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### Depth-KymographyFrom 2D to 3D in Voice Diagnostics

Vocal Folds Dynamics

Nibu A. George, Frits F.M. de Mul, Qinjun Qiu, Harm K. Schutte

Groningen Voice Research Lab.,

University of Groningen, University Medical Center UMCG,

Department of Biomedical Engineering BMSA,

Groningen, the Netherlands.

May 2008

FirstVideo-kymography project:

“Voice Diagnostics in a New Perspective”

- Goal:

To develop and apply a new type of video-camera

to image Vocal Folds and

their horizontal positions and movements

in patients.

- This (second) project:

To measure vertical positions and movements

of vocal folds.

- Experimental: develop instrumentation
- Numerical: develop simulation of dynamics
- Develop method to compare measurements and simulations

glass fiber light cable

mouth

light source

endoscope

optical adapter

camera

microphone

computer

EGG

glottis

throat

2D-Videokymography system

Vocal Folds: top view

1,2: Left and right vocal fold

3: Blood vessel

4: Glottis: opening between folds,

partly or completely closed

during phonation

Imaged line in Videokymography

Optical axis of Endoscope

Camera system of Kymograph

Vocal folds

2D-Videokymography system

Glass fiber from light source

Image of one camera line is recorded repeatedly.

Shown: imaging of one point.

NB. In this figure (and all following figures) the vocal folds are drawn after rotation over 900.

(In reality the glottal midline is parallel

to the endoscope axis).

Camera

system of Kymograph

Line triangulation

Semi-transparent mirror

Laser

Cylindrical mirror

Detector array

Vocal folds top view

Vocal folds

(900 rotated)

Videokymography system with 3D-extension

Detector array might be combined

with camera system.

Line triangulation

Vocal folds top view

Videokymography system with 3D-extension

Laser beam

mirror

Detector array

target

laserdriver

laser projection channel

high-speed

camera

endoscope

camera

control unit

optical fiber

vocal folds

white light source

Videokymography system with 3D-extension

Resolution: 50 m

(hor. & vert.)

Nibu A George, Frits F M de Mul, Qingjun Qiu, Gerhard Rakhorst and Harm K Schutte,

“Depth-Kymography: High-speed calibrated 3D imaging of human vocal fold vibration dynamics”,

Phys. Med. Biol. 53, May 2008, 2667-77.

Videokymography system with 3D-extension

- System characteristics
- Laser :658 nm, 90 mW (on vocal folds: 14 mW)
- Laser line on vocal folds :18 mm x 0.4 mm
- Triangulation angle :7 o
- Camera systems:
- High-speed camera (Wolf)
- 4000 fps, color, 256 x 256 pixels @ 13 x 13 m2
- Position-sensitive linear detector array (Hamamatsu)
- 256 x 2 pixels @ 13 m x 1 mm.

Vocal Folds Dynamics

one cycle

Left:Modal

Right:Falsetto

At left side of each:

Dotted region: solid lip

Open region: mucosal lip

time

From: Hirano (1968)

Nibu A George, Frits F M de Mul, Qingjun Qiu, Gerhard Rakhorst and Harm K Schutte, “Depth-Kymography: High-speed calibrated 3D imaging of human vocal fold vibration dynamics”, Phys. Med. Biol. 53, May 2008, 2667-77.

Numerical simulations:

Vocal Folds Dynamics

- Goals:
- To simulate the horizontal and vertical motions of the vocal folds, as functions of time
- To directly compare measurements and simulations
- Modeling:
- Vocal folds modelled as two masses,
- With horizontal and vertical freedom,
- Connected by springs and dampers,
- Driven by air pressures
- Simulate (as functions of time):
- Coordinates
- Pressures
- Flows

Numerical simulations:

Vocal Folds Dynamics

- Most important references:
- Ishizaka, K. and Flanagan, J.L.,Synthesis of voiced sound from a two-mass model of the vocal cords, Bell Syst. Tech. Journ. 51, 1972, 1233-1267.
- Titze, I.R.,The human vocal cords: A mathematical model I+II, Phonetica, 28, 1973, 129-170.
- Koizumi, T., Taniguchi, S., Hiromitsu, S.,Two-mass models of the vocal cords for natural sounding voice synthesis, J. Acoust. Soc. Amer. 82, 1987, 1179-1192 + corrections

F

open

closure

midline

x

x0

0

0

x0

x

linear term (prop. to displacement)

incl. non-linear term

incl. closure term

Spring forces:

also for y

x0,, y0 = position

at rest

open

closure

F

x

x0

0

0

x0

x

constant term ~ velocity

also for y

x0,, y0 = position at rest

incl. closure term

incl. singularity smoothing

Damping forces(prop. to velocity)

y, flow

x

Pressures in x-direction

Pressures in y-direction

Forces from pressures

Pressure forces F =

Pressure P * exposed area A

Pressures depend on

actual coordinates

y, flow

x

Combined Model

6 System variables:

for both masses:

x- and y-positions, thicknesses d

4 Equations of motion

( x and y for both masses):

