Pressures and Flows for a Convergent and Divergent Oblique Glottis of 15 Degrees

PRESSURES AND FLOWS FOR A CONVERGENT AND DIVERGENT OBLIQUE GLOTTIS OF 15 DEGREES

Jason A. Whitfield, B.A.

A Thesis

Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

May 2012

Committee:

Ronald Scherer, Advisor

John Folkins

Roger Colcord

Jason A. Whitfield

iii

ABSTRACT

Ronald Scherer, Advisor

Current high-speed imaging of vocal fold motion has shown vibrational

asymmetries in both individuals with and without voice disorders. However, empirical

data regarding aerodynamic pressure of asymmetric glottal configurations is limited. The

current investigation examined empirically derived intraglottal pressures of left-right

glottal asymmetry (obliquity) using the static constant flow model, M5. Two cases, one

convergent and one divergent, having an obliquity of 15o were examined. Seven

diameters along with a range of transglottal pressure were studied for each case.

For both cases of obliquity, when the diameter was small, the vocal folds were more aerodynamically entrained, with each vocal fold having similar intraglottal pressures. As the diameter increased, the aerodynamic coupling of the vocal folds decreased, leading to cross channel pressure differences at glottal entrance as large as

70% for the convergent Case I and 40% for the divergent Case II. These aerodynamic differences may potentially enhance out of phase motion of the vocal folds.

These data suggest that the aerodynamic effects of obliquity are highly dependent on diameter and angle. Results from this study should be incorporated into multimass computer simulation models to further examine the dynamic effects of obliquity on vocal

fold oscillation and glottal flow.

This study is dedicated in memory of my Grandfather, Ray Albertson.

ACKNOWLEDGMENTS

I would first like to thank my advisor, Ronald Scherer, for his time, guidance, and

support during this portion of my graduate education. In addition, I want to thank my

committee members, Roger Colcord and John Folkins for their time. Also, I want to

thank Alexander Goberman for his support and guidance during the past two years.

To my fellow Master’s students: thank you for your support and friendship as we

completed this degree together. Thank you to Elina Banzina, Ramya Konnai, Sabiha

Parveen, Siva Priya Santhanam, Lisa Shattuck, Eric Swartz, Stephanie Richards, and

Elizabeth Witter for being good friends and office-mates. Thank you to Brianna

Chapman, Katie Keenan, and Katharine Murphy for being such caring, supportive friends. To Charlie Hughes, thank you for your friendship and advice. Thank you to My

Family: Mom, Granny, Dad, Karen, Greg, and Dee for your love and continuous support during my education and throughout my life. A most special and loving thank you to my

wife Kathleen Whitfield; I could not have completed this phase of my education without

your loving kindness and understanding.

TABLE OF CONTENTS

Page

CHAPTER I. INTRODUCTION ...... 1

Basic Overview of Phonation for Voice and Speech ...... 1

Vocal fold motion and glottal geometries ...... 2

Clinical observations ...... 3

Glottal obliquity ...... 8

Overview of the Literature ...... 9

Effect of diameter ...... 11

Effect of glottal angle...... 12

Effect of obliquity ...... 12

Overview of the Current Study ...... 13

CHAPTER II. METHODS ...... 15

Glottal Configurations for the Current Study ...... 15

The M5 Model ...... 17

Setting Up the Model for Data Collection ...... 20

Measurement of Flow ...... 23

Calibration Procedures ...... 25

Calibration of the pressure transducers ...... 26

Calibration of the pneumotach with the flowmeter ...... 27

Data Collection with Model M5 ...... 28

Presentation of the Data ...... 34

vii

CHAPTER III: RESULTS ...... 37

Case I: Convergent Glottis; -20o Conv. Side and +10o Div. Side; Oblique 15o ...... 37

Normalized pressure distributions ...... 38

Glottal entrance pressures ...... 39

Summary of flow data ...... 59

Case II: Divergent Glottis; -10o Conv. Side and +20o Div. Side; Oblique 15o ...... 64

Normalized pressure distributions ...... 65

Glottal entrance pressures ...... 67

Bimodal pressure distributions ...... 71

Summary of flow data ...... 97

CHAPTER IV: DISCUSSION ...... 103

Similar Observation between Cases...... 103

Differences between Cases ...... 104

Extension and Comparison of the Findings ...... 105

Comparison of oblique data with symmetric data ...... 106

Small diameters: 0.005 to 0.04 cm...... 107

General overview ...... 107

Case I ...... 109

Case II ...... 110

Large diameters: 0.08 to 0.32 cm ...... 111

Case I ...... 111

Case II ...... 116

Effect of obliquity ...... 122 viii

Replication Comparisons ...... 122

CHAPTER V: CONCLUSIONS ...... 126

REFERENCES ...... 129

APPENDIX A...... 133

Pressure Transducer Calibration ...... 133

APPENDIX B...... 138

Comparison of the Oblique Glottis to the Symmetric ...... 138

Case I ...... 138

Case II ...... 152

LIST OF FIGURES

Figure Page

1 A normal cycle of vocal fold vibration as view in the mid-coronal plane ...... 4

2 Case I: A convergent glottis of -10 degrees with an obliquity angle of 15 degrees .. 16

3 Case II: A divergent glottis of +10 degrees with an obliquity angle of 15 degrees ... 16

4 Model M5 and its components ...... 17

5 Schematic diagram of M5 ...... 18

6 Locations of the pressure taps on a vocal fold piece ...... 19

7 Pressure taps on the vocal fold inserts ...... 21

8 Schematic representation of the setup for model M5 ...... 24

9 Mounted Flowmeter Configuration ...... 25

10 The human hair located just downstream of glottal exit ...... 33

11 Example 1 Pressure distribution displaying absolute pressure drop ...... 42

12 Example 2 Normalized pressure distribution displaying the ratio pressure drop with

respect to tap 16 ...... 36

13 Case I pressure distributions for the minimal nominal diameter 0.005 cm ...... 42

14 Case I normalized pressure distributions for the nominal diameter of 0.005 cm ...... 43

15 Case I pressure distributions for the minimal nominal diameter 0.01 cm ...... 44

16 Case I normalized pressure distributions for the nominal diameter of 0.01 cm ...... 45

17 Case I pressure distributions for the minimal nominal diameter 0.02 cm ...... 46

18 Case I normalized pressure distributions for the nominal diameter of 0.02 cm ...... 47

19 Case I pressure distributions for the minimal nominal diameter 0.04 cm ...... 48

20 Case I normalized pressure distributions for the nominal diameter of 0.04 cm ...... 49 x

21 Case I pressure distributions for the minimal nominal diameter 0.08 cm ...... 50

22 Case I normalized pressure distributions for the nominal diameter of 0.08 cm ...... 51

23 Case I pressure distributions for the minimal nominal diameter 0.16 cm ...... 52

24 Case I normalized pressure distributions for the nominal diameter of 0.16 cm ...... 53

25 Case I pressure distributions for the minimal nominal diameter 0.32 cm ...... 54

26 Case I normalized pressure distributions for the nominal diameter of 0.32 cm ...... 55

27 Case I normalized pressure distribution averaged across transglottal pressure and shown

for each glottal diameter ...... 56

28 Full range of transglottal pressures and flows for Case I...... 62

29 Reynolds number v. transglottal pressure coefficient for all diameters of Case I ..... 63

30 Case II pressure distributions for the minimal nominal diameter 0.005 cm ...... 74

31 Case II normalized pressure distributions for the nominal diameter of 0.005 cm ..... 75

32 Case II pressure distributions for the minimal nominal diameter 0.01 cm ...... 76

33 Case II normalized pressure distributions for the nominal diameter of 0.01 cm ...... 77

34 Case II pressure distributions for the minimal nominal diameter 0.02 cm ...... 78

35 Case II normalized pressure distributions for the nominal diameter of 0.02 cm ...... 79

36 Case II pressure distributions for the minimal nominal diameter 0.04 cm ...... 80

37 Case II normalized pressure distributions for the nominal diameter of 0.04 cm ...... 81

38 Case II pressure distributions for the minimal nominal diameter 0.08 cm ...... 82

39 Case II normalized pressure distributions for the nominal diameter of 0.08 cm ...... 83

40 Case II pressure distributions for the minimal nominal diameter 0.16 cm where the

divergent side is the flow side and the convergent side is the non-flow side ...... 84

41 Case II normalized pressure distributions for the nominal diameter of 0.16 cm where xi

the divergent side is the flow side and the convergent side is the non-flow side ...... 85

42 Case II pressure distributions for the minimal nominal diameter 0.16 cm where the

divergent side is the non-flow side and the convergent side is the flow side ...... 86

43 Case II normalized pressure distributions for the nominal diameter of 0.16 cm where

the divergent side is the non-flow side and the convergent side is the flow side ...... 87

44 Case II percent difference of the flow side versus non-flow side pressure for the

nominal diameter of 0.16 cm ...... 88

45 Case II pressure distributions for the minimal nominal diameter 0.32 cm where the

divergent side is the flow side and the convergent side is the non-flow side ...... 89

46 Case II normalized pressure distributions for the nominal diameter of 0.32 cm where

the divergent side is the flow side and the convergent side is the non-flow side ...... 90

47 Case II pressure distributions for the minimal nominal diameter 0.32 cm where the

divergent side is the non-flow side and the convergent side is the flow side ...... 91

48 Case II normalized pressure distributions for the nominal diameter of 0.32 cm where

the divergent side is the non-flow side and the convergent side is the flow side ...... 92

49 Case II percent difference of the flow side versus non-flow side pressure for the

nominal diameter of 0.32 cm ...... 93

50 Case II normalized pressure distribution averaged across transglottal pressure and shown

for each glottal diameter ...... 94

51 Full range of transglottal pressures and flows for Case I...... 100

52 Reynolds number v. transglottal pressure coefficient for all diameters of Case II .... 101 xii

53 Case I pressure distributions comparison for an oblique and symmetric convergent glottis

with an included angle (IA) of -10o and a minimal diameter of 0.005 cm for the

transglottal pressure of 10 H20 ...... 108

54 Case II pressure distributions comparison for an oblique and symmetric convergent

glottis with an included angle (IA) of -10o and a minimal diameter of 0.005 cm for the

transglottal pressure of 10 H20 ...... 108

55 Case I pressure distributions comparison for an oblique and symmetric convergent glottis

with an included angle (IA) of -10o and a minimal diameter of 0.04 cm for the transglottal

pressure of 10 H20 ...... 109

56 Case II pressure distributions comparison for an oblique and symmetric convergent

glottis with an included angle (IA) of -10o and a minimal diameter of 0.04 cm for the

transglottal pressure of 10 H20 ...... 110

57 Case I convergent glottis, comparison of pressure distributions among the oblique glottis

(0.32 cm) ...... 113

58 Case I convergent glottis, comparison of pressure distributions among the oblique glottis

(0.16 cm) ...... 114

59 Case I convergent glottis, comparison of pressure distributions among the oblique glottis

(0.08 cm) ...... 115

60 Case II convergent glottis, comparison of pressure distributions among the oblique glottis

(0.08 cm) ...... 117

61 Case II convergent glottis, comparison of pressure distributions among the oblique glottis

(0.16 cm, Convergent Vocal Fold is Flow Side) ...... 118 xiii

62 Case II convergent glottis, comparison of pressure distributions among the oblique glottis

(0.16 cm, Divergent Vocal Fold is Flow Side) ...... 119

63 Case II convergent glottis, comparison of pressure distributions among the oblique glottis

(0.32 cm, Convergent Vocal Fold is Flow Side) ...... 120

64 Case II convergent glottis, comparison of pressure distributions among the oblique glottis

(0.32 cm, Divergent Vocal Fold is Flow Side) ...... 121

65 Case I comparison of current empirical data with original M5 data ...... 124

66 Case I comparison of current empirical data with original M5 data ...... 125

xiv

LIST OF TABLES

Table Page

1 Voltage required at each gain setting for the prescribed transglottal pressures ...... 30

2 Calibration equations and ranges for each gain setting of the transducers in use ...... 31

3 Percent pressure drop at Tap 11 relative to transglottal pressure

(convergent vocal fold) ...... 39

4 Standard deviation of the normalized transglottal pressure at each tap of

the divergent vocal fold ...... 57

5 Standard deviation of the normalized transglottal pressure at each tap of

the convergent vocal fold ...... 58

6 Case I flow values when the pressures on the convergent vocal fold were recorded 60

7 Case I flow values when the pressures on the divergent vocal fold were recorded ... 61

8 Regression equations for pressure versus flow across diameters for Case I ...... 62

9 Regression equations for Re versus P* across diameters for Case I ...... 64

10 Percent pressure drop at Tap 7 relative to transglottal pressure for

the convergent vocal fold ...... 67

11 Percent pressure drop at Tap 7 relative to transglottal pressure for

the divergent vocal fold ...... 67

12 Percent pressure drop at Tap 6 relative to transglottal pressure

(convergent vocal fold) ...... 69

13 Percent pressure drop at Tap 6 relative to transglottal pressure

(divergent vocal fold) ...... 70 xv

14 Percent pressures difference relative prescribed transglottal pressure of the divergent and

convergent vocal fold ...... 71

15 Percent drop relative to the transglottal pressure of the first and second local minima for

convergent side ...... 73

16 Percent drop relative to the transglottal pressure of the first and second local minima for

divergent side ...... 73

17 Standard deviation of the normalized transglottal pressure at each tap of

the divergent vocal fold ...... 95

18 Standard deviation of the normalized transglottal pressure at each tap of

the convergent vocal fold ...... 96

19 Case II flows when the pressures on the convergent fold were recorded ...... 98

20 Case II flows when the pressures on the divergent fold were recorded ...... 99

21 Regression equations for pressure versus flow across diameters for Case II ...... 100

22 Regression equations for Re versus P* across diameters for Case I ...... 102

CHAPTER I: INTRODUCTION

Physically, speech is the interaction between moving biological structures and dynamic air pressures and flows that create a temporal sequence of acoustic events. These acoustic events are then interpreted by the listener as a linguistic message. A fundamental component of sound production for the communication process is the voice. Voicing is associated with oscillating

vocal folds, which create a wide range of glottal angles, both symmetric and asymmetric. This

thesis examines pressures and flows of two different snapshots of asymmetric voicing.

Basic Overview of Phonation for Voice and Speech

The larynx, a structure that is positioned atop the trachea, contains various cartilages, one

bone, a matrix of connective tissue, and the paired vocal folds. The three dimensional space

between the vocal folds is termed the glottis and contains two main portions. The anterior or

membranous glottis extends from the anterior commissure, where the two vocal folds meet tissue

entering the posterior lamina of the thyroid cartilage, to the vocal processes of the arytenoid

cartilages. The posterior or cartilaginous glottis is defined as the airway that lies between the two

arytenoid cartilages at the level of the membranous glottis; it extends to the posterior mucosal

membrane. The membranous glottis will be the focus of this discussion as it relates to the

oscillation of the vocal folds.

The vocal folds oscillate due to a number of synchronized physical and biological

interactions. The parameters that are involved in these interactions include the mechanical

properties of the vocal fold tissue, the configuration of the glottis, and the aerodynamic pressures

that communicate forces that act to displace the vocal folds. From a physical view point, the

vocal fold tissue in oscillation is dictated primarily by the passive tensions of the mucous

membranes and active tension of the vocalis muscles, as well as the distributed tissue masses, 2 damping characteristics, and vocal fold length. The glottal configuration refers to the geometrical arrangement of the glottis before and during phonation. This depends on the position of the vocal

processes (adduction), the anterior-posterior length of the glottis, the inferior-superior thickness

of the glottis, the medial vocal fold contour, and symmetry of the glottal walls. Air pressures are

generated by creating a pressure difference across the glottis by volume change of the respiratory

system. To create phonation, the vocal folds are positioned medially, narrowing the air space

enough to allow an interaction between the air pressure in the trachea and the surfaces of the

vocal fold tissue to set the elastic tissue of the vocal folds into quasi-periodic oscillation (Titze,

2000; Scherer, 1995).

Vocal fold motion and glottal geometries.

When the vocal folds are placed within the phonatory adductory range (Scherer, 1995)

and positive air pressure is generated in the lungs by a decrement in the volume of the respiratory

system, the air pressure created in the region just below the glottis communicates a force to the

surface of the vocal folds. If this pressure is at or above the phonation threshold pressure, the

tissue is set into quasi-periodic, sustained oscillation (Titze, 2000). The pressure difference

between the trachea and the superior vocal tract drives flow through the glottis.

As observed by Hirano’s stroboscopic observations (1981), the glottis may take on a

variety of glottal shapes and angles during phonation. During a cycle of phonation the lower

margin of the glottis leads the upper margin, first laterally then medially, resulting in a changing

sequence of the glottal wall angle from convergence to divergence, as seen in Figure 1. The

phonatory cycle includes glottal opening, glottal closing, and the most closed portion of the cycle

when present (Figure 1). These changing glottal shapes are repeated from cycle to cycle and create distinct portions of the cycle that can be defined by instantaneous angles created by the 3 two vocal fold medial surfaces. Prior research suggests that these glottal shapes result from the transfer of energy from the airstream to the vocal folds and vice versa (Titze, 1988). The vertical phase difference throughout the cycle has been called the mucosal wave. The mucosal wave more specifically refers to the wave-like motion of the vocal fold tissue that propagates during the cycle and results from the interaction of the tissue, the initial glottal configuration, and the

aerodynamic forces acting on the tissue (Titze, 2000).

According to Scherer, De Witt, and Kucinschi (2001), the pressures in the glottis during

opening, when the glottal angle is convergent, are relatively positive. When the glottis is closing,

the pressures in the glottis are primarily negative, due to the Bernoulli Effect and negative

(rarefaction) pressure above the folds (Titze, 1988), and shown to be negative in empirical

studies (Binh and Gauffin, 1983; Scherer, Titze, and Curtis, 1983; Scherer, Shinwari, DeWitt,

Zhang, Kucinschi, and Afjeh, 2001). The synergy of the recoil forces of the vocal fold tissue

during motion and the geometry-depended intraglottal pressures results in an in-phase force that creates the sustained vibration of the vocal folds. This oscillation valves the air flow through the glottis. The changing glottal flow creates an acoustic excitation that is propagated through the

superior vocal tract. Various characteristics of the changing glottal airflow waveform relate to

the source acoustic and thus perceptually to aspects of pitch, loudness, and voice quality.

Clinical observations.

