics "#"# "# A highly eﬃcient multigrid method is applied to solve A A ΔX ff fs f f = , ð11Þ equation (6). A A sf ss ΔX (3) The pressure and velocity ﬁeld is corrected by using pressure correction variable P where t is the step size of time; A , ΔX , and B denote sys- ff f f tem matrix of ﬂow ﬁeld, unsolved, and external force, respec- tively; and A and A represent the coupling matrix of ﬂuid- n+1 n sf fs P = P + P , structure. 1 δP The methods of FSI include direct coupling and sequen- n+1 ∗ u = u − Δt , i i tial coupling method. In fact, the direct coupling method cal- ρ δx ð7Þ cc culates the ﬂuid and solid equations at the same time, and there is no lag of calculation time. However, the direct cou- 1 δP n+1 ∗ U = U − Δt : pling method results in calculation divergence and a large i i ρ δx fc amount of calculation. Thus, we applied the sequential cou- pling method to ﬂuid-solid coupling. The computation of In this research, vocal folds and airway surface are repre- ﬂuid and structural domain is separate. Diﬀerent solvers are sented by the unstructured mesh with triangular elements. used to calculate their physical variables, and the common The boundary conditions are imposed on the nodes of the variables are updated asynchronously. When the ﬂuid solver triangular elements through either the prescribed motion or sends pressure to the solid solver, it receives displacement the computed motion from ﬂow-structure interaction. computed by the solid solver. 3.2. Structural Mechanics. Vocal folds are composed of mul- 4. Results tilayered tissue, which are nonlinear, transversely isotropic, and viscoelastic. Considering the fact that the deformation 4.1. Validation and Vocal Fold Vibration. The time history of of the vocal folds during normal phonation, it can be the displacement of a healthy vocal fold and sulcus vocalis in assumed that the relationship between stress and strain is lin- Y direction is shown in Figures 3(a) and 3(b). Figure 3(a) ear. Thus, the Kelvin-Voigt model  for linear viscoelastic suggests that the numerical simulation ran successfully for material is adopted for vocal fold tissue. providing quasisteady cycles. The result from Vazifehdoost- Based on the Kelvin-Voigt model, the constitutive law saleh et al.  is included here for comparison. Figure 3 can be written as follows: illustrates that the current results are in good agreement with previous simulation data. In addition, the displacement of σ = Eε + Cε_, ð8Þ the right side is greater than that of the left side in the sulcus vocalis, which also validates the credibility of the sulcus voca- where E and C are elasticity and damping matrix. lis model. The governing equation of solid dynamics is given by More importance is often attached to the glottal wave- form for voice quality assessment. Due to the incompressibil- ∂σ ∂ u ity of ﬂow, it can be measured by the equipment which cover t ij ρ = f + , ð9Þ s i 2 subject’s mouth and nose frequently. Several statistical ∂t ∂x parameters such as the fundamental frequency, the peak and mean glottal ﬂow rate, and the open and skewing quo- where i, j =1,2,3, σ is the stress tensor, ρ is the tissue tient  are usually extracted from this waveform to exam- density, f is the body force, and u is vocal fold tissue ine voice quality. The vibration frequency of the healthy displacement. vocal folds is estimated to be 107.5 Hz from Figure 3(a). The ﬂow parameters for healthy vocal folds and sulcus voca- 3.3. Fluid-Structure Coupling. In order to ensure that the lis (1 mm) were compared with other simulation and experi- ﬂuid-structure coupling follows the conservation principle, mental data in Table 1; this simulation could appear to be the the following equations should be applied on the ﬂuid- representation of real human phonation. structure coupling interface. The vibration of the vocal folds is much more complex, which behaves partly like string and partly like spring. The τ · n = τ · n f f s s : ð10Þ fundamental frequency F of vocal folds can be expressed d = d f s by equating the expressions for a vibrating string and spring. rﬃﬃﬃﬃ For the convenience of analysis, a general form of govern- rﬃﬃﬃ 1 σ 1 k ing equations was established. And we solved uniﬁed equa- F = = , ð12Þ 2L ρ 2π m tions with appropriate initial conditions and boundary conditions. This method solves the problem by coupling the ﬂuid-structure control equations to the same equation where L is the length of vocal folds, σ is the stress, ρ is tissue matrix, which solving the ﬂuid and structure governing