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Depth-Kymography From 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,

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Depth kymography from 2d to 3d in voice diagnostics

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


time

Vocal Folds: top view

Videokymography:

Imaged line as a function of time

Glottis

Blood vessel


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)


time

Conventional 2D - Kymography

time


What do we want to see:

time

time

2D Kymography line with extra:

vertical profile.


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.


What do we want to see Rakhorst and Harm K Schutte,:

time

depth

width

2D Kymography line with extra:

vertical profile.


Awarded Rakhorst and Harm K Schutte,

(for the novelty, significance

and potential impact

on future research)


  • Numerical simulations: Rakhorst and Harm K Schutte,

    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: Rakhorst and Harm K Schutte,

    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


Schematic time cycle Rakhorst and Harm K Schutte,

Modeling

time

From: Hirano (1968)

Blocks may also have vertical freedom


y, flow Rakhorst and Harm K Schutte,

x

=

spring and damper

2-masses

model


to Rakhorst and Harm K Schutte,mouth

y, flow

expansion

vocaltract

x

glottismidline

glottis

contraction

trachea

pressure

tolungs


F Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte, = 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 Rakhorst and Harm K Schutte,

  • 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


Input parameters of the simulations. Rakhorst and Harm K Schutte,


Output variables of the simulations Rakhorst and Harm K Schutte,


Example of screen output Rakhorst and Harm K Schutte,


VFDyn-program Rakhorst and Harm K Schutte,


Masses (averages, amplitudes) in various models Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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). Rakhorst and Harm K Schutte,

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). Rakhorst and Harm K Schutte,

Model 312.

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


Effects of different Vocal Tract Area Functions (VTAF’s). Rakhorst and Harm K Schutte,

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). Rakhorst and Harm K Schutte,

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 Rakhorst and Harm K Schutte,

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

Curve: overlay of the corresponding depth-Kymographic measurement.


Conclusions so far: Rakhorst and Harm K Schutte,

  • 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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