In his book Clinical Examination of Voice, Hirano (1981) provided one of the first

overviews of clinical instrumentation for the evaluation of voice, including visualization of the

vocal folds from above using videostroboscoy. Videostroboscoy captures the image of the vocal

folds during phonation at adjacent portions of each vibratory cycle to create a slow-motion visual

image. Included in the recommended observational criteria for clinical voice assessment is the 4 dynamic symmetry of the vocal folds during phonation. Hirano noted that if there were differences in the biomechanical properties of the two vocal folds (such as mass, stiffness, relative position, viscosity, and shape), the vibratory motion might be asymmetrical (Hirano,

1981, p.52). While the vocal folds move in a rather symmetric motion relative to each other during normal phonation (as shown in Figure 1), asymmetries of motion of the two folds across midline have been observed through visual evaluation of the larynx in pathological (Svec, Sram, and Schutte, 2007) and normal phonation (Shaw & Deliyski, 2006; Bonilha, Deliyski, and

Gerlach, 2008; Haben, Kost, andPapagiannis,2003).

end of glottal closing

glottal opening

closed glottis

glottal closing

Figure 1. A normal cycle of vocal fold vibration viewed in the mid-coronal plane. The vocal

folds separate (forming a convergent glottal shape) and later move toward each other (forming a

divergent glottal shape) with the inferior vibratory margin leading the superior vibratory margin

(after Hirano, M. Clinical Examination of Voice. 1981, Springer-Verlag). 5

Hirano and Bless (1993) discussed how small asymmetries relative to the amplitude and phase of each vocal fold was a common clinical finding when visualizing the motion of the vocal folds with videostroboscoy. Moreover, the authors state that because asymmetries may result from differences in morphological characteristics between the two vocal folds, asymmetric motion may be diagnostically telling (Hirano & Bless, 1993). Valid stroboscopic visualization of asymmetric cycles requires that the asymmetric motion from cycle to cycle be consistent, however; otherwise the stroboscopic method leads to inaccurate images. High speed imaging is

preferred when needing to visualize asymmetric motions.

The glottal asymmetries most relevant to this thesis are left-right asymmetries rather than

anterior-posterior asymmetries. The left-right asymmetries have been most commonly discussed

in regards to (1) differences in the medio-lateral excursion of the vocal folds from midline during

a cycle of vibration (Svec et al., 2007; Bonilha et al., 2008; Mehta, Deliyski, Zeitels, Quatieri,

and Hillman, 2010), (2) across midline differences in the vertical (inferior-superior) angle of each glottal wall (Svec et al., 2007; Bonilha et al., 2008; Mehta et al., 2010), (3) shift in the axis of glottal symmetry during closing (Svec et al., 2007; Mehta et al., 2010), (4) the speed of closure of each vocal fold (Hetegard, Larsson, and Wittenberg, 2003), and (5) differences in the frequency at which each fold is vibrating across cycles (Svec et al., 2007). Svec et al. (2007) provided a relatively comprehensive categorization of left-right asymmetries examining amplitude asymmetry, phase asymmetry, the shift of the glottal axis at closing, and frequency differences between the two vocal folds as observed by videokymography in a number of patients with voice disorders. 6

With more recent developments of digital kymography (DKG) and high speed videoendoscopy (HSV), visualization of the vibratory movement of the vocal folds during the entire cycle of vibration can be achieved. The use of high-speed laryngeal imaging has also shown asymmetry of motion of the two folds during normal phonation (Shaw & Deliyski, 2006;

Bonilha et al., 2008). Using a variety of laryngeal visualization techniques, Shaw & Deliyski

(2006) observed an atypical symmetry relative to phase and magnitude of the mucosal wave motion of the right and left vocal fold surfaces for individuals without vocal pathologies. Using

HSV Metha, Deliyski, Quatieri, and Hillman (2011) developed an automated process for extracting various parameters for the objective evaluation of glottal asymmetry including phase and amplitude asymmetry as well as degree of axial shift during closing. HSV asymmetric measures were extracted for 52 different participants without a history of voice or speech problems. Phase asymmetry was computed as the difference in the frame index when each vocal fold reached maximum lateral displacement relative to the number of frames in the period. The authors found a normal distribution of prevalence for phase asymmetry ratio ranging from 0.13%

to 22.20% and 0.00% to 20.2% in normal and pressed phonation, respectively. The mean phase

asymmetry ratio was 5.40 (4.63) % for pressed and 6.27 (4.33) % for normal phonation Thesis

results suggest that left-right asymmetries in individuals with no current or history of voice

problems experience left-right vocal fold wall asymmetry. The causes of these asymmetries have

been explored empirically and theoretically and various parameters have been proposed to

influence asymmetries in vocal fold vibration including differences in mass and stiffness

between the two vocal folds (Steinecke and Herzel, 1995), subglottal pressure (Berry, Herzel,

Titze, and Story, 1996), daily vocal load (Doellinger, Lohscheller, McWhorter, and Melda, 7

2009), and non-linear source-filter interaction (Zanartu, Mehta, Ho, Wodicka, and Hillman,

2011).

Large differences in the phase angles of each vocal fold may be diagnostically predictive

of various pathologic conditions including vocal fold mass lesions, paralysis (Sercarz, Berke,

Gerratt, Ming, and Natividad, 1992), and other voice disorders. While studies have observed a

relation between perceptual measures of deviant sound qualities and vocal fold phase asymmetry

when comparing individuals with and without voice disorders (Verdonck-de Leeuw et al., 2001),

direct relation between phase asymmetry and various acoustic measures has been limited. In a

study by Mehta et al. (2010)of 14 voice patients who had undergone phonosurgery for early

glottic cancer, the degree to which phase asymmetries related to clinical acoustic measures

including noise to harmonic ratio, jitter, and shimmer were determined. In that study the acoustic

analyses were compared to a variety of measures quantifying asymmetric vocal fold motion that

were obtained using HSV. An increase in jitter was observed but was accounted for by the

variability of the magnitude of asymmetry across a number of vibratory cycles. In a study by

Bonilha et al. (2008) of 52 speakers without a history of voice problems, the authors reported

left-right phase asymmetries in 79 percent for both pressed and normal phonation. In that study

three different raters rated samples that were obtained using a variety of laryngeal visualization

techniques. For all three raters, the stroboscopic recordings were judged to be asymmetric less

frequently than HSV, digital kymography (DKG), mucosal wave kymography (MKG), and

medial digital kymography (mDKG). In general, asymmetries were judged to be mild using a

visual-perceptual scale. It was also reported that the frequency of left-right asymmetry was

decreased for pressed phonation when compared to normal. The objective measures of left-right

asymmetry were similar to those of the raters for left-right asymmetries ranging from 0 percent 8 to 20 percent. The strongest correlations between the visual-perceptual ratings and objective measures were for HSV (.47-.71), DKG (.26-.76), and mDKG (.40-.70).

As indicated above, the occurrence of phase asymmetries in both normal and disordered phonation is common. Asymmetric glottal shapes are known to produce different pressure on the right and left vocal folds (Scherer et al., 2001b), but only a small number of asymmetric cases have been studied, and there is insufficient information to determine how the asymmetric forces affect vocal fold oscillation. This thesis explores the differences in aerodynamic forces acting upon two asymmetric glottal configurations to better understand the aerodynamic aspect of glottal asymmetry and add insight into practical applications of aerodynamic computational modeling of vocal fold motion.

Glottal obliquity.

As discussed above, glottal asymmetry broadly defined indicates some lack of symmetry in the glottal configuration across midline or axis of symmetry. Here glottal obliquity refers to the vertical “slant” of the glottal midline and will be defined by a calculated difference in the angles of each glottal wall relative to a vertical (inferior to superior) midline axis (Scherer et al.,

2001). The Plexiglas Model M5 can accommodate both symmetric and asymmetric, specifically

oblique, glottal geometries for a range of glottal angles and diameters. When the vocal fold

inserts have the same angle, the pressure distributions model those of the normal symmetric

glottis. However, the current investigation will use right-left vocal fold pieces that have different

angles. As a result, the glottal axis deviates from the vertical, laryngeal midline, allowing the

study of pressure distributions of asymmetric glottal geometries similar to those observed in both

normal and pathological conditions in the larynx. The degree of obliquity is then considered the

degree to which the mid-axis between the two folds deviates from the vertical axis. In this study, 9

we have define glottal obliquity as, OA=(aL-aR)/2, where OA is the oblique angle, aL is the angle

of the left glottal wall, and aR is the angel of the right glottal wall. It is important to note that

divergent angles are designated as positive angles and convergent angles as negative.

Overview of the Literature

The current project examines the intraglottal pressures for two cases of glottal obliquity,

each for a wide range of glottal diameters. A Plexiglas model, M5, of the vocal folds is used to

mimic the human larynx to obtain these pressures empirically. The model has vocal fold inserts

that are scaled 7.5 times larger than for a typical male. The vocal folds are placed within a wind tunnel and airflow is pulled through the model. M5 is a static, non-vibrating, constant flow model used to study aerodynamic pressures on the two vocal folds at various flow rates and

minimal glottal diameters. Constant flow modeling of the dynamic process of phonation is

supported by the quasi-steady approximation (McGowan, 1993). The quasi-steady assumption

states that continually time-varying aerodynamic oscillatory processes, such as phonation, can be

aerodynamically modeled in succession as discrete static geometries. Recent experimental

investigations have supported the quasi-steady assumption (Zhang, Mongeau, and Frankel, 2002;

Vilain, Pelorson, Fraysse, Deverge, Hirschberg, and Willems, 2003; Park and Mongeau, 2007).

Park and Mongeau (2007) found this assumption to be reasonably valid for 70% of the glottal

cycle, with discrepancy when the diameters were smallest during the cycle (i.e. at opening and

near closing).

Numerous investigations have examined empirical pressure distributions of static glottal-

shaped orifices using constant flow (van den Berg et al., 1957; Ishizaka and Matsudaira, 1972;

Scherer, et al., 1983; Binh and Gauffin, 1983; Scherer, Shinwari, DeWitt, Zhang, Kucinschi, and

Afjeh, 2001; Scherer, De Witt, and Kucinschi, 2001; Scherer, Shinwari, De Witt, Zhang, 10

Kucinschi, and Afjeh, 2002; Shinwari, Scherer, DeWitt, and Afjeh, 2003). Previous research has examined a series of vocal fold configurations including diverging (Scherer et al., 2001a) and

converging (Scherer et al., 2001b) glottal shapes, and uniform glottal shapes(van den Berg et al.,

1957; Scherer et al., 1983; Scherer et al., 2002), and symmetric and oblique glottal angles

(Scherer et al., 1983; Scherer et al., 2001a; Scherer et al., 2001b, Scherer et al., 2002), and

special cases of obliquity relating specifically to the hemilarynx (Alipour, and Scherer, 2002;

Fulcher, Scherer, De Witt, Thapa, Bo, and Kucinschi, 2010).

Many of the early studies assumed unidirectional flow exiting the glottis, thus

overlooking more complex flow behavior in the glottis (van den Berg et al., 1957; Ishizaka and

Matsudaira, 1972; Scherer et al., 1983; Binh and Gauffin, 1983). These studies assumed equal

pressure on both vocal folds and reported pressure distributions accordingly. For many glottal

geometries however, a bistability of the flow takes place when the flow separates from one vocal

fold wall, the “non-flow wall,” and remains attached to the other, “flow wall.” Erath and colleagues have examined asymmetric flow jets in both symmetric and asymmetric glottal- shaped orifices using pulsating flow and PIV imaging techniques in static models (Erath and

Plesniak, 2006a; Erath and Plesniak, 2006b) and driven models of the vocal folds (Erath and

Plesniak, 2009; Erath and Plesniak, 2010). These recent investigations, along with preliminary studies such as Shinwari et al. (2003), show that there is a rather complex pattern of the flow exiting the glottis. The pressures on the two vocal folds tend to differ (Scherer et al., 2001a;

Shinwari et al., 2003). The pressure on the flow wall tends to be lower than the non-flow wall

(Scherer et al., 2001a; Shinwari et al., 2003). In addition, bimodal pressure distributions on the flow wall side in the divergent symmetric configuration have been observed (Scherer, 2011).

From the findings of Erath and Plesniak (2006a) it seems flow exiting the asymmetric divergent 11 glottis is more likely to attach to the vocal fold wall with the lesser divergent angle. Investigation into other aspects of glottal aerodynamics such as separation point in the glottis has been studied

using static models.

Effect of diameter.

Previous research commonly examined glottal aerodynamics in models with a glottal

width of 0.04 cm. Exceptions are Alipour and Scherer (2002), who also included 0.08 and 0.16 cm, and Scherer et al., (1983) who included data for a uniform glottis with a minimal diameter of

0.104 and 0.1575 cm. In the study of the hemilarynx model, Lewis et al. (2010) included

symmetric M5 data for the minimal glottal diameters 0.04 and 0.08 cm. Symmetric glottal

configurations for M5 have been completed for numerous diameters ranging from 0.005 to 0.32 cm (Scherer, 2011). In general, as diameter decreases the pressures in the convergent glottis

decline more rapidly in the axial direction, with higher pressures upstream of the minimal glottal

width when the diameter is small. The declination in the pressure distribution contour occurs at a

more upstream location in the axial direction as diameter increases. For the largest diameter

studied, 0.32 cm, the pressure distributions of the divergent glottis closely resembles the uniform glottis rather than a diffuser.

Empirical pressures for three cases of obliquity are reported in a recent unpublished thesis by Li (2010) that also include these diameters. In an investigation of the oblique glottis, Li

(2010) examined intraglottal pressure of three oblique glottal configurations including a convergent and divergent oblique glottis using M5. For the -15o convergent glottis with an

obliquity of 2.5o, decreasing the glottal diameter resulted in increased intraglottal pressures as

well as increased pressures on the inferior surface of the vocal folds. For the 12.5o divergent

glottis with an obliquity of 3.75o, decreasing the glottal diameter resulted in increased pressure 12 on the inferior surface of the vocal folds. However, the pressures in the glottis did not increase as diameter decreased.

Effect of glottal angle.

General findings suggest that the pressure acting on the vocal folds within the glottis are higher on the convergent side than the divergent side for both the symmetric and asymmetric, or oblique, configurations. Thus, the vertical angle of the vocal fold wall has an effect on the pressures acting on the folds. For the symmetric case the pressure in the convergent glottis is

higher than the pressure when the glottis is divergent, as the largest pressure drop is near the minimal glottal diameter near glottal exit (Scherer et al., 2001b). Therefore, pressures in the convergent glottis are relatively positive with respect to supraglottal pressure. Pressures in the divergent glottis are negative and recover to atmospheric pressure between the minimal glottal

width to glottal exit. In the study of the hemilarynx model, Fulcher et al. (2010) included

symmetric M5 data across numerous convergent and divergent glottal angles. As the

convergences increased, the surface pressures in the upstream half of the glottis were higher

(Fulcher et al., 2010; Scherer, 2011). For the divergent glottis, the pressure recovery occurred

over less axial distance the greater the divergence (Fulcher et al., 2010; Scherer, 2011).

Effect of obliquity.

Likewise, relative to oblique glottis data, if there is a convergent and divergent fold

present geometrically, the pressure on the convergent fold is higher than the divergent fold

(Scherer et al., 2001; Scherer et al., 2002; Shinwari et al., 2003). This is especially meaningful at

the glottal entrance where the divergent fold is acted upon by a lower pressure than the

convergent fold which experiences a more positive pressure, thus driving each fold differently at

glottal entrance. These investigations reported cross channel differences as large as 27% in the 13 oblique divergent glottis and 21% in the oblique uniform glottis with a minimal diameter of 0.04 cm (Scherer et al. 2001; Scherer et al. 2002; Shinwari et al., 2003). Li (2010) observed the effect

of obliquity was related to diameter for the convergent glottis. For the smallest diameter, 0.005

cm and diameters larger than and including 0.04 cm, the pressure distributions were relatively

similar to the symmetric glottis, with differences less than 10% within the glottis. The author

concluded there was little effect of obliquity for the diameters of 0.005, 0.04, 0.08, 0.16, and

0.32 cm of the -15o convergent glottis with an obliquity of 2.5o. For the diameters of 0.01 and

0.02 cm, the pressures in the first half of the axial glottis were 12 to 16% higher than the symmetric glottis. For the divergent oblique glottis studied, the author reported little effect of obliquity as the symmetric and oblique pressure did not vary greatly (Li, 2010).

The Overview of the Current Study

This work serves to add to the current understanding of the aerodynamic effects of glottal obliquity, give practical insight into the nature of glottal obliquity, and provide empirical evidence that can be implemented in multimass computer models to further understand the mechanical significance of how the pressures acting on the oblique glottal geometry interact with dynamic tissue characteristics in the process of phonation. The current degrees of obliquity are not unrealistic in human phonation (Metha et al., 2011).

The present study will examine the pressure distributions for two cases of obliquity, one for a +10o divergent glottis, and the other for a -10o convergent glottis. Both cases have an

obliquity angle of 15o and are further discussed in Chapter 2. A special aspect of the study is the

use of numerous glottal diameters and transglottal pressures for each case. These diameters are

comparable to those studied in the literature (Fulcher et al., 2010; van den Berg et al., 1957; Li,

2010). Relative recent studies using advanced imaging techniques with calibrated distance 14 measures, these diameters appear to be within a reasonable range expected for the vibrational amplitude of the vocal folds (George, de Mul, Qiu, Rakhorst & Schutte, 2008; Popolo and Titze,

2008). This study then extends our information of driving pressures for the rather ubiquitous slanted larynx, and leads to a more complete implementation of empirical pressures with multimass models of simulated phonation.

CHAPTER II: METHODS

Glottal Configurations for the Current Study

The present study of pressure distributions along the mid-membranous vocal folds is

restricted to two cases of glottal angle, one convergent, one divergent, both having an oblique

angle (OA) of 15o. The angle between the two vocal folds, or included angle (IA), is defined as,

IA= aL + aR, where aL and aR are the angles the left and right medial surfaces make with the

vertical, midsagittal plane. The IA for the Case I is -10o convergent (shown in Figure 2 the minus

sign mean “divergent”). The Case II is a glottal duct with an IA of +10o divergent (shown in

Figure 3; the plus sign mean “divergent”). The diameters are a standard set chosen for other

studies, that is, 0.005, 0.01, 0.02, 0.04, 0.08, 0.16, and 0.32 cm. For diameters less than and including 0.04 cm, pressure distributions are recorded for transglottal pressures of 3, 5, 10, 15,

25, 50, and 75 cm H2O. For the diameter of 0.08 cm, the transglottal pressures studied were 3, 5,

10, 15, 25 and 50 cm H2O. For the diameter of 0.16 cm, the transglottal pressures of 3, 5, 8, 10,

and 15 cm H2O were studied. For the largest diameter (0.32 cm), the transglottal pressures

studied were 1, 3, 5, 8, and 10 cm H2O.

Figure 2. Case I: Convergent glottis of -10o with an oblique angle of 15o

Figure 3. Case II: Divergent glottis of +10o with an oblique angle of 15o

The M5 Model

The M5 experimental setup is comprised of several Plexiglas slabs, two removable vocal

fold pieces with 14 pressure taps on one side (left), a Scanivalve pressure scanner (Model

W0602/IP-24T), and a Validyne pressure transducer (DP-103), as shown in Figure 4. Figure 5 is a schematic of the set up and includes the dimensions of the wind tunnel. The upstream channel

(right side of Figure 5) is 15 cm in width and is open to atmospheric pressure. Downstream of

the glottal duct, a smaller opening 2.3 cm in width is connected to a vacuum source (Model

S14CL) that when turned on creates negative relative pressure that pulls air through the model.