equa- density, k is the stiﬀness of vocal folds, and m is the mass of tions in the same solver. vocal folds. Applied Bionics and Biomechanics 5 0.0004 0.00020 Present result Present result 0.00015 0.0003 0.00010 0.0002 0.00005 0.00000 0.0001 –0.00005 –0.00010 0.0000 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.01 0.02 0.03 0.04 0.05 Time (s) Time (s) Left side point Right side point (a) (b) 0.0008 0.0008 A. Vazifehdoostsaleh (2018) A. Vazifehdoostsaleh (2018) 0.0006 0.0006 0.0004 0.0004 0.0002 0.0002 0.0000 0.0000 –0.0002 –0.0002 0.00 0.01 0.02 0.03 0.04 0.05 0.00 0.01 0.02 0.03 0.04 0.05 Time (s) Time (s) Left side point Right side point (c) (d) Figure 3: Variation of healthy vocal fold displacement versus time from this work (a) and A. Vazifehdoostsaleh’s result (c). Variation of right and left side displacement of sulcus vocalis (1 mm) versus time from this work (b) and A. Vazifehdoostsaleh’s result (d). Table 1: Comparison of ﬂow parameters for healthy vocal folds and sulcus vocalis (1 mm). A. Vazifehdoostsaleh (2018) Present result Typical range for healthy vocal folds Healthy vocal folds Sulcus vocalis Healthy vocal folds Sulcus vocalis F (Hz) 65-260  104.2 83.3 107.5 85.0 Q (ml/s) 200-580  345.1 390.0 359.2 407.5 max Q (ml/s) 110-220  198.2 226.2 186.5 241.4 mean The expression of the mass of vocal fold is m = ρLTD, of sulcus vocalis k is ðπ /LÞσTðD − dÞ. The stress σ is con- where ρ and T are the density and thickness of vocal folds stant with the same elastic modulus and lung pressure. and D is the depth of the cover layer in that only the pliable Thereby, an increase in sulcus depth d will produce a lower cover of vocal folds is vibrating during soft talking. The eﬀec- vibrating frequency of vocal folds. tive stiﬀness of vocal folds k can be derived from equation The vibrating frequency of the sulcus vocalis is estimated (11), which is k = π σTD/L. Then, the expression for stiﬀness to be about 85 Hz from Figure 4. The vibrating frequency of Y (m) dis Y (m) dis Y (m) Y (m) dis dis 6 Applied Bionics and Biomechanics with a depth of 0 mm, 1 mm, and 2 mm. It should be noticed 0.00020 that the glottal jet was nearly symmetrical during three quar- ters of a cycle in the model with a depth of 3 mm. In addition, 0.00015 the jet deﬂection was decreasing when the depth of sulcus vocalis increased. 0.00010 Figure 6 exhibits a more quantitative comparison about total velocities between the laryngeal models with diﬀerent sulcus depths. The velocity data were extracted along cross- 0.00005 lines that are located in the X-Y plane of diﬀerent laryngeal models as Figure 6(a) shows. The max total velocity of 0.00000 0 mm laryngeal model was larger than other types of laryn- geal models on line 1 shown in Figure 6(a), which is in the –0.00005 centre of the glottis. It is also presented that the speed curve is symmetrical about y =10 mm from line 1 to 3 in 0.01 0.02 0.03 0.04 0.05 Figure 6(b). When the cross-line was in the region of inferior Time (s) glottis, the location of the max velocity was gradually chang- 1 mm ing to up or down side in the Y direction. It can be presented 2 mm that the glottal jet tended to be deﬂected into upper or lower 3 mm walls of the glottal tract, which indicated that the direction of the jet deﬂection is stochastic. Figure 4: The right side displacement of vocal folds in Y direction of sulcus vocalis(1 mm, 2 mm, and 3 mm). 4.3. Pressure Distribution and Phonation Threshold Pressure. Vibration of the vocal cord is governed primarily by the prin- ciples of aerodynamics, structural dynamics, and ﬂuid- the sulcus vocalis (1 mm) is lower than that of the healthy vocal cord (0 mm). A deeper sulcus vocalis in the cover layer structure interactions. It could assist in revealing the eﬀects of diﬀerent sulcus vocalis depths on phonation by studying decreases the fundamental frequency and amplitude of the glottal pressure distribution. With FSI numerical method in vibration. However, when the sulcus depth gets larger that extends into the ligament layer or deeper, the vibrating fre- a 3D computational model, phonation threshold pressure was estimated to study the eﬀects further. quency of vocal folds has almost no change, which is identical to the expression of fundamental frequency. Figure 7 illustrates the variation of glottal pressure distri- butions for the line (y =10 mm, z =7 mm) for the laryngeal models with diﬀerent sulcus depths at four diﬀerent time 4.2. Dynamics of the Glottal Jet. The glottal ﬂow could exhibit a variety of phenomena