Non linear dynamics of the glottic signal - Laboratoire d'Audio

Fitch WT, Neubauert J, Herzel HP. Calls out of chaos: the adaptative significance of nonlinear phenomena in mammalian vocal production. Animal Behaviour ...
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Non linear dynamics of the glottic signal : perspectives

Antoine Giovanni Maurice Ouaknine Elodie Chapus Laboratoire d’Audio-Phonologie Expérimentale et Clinique UPRES-EA 2668 Université de la Méditerranée Marseille (France)

Non-linearities of the vocal signal • • • •

Pathologic vocal signal (dysphonia) Infant cry Monkey calls (« coo ») Birdsongs – Biphonations – Subharmonics – Chaos

Fitch WT, Neubauert J, Herzel HP. Calls out of chaos: the adaptative significance of nonlinear phenomena in mammalian vocal production. Animal Behaviour, 2002;83:407-418

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Clinical evidence of nonlinearity : synchronization of the vocal folds • Normal vocal folds • Paralytic dysphonia Adduction position (« medial »)

Fo= 1 k 2π m

Fo= 1 k 2π m

Synchronization Synchronization is is aa highly highly nonlinear nonlinear phenomenon phenomenon due due to to contact contact between between the the vocal vocal folds folds and and to to the the Bernouilli’s Bernouilli’s effect effect

Theoretical physiological mechanism • Trend to desynchronization – Degrees of freedom • degree of assymetry between left and right • Presence of a mass (polyp, nodule)

– Subharmonics, noise and chaos

• Trend to synchronization – Contact during closure – Subglottic pressure

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Experimental bench with laser-reflectometers

Ouaknine M, Garrel R, Giovanni A. Separate detection of the vibration of the two vocal fold by optoreflectometry. Folia Phoniatr Logop 2003

Experimental data in case of assymetry 1- no interaction

Tension Tensionassymetry assymetry Low Lowsubglottal subglottalpressure pressure

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Experimental data in case of assymetry 2- interaction but no synchronization

Increased Increasedsubglottal subglottalpressure pressure Increased Increasedviscosity viscosityofofsuperficial superficialmucus mucus

Interactions : non-linear combination F1=250Hz

F2=100Hz

Combined Combinedvocal vocal signal signal

subharmonics subharmonics FFT FFTSpectrum Spectrum 100

150

250

350

F

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Experimental data in case of assymetry 3- interaction and synchronization 1/1

Increased Increasedsubglottal subglottalpressure pressure Increased Increasedviscosity viscosityofofsuperficial superficialmucus mucus

Strong interactions : « blind » non-linear combination

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Principles of a Phase Portrait ille) ) rsrseeille a M e ( Ma ninne ( uuaakknrisioionn O e s Labb Ota vver nal l La BBeeta SSigigna

Quantification of a Phase Portrait • Fractal dimensions – Number of degrees of freedom

• Lyapunov Exponent – Divergence of initially close trajectories

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Determination of Lyapunov exponent

After n iterations, error E E E E n = n n − 1 ... 1 amplification factor would be: E E E E 0 n −1 n − 2 0

Lyapunov coefficient characterizes the logarithm of E increase in relative error during 1 n λ = ∑ log k for iteration n k =1 E k −1

n → ∞ ; E →0 0

Giovanni A, Ouaknine M, Triglia JM. Determination of largest Lyapunov Exponents of Vocal Signal: application to unilateral laryngeal paralysis. J Voice, 1999;13:341-354

Problem : accurate determination of parameters • Measuring Lyapunov exponent is still challenging because of several choices to be made before computing – Exclusion radius – Inclusion radius – Time delay

• Results can be dramatically different if choices are uncorrect

X1, j+2

X1, j+1 1 X1, j

0

E0

E1

x1

E2

X2, j+1

X2, j

2

E2’ E3

x2

x0

X3, j

x3

3

E3’

Giovanni A, Ouaknine M, Triglia JM. Determination of largest Lyapunov Exponents of Vocal Signal: application to unilateral laryngeal paralysis. J Voice, 1999;13:341-354

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Handling non linear concepts •

Promising avenue for a new classification of dysphonic problems (see Orlikoff & Baken’s « Curing diagnosis ») : – Divergence (Lyapunov exponents) • Glottis is made of several moreless coupled oscillators • Sensitivity to initial conditions is a way towards chaos

– Convergence (attractors) • Loss of initial conditions (control) is a way towards stability • « Control » decreases the degrees of freedom



Baken’s lecture during next Voice Symposium in Boston (June 04)

Non-linearities of the vocal signal • • • •

Pathologic vocal signal (dysphonia) Infant cry Monkey calls (« coo ») Birdsongs – Biphonations – Subharmonics – Chaos

Fitch WT, Neubauert J, Herzel HP. Calls out of chaos: the adaptative significance of nonlinear phenomena in mammalian vocal production. Animal Behaviour, 2002;83:407-418

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Clinical experiment • Subject controls – Hypothesis : number of degrees of freedom is increased at phonatory threshold because of lack of « control » – Phase portrait : instability – Lyapunov exponent : increased

• Paralytic dysphonia – Hypothesis : number of degrees of freedom is decreased at a « louder » level of voicing if contact is obtained – Phase portrait : stability – Lyapunov exponent : decreased

Control subject # 1

3 e0 3 ooicice n0 V oss V rsioion AAtm tmeotaavveers BBet

threshold

normal

loud

shout

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Control subject # 1

threshold

normal

Lyapunov : 623 bits/s

Lyapunov : 187 bits/s

loud

Lyapunov : 145 bits/s

Abduction vocal fold paralysis

10

loud

normal

Lyapunov : 221 bits/s

Lyapunov : 667 bits/s

Conclusion « Curing diagnosis » Polyp in a 43 old man Sustained /a/

Same patient Sustained /a/

Comfortable pitch and intensity

Comfortable pitch and intensity during a session of speech therapy

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Next Meeting of the

International Conference for Voice Physiology and Biomechanics ICVPB

..ffrr e e e r f e . r f 4 . 2200004 v c i v / / c i : / / p : t hhtttp Marseille, 18 – 20 August 2004

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