The vocal fold insert on the left, as shown in Figure 4, contains a series of 14 pressure taps. The

14 pressure taps located on the left vocal fold insert, shown in Figure 6, were drilled

perpendicular to the surface of the vocal fold, and are used to measure the pressure normal (i.e.

perpendicular) to the vocal fold at specific locations.

Shim

Pressure Scanner

Pressure

Transducer Vocal folds inserts

Figure 4. Model M5 and its components 18

13 cm

81.5 cm

2.3 15 cm cm

T (0) T (16) T (15) 33.5 cm

43.5 cm 65.5 cm

Figure 5. Schematic diagram of M5 (after Scherer et al., 2001).

Taps 1 to 5 are located on the inferior vocal fold surface, tap 6 is located at the entrance

of the glottal duct and, taps 7 to 11 on the medial (straight) surface of the vocal fold. Tap 12 is on the exit rounding, tap 13 at the exit on the horizontal surface of the fold near the glottal exit

proper, and tap 14 near tap 13 but more distant from the glottal exit. Tap 0 is located just upstream of the vocal fold pieces and provides the reference pressure at the subglottal section, as

seen in Figure 5. Figure 5 also shows the locations of taps 15 and 16 downstream in the wind tunnel. Constant flow (the value of which depends primarily on the transglottal pressure and

glottal diameter) is pulled through the wind tunnel. The data measured at each of the 16 taps 19 create the pressure distributions that are the main focus of this research. The axial length of the glottal duct (tap 6 to the horizontal locations of taps 13 and 14) is 0.3 cm in real life.

A series of Plexiglas shims are available to vary the glottal diameter. The shim of appropriate thickness was placed in the wind tunnel between the vocal fold without the pressure taps (right side) and the wall of the tunnel as shown in Figures 4 and 5.

Figure 6. Locations of the pressure taps on a vocal fold piece (Scherer et al., 2001).

Setting Up the Model for Data Collection

First the top of the wind tunnel is removed by unscrewing the bolts that secure the top to

the model. The top is then placed on a soft towel or bubble sheet with the screws lined up with

their respective holes to reduce any change to the internal threads. The left vocal fold piece with

the desired angle is placed into the tunnel. The appropriate shim and the desired right vocal fold

piece are then placed in the wind tunnel and lightly secured to the right side of the wind tunnel as

shown in Figure 4. For the largest diameter (0.32 cm), no shim is required and the right vocal

fold is attached directly to the right wall of the wind tunnel. Plastic tubing is then connected to

the respective pressure ports on the left vocal fold piece. These ports and associated taps and ports are displayed in Figure 7. After the tubing is connected, the labeled locations of the tubes

are verified to insure that the numbers on each port correspond to the correct tube leading to the

pressure scanner. Once the tubing is connected and the connections are verified, the left and the

right vocal folds are secured to the respective wall of the wind tunnel by screws on each side.

Each screw is tightened but can be further adjusted to guarantee the correct minimal glottal

diameter.

The top of the wind tunnel is then secured to the model by tightening the screws with the

fingers. An electric screwdriver is then used to finish tightening the screws. When replacing the

top of the model, the pair of screws located adjacently across the duct is tightened first. This

process starts in the middle, nearest the location of the vocal fold inserts and continues outward,

to the ends of the model. This procedure is used to minimize undue stress on the top and thus

prevent any distortion of the shape of the lid as well as even pressure on the vocal fold inserts.

Once all 12 screws are secured, the model assembly is complete. 21

Figure 7. Pressure taps on the vocal fold inserts. Top: The medial wall of the left vocal fold

insert with 14 pressure taps. Bottom: The reverse side of the left vocal fold piece displaying the

pressure tap ports.

During the experimental runs for Case II, a microphone windscreen, modified to fit on the wall, was secured over tap 16 to decrease the effect of flow patterns local to that tap in the wind tunnel. Previous experiments had shown a more negative pressure at 16 when the flow exits the glottis toward the left downstream wall, changing the pressure at tap 16.

When model M5 is properly assembled, the minimal diameter of the glottal duct, formed by the two vocal fold inserts, is measured at four vertical locations along the anterior-posterior

glottal duct to obtain an average, diameter measure. A stack of feeler gauges that sums to a

height that is closest to the desired diameter is constructed. Careful conversion is performed prior

to measurement as the feeler gauges are measured in inches and the desired glottal diameter is

measured in cm. For example, if the desired diameter is 0.04 cm, one takes into consideration the

scaling factor (7.5) and the unit conversion factor so that (0.04 cm * 7.5) / 2.54 cm = 0.1181 in.

The feeler gauge configuration is inserted into the space between the two vocal folds, by passing

the operator’s arm into the upstream portion of the wind tunnel. The four measured locations

must be relatively close as the anterior-posterior dimension of the glottal duct should be uniform.

Position 1 is near the bottom of the glottal duct and position 4 near the top of the glottal duct.

The screws securing the vocal fold inserts to the wind tunnel wall can be turned to make minor

adjustments to the minimal glottal diameter. Once satisfied with the fit of the feeler gauge

configuration at the smallest separation between the vocal folds, the four values are recorded and

averaged. If the diameter is not measured to be within 1% of the desired minimal glottal diameter, adjustments are made. If the adjustments are small, the screws securing the vocal fold pieces to the wall of the wind tunnel may be adjusted. However, if this adjustment is not sufficient, the top of the wind tunnel must again be removed to adjust the location of the right vocal fold by securing additional feeler gauges between the large shim and the right wall of the 23 wind tunnel with thin tape. The top of the wind tunnel is then replaced following the above procedures. If the correct minimal diameter was measured after placing additional feeler gauges

between the shim and the right wall of the wind tunnel, scotch tape is placed on the upstream

edge of the shim and the wind tunnel entrance to seal the space created by the additional feeler

gauges.

Measurement of Flow

Figure 8 provides a schematic representation of the experimental setup used during data

collection. During an experimental run, the airflow is created by a vacuum sweeper source so

that the air travels through the wind tunnel and is measured by a downstream pneumotach (Hans

Rudolph Inc. 4700 Series & Model 4813) connected to a Validyne differential pressure

transducer (MP45-16). The pneumotach has a series of screens that act as a resistor to the flow

through the connected system. The high and low side of the pneumotach are connected,

respectively, to the pressure transducer via flexible rubber tubing. When operating within the linear range, the pressure transducer outputs a voltage that is directly proportional to the pressure drop across the pneumotach. The pressure drop across the pneumotach is directly proportional to the flow through the pneumotach if the pneumotach is operating in the linear range. Thus, the

voltage output of the pressure transducer connected to the pneumotach is directly proportional to the flow through the pneumotach.

Prior to an experimental run the pneumotach is calibrated and a voltage-flow coefficient

is calculated for the experiment. The wire mesh of the pneumotach collects particulates in the air

over time due to the airflow through it. Thus, the pneumotach is removed from the system and cleaned with alcohol to remove the particulates that have collected on the screen. 24

A flowmeter (Gilmont #5), in line with connecting tubes, is mounted on a thin vertical board, as shown in Figure 9. The flowmeter contains a small steel ball that lies at the bottom when no flow is pulled through the system. Once acted upon by the resulting forces generated by the vacuum source that create flow through the system, the ball rises to a height relative to the pressure drop across the ball or the flow in the tube. The flowmeter has ball-height markings that are used to specify the flow rate through the flowmeter by using the manufacture’s calibration details for the flowmeter.

M5 Model

Pressure Scanner Air

Pn PT Signal Conditioner PT V

Wet/Dry Vac. DM

Figure 8. Schematic representation of the setup for model M5 (From: Scherer et al., 2001). 25

Relief valve

Regulating valve

Flow meter

Vacuum

Figure 9. Mounted flowmeter configuration

Calibration Procedures

A series of calibrations are made over the course of the experimental runs. These include

the regular calibration of the pneumotach as the flow-voltage coefficient changes over time, as

discussed above, and calibration of the pressure transducers currently in use. Prior to any of the

experimental runs for this thesis, the Validyne DP-103 differential pressure transducer and the

Validyne MP45-16 differential pressure transducer were calibrated (see below). The DP-103

differential pressure transducer is used to measure the pressure difference between the referential

upstream pressure (tap 0) and each tap along the left vocal fold inserts. The MP45-16 differential

pressure transducer is used to measure the pressure drop across the pneumotach when measuring

the volume flow.

Calibration of the pressure transducers.

Prior to the experimental run, the DP-103 differential pressure transducer and the MP45-

16 were recalibrated using a Dwyer micromanometer (Model 1430). An air-tight tubing system was arranged using rubber tubing that was connected from the pressure transducer to the high side of the Dwyer micromanometer. The recalibration was performed for both the high and low side of the pressure transducer. When calibrating the positive pressure, the negative side was left open to atmospheric pressure, and vice versa. The voltage of the pressure transducers were zeroed and recorded with the relief valve open to atmospheric pressure prior to calibration.

Once the apparatus containing the closed tubing system with relief was properly connected to the high side of the micromanometer and to the pressure transducer, a data sheet was used to record the ambient conditions including the operator’s name, time, date, temperature, barometric pressure, and relative humidity. The zeroed voltage was recorded while the relief valve was open to atmospheric pressure. The Dwyer micromanometer contains a cylindrical barrel that when turned clockwise descends into a column filled with water. The barrel’s full extension is equivalent to one inch of water and is divided into 1000 units. When the point of the descending barrel touches the surface of the column of water, an electrical circuit is closed and the needle of an ampere meter on the micromanometer jumps, and the height of the column of water is obtained so that the pressure reading can be determined. The reading is accurate within 0.00025 in (0.000635 cm) of water (estimates within a unit can be read), reflecting an accuracy sufficient for the calibration purposes here. When the tubing system is open to atmospheric pressure, the zero value of the relative height of the micromanometer barrel is recorded to later calculate the height difference that is proportional to the differential pressure. 27

Once the zero values are recorded, the relief valve is closed and constant pressure is applied to the system by using a number of vice grip wrenches (applied to the flexible tubing) to decrease the volume of the system, thereby increasing the air pressure. The operator slowly turns the barrel of the micromanometer and watches the ampere meter until the tip of the measurement device closes the circuit as it touches the meniscus of the water column. Once the approximate value is found, the operator rotates the barrel counterclockwise to open the circuit. The operator again slowly lowers the measurement device by rotating the barrel clockwise and presses the

HOLD button on the multimeter displaying the voltage reading from the pressure transducer at the moment the circuit is closed. The value on the barrel and voltage are recorded. This procedure is repeated a number of times at various pressures to obtain enough data to determine the extension of the linear range of the transducer. The values are then used to generate a best-fit linear equation that is the calibration of the transducer for that gain setting. This procedure is repeated for all gain settings of the Validyne pressure transducer. The results of the calibration will be reported in Appendix A.

Calibration of the pneumotach with the flowmeter.

To calibrate the pneumotach, the tubing downstream of the Plexiglas model containing

the inline pneumotach is detached from the wind tunnel and the exit side of the pneumotach is connected to tubing leading to the flowmeter configuration as shown in Figure 9. The

pneumotach and flowmeter are now inline with each other. The rubber tube connecting the

system has enough flexibility to bend gradually to promote laminar flow between the

pneumotach and the flow meter. The joints of the tubing are sealed with duct tape to ensure no

air escapes the system. The vacuum source is then connected to the downstream side of the 28 tubing on the board, as shown on the lower right of Figure 9. The relief valve is left open and the regulating valve on the board is closed.

Once the apparatus is connected, a data sheet is used to record the current calibration details. Recorded are the ambient conditions of the lab such as the time, date, temperature, barometric pressure, and relative humidity. The model and serial numbers of the lab equipment in use are also recorded. The voltage from the MP45-16 is zeroed and recorded while there is no flow through the system. Small relief valves of the tubing connecting the pressure transducer to the pneumotach are left open to atmospheric pressure. These small valves are then closed and the vacuum source is turned on. The regulating valve shown in Figure 9 along with the variable

control on the vacuum source, are used to vary the flow during the calibration. Ten equidistant data points are obtained that reveal the relationship of flow relative to the ball height of the flowmeter and the corresponding voltage; these data are monotonic with the pressure drop across the pneumotach and are used to generate a calibration equation that gives the voltage-flow relationship.

Data Collection with Model M5

Once the current calibration of the pneumotach is found and the experimental setup of the

model is complete, the operator is ready for data collection. First, the wind tunnel is reconnected

to the tubing, as shown in Figure 8. The operator uses a data sheet containing geometric parameters of the vocal fold pieces (the chosen angles of the vocal fold inserts and the minimal

diameter) and the expected pressure. The operator then sets the appropriate gain on the Validyne

signal conditioner based on the prescribed transglottal pressure. In most instances, a larger transglottal pressure and higher flow will require a larger gross gain value on the amplifier

(signal conditioner). The gain is a parameter relates the value of the transglottal pressure to the 29 flow rate using the appropriate calibration equations. The no-pressure, no-flow voltages of the

DP-103 and MP45-16 multimeters are then zeroed by adjustment of the resistance of the signal

conditioners. The zeroed values are recorded with the entire system open to atmospheric pressure. The data sheet allowed for the recording of all information for the experimental run,

that is, the nominal transglottal pressure, the gain of the signal conditioner for both pressure

transducers, the ambient conditions of the lab, and the voltages associated with the pressures at

each tap location.

Table 1 was generated using the calibration equation for the DP-103 for reference when

recording and setting the transglottal pressure. This table displays the various nominal

transglottal pressures used in this study and their relationship to the corresponding voltages

required at each gain setting. Table 2 includes an overview of the calibration equations in use for

each of the pressure transducers that were used in this study. The information that has been

obtained from the above calibrations of the pneumotach is used to calculate the volume velocity

in cc/s after the run from an (average visual) voltage (see below) recorded during the run.

Once the experimental apparatus is set up and all information is recorded, the vacuum

source is slowly turned on and adjusted until the voltage expected for the given transglottal

pressure value is reached on the DP-103 meter. As clarification, the transglottal pressure is set as the difference between the referential upstream tap (tap 0) and tap 16. Once the desired transglottal pressure is set, the operator simultaneously presses HOLD on both multimeters, and records the voltage value from the MP45-16 that corresponds to the flow through the

pneumotach, and the voltage value from the DP-103 corresponding to the pressure at the tap

being measured. Four independent measures are taken as small fluctuations in the voltage occur.

Each of the four reading is taken after an interval of 60 seconds, typically. These small 30 fluctuations of the pressures and airflows, due to the complexity of the setup and inevitable unsteadiness of the flow (even when “constant”), are expected during experimental runs. In order

to allow for such changes, 4 voltage values are recorded for each of the 16 pressure taps.

Averages of these voltages corresponding to pressure and flow rate for the given glottal geometry (diameter and angle) are calculated to obtain a representative value. The standard deviation of the 4 voltages is also calculated to provide a measure of relative consistency of the data.

Table 1

Voltage required at each gain setting for the prescribed transglottal pressures

Pt (cm H20) 2.5 mV/V 5 mV/V 10 mV/V 25 mV/V 50 mV/V 1 0.9197 - - - -

3 2.7592 - - - -

5 4.5987 2.3016 1.1577 - -

8 - 3.6825 1.8523 - -

10 - 4.6032 2.3154 - -

15 - - 3.4730 1.3893 -

25 - - 5.7884 2.3155 1.1700

50 - - - 4.6310 2.3401

75 - - - 6.9465 3.5101 Note. Transglottal pressure values are converted to real life values 31

Table 2

Calibration equations and ranges for each gain setting of the transducers in use.

Transducer Gain Equation Range 2.5 mV/V V= 51.7357*P (-10.50v,+10.78v)=(-0.20cm,+0.21cm)

5 mV/V V= 25.8928*P (-11.0V,+11.9V)=(-0.43cm,+0.46cm)

CD12#1 10 mV/V V= 13.0239*P (-10.0v,+10.0v)=(-0.77cm,+0.77cm)

DP103 25 mV/V V= 5.2099*P (-8.01v,+8.04v)=(-1.56cm,+1.52cm)

V= 2.6326*P (-4.0v,+4.0v)=(-1.53cm,+1.49cm) 50 mV/V 2.5 mV/V V= 12.4638*P (-8.0v,+5.9v)=(-0.64cm,+0.5cm)

5 mV/V V= 6.2739*P (-8.0v,6.0v)=(-1.28cm,0.94cm)

CD12a 10 mV/V V = 3.1834*P (-8.0v,+7.1v)=(-2.54cm,2.24cm)

MP45-16 25 mV/V V= 1.2612*P (-5.9v,+6.5v)=(-4.79cm,+5.08cm)

50 mV/V V = 0.6319*P (-3.0v,+3.05v)=(-4.81cm,+4.8cm)

During the data collection for Case II, an automatic method for collecting voltages at

each tap was developed using a real-time streaming feature of the Data Translation (DT) product,

DT Measure Foundry. Using the DT DT98401 USB Data Acquisition A-to-D converter as the

hardware component, and the DT Measure Foundry software package, an interface program was

Excel. The output signal from the Validyne signal conditioners was connected to the DT

DT98401 A-to-D converter for real-time streaming of the voltages from each of the Validyne

pressure transducers used during data collection. An interface was created that allowed the

operator to monitor the voltage signal using a digital oscilloscope display with accompanying

voltmeter, to ensure that the pressure was stable at each tap before recoding data into Excel. A

text box was linked to the interface that allowed the user to choose which column the data would 32 be entered into Excel worksheet. The Excel template used during data collection was set up such that the pressure and flow voltages from the pressure transducers were recorded in adjacent columns, so they could be recorded simultaneously during data collection. As the data of interest are static voltages, a sampling frequency of 20000-25000 Hz was chosen to collect data for an appropriate duration at each tap, approximately 3-4 seconds. The interface program would transfer each buffer, the size of which was related to the sampling frequency, into Excel until the final row of the excel worksheet was reached. This sampling frequency and duration were chosen to allow adequate sampling of the voltages at each tap. Once a column of Excel was filled, data collection for that column stopped until the operator entered the next column and again executed the real-time streaming function. During an experimental run, the operator would enter the column number corresponding to each tap and once a static pressure was established, the user recorded the pressure and flow voltages for that tap. The average, along with standard deviation, and coefficient of variation of each column of data, representing the voltages proportional to the pressure and flow, were automatically calculated on the Excel worksheet.

These descriptive statistics were copied into an accompanying Excel file for each run. The files just discussed were saved.

When the flow jet leaves the glottal exit, it will go towards one wall of the wind tunnel.

