Influence of Acoustic Loading on the Flow-Induced Oscillations of Single Mass Models of the Human Larynx

Matías Zañartu SalasSchool of Electrical and Computer EngineeringPurdue University

Outline

Introduction Objectives Wave Reflection Analog Model for the

Acoustics of the Tracts Effective Single Degree of Freedom Model of

the Vocal Folds Results of the Coupled Models Conclusions Suggestions for Future Research

Motivation

Applications of early models of voice production: speech synthesis, speech recognition, speech coding.

Applications of current research on voice production : Improve upon previous applications, Early detection and better treatment of voice pathologies, Development of bioimplants, Optimization of voice prosthesis, Voice enhancements for singers, Better tools for voice simulation and speech perception, Phonosurgical modeling.

Voice production system

Typical phonation cycle

One-mass model Multi-mass model

The linear source-filter theory of voice production

Introduction

Forces in phase with the velocity of the tissue (mass) are favorable to phonation. A “mucosal wave” in the cover of the vocal fold An inertive impedance in the vocal tract

The relative importance is unknown.

The role of other supraglottal loadings and the subglottal tract is not clear.

One-mass models cannot reach SSO without acoustic loading, since no mucosal wave is present.

Objectives

Model for the acoustics of the tracts: Subglottal and the supraglottal tracts. Static representation of non-nasal vowels Produce synthesized speech Time domain based

Model of the vocal folds vibration: One-mass model Able to produce SSO without acoustic loading

Coupling of the two models: Role of acoustic loadings Flow-sound interactions vs. flow-structure

Model for the Acoustics of the Tracts

Wave Reflection Analog Model (Kelly & Lochbaum, 1962; Liljencrants, 1985; Rahim, 1994; Story, 1995)

Originally designed for speech synthesis

Time domain based technique

Instantaneous acoustic pressure and volumetric flow rate at any time in any place

Radiation impedance and different types of energy dissipation

Revealed acoustic differences due to detailed geometries. MRI shapes of the tracts

Vocal Tract Representation

Wave Reflection Analog

Connection with the source model

Termination impedance

Sound waves: αk sub

Sound waves: αk supra

Loss Factor for each Tract

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Frequency in [Hz]

Att

enu

atio

n f

acto

r [c

m-1

]

13 2

(supraglottal) 3.8 x 10k kA

1 15 22 2(5.23 x 10 439 )k kf f A

1 15 2 2

2 2

23041(5.23 x 10 )

6500 6.31k kf Af

13 2

(subglottal) 11.2 x 10k kA

αk (supraglottal)

Rahim, 1994

αk (subglottal)

Supraglottal

Subglottal

Evaluation of the complete scheme

Effects of boundary conditions Closed-open Closed-closed Open-open

Effects of radiation impedance Adjusted magnitude of reflected pressures Added a positive slope

Effects of the global loss factor Reduced magnitude and bandwidth of formants More pronounced in narrow-band formants

Acoustic coupling between tracts Both linear and non-linear showed poles and zeros Non-linear approach introduced more variations

Evaluation Tests

Basic Approach:

Matlab animations:

Comparison with theoretical complex solution of the planar wave equation

Wave reflection analog

Theoretical complex solution

No lossesWith losses

Closed-open uniform tube with termination impedance

Theoretical complex solution

Piston with at x=0, operating at all frequencies. Pressure measured at x=L

Wave reflection analog

Closed at x=0, impulse injected at x=0 and t=0. Pressure measured at x=L

Proposed Subglottal Tract Design

Weibel, 1963

Proposed subglottal tract design

F1 F2 F3

Typical subglottal resonances (Ishizaka, 1976; Stevens,2000; Harper, 2000)

x=0Spectrum of the acoustic

pressure at x=0

One-Mass Model of the Vocal Folds

Based on Fulcher’s model (2005). Upgrades: Fluid-structure interactions Fluid-sound interactions Collision effects

Used Bernoulli’s equation and obstruction theory.

A smooth time-varying ODC resembled the effects of the mucosal wave.

The ODC for converging and diverging glottal shapes were taken from experimental data.

Material properties were taken from previous studies.