such as jet deﬂection, ﬂow transition, instants during one vibration cycle, respectively. It is pre- sented that glottal pressure has one pressure drop at x =30 and instability of jet. These phenomena have a close relation with the quality of voice and phonation. And the spatial and mm in Figure 7(a), which is the centre of the glottis. How- temporal details of the glottal jet could be performed by ever, the glottal pressure occurs two pressure drops for sulcus numerical simulation with ﬁnite element analysis methods. vocalis; one is at the entrance of sulcus vocalis, and the other Figure 5 illustrates the contours of the glottal jet for healthy is at the exit of sulcus vocalis. Based on the inference of Ber- vocal folds (0 mm) and sulcus vocalis with the typical depth noulli’s principle, the airﬂow in the vocal tract accelerates due of 1 mm, 2 mm, and 3 mm during one vibration cycle. to the reduction of ﬂuid area, which makes the pressure of In Figure 5, time instants of one cycle were selected airﬂow falls quickly. After entering the sulcus vocalis, the instead of speciﬁc time due to the diﬀerent vibration fre- pressure of airﬂow rises slowly until the airﬂow arrives at quency of healthy vocal fold and three types of the sulcus the exit of sulcus vocalis. What is more, it should be noted vocalis. At the time instant of 0.1 T, a glottal jet emanated that with sulcus vocalis depth increasing, the minimal glottal from the glottal gap as the vocal folds were diverging. What pressure gradually gets larger and the gradient of glottal pres- is more, the glottal jet was symmetrical whether the compu- sure became smaller. tational model is healthy vocal fold or sulcus vocalis at the Phonation threshold pressure is associated with patho- beginning of the cycle. However, when the glottis further logical voice frequently, which is the minimal glottal pressure needed to initiate and sustain vocal fold vibration , for opened, the front of the glottal jet was attaching to one side of the glottal tract, which is a notable phenomenon called the sake of the sensitivity in laryngeal biomechanics’ changes. the Coanda Eﬀect. The existence of the glottal jet deﬂection In this research, the validated computational model was is debated now. Comparing with other studies that per- applied to obtain phonation threshold pressure. Figure 8 formed the glottal jet deﬂection [36, 37], Xue et al.  found shows the time evolution of the pressure at the entrance of the glottis. that the glottal jet was almost symmetric, which had no strong jet deﬂection for the sake of the application of more According to Titze’s derivations for phonation threshold realistic geometric conﬁguration. pressure , phonation threshold pressure P for sulcus th In our research, the laryngeal models with simpliﬁed geo- vocalis is k Bcðξ + dÞ/T, where k is a transglottal pressure t 0 t metric conﬁguration and isotropic material properties were coeﬃcient, B is the viscous damping coeﬃcient, c is the veloc- applied. The ﬂow deﬂection occurred in the laryngeal models ity of the mucosal wave, and ξ is the prephonatory glottal Y (m) dis Applied Bionics and Biomechanics 7 0 mm 1 mm 2 mm 3 mm Figure 5: Contours of velocity at four diﬀerent time instants in one cycle for healthy vocal fold (0 mm) and sulcus vocalis with diﬀerent depths (1 mm, 2 mm, and 3 mm). half-width. For the vocal fold model with sulcus depth of vocal fold vibration, when the pressure on the inlet surface 0 mm, the vocal fold starts to vibrate when the pressure at was 1000 Pa. As the vocal folds started to converge and the entrance of the glottis is up to 450 Pa. The general diverge, the pressure curves were quasi-periodic waveforms description for the variation of pressure with time is the fol- based on phonation threshold pressure. (2) For sulcus depths lowing: (1) the pressures at the entrance of the glottis of 0 mm, 1 mm, 2 mm, and 3 mm, the phonation threshold dropped to diﬀerent suitable values to initiate and sustain pressures in the sulcus vocalis were obviously larger than in 0.7T 0.5T 0.3T 0.1T 0.7T 0.5T 0.3T 0.1T 8 Applied Bionics and Biomechanics 12 3 4 5 6 (a) 12 3 4 5 6 0 20 40 60 0 20 40 60 0 20 40 60 0 20 40 60 0 20 40 60 0 20 40 60 V (m/s) 0 mm 2 mm 1 mm 3 mm (b) Figure 6: Total velocities, plotted along the six lines located in the X-Y plane. depth increases from 1 mm to 3 mm. The lower velocity of the healthy vocal folds. The phonation threshold pressure raise at glottal entry became more prominent with increasing the jet reduces the