For some geometric configurations, the operator can guide the flow toward the other wall as well. The flow direction can be guided by inserting a small piece of paper into the glottal duct from the entrance of the wind tunnel. The flow pattern in the wind tunnel downstream of the

glottal duct is monitored by an array of black human hairs that are distributed across the width of

the wind tunnel, as shown in Figure 10. Past experience has shown that the flow direction is

stable for either wall for certain glottal geometries. 33

hair

Figure 10. The human hair located just downstream of glottal exit.

If bistability of the flow is possible, the pressure distribution for both the flow wall and the non-

flow wall (stall side) will need to be recorded as these pressures differ. During the run, the

operator monitors the direction of the flow through the glottis to insure that the direction does not

change.

Using the flow voltage obtained when setting the transglottal pressure, the operator

maintains the flow voltage to ensure constant flow while subsequently shifting between each

pressure tap using the pressure scanner. After recording the voltages at each tap, if the voltage

value at tap 16 is again near the value expected from the DP-103 initial reading, the

measurements can be regarded as acceptable after a confirmation that the zero for each 34 transducer has not shifted, when the vacuum source is turned off. Subsequently, the zero values for both transducers at atmospheric pressure are recorded again. If they are close (within 10 mV)

to the values recorded at the beginning of the experiment and, the measurements can be regarded

as reasonable. Otherwise, the experiment is repeated until the operator is satisfied with all of the

voltage readings.

Presentation of the Data

In Chapter 3 and 4 pressure distributions like Figures 11 and 12 will be used to graphically represent the data collected for the thesis experiments. Note the vertical axis (y-axis) is in pressure drop for Figure 11 and percent pressure drop for Figure 12. For both Figures, the horizontal axis (x-axis) displays the axial distance. The axial location of the glottal entrance and exit are shown with a dashed vertical line (red arrows). As Shown in Figure 11, pressure distributions for the divergent oblique vocal fold are plotted with a dashed black line and filled squares. The pressure distributions for the convergent oblique vocal fold are plotted with a solid black line and unfilled squares. These graphing designations are referenced in the legend of the

Figure. The data points are the pressures taken at the 16 pressure taps. Displayed on Figure 11 are two pressure distributions. The first pressure distribution (higher on the page) is for the

transglottal pressure of 3 cm H20 and the second pressure distribution (lower on the page) is for

the transglottal pressure of 15 cm H20, as shown on the vertical axis (y-axis). 35

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 3 cm H20 2 O) 2 4 6 Convergent Side 8 10 Divergent Side 12

15 cm H20

Pressure Drop (cm H 14 16 Entrance Exit 18 Divergent Side Convergent Side

Figure 11. Example 1. Pressure distribution displaying absolute pressure drop.

Figure 12 displays the normalized pressure for the convergent and divergent folds. The

normalized pressure distributions are stacked vertically. The upper normalized pressure

distributions (higher on the page) are for the convergent fold and the lower normalized pressure

distributions (lower on the page) are for the divergent fold.

Note that the vertical axis for the divergent fold is located on the vertical left axis (y-axis)

and the vertical axis for the convergent fold is located on the right vertical axis (y-axis). Arrows

have been placed on the all Figures to remind the reader of which axis corresponds to the each

set of normalized pressure distributions as seen in Figure 12. For Figure 12, the normalized

pressure distributions for the transglottal pressures of 3, 5, 10, and 15 cm H20 are shown. As up to seven transglottal pressures are studied per diameter, these normalized pressure distributions have been color coded and are shown in the legend (boxed in red). Sets of figure like Figures 11 and 12 are generated for each diameter of the two cases in this thesis. 36

Axial Distance

0 0.2 0.4 0.6 0.8 -0.25 0

0 0.25

0.25 0.5

Convergent Side

0.5 0.75

Divergent Side 0.75 1 Percent Pressure Drop

1 1.25

1.25 1.5

Entrance Exit 1.5 1.75

3 cm H20 5 cm H20 10 cm H20 15 cm H20

Figure 12. Example 2. Normalized pressure distribution displaying the ratio pressure drop with respect to tap 16.

CHAPTER III: RESULTS

Using model M5, two cases of glottal obliquity were examined at seven minimal glottal diameters and a number of transglottal pressures. For Case I model M5 has a -10o convergent glottis with an obliquity of 15o. For Case II model M5 has a +10o divergent glottis with an

obliquity of 15o.

Figures displaying the measured pressures across all prescribed transglottal pressures will

be given along with a companion figure of the normalized pressure distribution. A normalized

pressure distribution is generated using the pressure at tap 16 as the reference. The pressure drop at each tap is divided by the pressure drop at tap 16 to provide a percentage of pressure drop

relative to tap 16. Included are data summarizing the flow through the glottis at each transglottal

pressure and corresponding non-dimensional Reynolds Numbers (Re) and pressure coefficients

(P*) for each case. All unit values are reported in human “real-life” physical units.

Case I: Convergent Glottis; -20o Conv. Side, +10o Div. Side; Obliquity 15o

For Case I (Figure 2), no bistability was observed. The pressure distributions on the -20o

convergent fold and +10o divergent fold are given in Figures 13 through 26. The flow exiting the

glottis went toward the side of the model to which the divergent fold was attached. For diameters

equal to and larger than 0.04 cm, the divergent vocal fold exhibited lower pressures than the

convergent fold throughout the glottis (Figures 19 through 26). For example, the pressure

distribution displayed in Figure 19 shows a larger pressure drop in the glottis (taps 6 through 12)

for the divergent fold (dashed curve with filled squares) than for the convergent fold (solid curve

with unfilled squares). When the minimal diameter was equal to or smaller than 0.01 cm,

pressures in the glottis on each vocal fold were relatively similar. Figure15 clearly shows the similarity in the pressure distributions of the two folds especially for taps1 through 9. For these 38 diameters the convergent side had the greatest recorded pressure drop near the minimal glottal diameter measured at tap 11 (Figures 13 through 16). For example, Figure 13 shows the pressure

at tap 11 on the convergent fold as the largest drop in pressure for this diameter rather than tap

11 on the divergent fold. Notice, also, pressure tap 11 on the convergent fold is slightly advanced

in the axial direction (downstream) compared to the divergent fold.

Normalized pressure distributions.

When normalized, the pressure distributions for Case I were relatively similar. This is

seen in Figure 16 by the relatively small difference in the normalized pressure drop at each tap.

The largest differences in the normalized pressure distributions were noted at tap 11 on the

convergent fold highlighted in Figure 16. Though the variability of the normalized pressure at

tap 11 across all transglottal pressures was relatively low, patterns related to the transglottal

pressure were observed for some diameters. Table 3 outlines the percent pressure drop at tap 11

relative to the transglottal pressure to further highlight these trends. For example, for the

diameter of 0.01 cm shown in Figure 16, as transglottal pressure increased, the percent drop

decreased (Table 3). This is also the case for the diameters of 0.02, 0.04, and 0.08 cm as shown

in Figures 18 through 22 and Table 3.

As the normalized distributions were relatively similar, the average normalized pressure

at each tap was calculated for all seven normalized transglottal pressures and diameters. Figure

27 displays the average normalized transglottal pressure for each the seven minimal glottal

diameters. The standard deviation of the seven normalized transglottal pressures at each pressure

taps are provided in Table 4 and Table 5 (placed after Figure 27 in this thesis). These tables

provide the average variability for each transglottal pressure of the normalized values at each

pressure tap shown in Figure 27. 39

Table 3

Percent pressure drop at Tap 11 relative to transglottal pressure (convergent vocal fold)

Diameter 3 cm H20 5 cm H20 10 cm 15 cm 25 cm 50 cm 75 cm H20 H20 H20 H20 H20 0.005 cm 100.32% 103.91% 107.10% 107.21% 106.16% 103.13% 102.11%

0.01 cm 110.39% 108.79% 107.07% 104.96% 103.84% 102.16% 100.91%

0.02 cm 109.35% 106.39% 105.05% 104.25% 103.22% 102.11% 101.25%

0.04 cm 108.35% 106.69% 104.97% 103.63% 102.51% 100.93% 100.06%

0.08 cm 105.35% 104.46% 102.74% 101.91% 101.99% 99.53% - Diameter 1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm 15 cm - H20 H20 0.16 cm - 102.84% 102.52% 101.07% 101.20% 100.13% -

0.32 cm 104.63% 102.03% 101.09% 102.11% 100.49% - -

Glottal entrance pressures.

One of the largest measured pressure differences between the two vocal folds occurred at the glottal entrance, tap 6 (see Figures 13 through 26). This tap is at the same axial location on each fold allowing for direct cross channel comparison. At this location the normalized average pressure difference between the two folds increased as diameter increased. At this location, the standard deviation across all normalized transglottal pressure was less than one percent. A positive correlation was found for diameter and the difference of the average normalized pressures between the convergent and divergent fold at glottal entrance: r(7)=.9879. The pressure on the convergent side at glottal entrance was larger than the pressure on the divergent side.

For the 0.005 cm diameter, the pressure drop at glottal entrance for the convergent fold and divergent fold was within 1.5% of the transglottal pressure for all of the prescribed transglottal pressures. As seen in Figures 13 and 14, the pressures in the glottis, especially at 40 entrance, are very similar for the convergent and divergent folds. The cross channel pressure difference at entrance was less than 1 cm H20 for all transglottal pressures. The data suggest that driving pressures at the entrance for this small diameter are very similar as this difference was well within 1% of the prescribed transglottal pressure.

Likewise for the 0.01 cm diameter, the cross channel entrance pressures are relatively similar, within 1 cm H20, except for the largest transglottal pressure of 75 cm H20. At this pressure drop the actual pressure difference is 1.07 cm H20, within 1.5% of the transglottal pressure. The cross channel difference was well within 1% of the prescribed transglottal pressure for all transglottal pressures as seen in Figures 15 and 16. The pressure drop at glottal entrance for the convergent fold ranged between 2.11 to 2.65% of the transglottal pressure. For the divergent fold at this axial location, the pressure drop ranged from 3.52 to 4.04% of the prescribed transglottal pressure.

For the diameter of 0.02 cm shown in Figures 17 and 18, the pressure drop at the glottal entrance for the convergent fold ranged between 6.78 to 7.93% of the prescribed transglottal pressure. For the divergent fold, the pressure drop ranged from 11.82 to 13.85% of the transglottal pressure at entrance. The cross channel difference at entrance was within 6% of the prescribed transglottal pressure.

For the 0.04 cm diameter, the cross channel difference at the entrance was within 14% of the prescribed transglottal pressure as shown in Figures 19 and 20. The pressure drop at glottal entrance for the convergent fold ranged between 17.69 to 18.04% of the transglottal pressure.

For the divergent fold at the entrance, the pressure drop ranged from 30.71 to 31.66% of the transglottal pressure. 41

For the diameter of 0.08 cm, the pressure drop at glottal entrance for the convergent fold ranged between 32.08 to 32.81% of the transglottal pressure. For the divergent fold at this axial location, the pressure drop was higher, ranging from 58.59 to 58.92% of the transglottal pressure.

This cross channel difference was 26.00 to 26.85% of the prescribed transglottal pressure, suggesting large differences in the amount of pressure driving each fold laterally, indicated in

Figures 21 and 22.

The cross channel entrance difference in pressure for the diameter of 0.16 cm displayed in Figures 22 and 23 ranged from 47.56 to 48.34% of the prescribed transglottal pressure, suggesting large differences in the amount of pressure driving each fold laterally. The pressure drop at glottal entrance for the convergent fold ranged between 46.59 to 47.06% of the transglottal pressure. For the divergent fold, the pressure drop ranged from 94.49 to 95.02% of

the transglottal pressure.

For the diameter of 0.32 cm, the pressure drop at entrance for the convergent fold ranged

between 59.91 to 60.97% above the transglottal pressure. For the divergent fold at this axial

location, the pressure drop ranged from 35.42 to 36.11% below of the transglottal pressure. As

shown in Figures 25 and 26, this was the only diameter of Case I in which the entrance pressure

for the divergent fold was negative relative to transglottal pressure and the cross channel

entrance pressure for the convergent fold was positive. This difference at entrance ranged

between 74.43 to 75.94% of the prescribed transglottal pressure. This difference in polarity

relative to transglottal pressure would result in an out of phase aerodynamic force pushing the

convergent fold laterally and pulling the divergent fold medially at entrance.

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O) 2 4 6 8 10 12 14 Pressure Drop (cm H 16 Entrance Exit 18 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 10

O) 20 2 30 40 50 60 70

Pressure Drop (cm H 80 Entrance Exit 90 Divergent Side Convergent Side

Figure 13. Case I pressure distributions for the minimal nominal diameter 0.005 cm for

transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 43

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.5 0

-0.25 0.25

0 0.5

0.25 0.75

0.5 1

0.75 1.25 Normalized Normalized Pressure Drop

Entrance Exit 1.25 3 cm H20 5 cm H20 10 cm H20 15 cm H20

25 cm H20 50 cm H20 75 cm H20

Figure 14. Case I normalized pressure distributions for the -20o convergent side (upper curves

corresponding to the right vertical axis) and +10o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.005 cm. 44

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O) 2 4 6 8 10 12 14 Pressure Drop (cm H 16 Entrance Exit 18 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 10

O) 20 2 30 40 50 60 70

Pressure Drop (cm H 80 Entrance Exit 90 Divergent Side Convergent Side

Figure 15. Case I pressure distributions for the minimal nominal diameter 0.01 cm for transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 45

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop

0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75 3 cm H20 5 cm H20 10 cm H20 15 cm H20

25 cm H20 50 cm H20 75 cm H20

Figure 16. Case I normalized pressure distributions for the -20o convergent side (upper curves

corresponding to the right vertical axis) and +10o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.01 cm. 46

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O) 2 4 6 8 10 12 14 Pressure Drop (cm H 16 Entrance Exit 18 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 10

O) 20 2 30 40 50 60 70

Pressure Drop (cm H 80 Entrance Exit 90 Divergent Side Convergent Side

Figure 17. Case I pressure distributions for the minimal nominal diameter 0.02 cm for

transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 47

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop 0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75 3 cm H20 5 cm H20 10 cm H20 15 cm H20

25 cm H20 50 cm H20 75 cm H20

Figure 18. Case I normalized pressure distributions for the -20o convergent side (upper curves

corresponding to the right vertical axis) and +10o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.02 cm. 48

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O) 2 4 6 8 10 12

Pressure Drop (cm H 14 16 Entrance Exit 18 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 10

O) 20 2 30 40 50 60 70 Pressure Drop (cm H 80 Entrance Exit 90 Divergent Side Convergent Side

Figure 19. Case I pressure distributions for the minimal nominal diameter 0.04 cm for

transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 49

Axial Distance

0 0.2 0.4 0.6 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop

0.75 1

1.25

Normalized 1

1.25 1.5

Entrance Exit 1.5 1.75 3 cm H20 5 cm H20 10 cm H20 15 cm H20

25 cm H20 50 cm H20 75 cm H20

Figure 20. Case I normalized pressure distributions for the -20o convergent side (upper curves

corresponding to the right vertical axis) and +10o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.04 cm. 50

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

O) 2 2

Pressure Drop (cm H 10

Entrance Exit 12 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 O) 2 20

50 Pressure Drop (cm H Entrance Exit 60 Divergent Side Convergent Side

Figure 21. Case I pressure distributions for the minimal nominal diameter 0.08 cm for

transglottal pressures of 3, 5, and 10cm H20 (top) and 15, 25, and 50 cm H20 (bottom). 51

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop 0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75 3 cm H20 5 cm H20 10 cm H20

15 cm H20 25 cm H20 50 cm H20

Figure 22. Case I normalized pressure distributions for the -20o convergent side (upper curves

corresponding to the right vertical axis) and +10o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.08 cm. 52

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 2

5 Pressure Drop (cm H PressureDrop (cm 6 Entrance Exit 7 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2

4 O) 2 6 8 10 12 14 Pressure Drop (cm H PressureDrop (cm 16 Entrance Exit 18 Divergent Side Convergent Side

Figure 23. Case I pressure distributions for the minimal nominal diameter 0.16 cm for

transglottal pressures of 3 and 5cm H20 (top) and 8, 10, and 15 cm H20 (bottom). 53

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop

0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75

3 cm H20 5 cm H20 8 cm H20 10 cm H20 15 cm H20

Figure 24. Case I normalized pressure distributions for the -20o convergent side (upper curves

corresponding to the right vertical axis) and +10o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.16 cm. 54

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 1

2 O) 2 3 4 5 6 Pressure Drop (cm H PressureDrop (cm 7 Entrance Exit 8 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2

4 O) 2 6 8 10 12 Pressure Drop (cm H PressureDrop (cm 14 Entrance Exit 16 Divergent Side Convergent Side

Figure 25. Case I pressure distributions for the minimal nominal diameter 0.32 cm for

transglottal pressures of 1, 3, and 5 cm H20 (top) and 8and 10 cm H20 (bottom).

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop 0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75

1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm H20

Figure 26. Case I normalized pressure distributions for the -20o convergent side (upper curves

corresponding to the right vertical axis) and +10o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.32 cm.

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -1 0 0.005 cm -0.75 0.25 -20o Conv. -0.5 Side 0.5

-0.25 0.75 0.32 cm

0 1

0.25 0.005 cm 1.25 Pressure Drop

0.5

0.75 Normalized +10o Div. 1 Side

1.25 0.32 cm

Entrance Exit 1.5 Dn:0.005 Dn:0.01 Dn:0.02 Dn:0.04

Dn:0.08 Dn:0.16 Dn:0.32

Figure 27. Case I normalized pressure distribution averaged across transglottal pressure and

shown for each glottal diameter for the -20o convergent side (upper curves corresponding to the

right vertical axis) and +10o divergent side (lower curves corresponding to the left vertical axis).

Table 4

Standard deviation of the normalized transglottal pressure at each tap of the divergent vocal fold

Tap Dn: 0.005 Dn: 0.01 Dn: 0.02 Dn: 0.04 Dn: 0.08 Dn: 0.16 Dn: 0.32 1 0.0032 0.0025 0.0018 0.0023 0.0005 0.0020 0.0061

2 0.0021 0.0027 0.0007 0.0022 0.0016 0.0017 0.0066

3 0.0034 0.0037 0.0027 0.0019 0.0005 0.0031 0.0064

4 0.0034 0.0043 0.0022 0.0013 0.0011 0.0017 0.0066

5 0.0036 0.0052 0.0020 0.0029 0.0037 0.0089 0.0241a

6 0.0021 0.0018 0.0068 0.0033 0.0014 0.0022 0.0041

7 0.0022 0.0035 0.0021 0.0041 0.0068 0.0104 0.0071

8 0.0029 0.0028 0.0018 0.0069 0.0113 0.0120 0.0098

9 0.0059 0.0023 0.0041 0.0112 0.0104 0.0154 0.0044

10 0.0178 0.0050 0.0034 0.0144 0.0132 0.0124 0.0127

11 0.0790 a 0.0078 0.0066 0.0118 0.0145 0.0100 0.0159

12 0.0109 0.0159 0.0096 0.0086 0.0094 0.0082 0.0120

13 0.0070 0.0078 0.0029 0.0109 0.0053 0.0084 0.0090

14 0.0038 0.0138 0.0058 0.0104 0.0058 0.0079 0.0056

15 0.0048 0.0245 a 0.0027 0.0111 0.0058 0.0078 0.0072

16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 a Indicates SD is larger than 0.02 of the normalized pressure.

