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
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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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