Matías Zañartu Salas School of Electrical and Computer Engineering Purdue University

1. Influence of Acoustic Loading on the Flow-Induced Oscillations of Single Mass Models of the Human Larynx Matías Zañartu Salas School of Electrical and Computer Engineering Purdue University

2. 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

3. 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.

4. Voice production system Typical phonation cycle

5. One-mass model Multi-mass model

6. The linear source-filter theory of voice production

7. 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.

8. 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

9. 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

10. Vocal Tract Representation

11. Sound waves: αk supra Termination impedance Connection with the source model Sound waves: αk sub Wave Reflection Analog

12. Supraglottal Subglottal αk (subglottal) αk (supraglottal)Rahim, 1994 Loss Factor for each Tract

13. 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

14. Evaluation Tests Basic Approach: Matlab animations:

15. Wave reflection analog Theoretical complex solution Comparison with theoretical complex solution of the planar wave equation 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 No losses With losses Closed at x=0, impulse injected at x=0 and t=0. Pressure measured at x=L

16. F1 F2 F3 Proposed Subglottal Tract Design Spectrum of the acoustic pressure at x=0 x=0 Weibel, 1963 Proposed subglottal tract design Typical subglottal resonances (Ishizaka, 1976; Stevens,2000; Harper, 2000)

17. 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.

18. SDOF Self-Oscillating Model Symmetric vocal folds Shape comparison M5 shape: Scherer, 2001

19. 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

20. Simplified Flow Diagram of Source Model Coupled with the WRA Model Notes:

21. SDOF Self-Oscillating Model Starting the cycle Maximum opening Maximum collision

22. Results of the source model with no acoustic loading fo=180 Hz

23. 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

24. 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/

25. a b c d MRI vowel /i/Acoustic coupling only fo=170 Hz F1=225 Hz F2=2486 Hz

26. a b c d MRI vowel /A/Acoustic coupling only fo=190 Hz F1=786 Hz F2=1147 Hz

27. a b c d MRI vowel /i/Acoustic coupling and time varying ODC fo=170 Hz F1=225 Hz F2=2486 Hz

28. a b c d MRI vowel /A/Acoustic coupling and time varying ODC fo=190 Hz F1=786 Hz F2=1147 Hz

29. 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

30. 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

31. Effects of acoustic loading on SSO Supraglottal and subglottal loadings, with no time varying ODC

32. 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 an infinitely long tube. • Its design (shape, boundary conditions, losses) could severely affect phonation. • The effects are combined when using both tracts.

33. 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

34. 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

35. 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)

36. 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

37. Influence of Acoustic Loading on the Flow-Induced Oscillations of Single Mass Models of the Human Larynx Matías Zañartu Salas School of Electrical and Computer Engineering Purdue University