Table 5

Standard deviation of the normalized transglottal pressure at each tap of the convergent vocal fold

Tap Dn: 0.005 Dn: 0.01 Dn: 0.02 Dn: 0.04 Dn: 0.08 Dn: 0.16 Dn: 0.32 1 0.0011 0.0015 0.0041 0.0015 0.0011 0.0036 0.0049

2 0.0014 0.0007 0.0033 0.0030 0.0031 0.0023 0.0027

3 0.0029 0.0006 0.0045 0.0041 0.0019 0.0064 0.0051

4 0.0015 0.0032 0.0029 0.0023 0.0016 0.0021 0.0037

5 0.0009 0.0021 0.0020 0.0022 0.0035 0.0047 0.0057

6 0.0020 0.0022 0.0041 0.0013 0.0032 0.0019 0.0050

7 0.0027 0.0052 0.0027 0.0029 0.0044 0.0043 0.0056

8 0.0051 0.0050 0.0034 0.0086 0.0097 0.0032 0.0081

9 0.0115 0.0070 0.0029 0.0084 0.0093 0.0063 0.0089

10 0.0395 a 0.0122 0.0042 0.0132 0.0167 0.0093 0.0079

11 0.0264 a 0.0347 a 0.0275 a 0.0301 a 0.0206 0.0111 0.0158

12 0.0097 0.0029 0.0042 0.0094 0.0118 0.0079 0.0079

13 0.0028 0.0036 0.0049 0.0120 0.0086 0.0045 0.0085

14 0.0019 0.0054 0.0147 0.0085 0.0071 0.0043 0.0082

15 0.0014 0.0014 0.0027 0.0078 0.0059 0.0039 0.0071

16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 a Indicates SD is larger than 0.02 of the normalized pressure.

Summary of flow data.

As expected, there is a quadratic relationship between pressure and flow, of which the dominate term decreased as the diameter increased (Figure 28 and Table 8). Tables 6 and 7 give the flows for Case I which ranged from 10.95 cc/s to 1680.11 cc/s, which are comparable to realistic values for flows in phonation. The larger values are comparable to peak flows produced in very breathy phonation. The equations in Table 8 were used to derive a general equation for pressure as a function of flow and diameter:

P= C1*U2 + C2*U

-1.9837 C1Divergent= 3.0806E07D , R² = .9866

3 2 C2Divergent = -0.1568(log10D) - 0.5295(log10D) - 0.5744(log10D) - 0.1819, R² = .9576

-2.0001 C1Convergent = 2.6651E07D , R² = .9853

3 2 C2Convergent = -0.1378(log10D) - 0.4302(log10D) - 0.4443(log10D) - 0.1358, R² = .9918 where P is equal to the transglottal pressure in cm H20, u is equal to the flow in cc/s, and D is equal to the to the diameter in cm. Coefficients were calculated for when the pressures were collected from both the divergent and convergent folds. The subscript of the coefficients denotes for which vocal fold pressure data were collected.

Across all transglottal pressures, the Reynolds number ranged from 121.14 to 14735.81 and the transglottal pressure coefficient ranged from 0.65 to 1.59 (Figure 29). Regression equations are given in Table 9. These Reynolds numbers suggest that even for a large subglottal pressure, the flow regime when the glottal diameter is relative small is still laminar. In this static model for this configuration, the largest Reynolds numbers occurred at the larger diameters.

Table 6

Case I flow values when the pressures on the convergent vocal fold were recorded

Pt 0.005 0.01 cm 0.02 cm 0.04 cm 0.08 cm 0.16 cm 0.32 cm cm H20 cm 1 ------479.32

3 11.48 20.99 43.46 85.44 184.14 402.00 954.75

5 14.18 28.01 57.06 111.76 245.71 540.23 1287.01

8 - - - - - 730.00 1486.22

10 21.92 40.97 83.59 162.69 363.39 843.17 1680.11

15 28.48 52.67 103.40 205.33 462.46 1174.23 -

25 39.49 69.96 139.53 274.44 641.83 - -

50 61.76 105.70 209.17 414.64 982.71 - -

75 80.18 135.39 271.63 531.38 - - - Note. The nominal transglottal pressures are reported rather than empirical values.

Table 7

Case I flow values when the pressures on the divergent vocal fold were recorded

Pt 0.005 0.01 cm 0.02 cm 0.04 cm 0.08 cm 0.16 cm 0.32 cm cm H20 cm 1 ------492.36

3 10.95 23.84 46.24 87.52 188.26 408.60 997.68

5 15.05 29.91 60.14 116.24 252.63 555.60 1261.98

8 - - - - - 764.11 1431.83

10 23.20 41.87 84.98 169.29 366.52 875.21 1645.28

15 29.82 51.57 106.25 213.42 467.50 1142.06 -

25 40.88 68.43 139.93 286.47 640.58 408.60 -

50 62.32 100.76 208.90 425.75 1008.54 - -

75 81.06 126.62 272.18 543.42 - - - Note. The nominal transglottal pressures are reported rather than empirical values.

80 D:0.005

70 D:0.01 0) 2 D:0.02 60 D:0.04 D:0.08 50 D:0.16 D:0.32 40

Transglottal Pressure (cmH Pressure Transglottal 10

0 0 200 400 600 800 1000 1200 1400 1600 1800 Flow (cc/s)

Figure 28. Full range of transglottal pressures and flows for Case I. 62

Table 8

Regression equations for pressure versus flow across diameters for Case I

Diameter Convergent Side on the Left Divergent Side on the Left 2 2 Dn : 0.32 P = 3.8192E-06u - 0.0005u, R² = .9909 P = 4.3872E-06u - 0.0011u, R² =.9868

2 2 Dn : 0.16 P = 5.3926E-06u + 0.0067u, R² = .9946 P = 7.3295E-06u + 0.0048u, R² = .9995

2 2 Dn : 0.08 P = 3.8372E-05u + 0.0135u, R² = .9991 P = 3.5019E-05u + 0.0148u, R² = .9980

2 2 Dn : 0.04 P = 0.0002u + 0.0293u, R² = .9990 P = 0.0002u + 0.0254u, R² = .9992

2 2 Dn : 0.02 P = 0.0008u + 0.0618u, R² = .9981 P = 0.0008x + 0.0561x, R² = .9974

2 2 Dn : 0.01 P = 0.0033u + 0.1179u, R² = .9990 P = 0.0042u + 0.0698u, R² = .9993

2 2 Dn : 0.005 P = 0.0081u + 0.2943u, R² = .9989 P = 0.0084u + 0.2591u, R² = .9990 Note. u is the flow in cc/s and P is pressure in cm H20

1.8 D:0.005 D:0.01 1.6 D:0.02 D:0.04 1.4 D:0.08 D:0.16 D:0.32 1.2

0.8

0.6 Transglottal Pressure Coefficient P* Coefficient Pressure Transglottal 0.4 0 2000 4000 6000 8000 10000 12000 14000 16000 Reynolds Number Re

1.8

D:0.005 D:0.01 1.6 D:0.02 D:0.04 1.4 D:0.08 D:0.16 1.2 D:0.32

0.8

Transglottal Pressure Coefficient P* Pressure Transglottal 0.6

0.4 1.5 2.5 3.5 4.5 Log10(Re)

Figure 29. Reynolds number versus transglottal pressure coefficient for all diameters of Case I.

Table 9

Regression equations for Re versus P* across diameters for Case I

Diameter Convergent Side on the Left Divergent Side on the Left 2 2 Dn : 0.32 P* = 2.4685*log10(Re) - P* = 3.3362*log10(Re) -

19.587*log10(Re) + 39.624, R² = .8875 26.116*log10(Re) + 51.848, R² = .7826

Dn : 0.16 P* = -0.9975*log10(Re) + 4.7411, P* = -0.9034*log10(Re) + 4.3493,

R² = .9814 R² = .9964

Dn : 0.08 P* = -0.7757*log10(Re) + 3.9042, P* = -0.7212*log10(Re) + 3.6764,

R² = .9948 R² =.9816

Dn : 0.04 P* = -0.7011*log10(Re) + 3.648, P* = -0.6637*log10(Re) + 3.461,

R² = .9837 R² = .9810

2 Dn : 0.02 P* = -0.6995*log10(Re) + 3.4344, P* = -0.7614*log10(Re) +

R² = .9781 4.212*log10(Re) - 4.4605, R² = .9969

2 Dn : 0.01 P* = -0.783*log10(Re) + 3.4402, P* = -1.0447*log10(Re) +

R² = .9982 5.5742*log10(Re) - 6.1208, R² = .9630

Dn : 0.005 P* = -0.8869*log10(Re) + 3.2896, P* = -0.8826*log10(Re) + 3.2245,

R² = .9524 R² = .9858

Case II: Divergent Glottis; -10o Conv. Side and +20o Div. Side; Obliquity 15o

For Case II (Figure 3), a bistability was observed at the largest diameters of 0.16 cm and

0.32 cm where the flow exiting the glottis could go either to the right or to the left. Therefore for

these data, two sets of figures have been generated, one displaying the pressures on the folds

when the divergent side was the flow side and the convergent side was the non-flow side, and the

other displaying the opposite condition. The side of the model to which the flow exited the 65 glottis was considered the flow side. At the 0.01 cm diameter for the highest transglottal pressure of 75 cm H20, two stable pressure distribution patterns were observed for the divergent fold

(Figures 32 through 33). The measured pressures for this case are displayed in Figures 30

through 39. As in Case I, when the diameter increased to 0.16 and 0.32 cm, each vocal fold wall

became somewhat aerodynamically decoupled from the other. The pressure distributions at these

diameters reflect the geometric configuration of each fold, with the convergent having the larger

drop further downstream in the axial direction than the divergent fold (Figures 40 through 48).

For example, Figure 40 shows the largest pressure drop for the divergent fold at the glottal

entrance (near tap 6) and the largest pressure drop for the convergent fold closer to the glottal

exit, near tap 10.

Normalized pressure distributions.

When normalized by the pressure at tap 16, the pressure distributions for Case II were

rarely similar and thus the average variability was higher. The standard deviations of the seven

normalized transglottal pressures at each pressure tap are provided in Tables 17 and 18 (placed

after Figure 50 in this thesis). Figure 50, comparable to Figure 27, displays the average normalized transglottal pressure across the seven minimal glottal diameters. Again table Tables

17 and 18 report the average variability for each transglottal pressure of the normalized values at each pressure tap shown in Figure 50. The effect of the bimodal pressure distributions

(discussed below) are see in the averaging of these data. For example, as shown in Figure 50 at tap 12 for the 0.04 cm diameter for the divergent fold, displayed in red, the pressure drop is increased (lower on the page) because of the bimodal pressure distributions observed at this diameter at the highest transglottal pressure (shown in Figure 37). This is the largest variability

(SD= 0.1977) in the average normalized pressure at tap 12 of the divergent fold (Table 17). 66

When the glottal diameter was less than or equal to 0.04 cm, patterns relative to pressure drop near the minimal glottal diameter at tap 7 were present (Figures 20 through 37) for both the convergent and divergent folds. These data indicate a relationship between the relative magnitude of the pressure drop just past the minimal constriction and transglottal pressure for these smaller diameters. For these diameters, the relative percent of the transglottal pressure drop at tap 7 for all transglottal pressures is reported for the convergent fold in Table 10 and for the divergent fold in Table 11. Note that values below 100% indicate a positive pressure at tap 7 and values above 100% indicate a negative pressure at tap 7, relative to the pressure at tap 16. These data trends can be seen graphically in Figures 30 to 37. For the two lowest transglottal pressures of the 0.005 diameter glottis, the maximum pressure drop did not occur near tap 7 (Figure 31).

For the diameter of 0.005 cm, the percent pressure drop at tap 7 increased with transglottal pressure from 3 to 25 cm H20. Beyond that point, the percent drop at tap 7 for the three highest transglottal pressures were relatively similar (Figure 31). For the diameter of 0.01 cm, the percent pressure drop increased from 3 to 10 cm H20, then decreased from 15 to 75 cm

H20 (Figure 33). For the diameter of 0.02 cm, the percent pressure drop decreased as transglottal pressure increased except for the highest transglottal pressure of the divergent fold (shown in

Table 11 and Figure 35).

For the diameter of 0.04 cm, the percent pressure drop at tap 6 and 7decreased as

transglottal pressure increased from 3 to 15 cm H20, then increased from 15 to 50 cm H20, with

75 cm H20 being relatively similar to 50 cmH20 (Table 12 through 14 and Figure 37). For the minimal glottal diameter of 0.08 cm, the largest pressure drop for the divergent fold moves tap 7 to tap 6 (Figure 39). The convergent fold at this diameter shows a shift in the location of the maximal pressure drop related to the magnitude of the transglottal pressure. For lower 67 transglottal pressures, below and including 15 cm H20, the largest recorded pressure drop occurs at tap 6 (Figure 39). At higher transglottal pressures, above and including 25 cmH20, the largest recorded pressure drop occurred at tap 7 (Figure 39). For the two largest glottal diameters, 0.16 and 0.32 cm, the largest drop occurred at tap 6 for the divergent fold and tap 11 for the convergent fold (Figures 41 through 48).

Table 10

Percent pressure drop at Tap 7 relative to transglottal pressure for the convergent vocal fold

Diameter 3 cm H20 5 cm H20 10 cm 15 cm 25 cm 50 cm 75 cm H20 H20 H20 H20 H20 0.005 cm 80.86% 86.98% 102.70% 114.48% 125.47% 125.17% 124.85%

0.01 cm 119.73% 129.78% 127.02% 125.44% 122.89% 120.54% 119.03%

0.02 cm 125.04% 124.27% 121.51% 119.17% 115.54% 114.05% 115.28%

0.04 cm 121.81% 117.12% 113.73% 112.49% 119.22% 121.18% 120.87%

Table 11

Percent pressure drop at Tap 7 relative to transglottal pressure for the divergent vocal fold

Diameter 3 cm H20 5 cm H20 10 cm 15 cm 25 cm 50 cm 75 cm H20 H20 H20 H20 H20 0.005 cm 88.73% 94.31% 102.73% 110.32% 120.09% 119.94% 117.79%

0.01 cm 117.87% 127.30% 126.58% 123.01% 120.54% 116.03% 113.59%

0.02 cm 130.06% 126.36% 124.86% 122.30% 119.85% 116.21% 125.03%

0.04 cm 132.91% 127.51% 123.01% 120.65% 129.13% 132.32% 131.61%

Glottal entrance pressures.

Near glottal entrance (tap 6) the normalized average pressure difference between the two

folds increased as diameter increased up to 0.08 cm. The difference for the largest two diameters 68 did not follow this same trend as in Case I. For diameters larger than and including 0.02 cm, the

divergent vocal fold exhibited lower pressures than the convergent side at glottal entrance, near

the minimal glottal diameter (Figures 34 through 48). For diameters larger than and including

0.04 cm, the divergent vocal fold exhibited a negative pressure at entrance while the convergent

side exhibits a positive pressure glottal entrance (Figures 36 through 48). When the minimal

diameter was smaller than 0.02 cm, pressures in the glottis on each vocal fold were relatively

similar within the glottis. For these diameters the convergent side had the greatest recorded

pressure drop near the minimal glottal diameter measured at tap 11 (Figure 30 through Figure

33).

Tables 12 to 15 provide a summary of pressure differences between the two vocal folds at

tap 6. These tables indicate increasing percentages in the entrance pressure drop across

transglottal pressures. The data supplement figures displaying the normalized pressure

distributions. Table 12 reports the percent of the pressure drop of at tap 6 of the convergent vocal

fold while Table 13 reports the analogous data for the divergent vocal fold. Table 14 reports

cross channel pressure differences as a percentage of transglottal pressure.

The percent pressure drop at entrance increased with transglottal pressure for both vocal

folds at 0.005 cm (Figure 31). An increasing trend from 3 to10 cm H20 is observed for 0.01 cm,

with higher transglottal pressures being relatively similar (Figure 33). At 0.02 cm, the entrance

pressures are similar in proportion across all transglottal pressures (Figure 35). Entrance

pressures for 0.04 and 0.08 cm vary within 10% and 15% of the transglottal pressure,

respectively, for the divergent fold and 8% for the convergent fold. No observable trend is found

in the percent pressure drop for the 0.16 diameter across transglottal pressure (Table 12 and 13

and Figures 41 and 43). As seen in Table 12 and 13, for 0.32 cm there is a slight decrease in the 69 percent pressure drop at entrance as transglottal pressure increases (Figure 46 and 48). For the diameters where a bistability was observed, there was a greater pressure drop at entrance on the

flow side compared to the non-flow side (Table 12 and 13).

Table 12

Percent pressure drop at Tap 6 relative to transglottal pressure (convergent vocal fold)

Diameter 3 cm H20 5 cm H20 10 cm 15 cm 25 cm 50 cm 75 cm H20 H20 H20 H20 H20 0.005 cm 11.27% 11.91% 16.91% 20.02% 24.11% 26.20% 26.68%

0.01 cm 44.01% 49.72% 50.64% 51.08% 51.17% 51.64% 51.30%

0.02 cm 72.94% 72.93% 72.76% 72.30% 70.54% 70.30% 71.02%

0.04 cm 91.81% 88.24% 85.98% 85.99% 92.64% 94.01% 93.87%

0.08 cm 85.07% 83.19% 80.44% 85.79% 91.44% 89.80% - Diameter 1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm 15 cm - H20 H20 0.16 cma - 84.03% 78.91% 78.79% 79.49% - -

0.16 cmb - 84.12% 82.67% 81.64% 80.49% 81.52% -

0.32 cma 88.58% 87.48% 83.87% 83.76% 82.81% - -

0.32 cmb 85.37% 83.90% 83.11% 82.80% 81.87% - - a Flow Side b Non-Flow Side

Table 13

Percent pressure drop at Tap 6 relative to transglottal pressure (divergent vocal fold)

Diameter 3 cm H20 5 cm H20 10 cm 15 cm 25 cm 50 cm 75 cm H20 H20 H20 H20 H20 0.005 cm 13.02% 18.08% 24.91% 30.46% 37.15% 40.91% 41.25%

0.01 cm 52.71% 61.46% 66.09% 66.40% 67.35% 66.70% 66.46%

0.02 cm 91.26% 91.82% 91.79% 92.85% 91.11% 89.87% 96.23%

0.04 cm 115.37% 113.89% 111.07% 110.98% 117.67% 121.66% 121.65%

0.08 cm 126.35% 121.64% 120.02% 125.25% 135.00% 134.98% - Diameter 1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm 15 cm - H20 H20 0.16 cmb - 125.52% 118.48% 123.54% 115.19% - -

0.16 cma - 131.13% 122.89% 124.74% 123.42% 128.85% -

0.32 cmb 110.52% 108.88% 106.29% 106.29% 103.93% - -

0.32 cma 124.12% 114.38% 112.25% 110.40% 109.37% - - a Flow Side b Non-Flow Side

Table 14

Percent pressures difference relative prescribed transglottal pressure of the divergent and convergent fold

Diameter 3 cm H20 5 cm H20 10 cm 15 cm 25 cm 50 cm 75 cm H20 H20 H20 H20 H20 0.005 cm 1.73% 6.15% 7.99% 10.38% 13.03% 14.75% 14.64%

0.01 cm 9.05% 11.68% 15.49% 15.27% 15.97% 14.58% 15.38%

0.02 cm 18.18% 19.15% 18.40% 20.50% 20.50% 19.59% 25.19%

0.04 cm 23.46% 25.40% 25.09% 24.94% 24.98% 27.50% 27.57%

0.08 cm 41.33% 39.49% 40.80% 39.39% 43.54% 44.91% - Diameter 1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm 15 cm - H20 H20 0.16 cma - 40.96% 39.65% 44.08% 35.93% - -

0.16 cmb - 46.80% 39.87% 42.25% 43.16% 46.84% -

0.32 cma 21.93% 22.58% 22.47% 22.73% 21.37% - -

0.32 cmb 38.34% 30.58% 29.79% 28.30% 27.41% - - a Divergent side is the flow side b Convergent side is the flow side

Bimodal pressure distributions.

