Factors affecting the phonation threshold pressure and frequency

Transcription

1 3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch supported by NIH R-DC99 nd R-DC37

2 Motivtion/Objective How vocl fold geometry nd mteril properties ffect voice production Phontion threshold pressure Phontion onset frequency A better understnding of physicl mechnisms of phontion Provide theoreticl knowledge bse towrds better plnning of thyroplstic surgery.

3 Previous work Mucosl wve model: Titze (988) P th ( kt / T ) Bcξ /( ξ + ξ ) k t : trnsglottl pressure coefficient B: men dmping coefficient c: mucosl wve velocity ξ, : prephontory glottl hlf-width T: vocl fold thickness. The mucosl wve velocity is dynmic vrible of the coupled fluid-structure system, nd its dependence on biomechnicl properties is uncler

4 Previous work cont d Two-mss model, Ishizk (98) Liner stbility nlysis of the two-mss model Phontion onset occurs s two modes of the two-mss model re synchronized by the glottl flow Synchroniztion of two modes leds to phse difference between the motions of the two msses. Lumped model: model prmeters not directly relted to physicl vribles of the vocl system.

5 Previous work cont d Continuum model of the coupled irflow-vocl fold system: Zhng et l. (7) Continuum model of the vocl folds llow the effect of individul geometric prmeter on phontion threshold pressure to be studied. Liner stbility nlysis of the continuum model showed: Phontion onset occurs s two structurl modes of the vocl fold re synchronized by the flow-induced stiffness of the glottl flow Synchroniztion of two modes llows the flow pressure of one mode to interct with the velocity field of the other mode, nd estblishes n energy trnsfer from the flow into the vocl folds

6 Phontion onset occurs s two modes re synchronized by the flow-induced stiffness Q.5 Frequency Two eigenmodes merge nd led to phontion onset Work done on Growth Rte the vocl fold Jet Velocity Subglottl Pressure The net work done by the irflow on the vocl folds remins zero until the two modes synchronize Wht determines how nd which eigenmodes get synchronized?

7 In This Study Exmine the fctors ffecting the synchroniztion process: Use the continuum model of Zhng et l. (7). To illustrte the fctors ffecting Pth nd F, Two-mode pproximtion of the vocl fold motion No structurl or flow-induced dmping. Include more modes nd dmping terms Exmple: geometric dependence of PTP will be studied: Medil surfce thickness Depth of cover lyer Over ll depth of the vocl folds

8 Body-cover Vocl Fold Model t α b T bse α b α c αc Superior D D Inferior r α r T/ t T/5 α b 83º α c 85º α b 5º α c 5º Flow g T Plne-strin isotropic for ech lyer Control Prmeters: Thickness: T Divergent ngle: α Depths: D b nd D c Young s moduli: E b nd E c Minimum glottl hlf width t rest: g Glottl entrnce ngles Glottl exit ngles

9 Model Prmeters Used Structurl Dmping Loss fctor VF Lterl Thickness T bse VF Cover Depth VF Body Depth Glottl Chnnel Gp VF Density Flow Density Non-dimensionl vlues -.4 vrible vrible.. Physicl vlue mm.9 mm 3 kg/m 3. kg/m 3

10 Model ssumptions nd Derivtion of governing Equtions of the coupled irflow-vocl fold system For detils see Zhng et l., 7, JASA,, Two-dimensionl simplifiction Vocl fold Plne strin isotropic for ech lyer Glottl flow One-dimensionl potentil flow up to the point of flow seprtion; Flow seprtion ws ssumed to occur t point s determined by seprtion constnt H s /H min. At point downstrem of the minimum glottl constriction with glottl width equl to. times the minimum glottl width. Zero pressure recovery for the flow downstrem the flow seprtion point, nd no vocl trct zero pressure fluctution boundry condition t the vocl fold outlet; Constnt flow rte t the vocl fold inlet zero velocity fluctution. Liner stbility nlysis (Zhng et l., 7) Linerize system equtions round the men deformed stte Control equtions derived from Lngrnge s equtions Solve the eigenvlue problem, checking for phontion onset: Onset occurs when the growth rte of one of the eigenvlues first becomes positive Simultions Procedure. Solve for stedy stte for given flow rte t glottl entrnce. Perform liner stbility nlysis of the deformed stte of the coupled irflow-vocl fold system. Solve the eigenvlue problem, checking for phontion onset. If no onset, increse flow rte, nd repet steps nd. If onset, stop.

11 Eigenvlue Problem Q ) q&& + ( C Q ) q& + ( K Q ) q ( M Structure Mss: Stiffness: Dmping: Flow: M K C σωm Q Q q&& + Qq& + Qq Phontion onset occurs when the growth rte of one of the eigenvlues first becomes positive (linerly unstble)

12 Vocl fold motion [ξ, η] is pproximted s the liner superposition of the first two nturl modes of the vocl fold ξ: medil-lterl direction; η: inferior-superior direction; φ: nturl modes of the vocl fold structure; q: coefficients The flow-induced stiffness mtrix Q : Two-mode pproximtion z z x x q q q q,,,, ; ϕ ϕ η ϕ ϕ ξ + + Q γ dv dl n H g n H g g U V z i x i vf l z z i x j x j x x i x j x j ij f fsi + + ) ( )] ) ( ) [( 4,,,,,,,,, ϕ ϕ ρ ϕ ϕ ϕ ϕ ϕ ϕ ρ γ