SDOF Self-Oscillating Model

Symmetric vocal folds

Shape comparison

M5 shape: Scherer, 2001

Equation of motion

Equation of motion of the mass is given by:

Fp is the pressure force acting on the open cycle, including

Fluid-structure interactions Fluid-sound interactions

FH are the forces acting during collision, including

Hertz impact forces Increased damping ratio (thus b) Upstream pressure force on the surface

( )o p Hmy by k y y F F

Simplified Flow Diagram of Source Model Coupled

with the WRA Model

Notes:

y Displacement

v Velocity

Q Volumetric flow rate

cd(t) ODC

Fp Pressure Force

FH Impact forces

SDOF Self-Oscillating

ModelStarting the

cycle

Maximum opening

Maximum collision

fo=180 Hz

— : ODC OFF (no fluid-structure interactions)--- : ODC ON (with fluid-structure interactions)

Results of the source model with no acoustic loading

Evaluation of the model: no load case

Effects of orifice discharge coefficient Continuous vs. discontinuous ODC functions ODC modified Q: amplitude and skewing Without time-varying ODC the model did not reach SSO

Effects of collision forces Increased the fundamental frequency of oscillation Reduced of the amplitude Importance: (1º) Change in damping, (2º) upstream

pressure, (3º) Hertz force

Effects discontinuity in the glottal entrance Minor differences compared with a continuous profile

Results for the Coupled Models

What was the relative importance between fluid-structure interactions and fluid-sound interactions?

What was the role of each tract?

Cases: Only fluid-structure interactions Only fluid-sound interactions Both type of interactions together

Notes: No time varying ODC meant cd(t)=1 Subglottal tract + two vocal tract loadings: MRI /i/ and /A/

MRI vowel /i/

fo=170 Hz

F1=225 Hz

F2=2486 Hz

— : ODC OFF (no fluid-structure interactions)--- : ODC ON (with fluid-structure interactions)

fo=190 Hz

F1=786 Hz

F2=1147 Hz

MRI vowel /A/— : ODC OFF (no fluid-structure interactions)--- : ODC ON (with fluid-structure interactions)

Remarks

Acoustic loading with no time varying ODC Large coupling: source and supraglottal tract Subglottal tract: less pronounced effects in the source Modified source properties (Q):

• Ripple or depressions=> more harmonics.• Changes in fo

Acoustic loading with time varying ODC Similar with the no time varying ODC case Results comparable with other studies using high order

models (Story, 2002)=> Effects of fluid-sound interaction were more significant than the fluid-structure interaction

Results for the Coupled Models

What were the effects of different acoustic loadings in SSO?

Cases No time varying ODC were considered Phase plot only Different loading profiles

• Infinitely long tubes• Uniform tubes with variable area and length• MRI vowels• Subglottal tract designs

Cases tested:• Supraglottal tract• Subglottal tract• Both tracts simultaneously

Effects of acoustic loading

on SSO

Supraglottal and subglottal loadings, with no time varying ODC

(a) Vocal Tract: Infinitely long, 4 cm2 (b) Subglottal tract: Infinitely long, 4 cm2

(c) Vocal Tract: Uniform 17cm, 1 cm2 (d) Subglottal tract: Uniform 17cm, 1 cm2

(e) Vocal tract: MRI /i/ (f) Subglottal tract: Proposed design

Remarks

Effect of supraglottal loading in SSO It meets inertance theory. It leads to SSO in relatively narrow shapes (≤1cm2). The area is the most sensible variable.

Effect of subglottal loading in SSO It does not meet the inertance theory. It does not reach to SSO, but shows favorable. Realistic shapes are comparable to a infinitely long tube. Its design (shape, boundary conditions, losses) could

severely affect phonation. The effects are combined when using both tracts.

Conclusions

Time domain model for the acoustics of the tracts: New subglottal attenuation factor New subglottal tract design Complete set of tests to evaluate the scheme Flexible and with multiple applications

Design of a source model for the vocal folds: One-mass model able to reach SSO without acoustic load Allowed fluid-structure interactions Allowed fluid-sound interactions It was able to illustrate effects only seen in high order

models. Collision effects were significant

Conclusions

Results of the coupled models: non-linear voice production Effects of the acoustic loading also led to SSO The effects of the fluid-sound interaction were more

significant than the fluid structure interaction Important changes were observed in the source The supraglottal and subglottal tracts played different roles The inertance theory was met only in the vocal tract The vocal tract was more dominant than the subglottal tract The subglottal tract reduced the effects introduced by the

vocal tract in Q

Suggestions for Future Research

Improvements in the wave reflection analog: Frequency dependent losses Tube branching Other sources of radiation

=>Coupling with piriform sinus, nasal tract.=>Better subglottal tract design.

Improvements in the source model: Pressure distribution codebook Use interactive high order model (finite element model) Include perturbation analysis (jitter, shimmer, SHR, etc)

Suggestions for Future Research

Theoretical perspective: Develop a complete impedance analysis Interactive state model for the improved source

Experimental perspective: Use synthetic models of the vocal folds. Measure Q,

pup, pdn as function of the acoustic loadings DIC is suggested, but the procedure should be adapted

Influence of Acoustic Loading on the Flow-Induced Oscillations of Single Mass Models of the Human Larynx

Matías Zañartu SalasSchool of Electrical and Computer EngineeringPurdue University