Bimodal pressure distributions, where there existed two local pressure minima within the glottis, were observed for high transglottal pressures at some diameters. Specific data comparing the percent pressure drop relative to the transglottal pressure drop of each local minimum for the convergent fold and divergent fold are available in Table 15 and 16, respectively. Figures 31 through 37 show the bimodal pressure distributions.

For the convergent fold, bimodal pressure distributions with the second local minimum occurring around tap 11 and 12 were recorded for the minimal glottal diameters of 0.005, 0.01, and 0.02 cm. The magnitude of the second local pressure minimum increased with diameter as 72 shown in Figures 31 through 35. For the diameters of 0.005 and 0.01 cm bimodal pressure distributions were recorded at transglottal pressures of 50 and 75 cm H20. At the 0.02 cm diameter, the bimodal pressure distribution occurred at transglottal pressures of 25, 50, and 75 cm H20.

For the divergent fold, bimodal pressure distributions with the second local minimum occurring around tap 12 were recorded for the minimal glottal diameters of 0.01, 0.02, and 0.04 cm. The magnitude of the second local pressure minimum increased with diameter as shown in

Figures 33 through 37. For the diameters of 0.01 and 0.02 cm bimodal pressure distributions were recorded at the transglottal pressure of 75 cm H20 where at the 0.04 cm diameter, the

bimodal pressure distribution occurred at transglottal pressures of 50 and 75 cm H20.

Table 15

Percent drop relative to the transglottal pressure of the first and second local minima for convergent side

Diameter First Local Minimum Second Local Minimum Dn : 0.02 15.54% (Pt =25; Tap 7) 9.07% (Pt =25; Tap 11)

14.05% (Pt =50; Tap 7) 21.85% (Pt =50; Tap 11)

15.28% (Pt =75; Tap 7) 27.03% (Pt =75; Tap 12)

Dn : 0.01 20.54% (Pt =50; Tap 7) 11.71% (Pt =50; Tap 12)

19.03% (Pt =75; Tap 7) 11.61% (Pt =75; Tap 11)

Dn : 0.005 25.17% (Pt=50; Tap 7) 2.54% (Pt=50; Tap 11)

24.85% (Pt=75; Tap 7) 2.88% (Pt=75; Tap 11)

Table 16

Percent drop relative to the transglottal pressure of the first and second local minima for

divergent side

Diameter First Local Minimum Second Local Minimum Dn : 0.04 32.32% (Pt=50; Tap 7) 39.84% (Pt =50; Tap 12)

31.61% (Pt=75; Tap 7) 43.99% (Pt =75; Tap 12)

Dn : 0.02 - -

25.03% (Pt =75; Tap 7) 13.07% (Pt =75; Tap 12)

Dn : 0.01 - -

a 1 19.25% (Pt=75 ; Tap 7) 4.78% (Pt =75 ; Tap 12)

Dn : 0.005 19.94% (Pt=50; Tap 7) 1.44% (Pt=50; Tap 12)

17.79% (Pt=75; Tap 7) 1.58% (Pt=75; Tap 12) a For this transglottal pressure, two stable distributions were possible, the second local minimum only occurred for this distribution

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O)

2 4 6 8 10 12 14 16 Pressure Drop (cm H 18 Entrance Exit 20 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 O)

2 20 30 40 50 60 70 80 90 Pressure Drop (cm H 100 110 Entrance Exit 120 Divergent Side Convergent Side

Figure 30. Case II pressure distributions for the minimal nominal diameter 0.005 cm for

transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 75

Axial Distance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.75 0

-0.5 0.25

-0.25 0.5

0.75 0

0.25 1

Pressure Drop 0.5 1.25

0.75 1.5

Normalized 1

1.25

Entrance Exit 1.5 3 cm H20 5 cm H20 10 cm H20 15 cm H20

25 cm H20 50 cm H20 75 cm H20

Figure 31. Case II normalized pressure distributions for the -10o convergent side (upper curves

corresponding to the right vertical axis) and +20o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.005 cm. 76

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O)

2 4 6 8 10 12 14

Pressure Drop (cm H 16 18 Entrance Exit 20 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 O)

2 20 30 40 50 60 70 80

Pressure Drop (cm H 90 100 110 Entrance Exit 120 Divergent Side Convergent Side

Figure 32. Case II pressure distributions for the minimal nominal diameter 0.01 cm for

transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 77

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.5 0

-0.25 0.25

0 0.5

0.25 0.75

0.5 1 Pressure Drop

0.75 1.25

Normalized 1 1.5

1.25

Entrance Exit 1.5 3 cm H20 5 cm H20 10 cm H20 15 cm H20 25 cm H20 50 cm H20 75 cm H20 75 cmH20 (2)

Figure 33. Case II normalized pressure distributions for the -10o convergent side (upper curves

corresponding to the right vertical axis) and +20o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.01 cm. 78

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O)

2 4 6 8 10 12 14

Pressure Drop (cm H 16 18 Entrance Exit 20 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 O)

2 20 30 40 50 60 70 80 90 Pressure Drop (cm H 100 110 Entrance Exit 120 Divergent Side Convergent Side

Figure 34. Case II pressure distributions for the minimal nominal diameter 0.02 cm for transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 79

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.5 0

-0.25 0.25

0 0.5

0.25 0.75

0.5 1 Pressure Drop

0.75 1.25

Normalized 1 1.5

1.25

Entrance Exit 1.5 3 cm H20 5 cm H20 10 cm H20 15 cm H20

25 cm H20 50 cm H20 75 cm H20

Figure 35. Case II normalized pressure distributions for the -10o convergent side (upper curves

corresponding to the right vertical axis) and +20o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.02 cm. 80

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O)

2 4 6 8 10 12 14 16 Pressure Drop (cm H 18 Entrance Exit 20 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 O)

2 20 30 40 50 60 70 80 90 Pressure Drop (cm H 100 110 Entrance Exit 120 Divergent Side Convergent Side

Figure 36. Case II pressure distributions for the minimal nominal diameter 0.04 cm for transglottal pressures of 3, 5, 10, and 15 cm H20 (top) and 25, 50, and 75 cm H20 (bottom). 81

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop 0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75 3 cm H20 5 cm H20 10 cm H20 15 cm H20

25 cm H20 50 cm H20 75 cm H20

Figure 37. Case II normalized pressure distributions for the -10o convergent side (upper curves

corresponding to the right vertical axis) and +20o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.04 cm. 82

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 O) 2 4

Pressure Drop (cm H 12 Entrance Exit 14 Divergent Side Convergent Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 O) 2 20 30 40 50 60 Pressure Drop (cm H 70 Entrance Exit 80 Divergent Side Convergent Side

Figure 38. Case II pressure distributions for the minimal nominal diameter 0.08 cm for transglottal pressures of 3, 5, and 10cm H20 (top) and 15, 25, and 50 cm H20 (bottom). 83

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop 0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 3 cm H20 5 cm H20 10 cm H20

15 cm H20 25 cm H20 50 cm H20

Figure 39. Case II normalized pressure distributions for the -10o convergent side (upper curves

corresponding to the right vertical axis) and +20o divergent side (lower curves corresponding to

the left vertical axis) for the nominal diameter of 0.08 cm.

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 2

5 Pressure Drop (cm H PressureDrop (cm 6 Entrance Exit 7 Divergent Side - Flow Side Convergent Side - Non-Flow Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

2 6 8 10 12 14 16

Pressure Drop (cm H PressureDrop (cm 18 20 Entrance Exit 22 Divergent Side - Flow Side Convergent Side - Non-Flow Side

Figure 40. Case II pressure distributions for the minimal nominal diameter 0.16 cm for transglottal pressures of 3 and 5 cm H20 (top) and 8, 10, and 15 cm H20 (bottom) where the

divergent side is the flow side and the convergent side is the non-flow side.

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop

0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75

3 cm H20 5 cm H20 8 cm H20 10 cm H20 15 cm H20

Figure 41. Case II normalized pressure distributions for the non-flow side -10o convergent fold

(upper curves corresponding to the right vertical axis) and flow side +20o divergent fold (lower

curves corresponding to the left vertical axis) for the nominal diameter of 0.16 cm. 86

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 2

5 Pressure Drop (cm H PressureDrop (cm 6 Entrance Exit 7 Divergent Side - Non-Flow Side Convergent Side - Flow Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2

4 O) 2 6 8 10 12 14 Pressure Drop (cm H PressureDrop (cm 16 Entrance Exit 18 Divergent Side - Non-Flow Side Convergent Side - Flow Side

Figure 42. Case II pressure distributions for the minimal nominal diameter 0.16 cm for transglottal pressures of 3, and 5 cm H20 (top) and 8 and 10 cm H20 (bottom) where the

divergent side is the non-flow side and the convergent side is the flow side.

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop

0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75

3 cm H20 5 cm H20 8 cm H20 10 cm H20 15 cm H20

Figure 43. Case II normalized pressure distributions for the flow side -10o convergent fold

(upper curves corresponding to the right vertical axis) and non-flow side +20o divergent fold

(lower curves corresponding to the left vertical axis) for the nominal diameter of 0.16 cm. 88

Axial Distance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.2

0.15

0.1

0.05

-0.05

Percent Difference -0.1

-0.15 Entrance Exit -0.2 3 cm H20 5 cm H20 8 cm H20 10 cm H20

Axial Distance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.2

0.15

0.1

0.05

-0.05

Percent Difference -0.1

-0.15 Entrance Exit -0.2 3 cm H20 5 cm H20 8 cm H20 10 cm H20

Figure 44. Case II percent difference of the flow side versus non-flow side pressure for the -10 o convergent fold (above) and +20o divergent fold (below) for 0.16 cm nominal diameter. 89

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 2

5 Pressure Drop (cm H PressureDrop (cm 6 Entrance Exit 7 Divergent Side - Flow Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 4

10 Pressure Drop (cm H PressureDrop (cm 12 Entrance Exit 14 Divergent Side - Flow Side Convergent Side - Non-Flow Side

Figure 45. Case II pressure distributions for the minimal nominal diameter 0.32 cm for

transglottal pressures of 1, 3, and 5 cm H20 (top) and 8 and 10 cm H20 (bottom) where the

divergent side is the flow side and the convergent side is the non-flow side.

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop

0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75

1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm H20

Figure 46. Case II normalized pressure distributions for the non-flow side -10o convergent fold

(upper curves corresponding to the right vertical axis) and flow side +20o divergent fold (lower

curves corresponding to the left vertical axis) for the nominal diameter of 0.32 cm. 91

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

2 2

5 Pressure Drop (cm H PressureDrop (cm 6 Entrance Exit 7 Divergent Side - Non-Flow Side Convergent Side - Flow Side

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2

4 O) 2 6 8 10 12 14 Pressure Drop (cm H PressureDrop (cm 16 Entrance Exit 18 Divergent Side - Non-Flow Side Convergent Side - Flow Side

Figure 47. Case II pressure distributions for the minimal nominal diameter 0.32 cm for transglottal pressures of 1, 3, and 5 cm H20 (top) and 8 and 10 cm H20 (bottom) where the

divergent side is the non-flow side and the convergent side is the flow side.

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.25 0

0 0.25

0.25 0.5

0.5 0.75 Pressure Drop

0.75 1

1 1.25 Normalized

1.25 1.5

Entrance Exit 1.5 1.75

1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm H20

Figure 48. Case II normalized pressure distributions for the flow side -10o convergent fold

(upper curves corresponding to the right vertical axis) and non-flow side +20o divergent fold

(lower curves corresponding to the left vertical axis) for the nominal diameter of 0.32 cm. 93

Axial Distance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.2

0.15

0.1

0.05

-0.05

Percent Difference -0.1

-0.15 Entrance Exit -0.2 1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm H20

Axial Distance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.2

0.15

0.1

0.05

-0.05

Percent Difference -0.1

-0.15 Entrance Exit -0.2 1 cm H20 3 cm H20 5 cm H20 8 cm H20 10 cm H20

Figure 49. Case II percent difference of the flow side versus non-flow side pressure for the -10 o convergent fold (above) and +20o divergent fold (below) for 0.32 cm nominal diameter. 94

Axial Distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -1 0

o -0.75 -10 0.25 0.005 cm Conv. Side -0.5 0.5

-0.25 0.75

0.32 cm 0 1

0.25 1.25 Pressure Drop

+20o 0.5 0.005 cm Div. Side 0.75 Normalized

1 0.32 cm

1.25

Entrance Exit 1.5 Dn:0.005 Dn:0.01 Dn:0.02 Dn:0.04 Dn:0.08 Dn:0.16 (CFS) Dn:0.16 (DFS) Dn:0.32 (CFS) Dn:0.32 (DFS)

Figure 50. Case II normalized pressure distribution averaged across transglottal pressure and

shown for each glottal diameter for the -10o convergent side (upper curves corresponding to the

right vertical axis) and +20o divergent side (lower curves corresponding to the left vertical axis).

Table 17

Standard deviation of the normalized transglottal pressure at each tap of the divergent vocal fold

Tap Dn: Dn: Dn: Dn: Dn: Dn: Dn: Dn: Dn: 0.005 0.01 0.02 0.04 0.08 0.16c 0.16d 0.32c 0.32d 1 0.0011 0.0019 0.0034 0.0018 0.0023 0.0067 0.0045 0.0084 0.0051

2 0.0021 0.0023 0.0048 0.0037 0.0023 0.0041 0.0071 0.0197 0.0091

3 0.0031 0.0034 0.0033 0.0020 0.0038 0.0095 0.0043 0.0153 0.0084

4 0.0030 0.0020 0.0073 0.0018 0.0056 0.0080 0.0141 0.0190 0.0111

5 0.0032 0.0072 0.0067 0.0169 0.0409a 0.0175 0.0191 0.036a 0.0183

6 0.1119b 0.0530a 0.0202a 0.0449a 0.0646a 0.0361a 0.0471a 0.0592a 0.0256a

7 0.1275b 0.0523a 0.0453a 0.0476a 0.0652a 0.0300a 0.0322a 0.0413a 0.0154

8 0.0364a 0.0429a 0.0490a 0.0418a 0.0612a 0.0272a 0.0279a 0.0278a 0.0081

9 0.0182 0.0217a 0.0307a 0.0321a 0.0613a 0.0332a 0.0234a 0.0218a 0.0087

10 0.0091 0.0080 0.0190 0.0133 0.0420a 0.0355a 0.0194 0.0279a 0.0083

11 0.0058 0.0059 0.0114 0.0461a 0.0417a 0.0446a 0.0148 0.0269a 0.0100

12 0.0104 0.0073 0.0487a 0.1977b 0.0155 0.0095 0.0152 0.0165 0.0114

13 0.0100 0.0036 0.0133 0.0703a 0.0369a 0.0144 0.0195 0.0196 0.0255a

14 0.0050 0.0033 0.0076 0.0365a 0.0295a 0.0181 0.0202a 0.0215a 0.0101

15 0.0066 0.0072 0.0228a 0.1059b 0.0341a 0.0169 0.0155 0.0250a 0.0107

16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 a Indicates SD is larger than 0.02 of the normalized pressure. b Indicates SD is larger than 0.10 of the normalized pressure c Flow Side. d Non-Flow Side.

Table 18

Standard deviation of the normalized transglottal pressure at each tap of the convergent vocal fold

Tap Dn: Dn: Dn: Dn: Dn: Dn: Dn: Dn: Dn: 0.005 0.01 0.02 0.04 0.08 0.16c 0.16d 0.32c 0.32d 1 0.0019 0.0005 0.0007 0.0011 0.0019 0.0041 0.0059 0.0118 0.0062

2 0.0009 0.0005 0.0013 0.0009 0.0024 0.0030 0.0029 0.0028 0.0042

3 0.0018 0.0003 0.0006 0.0016 0.0063 0.0074 0.0040 0.0073 0.0030

4 0.0029 0.0003 0.0011 0.0030 0.0105 0.0095 0.0058 0.0101 0.0063

5 0.0029 0.0021 0.0027 0.0181 0.0423a 0.0265a 0.0114 0.0219a 0.0064

6 0.0646a 0.0067 0.0117 0.0355a 0.0409a 0.0250a 0.0137 0.0255a 0.0131

7 0.1884b 0.0406a 0.0448a 0.0374a 0.0494a 0.0262a 0.0159 0.0294a 0.0211a

9 0.0080 0.0223a 0.0336a 0.0410a 0.0234a 0.0219a 0.0152 0.0288a 0.0132

10 0.0019 0.0049 0.0131 0.0299a 0.0424a 0.0225a 0.0147 0.0252a 0.0198

11 0.0142 0.0451a 0.0941a 0.0148 0.0285a 0.0228a 0.0143 0.0318a 0.0137

12 0.0026 0.0547a 0.1046b 0.0094 0.0166 0.0281a 0.0061 0.0198 0.0152

13 0.0049 0.0299a 0.0485a 0.0095 0.0091 0.0222a 0.0096 0.0201a 0.0110

15 0.0020 0.0146 0.0196 0.0062 0.0124 0.0173 0.0076 0.0181 0.0053

Summary of flow data.