interactions of vortices with each other. sulcus vocalis depth. The change of sulcus vocalis depth When the sulcus vocalis depth gets biggest, the motion of expands the prephonatory glottal half-width, which is a sig- vortices emerging downstream of the glottis is rarely inﬂu- niﬁcant factor of phonation threshold pressure according to enced by the mutual induction. This hardly brings about asymmetric vortex structures, and there is almost no change its expression. These results suggest that pressure distribu- tion and phonation threshold pressure will be highly sensi- in the ﬂow direction. On the other hand, the increase of sul- tive to sulcus vocalis with diﬀerent depth. The deeper cus vocalis expands the geometry in the vertical direction sulcus vocalis will increase phonation threshold pressure, suddenly. More airﬂow is gathered in the sulcus vocalis making it diﬃcult to vibrate and phonate. which could aﬀect the supra-glottal vortex structure that is related to the glottal jet deﬂection. The pressure in the glottis occurs unstable ﬂuctuations 5. Discussion for sulcus vocalis. When there is a sulcus vocalis, the pressure The increase in depth of sulcus vocalis changes the biome- appears two short-term rebounds and returns to 0 Pa ﬁnally. chanical properties of the vocal folds, which compromises Due to the discrepancy of sulcus vocalis depth, phonation threshold pressure reaches a diﬀerent value. In the condition the pliability of the vocal fold. The glottis closure is crippled by the indentation that extends into the ligament layer or of the same lung pressure, phonation threshold pressure deeper. Thus, the superior glottal angle becomes larger which increases with deeper sulcus vocalis. The larger phonation leads to the lower velocity in the glottis as the sulcus vocalis threshold pressure becomes, the more energy to overcome Y (mm) Applied Bionics and Biomechanics 9 1000 1000 –500 200 –1000 –200 –1500 –400 –2000 –600 0.020 0.025 0.030 0.035 0.040 0.020 0.025 0.030 0.035 0.040 X (m) X (m) 0.1T 0.5T 0.1T 0.5T 0.3T 0.7T 0.3T 0.7T (a) (b) 1000 1000 –200 –200 –400 –400 0.020 0.025 0.030 0.035 0.040 0.020 0.025 0.030 0.035 0.040 X (m) X (m) 0.1T 0.5T 0.1T 0.5T 0.3T 0.7T 0.3T 0.7T (c) (d) Figure 7: Glottal pressure distribution at diﬀerent time-instant of one cycle. (a) 0 mm. (b) 1 mm. (c) 2 mm. (d) 3 mm. the viscous resistance and friction of the airﬂow is required. structure coupling method for healthy vocal folds are veriﬁed Hence, the sulcus vocalis and increased sulcus vocalis depth to be within the normal physiological range. And then, three will cause vocal fatigue and harsh vocal quality. models with diﬀerent sulcus vocalis are developed to study The sulcus vocalis models with diﬀerent depths could be the vibration of vocal folds, the glottal jet dynamics, pressure a tool to observe and connect the physical mechanism of the distribution, and phonation threshold pressure. In addition, disorder and their causes to symptoms, furtherly conducting with increasing sulcus vocalis depth, the glottal jet deﬂection qualitative and quantitative comparison of healthy and sul- is not obvious and the glottal jet tends to be symmetrical. cus vocalis. This method is noninvasive, which provides cli- Finally, the glottal pressure has dropped twice in the direc- nicians with guidelines about the treatment of sulcus vocalis. tion of airﬂow for the sake of sulcus vocalis. As the sulcus vocalis depth increases, the phonation threshold pressures in the diﬀerent types of laryngeal models get larger, which 6. Conclusion disturbs phonation and leads to poor voice quality. The primary contributions of this study are the following: Three-dimensional FSI laryngeal models that consist of fully coupled vocal folds have been applied to enhance the under- (1) under the promise of the same lung pressure, the deeper standing of the eﬀects of sulcus vocalis depth on phonation. sulcus vocalis in the cover layer decreases the vibrating fre- The simulation results computed by the sequential ﬂuid- quency of vocal folds. It also increases the phonation P (Pa) P (Pa) P (Pa) P (Pa) 10 Applied Bionics and Biomechanics management,” The Annals of Otology, Rhinology, and Laryn- gology, vol. 105, no. 3, pp. 189–200, 1996.  S. H. Dailey and C. N. Ford, “Surgical management of sulcus vocalis and vocal fold scarring,” Otolaryngologic Clinics of North America, vol. 39, no. 1, pp. 23–42, 2006.  N. V. Welham, S. H. Dailey, C. N. Ford, and D. M. 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Published: Apr 9, 2021