2 Additional constraining equations:

1. Conservation of total mass

2. y1 , y2 , d1and d2 connected

=> 4 Independent variables

y, flow

x

Combined Model

- Other models:
- Ishizaka & Flanagan:
- Only x-dependence
- Fixed depths ( d ) and widths ( w )
- Forces not in center-of-masses
- Koizumi:
- No wall connection for upper mass
- Forces not in center-of-masses

y, flow

P2,y

x

F1x

F2x

x1

0

x2

x10

0

x20

P2,x

2

F2y

F1y

x2(t)

0

x1

P1,x

1

x1

0

x2(t)

F2y

F1y

x1(t)

0

x2

P1,y

x2

0

x1(t)

Pressure forces

vocal tract part n

vocal tract part 1

vocal tract part 2

lungs

trachea

glottis

mouth

Rg

Lg

Rg = Rcontraction + Rmass1 +

R1→2 + Rmass2 + Rexpansion

Lg = Lcontr + Lmass1 + Lmass2

Electrical analogon for pressures and flows

All resistances, compliances and inertias:

expressions according to air flow in tubes with dynamic lengths and diameters.

Static situation (DC): all inertia’s (L) = 0 and all compliances (C) = ∞.

Vocal tract: components dependent on vowel characteristics ( 45 comp.)

A = cross-sectional area

l = length

R = flowresistance = f ( A,l,Ug )

L = flow inertia = f ( A,l )

y, flow

x

Ug

2

2

1

1

Glottis area

Ug = flow [m3/s]

Vg = dUg / dt

P = pressure [Pa]

P =Rexp.Ug

expansion

P = R2 .Ug + L2 . Vg

glottis

P = Rmid .Ug

A

P = R1 .Ug + L1 . Vg

contraction

P = Rcontr .Ug

pressure

Calculations

- Initial conditions:
- Zero’s; build-up of Plungs at t > 0.
- Stable (DC) situation.

(*) Electrical analogon

of coupled circuits:

set of 2.(n+2)

linear equations

to solve

(n = no. of vocal

tract compartments)

New circuit elements ( R, L, C )

New flows (*)

New pressures and forces

(+) 4 coupled non-linear

equations of motion,

with 2 additional

constraining equations

(total mass, and

y-positions);

iterative approach.

New coordinates (+)

no

End time reached?

Time step

yes

End

Masses (averages, amplitudes) in various models

Models: (ABC)

A = 1: Ishizaka/Flanagan

2: Koizumi

3: Combined

B: lower mass

C: upper mass

B,C = 1: d & w var.

2: d var., w fixed

3: d & w fixed

“

“Error bars” denote

oscillation amplitudes

Coordinates (averages, amplitudes) in various models

Models:(ABC)

A = 1: Ishizaka/Flanagan, 2: Koizumi, 3: Combined

B: lower mass; C: upper mass

B,C = 1: d & w var.; 2: d var., w fixed; 3: d & w fixed

“Error bars” denote

oscillation amplitudes

Flows, pressures and frequencies

in various models

Models: (ABC)

A = 1: Ishizaka/Flanagan, 2: Koizumi, 3: Combined

B: lower mass; C: upper mass

B,C = 1: d & w var.; 2: d var., w fixed; 3: d & w fixed

Ref: model 333

Frequency peaks: intensity ratios in various models

Models:(ABC)

A = 1: Ishizaka/Flanagan, 2: Koizumi, 3: Combined

B: lower mass; C: upper mass

B,C = 1: d & w var.; 2: d var., w fixed; 3: d & w fixed

Ref: model 333

Effects of different Vocal Tract Area Functions (VTAF’s).

Mouth opening

Top glottis

Vocal Tract Area Functions (according to Story & Titze).

Component length: 0.40 cm.

Effects of different Vocal Tract Area Functions (VTAF’s).

Model 312.

The variable values are relative to the values of VTAF no. /o/.

Effects of different Vocal Tract Area Functions (VTAF’s).

Vowels /i/, /o/, /a/ (for components: ref. Story & Titze).

/o/

/i/

/a/

Flow in mouth (time)

Pressure in mouth (gray)andglottis (purple; shifted over 1/20 scale) (freq.)

Effects of different Vocal Tract Area Functions (VTAF’s).

Vowels /i/, /o/, /a/ (for components: ref. Story & Titze).

Pressure in mouth (gray) and glottis (purple; shifted over 1/20 scale) (freq.)

/a/

/o/

/i/

Comparison of measurements and simulations

Successive vertical cross sections of the simulations, during one vibration cycle.

Curve: overlay of the corresponding depth-Kymographic measurement.

Conclusions so far:

- 1. Laryngoscope for Depth-Kymography:
- Design and developmentready
- Successful tests with human subjects

- 2. The program seems to be capable of simulating
- the vocal fold dynamics:
- In horizontal and vertical directions
- With mass exchange between solid mass (lower) and mucosal mass (upper)

- 3. Additional result:
- Direct comparison between simulations and measurements.

The end

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