As expected, the flow data showed a quadratic relationship between pressure and flow, of which the dominate term decreased as the diameter increased (Figure 48 and Table 16). The flows for Case II ranged from 9.78 cc/s to 1591.66 cc/s, which are likewise comparable to realistic values phonation. The equations in Table 20 were used to derive a general equation for pressure as a function of flow and diameter:

P= C1*U2 + C2*U

-2.0059 C1Divergent= 2.5780E07D , R² = .9877

3 2 C2Divergent = -0.2109(log10D) - 0.7047(log10D) - 0.7515(log10D) - 0.2342,R² =.9651

-2.0179 C1Convergent = 2.7054E07D , R² = .9877

3 2 C2Convergent = -0.2199(log10D) - 0.7611(log10D) - 0.8348(log10D) - 0.2643,R² = 0.9705 where P is equal to the transglottal pressure in cm H20, u is equal to the flow in cc/s, and D is equal to the to the diameter in cm. Coefficients were calculated for when the pressures were collected from both the divergent and convergent folds. The subscript of the coefficients denotes for which vocal fold pressure data were collected.

Across all transglottal pressures, the Reynolds number ranged from 108.1979 to

13963.0760 and the transglottal pressure coefficient ranged from 0.57 to 1.79 (Figure 49).

Regression equations are given in Table 22. These Reynolds numbers suggest that even for a large subglottal pressure, the flow regime when the glottal diameter is relative small is still laminar. In this static model for this configuration, the largest Reynolds numbers occurred at the larger diameters.

Table 19

Case II flows when the pressures on the convergent vocal fold were recorded

Pt 0.005 0.01 0.02 0.04 0.08 0.16 0.16 0.32 0.32 a b a b cm H20 cm cm cm cm cm cm cm cm cm 1 ------441.14 438.93 3 10.06 21.23 44.73 92.15 194.35 398.57 397.15 851.85 850.03

5 13.08 29.13 57.53 119.99 257.91 540.17 538.60 1197.70 1193.27

8 - - - - - 727.69 725.95 1343.42 1341.89

10 19.90 43.37 82.22 172.66 383.30 828.71 824.00 1586.42 1591.66

15 24.94 54.81 102.66 217.18 507.83 1095.34 - - -

25 35.26 69.53 136.27 300.67 733.86 - - - -

50 57.12 104.83 203.31 462.89 1150.13 - - - -

75 73.46 134.02 269.04 591.50 - - - - - Note. The nominal transglottal pressures are reported rather than empirical values. a Flow Side. b Non-Flow Side.

Table 20

Case II flows when the pressures on the divergent vocal fold were recorded

Pt 0.005 0.01 0.02 0.04 0.08 0.16 0.16 0.32 0.32 a b a b cm H20 cm cm cm cm cm cm cm cm cm 1 ------470.91 466.50 3 9.78 21.58 44.64 91.71 192.97 401.73 403.85 895.58 896.02

5 12.65 29.40 57.38 118.92 256.33 538.78 546.80 1206.35 1205.27

8 - - - - - 715.45 722.44 1332.53 1338.19

10 19.20 43.26 81.98 171.07 379.54 832.43 833.86 1566.18 1574.58

15 25.06 54.61 102.13 215.01 508.51 - 1084.99 - -

25 35.17 69.93 134.23 299.84 733.47 - - - -

50 54.32 104.03 199.32 457.89 1147.15 - - - -

75 69.92 133.00 255.65 585.98 - - - - - Note. The nominal transglottal pressures are reported rather than empirical values. a Flow Side. b Non-Flow Side.

100

90 D:0.005

80 D:0.01 0)

2 D:0.02 70 D:0.04 D:0.08 60 D:0.16 D:0.32 50

Transglottal Pressure (cmH Pressure Transglottal 20

0 0 200 400 600 800 1000 1200 1400 1600 1800 Flow (cc/s)

Figure 51. Full range of transglottal pressures and flows for Case II.

Table 21

Regression equations for pressure versus flow across diameters for Case II

Diameter Convergent Side on the Left Divergent Side on the Left 2 2 Dn : 0.32 P = 4.4574E-06u - 0.0006u, R² = .9821 P = 3.9128E-06u + 0.0002u, R² = .9843

2 2 Dn : 0.16 P = 8.7092E-06u + 0.0046u, R² = .9984 P = 8.2368E-06u + 0.0049u, R² = .9977

2 2 Dn : 0.08 P = 2.3933 E-05u + 0.0126u, R² = .9988 P = 2.3590E-05u + 0.0164u, R² = .9987

2 2 Dn : 0.04 P = 0.0002x + 0.0315u, R² = .9991 P = 0.0002u + 0.0317u, R² = .9991

2 2 Dn : 0.02 P = 0.001u + 0.0491u, R² = .9986 P = 0.0008u + 0.066u, R² = .9963

2 2 Dn : 0.01 P = 0.0036u + 0.089u, R² = .9988 P = 0.0035u + 0.0963u, R² = .9992

2 2 Dn : 0.005 P = 0.0109u + 0.3175u, R² = .9994 P = 0.0092u + 0.3482u, R² = .9989 Note. u is the flow in cc/s and P is pressure in cm H20 101

D:0.005 D:0.01 1.8 D:0.02 D:0.04 1.6 D:0.08 D:0.16 1.4 D:0.32

1.2

0.8 Transglottal Pressure Coefficient P* Coefficient Pressure Transglottal 0.6

0.4 0 2000 4000 6000 8000 10000 12000 14000 16000 Reynolds Number Re

1.8

1.6

1.4

1.2

0.8

Transglottal Pressure Coefficient P* Coefficient Pressure Transglottal 0.6

0.4 1.5 2.5 3.5 4.5 5.5 Log (Re) 10

Figure 52. Reynolds number versus transglottal pressure coefficient for all diameters of Case II.

102

Table 22

Regression equations for Re versus P* across diameters for Case II

Diameter Convergent Side on the Left Divergent Side on the Left 2 2 Dn : 0.32 P* = 2.3779*log10(Re) - P* = 1.6884*log10(Re) -

18.591*log10(Re) + 37.233, R² =.4959 13.526*log10(Re) + 28.048, R² =.7071

Dn : 0.16 P* = -0.8133*log10(Re) + 4.0599, P* = -0.8766*log10(Re) + 4.302,

R² =.9894 R² =.9922

Dn : 0.08 P* = -0.8831*log10(Re) + 4.1697, R² P* = -0.8691*log10(Re) + 4.1125,

=.9821 R² =.9807

2 2 Dn : 0.04 P* = -0.5995*log10(Re) + P* = -0.5869*log10(Re) +

3.3685*log10(Re) - 3.3415, R² =.9833 3.2901*log10(Re) - 3.2309, R² =.9877

2 2 Dn : 0.02 P* = -0.7206*log10(Re) + P* = -0.8695*log10(Re) +

3.9688*log10(Re) - 4.0267, R² =.9988 4.8014*log10(Re) - 5.2037, R² =.9971

Dn : 0.01 P* = -0.5954*log10(Re) + 2.8915, R² P* = -0.6633*log10(Re) + 3.0765,

=.9532 R² =.9500

Dn : 0.005 P* = -1.1718*log10(Re) + 4.2369, P* = -1.1366*log10(Re) + 4.1158,

R² = .9854 R² =.9862

103

CHAPTER IV: DISCUSSION

The current investigation examined intraglottal pressures for two asymmetric static glottal configurations using constant flow. The left-right asymmetry, called obliquity, here was comprised of a glottal configuration with walls differing in angle relative to the vertical axis, with one convergent vocal fold and one divergent vocal fold. The sum of the angles of the two walls formed a convergent and divergent glottal geometry for the two cases examined.

Similar Observations between Case I and Case II

The findings of this investigation suggest that as the diameter increases, the pressure distribution on the medial surfaces of the two vocal folds become less similar, resembling the pressure distribution pattern more typically expected for the individual convergent and divergent geometry of each fold. That is, there was aerodynamic uncoupling as the diameter increased. For small diameters and transglottal pressures within the speech rage, 1 to 15 cm H20, the pressure

distributions acting on each fold were more similar than for the larger diameters. Because of this

similarity in pressure on the two sides, the folds may be caused to move more synchronously

(i.e., similarly), a phenomena that can be called aerodynamic entrainment of the vocal folds.

In the oblique divergent glottis (Case II) at diameters larger than and including 0.04 cm,

the divergent vocal fold at entrance exhibited a negative pressure while the convergent side exhibited a positive pressure. For the convergent oblique glottis studied (Case I), only at the largest diameter, 0.32 cm, was there a negative pressure on the divergent fold and a positive

pressure on the convergent fold relative to transglottal pressure. The finding that the entrance

pressure of each vocal fold can differ in polarity suggests that these configurations would result

in aerodynamic forces that are strongly out of phase. That is the pressure at entrance for the

above mentioned configurations would result in a pushing force driving the inferior margin of 104 the convergent fold laterally, and in pulling forces driving the inferior margin of the divergent fold medially, potentially enhancing obliquity.

In general, the divergent fold for both cases exhibited lower pressures when compared to the convergent fold. At the smallest diameters, however, a greater pressure drop (lower pressure) was observed on the convergent fold near the location of the minimal diameter. For Case I the tap nearest the minimal diameter, tap12, was more downstream on the convergent fold than the divergent fold because the exit radius of the convergent fold was smaller than that of the divergent fold. This may be due in part to the fact that the convergent wall was the “near” wall to which the flow may have been attached in accordance with Erath and Plesniak (2006a). Previous research has indicated that the pressures on the wall to which the flow is attached are lower than the pressures on the stalled or non-flow side (Scherer et al., 2001).

Differences between Case I and Case II

One clear difference between the two cases in the current investigation is the effect of the

overall convergence or divergence of the glottal configuration. This difference dictated the

location of the minimal diameter and in most cases the location of the largest pressure drop.

Thus, for the convergent oblique glottis (Case I) at diameters smaller than 0.32 cm, the largest

pressure drop occurred near the glottal exit. For the divergent oblique glottis (Case II) the largest

pressure drop occurred near the entrance. At typically higher transglottal pressures for the divergent case, there were bimodal pressure distributions in the glottis for diameters below 0.04 cm, with the first local pressure drop near the entrance and the second local pressure drop occurring near taps 11 and 12 just before the glottal exit. The bimodal pressure distributions occurred for both the convergent side (for diameters 0.01 and0.02 cm) and the divergent side (for 105 diameters 0.02 and 0.04 cm). It is hypothesized that the second pressure dip is also due to flow acceleration near the glottal exit expansion where the flow is near the wall with the pressure dip.

A second difference between the two cases in the current investigation was the range of the pressure distributions when normalized by the transglottal pressure. For the convergent case, the pressure distributions were relatively similar when normalized, while the divergent case

exhibited less overlap when normalized. Because the pressure distributions are highly similar

when replicated, the variation in the distributions appears quite valid, suggesting that the

divergent case is more sensitive to diameter and transglottal pressure changes. The pressure

distributions are dependent on the direction of the flow out of the glottis (Erath and Plesniak

2006a).

Another difference between the convergent and divergent case presented in this

investigation is that a bistability of the flow (where the flow exiting the glottis could essentially

go toward the right or toward the left) was only observed in the divergent case, for the two

largest diameters. The decreased probability of bistability for all but the latter two cases is most

likely due to the obliquity angle itself, because bistability has been studied in M5 for the

symmetric cases of +10 divergent and -10 convergent, where bistability was present for both

angles (see below), for diameters greater than or equal to 0.02 cm. The bistability was tested by

the insertion of a sheet of paper into the glottal duct to direct the flow exiting the glottis to the

right or the left. For both cases, the robust tendency was for the flow exiting the glottis to go

towards the downstream wall to which the divergent fold was attached as both folds were angled

in that direction.

106

Extension and Comparison of the Findings

The main inquiry of the systematic study of glottal asymmetry and obliquity relates to the consequence of intraglottal pressure differences and their effects on vocal fold oscillation. This includes the question of how glottal obliquity promotes or inhibits the motion of the vocal folds.

Dynamic motion, involving both tissue and aerodynamic forces (that vary in value and

dominance throughout the cycle of vibration), must be considered. A direct answer exceeds the

scope of the current investigation, as this study provides the aerodynamic information for two

static geometries across a range of pressures and diameters, but not the simulation of voicing.

However, comparison of the findings to intraglottal pressure in the symmetric glottis is a first

step in examining the significance of obliquity.

Comparison of oblique data with symmetric data.

When the data obtained for the two cases of glottal obliquity are compared to the

previous research of the symmetric glottis, many trends are apparent. The following discussion

highlights specific cases for comparison. This discussion is supplemented with Appendix B,

which provides a complete inventory of figures comparing the oblique and symmetric data for

the two cases. The pressure distributions of convergent and divergent vocal fold walls of the 15o oblique convergent (-10o) glottis (Case I) are compared to the flow wall and non-flow wall data of the -10o degree convergent symmetric glottis. As a reminder, the symmetric case includes two

vocal fold walls, each having a convergent angle of -5o. The pressure distributions of convergent and divergent vocal fold walls of the 15o oblique divergent (+10o) glottis (Case II) is compared to the flow wall and non-flow wall data of the +10o degree divergent symmetric glottis. Symmetric data are limited to the transglottal pressure below 15 cm H20 for all diameters except the largest diameter, 0.32 cm, for which only the three transglottal pressure drops 1, 3, and 5 cm H20. 107

The findings suggest that when the diameter is small, the pressures in the oblique glottis, for both cases, are similar to the pressures in the symmetric glottis, indicating increased aerodynamic coupling for heightened entrainment of the vocal fold motion. Effectively, the intraglottal pressures are “blind” to the obliquity angles. When the glottal diameter is large, however, the glottis is less aerodynamically entrained, and the pressure distributions on each fold differ, and the pressures therefore “see and are affected by the obliquity.”

Subsequent figures in this discussion display the symmetric flow wall data using a black

dotted curve with unfilled circle data points; symmetric non-flow wall data using a grey dashed

curve with filled circle data points; the divergent side of the oblique glottis using a black dashed

curve with filled square data points; and the convergent side of the oblique glottis using a black

solid curve with unfilled square data points.

Small diameters: 0.005 to 0.04 cm.

General overview.

When comparing the oblique and symmetric data for the diameters less than and

including 0.04 cm, the fit for both cases are relatively similar. For example, Figures 53 and 54

display comparative data for Case I and Case II for the diameter of 0.005 cm and a transglottal

pressure of 10 cm H20. For 0.005 and 0.01 cm diameters, the largest difference from symmetric

data occurs near the minimal glottal diameter. For the mid-size glottal diameters, 0.02 and 0.04

cm, the pressure differs most from symmetric data at glottal entrance. Figures 55 and 56 display

Case I and Case II, respectfully, at the diameter of 0.04 and a transglottal pressure of 10 cm H20.

At these small diameters the vocal folds are more aerodynamically entrained as the intraglottal pressures are similar. 108

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure

Figure 53. Case I pressure distributions comparison for an oblique and symmetric convergent glottis with an included angle (IA) of -10o and a minimal diameter of 0.005 cm for the

transglottal pressure of 10 H20.

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Pressure Drop (cm H20) (cm Drop Pressure 10

Figure 54. Case II pressure distributions comparison for an oblique and symmetric divergent

glottis with an IA of +10o and a minimal diameter of 0.005 cm for the transglottal pressure of 10

H20.

109

Case I.

For the 0.005 and 0.01 cm diameter near the location of the minimal diameter for the convergent glottis case, the pressure on the divergent fold is higher than in the symmetric glottis corresponding to the same included angle, while the pressure on the convergent fold is lower

(Figure 53). Notice, however, that the locations of the tap nearest the minimal diameter (tap 11) are located at different axial distances. As this region near the minimal diameter is a sensitive location, pressure at the same axial location on each fold may actually be similar. Thus the spline curves (from Excel) interpolated between the data points may not be valid representations of the data at this location. For the diameters 0.02 and 0.04 cm (Figure 55) the pressures on the divergent fold are lower than for the corresponding symmetric glottis, while the pressures on the convergent fold are higher.

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Figure 55. Case I pressure distributions comparison for an oblique and symmetric convergent glottis with an IA of -10o and a minimal diameter of 0.04 cm for the transglottal pressure of 10

H20.

110

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Figure 56. Case II pressure distributions comparison for an oblique and symmetric divergent

glottis with an IA of +10o and a minimal diameter of 0.04 cm for the transglottal pressure of 10

H20.

Case II.

Aside from pressures at glottal entrance, the pressure distributions for the divergent

oblique glottis at small diameters are similar to that of the symmetric glottis with the same

included angle. Thus, the pressures in the second half or downstream portion of the oblique

glottis and symmetric glottis are similar (Figure 54). The pressure at the entrance of the glottis

for these small diameters is higher for both the convergent and divergent fold of the oblique

glottis compared to the symmetric data. This is most likely due to the shift in the axial direction

near the location of the minimal diameter. The different entrance radii of the convergent and divergent fold in the oblique condition shift the minimal gap (just past tap 6) downstream of the corresponding location in the symmetric configuration (at tap 6). If this oblique divergent geometry occurred during the closing portion of the cycle, as glottal closing is dominated by the 111 divergent glottal geometry, pressure of the asymmetric glottis would inhibit the depth of closure near entrance as they are pushing forces acting on the vocal folds.

Large diameters: 0.08 to 0.32 cm.

As stated previously, when the diameter is large, the vocal folds are less entrained

because the contour and size of the pressure distributions differ on the two sides of the glottis.

The pressure distributions for the symmetric data with the same included angle differ from those

of the oblique glottis, with the convergent fold of the oblique glottis exhibiting higher pressures at entrance and the divergent fold of the oblique glottis exhibiting lower pressures at entrance.

Figures 57 through 64 display these differences among pressure distributions. The distributions from the symmetric studies are shown for two general considerations, one for the same

intraglottal angles (+10o and -10o), as well as from various angles and diameters that more closer

match the pressure distributions of each vocal fold for the oblique cases. The latter is an exercise

that asks, are there any symmetric situations that give pressure distributions that are close to

those of the oblique glottis?

Case I.

When compared to the pressures within the symmetric glottis of the same included angle,

there exist higher pressures on the convergent fold and lower pressures on the divergent fold of

the oblique configuration (Figures 57 through 59).

For the -20o convergent fold of Case I, the pressure distribution of the convergent fold is

matched best by the intraglottal pressures acting on the 10o convergent fold in a symmetric 20o

convergent glottis at the largest diameters of 0.16 and 0.32 cm as seen in Figures 57 and 58.

Only near glottal entrance for 0.08 cm and 0.16 cm, are the pressures on the convergent oblique

fold close to the distribution from symmetric cases (Figures 58 and 59). According to Figure 59 112 for a diameter of 0.08 cm, the middle portion of the glottis is more similar to the pressure distribution symmetric glottis with the same included angle (-10o). The +10o divergent fold of

Case I mirrors other convergent pressure distributions except at the largest diameter of 0.32 cm.