13 Two-mode pproximtion nd no dmping terms Neglecting dmping nd flow inertil terms: Two-mode pproximtion: ) ( ) ( ) ( + + q Q K q Q C q Q M & && ) ( + q Q K q M & &,, q q q q γ ω γ γ γ ω && &&

14 Solving the eigenvlue problem Assuming qq e st, the chrcteristic eqution of the eigenvlue problem is: s 4 + [( ω, + γ) + ( ω, + γ )] s + [( ω, + γ)( ω, + γ ) γ ] s [( ω, + γ) + ( ω, + γ )] ± [( ω, + γ) ( ω, + γ )] + 4γ Onset conditions: eigenvlues lie on the imginry xis in the stte spce until onset. At onset: ω + γ ) ( ω + γ )] + 4γ [(,,

15 Solving the eigenvlue problem - II [( ω, + γ) ( ω, + γ )] + 4γ Phontion threshold pressure P th γ th ω, ω, + Phontion onset frequency F ω th ω, + ω, + γ th ( + ) P th nd F γ th (ω ω, ω, + th )

16 Phontion threshold pressure γ th ω, ω, + ω, ω α, Phontion threshold pressure depends on: Frequency spcing between the two nturl modes being synchronized: ω, - ω, ; Coupling strength between these two modes due to fluid-structure coupling. Both two re completely determined by the properties of the vocl folds, including: Mteril properties: stiffness Geometry

17 Phontion onset frequency ω th ω, + ω, + γ th ( + ) Phontion onset frequency depends on: Nturl frequency of the two nturl modes being synchronized: ω, nd ω, ; Ability of the flow to merge the two modes. The vlue of phontion onset frequency cn be in between the two nturl frequencies, or quite lower thn either of the two, depending on the threshold pressure or presence of dmping.

18 Fctors ffecting P th nd F Vocl fold geometry Vocl fold stiffness Other properties Nturl modes: Frequency & Modl shpe Glottl opening Frequency spcing Coupling strength P th nd F

19 Exmple Effects of Medil Surfce Thickness T Flow Flow

20 Medil surfce thickness T D.7, D.67, convergent.4.76 P th F : two-mode, no dmping T T Nturl Frequency T Coupling Strength T Coupling strength: Blue: &

21 Effects of high-order modes When there re more thn two modes present: Synchroniztion cn occur t different pir of eigenmodes Competition between different pirs of eigenmodes to rech onset first Sudden chnges in phontion onset frequency F

22 Coupling Strength T.33 D.7 D.67 convergent Couplin g Strength Mode Mode Mode Mode 767. Mode Mode Mode Mode 3 S.D. 94. Mode Mode 5 S.D.: sttic divergence, or zero-frequency instbility

23 Medil surfce thickness T P th F.5 Modes nd Modes 4 nd 5 : two-mode, no dmping; : -modes, no dmping; T T 5 Nturl Frequency.5.5 Coupling Strength 5 Coupling strength: Blue: & Red: &3; Purple: 4& T..4.6 T

24 Effects of dmping When dmping (structurl or flow) is included: Dely phontion onset to higher threshold pressure My chnge the reltive dominnce of one pir of eigenmode over the other t onset, cusing sudden chnges in phontion onset frequency F Stbilize higher-order modes so tht phontion onset is more likely to occur s two lower-order modes become synchronized if the dmping is lrger t higher frequencies so tht strong coupling nd high threshold pressure re needed to rech onset

25 Inclusion of dmping my chnge the reltive dominnce of eigenmode groups t onset Phontion threshold pressure Phontion onset frequency Modes 4 nd 5.4. P th.3.. F.8 Modes nd Dmping Dmping vocl fold geometry remined unchnged when the dmping ws vried

26 Lrge dmping t high frequencies lowers the chnce for higher-order modes to be destbilized t onset.8 P th T F Modes nd Modes nd T : two-mode, no dmping; : -modes, no dmping; : -modes, with dmping, σ.4 Nturl Frequency.5.5 Coupling Strength Coupling strength: Blue: & Red: &3; Purple: 4& T T

27 Fctors ffecting P th nd F -- updted Vocl fold geometry Vocl fold stiffness Other properties Nturl modes: Frequency & Modl shpe Vocl fold dmping Glottl opening Frequency spcing Coupling strength P th nd F

28 Summry Phontion threshold pressure depends on the frequency spcing nd coupling strength between corresponding nturl modes of the vocl fold structure. For ccurte prediction of P th nd F : Higher-order modes need to be modeled More thn two modes cn interct with ech other There re more thn one group of eigenmodes tht re synchronized nd compete for dominnce. Accurte description of vocl fold biomechnicl properties (geometry, mteril properties, in prticulr structurl stiffness nd dmping) Dmping in the coupled system delys onset to higher threshold pressure, Dmping my lso determine which group of intercting eigenmodes becomes unstble nd reches onset first.

29 Reference Ishizk, K. (98). Significnce of Kneko s mesurement of nturl frequencies of the vocl folds, in Vocl Physiology: Voice Production, Mechnisms nd Function, edited by Osmu Fujimr (Rven, New York), pp Titze, I.R. (988), The physics of smll-mplitude oscilltion of the vocl folds, JASA, 83, Zhng, Z., Neubuer, J., Berry, D., (7), Physicl mechnisms of phontion onset: A liner stbility nlysis of n eroelstic continuum model of phontion, JASA,,