At this diameter, the pressure distribution on the +10o divergent fold best matches the pressures

acting on the flow wall of a symmetric 20o divergent glottis (Figure 57).

113

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW -10 Deg 0.32 0.5 Sym NFW -10 Deg 0.32 Obl Conv Side 0.32 1 Obl Div Side 0.32 1.5 Sym FW +20 Deg 0.16 Sym NFW -20 Deg 0.32 2 Sym NFW -40 Deg 0.32 2.5 3

Pressure Drop (cm H20) (cm Drop Pressure 3.5 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW -10 Deg 0.32 Sym NFW -10 Deg 0.32 1 Obl Conv Side 0.32 Obl Div Side 0.32 2 Sym FW +20 Deg 0.16 Sym NFW -20 Deg 0.32 3 Sym NFW -40 Deg 0.32 4

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure 57. Case I convergent glottis, comparison of pressure distributions among the oblique

glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.32 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

pressures of 3 and 5 cm H20.

114

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW +10 Deg 0.32

0.5 Sym NFW -10 Deg 0.16 1 Obl Conv Side 0.16 Obl Div Side 0.16 1.5 Sym FW -10 Deg 0.32 2 Sym NFW -20 Deg 0.16

2.5

Pressure Drop (cm H20) (cm Drop Pressure 3

3.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW -10 Deg 0.16

Sym NFW -10 Deg 0.16 1 Obl Conv Side 0.16 Obl Div Side 0.16 2 Sym FW -10 Deg 0.32 Sym NFW -20 Deg 0.16 3

4 Pressure Drop (cm H20) (cm Drop Pressure 5

Figure 58. Case I convergent glottis, comparison of pressure distributions among the oblique glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.16 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

pressures of 3 and 5 cm H20. 115

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5 Sym FW -10 Deg 0.08 1 Sym NFW -10 Deg 0.08 1.5 Obl Conv Side 0.08 2 Obl Div Side 0.08 2.5 3 Sym NFW -5 Deg 0.08 3.5 Sym NFW -20 Deg 0.08 4 4.5 Pressure Drop (cm H20) (cm Drop Pressure 5 5.5 6

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW -10 Deg 0.08 1

Sym NFW -10 Deg 0.08 2 Obl Conv Side 0.08 3 Obl Div Side 0.08 4 Sym NFW -5 Deg 0.08 5 Sym NFW -20 Deg 0.08 6 7 8

Pressure Drop (cm H20) (cm Drop Pressure 9 10 11 12

Figure 59. Case I convergent glottis, comparison of pressure distributions among the oblique glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.08 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

pressures of 5 and 10 cm H20.

116

Case II.

For the divergent oblique glottis (Case II with a -10o convergent side and a +20o divergent side) and diameter of 0.08 and 0.16 cm (Figures 60 through 62), the pressure distributions on both the flow wall and non-flow wall of the +10o divergent were similar, within

10%, to the pressure distribution on the +20o divergent oblique fold.

The convergent oblique fold however, was not matched well by the symmetric case with the same included angle, with higher pressures for the oblique convergent fold in the first half of the glottal duct. The symmetric data that best matched the convergent oblique fold included the uniform glottis for 0.08 cm (Figure 60), the -5o convergent glottis for 0.16 cm (Figures 61 and

62), and the -10o convergent glottis for 0.32 cm (Figures 63 and 64). For the convergent fold of

Case II, as the diameter increased from 0.08, the symmetric pressure distribution, having the same diameter which was a best match, increased in degree of convergence from the half angles of uniform at 0.08 cm to -5 degree convergence at 0.32 cm. According to Figures 63 and 64, for the 0.32 cm diameter, the pressure acting on the symmetric -5o convergent glottis for the diameter of 0.16 cm, was also a good match for the pressure distribution on the convergent fold of Case II.

117

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.08

1 Sym NFW 10 Deg 0.08 Obl Conv Side 0.08 2 Obl Div Side 0.08 3 Sym NFW Uniform 0.08 Sym NFW Uniform 0.04 4

5 Pressure Drop (cm H20) (cm Drop Pressure

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.08

2 Sym NFW 10 Deg 0.08 Obl Conv Side 0.08 4 Obl Div Side 0.08 6 Sym NFW Uniform 0.08 Sym NFW Uniform 0.04 8

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Figure 60. Case II divergent glottis, comparison of pressure distributions among the oblique glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.08 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

pressures of 5 and 10 cm H20.

118

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.16 0.5 Sym NFW 10 Deg 0.16

1 Obl Conv Side 0.16 FS 1.5 Obl Div Side 0.16 NFS Sym FW -5 Deg 0.16 2

2.5

Pressure Drop (cm H20) (cm Drop Pressure 3

3.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.16 1 Sym NFW 10 Deg 0.16 Obl Conv Side 0.16 FS 2 Obl Div Side 0.16 NFS 3 Sym NFW -5 Deg 0.16

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure 61. Case II divergent glottis, comparison of pressure distributions among the oblique glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.16 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

o o pressures of 3 and 5 cm H20 (-10 convergent side is the flow side and +20 divergent side is the

non-flow side). 119

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.16

0.5 Sym NFW 10 Deg 0.16

1 Obl Conv Side 0.16 NFS 1.5 Obl Div Side 0.16 FS Sym FW -5 Deg 0.16 2

2.5

Pressure Drop (cm H20) (cm Drop Pressure 3

3.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.16

1 Sym NFW 10 Deg 0.16 Obl Conv Side 0.16 NFS 2 Obl Div Side 0.16 FS 3 Sym NFW -5 Deg 0.16

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure 62. Case II divergent glottis, comparison of pressure distributions among the oblique glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.16 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

o o pressures of 3 and 5 cm H20 (+20 divergent side is the flow side and the -10 convergent side is

the non-flow side). 120

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.32 0.5 Sym NFW 10 Deg 0.32 Obl Conv Side 0.32 FS 1 Obl Div Side 0.32 NFS 1.5 Sym NFW +20 Deg 0.32 Sym FW -10 Deg 0.32 2 Sym FW -5 Deg 0.16 2.5 3 Pressure Drop (cm H20) (cm Drop Pressure 3.5 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.32

1 Sym NFW 10 Deg 0.32 Obl Conv Side 0.32 FS 2 Obl Div Side 0.32 NFS Sym NFW +20 Deg 0.32 3 Sym FW -10 Deg 0.32 Sym FW -5 Deg 0.16 4

5 Pressure Drop (cm H20) (cm Drop Pressure

Figure 63. Case II divergent glottis, comparison of pressure distributions among the oblique glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.32 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

o o pressures of 3 and 5 cm H20 (-10 convergent side is the flow side and +20 divergent side is the

non-flow side). 121

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.32 0.5 Sym NFW 10 Deg 0.32 Obl Conv Side 0.32 NFS 1 Obl Div Side 0.32 FS 1.5 Sym NFW +20 Deg 0.32 Sym NFW -10 Deg 0.32 2 Sym FW -5 Deg 0.16 2.5 3

Pressure Drop (cm H20) (cm Drop Pressure 3.5 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 Sym FW 10 Deg 0.32 Sym NFW 10 Deg 0.32 1 Obl Conv Side 0.32 NFS 2 Obl Div Side 0.32 FS Sym NFW +20 Deg 0.32 3 Sym NFW -10 Deg 0.32 Sym FW -5 Deg 0.16 4

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure 64. Case II divergent glottis, comparison of pressure distributions among the oblique glottis. The symmetric glottis with -10o convergent , for the minimal diameter of 0.32 cm and the

symmetric glottis cases that best match the two sides of the oblique glottis for the transglottal

o o pressures of 3 and 5 cm H20 (+20 divergent side is the flow side and the -10 convergent side is

the non-flow side).

122

Effect of obliquity.

In the current investigation the effect of obliquity is largely related to diameter. When the diameter is small there is less effect of obliquity as the intraglottal pressures are similar to those of the symmetric glottis. For the divergent case the only effect of obliquity at small diameters,

the higher pressure acting at the glottal entrance for the oblique case. As the diameter increases,

however, the there is an effect of obliquity. For Case I, the pressures acting on the divergent

oblique fold are 24 to 40% lower at the glottal entrance than the pressure for the symmetric

glottis with a -10o convergence. For Case I, the driving pressures acting on the convergent fold of the oblique glottis are 30 to 40% higher at the glottal entrance than the symmetric glottis of the same included angle. For Case II, the driving pressures acting on the convergent fold of the oblique glottis are 30 to 40% higher at the glottal entrance than the symmetric glottis with a +10o divergence. The pressures acting on the divergent oblique fold are relatively similar to the symmetric glottis with a +10o divergence. For these larger diameters, the data suggest that there

is the potential for increased asymmetric motion because the pressure on the vocal folds differ

greatly from the symmetric glottis.

Replication comparisons.

The current investigation expanded on previous work regarding pressure distributions in

the oblique glottis. Scherer et al., 2001 examined one diameter included in the current study.

These authors examined the 0.04 cm diameter of Case II along with a later publication, Shinwari

et al., 2003. The current investigation replicated this glottal configuration along with previously

collected data for Case I and the 0.04 cm diameter. The pressure distributions comparing the

original M5 Data and Current M5 data for Case I and Case II are shown in Figure 65 and 66,

respectively. 123

The pressures in the glottis for Case I (Figure 65) were well within 2% of previous results with the average pressure difference being less than 1% at each pressure tap in the glottis (taps 6-

12) for the convergent fold and less than 1.6% at each pressure tap in the glottis (taps 6-12) for the divergent fold. The largest percent difference in the glottis for the each was within 2% of the transglottal pressure (Figure 66). The flow values were within 3.2%.

The pressures in the glottis for Case II were well within 2% of previous results with the average pressure difference being 1% at each pressure tap in the glottis (taps 6-12) for the convergent fold and less than 1% at each pressure tap in the glottis (taps 6-12) for the divergent fold. The largest percent difference for the convergent fold was 2.6% and 1.3% for the divergent fold. The flow data were within 6%. This large difference in flow values is most likely due to the addition of the windscreen over tap 16 compared to previous experimental runs. When flow exits the glottis toward the left wall, there is a tendency for the pressure drop at tap 16 to be lower than when the flow goes toward the right wall. If there is a local negative pressure at tap 16, a higher flow is required to increase the pressure drop at tap 16 to the prescribed transglottal pressure.

The addition of the windscreen over tap 16 decreased this local flow effect. The largest differences in the flow measurements for Case II of the current investigation and previous data are observed when the pressures are measured on the divergent fold. In the Case II configuration, when the divergent vocal fold is placed on to the left side of the wind tunnel for pressure measurement, the flow exiting the glottis moves toward the left wall, downstream. This is the condition for which the pressure at tap 16 may be affected by local flow patterns that create an apparent pulling, or negative pressure, at tap 16. Thus the addition of the modified windscreen over tap 16 may be one explanation as to why previous data reported flows that were 4 to 5% higher than the current investigation for this condition. The use of the windscreen is considered 124 to be a significant improvement in the methodology, and adjust of prior data using model M5 need to be considered in light of this finding.

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0) 2

10 Pressure Drop (cm H PressureDrop (cm

18 Entrance Exit Original M5 Data (Div.) Current M5 Data (Div.) Original M5 Data (Conv.) Current M5 Data (Conv.)

Figure 65. Case I comparison of current empirical data with original M5 data. 125

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0) 2 8

12 Pressure Drop (cm H PressureDrop (cm

20 Entrance Exit Original M5 Data (Div.) Current M5 Data (Div.) Original M5 Data (Conv.) Current M5 Data (Conv.)

Figure 66. Case II comparison of current empirical data with original M5 data. 126

CHAPTER V: CONCLUSIONS

The current study expanded the body of work concerning pressure distributions and flows

for two cases of asymmetry in which the vocal fold walls differ in convergence and divergence.

Two cases of glottal obliquity were studied, one convergent and one divergent. An obliquity of

15o from the vertical axis was used in both cases. Intraglottal pressures were measured along the

medial surface of the vocal folds. This study examined seven different glottal diameters an a

number of transglottal pressures for each case.

The intraglottal pressure distributions were highly dependent on both angle and diameter.

For both cases, the main effect of increasing diameter was decreased aerodynamic entrainment of

the two vocal folds, characterized by pressure distributions that became more dissimilar from

each other, but more similar relative to the geometry of each side, either convergent or divergent.

Thus, when the diameter was small, the pressure distributions on the two folds were relatively

similar, indicating aerodynamic entrainment, and, except at the entrance location for the

divergent case (Case II), similar to the symmetric glottis. When the diameter was large, however,

the vocal folds are aerodynamically uncoupled, and the pressures on the two vocal folds were significantly different from the pressure within the symmetric glottis with higher pressure on the

convergent fold and lower on the divergent fold.

The normalization overlap of the pressure distributions differed for the convergent and divergent oblique glottis. The convergent glottis demonstrated considerable overlap when

normalized by transglottal pressure, whereas the divergent glottis did not. The significance of

this is that when there is consistent overlap of the pressure distributions when divided by the

transglottal pressure (when they all look alike), the physical properties are similar for each (e.g.,

no shift from laminar to highly turbulent flow within the glottis), and the prediction of the 127 pressure distribution can be made for any realistic transglottal pressure (note the very large range of transglottal pressures in this study, 3 to 75 cm H20). This consistency held more for the convergent oblique glottis, and less for the divergent oblique glottis, and thus care must be taken when predicting or oversimplifying the results for modeling purposes.

For the divergent glottis, at high transglottal pressures, a bimodal pressure distribution was observed at small to midsized diameters. This finding indicates significant pulling forces at these locations that may affect the torque and motion of the vocal fold tissue.

The specific effects of obliquity on the pressure distributions and resultant aerodynamic

forces on the vocal folds can only be determined when the time-varying tissue recoil, tissue

viscous forces, and acceleration forces are known. Inclusion of the data from this study into

computer simulation models of phonation will allow a more in-depth study of the effects on

vibrational asymmetry. These data can be used to test the accuracy of computational models by comparing the pressure values these models predict with the empirical results here.

However, these data suggest several characteristics of this type of glottal asymmetry: 1.

The cross channel pressures in the glottis are relatively similar at small diameters, and

comparable to the symmetric glottis, except possibly at entrance; 2. The cross channel pressure

differences at the entrance increase as glottal diameter increases. 3. For medium to large

diameters for the divergent oblique glottis, pressure acting on the focal folds at glottal entrance

differ in polarity relatively to the transglottal pressure, potentially enhancing out of phase

motion; 4. Pressure distributions in the divergent oblique glottis exhibit increased variability

relative to transglottal pressure.

Further research should model asymmetric vocal fold motion using computer simulation

with empirical pressure distributions and flows to further study the effect of obliquity. Future 128 empirical research in the study of glottal asymmetry should aim to further categorize obliquity relative to vocal fold contour, as well as extend computer models to include more valid intraglottal driving forces.

129

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133

APPENDIX A

Pressure Transducer Calibration Results

This appendix provides figures that show calibration data for the DP-103 and MP-45

Validyne pressure transducers. The calibration procedures and calibration equations can be found

in the Methods section of this thesis (Chapter 2). Below are figures that show the calibration data

for only the best fit and words fit for both transducers. The r-squared (R2) values for are reported.

134

Voltage vs Pressure, DP-103, gain 10mV/V 20

0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Voltage (V) Voltage -5

-10

-15

-20 Pressure (cm H2O)

Voltage vs Pressure, DP-103, gain 10mV/V 10

0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Voltage (V) Voltage -2

-4

-6

-8

-10 Pressure (cm H2O)

Figure A1.Best fit (R2=1.0000) calibration for the DP-103. 135

Voltage vs Pressure, DP-103, gain 50mV/V

0 -3 -2 -1 0 1 2 3 Voltage (V) Voltage

-2

-4

-6 Pressure (cm H2O)

Voltage vs Pressure, DP-103, gain 50mV/V 4.0

3.0

2.0

1.0

0.0 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6

Voltage (V) Voltage -1.0

-2.0

-3.0

-4.0 Pressure (cm H2O)

Figure A2.Worst fit (R2=0.9998) calibration for the DP-103. 136

Voltage vs Pressure, MP45-16, gain 10mV/V 12

0 -5 -3 -1 1 3 5 Voltage (V) Voltage -4

-8

-12 Pressure (cm H2O)

Voltage vs Pressure, MP45-16, gain 10mV/V 10

0 -3 -2 -1 0 1 2 3

Voltage (V) Voltage -2

-4

-6

-8

-10 Pressure (cm H2O)

Figure A3. Best fit (R2=1.0000) calibration for the MP-45. 137

Voltage vs Pressure, MP45-16, gain 2.5mV/V 12

0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Voltage (V) Voltage -4

-8

-12 Pressure (cm H2O)

Voltage vs Pressure, MP45-16, gain 2.5mV/V 8

0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Voltage (V) Voltage -2

-4

-6

-8 Pressure (cm H2O)

Figure A4. Worst fit (R2=0.9995) calibration for the MP-45. 138

APPENDIX B

Comparison of the Oblique Glottis to Symmetric Glottis

This appendix provides a complete inventory of figures comparing the two cases of

glottal obliquity with data from the symmetric glottis with the same included angel.

Case I

The pressure distributions of the 15 degree oblique convergent glottis of -10o (Case I) are

displayed with data of the -10o degree convergent symmetric glottis. The pressure distributions

of -20o convergent and +10o divergent vocal fold walls of the 15 degree oblique convergent

glottis is compared to the flow wall and non-flow wall data of the -10o degree convergent

symmetric glottis. Symmetric data are limited to the transglottal pressure below 15 cm H20 for all diameters except the largest diameter, 0.32 which only include the three transglottal pressure drops 1, 3, and 5 cm H20.

139

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.5

1.5

2.5 Pressure Drop (cm H20) (cm Drop Pressure 3

3.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Pressure Drop (cm H20) (cm Drop Pressure 5

Figure B1. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.005 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20. 140

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Pressure Drop (cm H20) (cm Drop Pressure 10

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2

4 6 8 10 12 14 Pressure Drop (cm H20) (cm Drop Pressure 16 18

Figure B2. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.005 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 141

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.5

1.5

2.5

3 Pressure Drop (cm H20) (cm Drop Pressure 3.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B3. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.01 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 142

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B4. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.01 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 143

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B5. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.02 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 144

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B6. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.02 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 145

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B7. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.04 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 146

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B8. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.04 cm

for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 147

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B9. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.08 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 148

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B10. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.08 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 149

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B11. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.16 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 150

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B12. Case I comparison of the pressure distributions for an oblique and symmetric

convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.16 cm

for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 151

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.25

0.5

0.75

Pressure Drop (cm H20) (cm Drop Pressure 1.25

1.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Figure B13. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.32 cm for the transglottal pressures of 1 (top) and 3 (bottom) cm H20 152

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

6 Pressure Drop (cm H20) (cm Drop Pressure 7

Figure B14. Case I comparison of the pressure distributions for an oblique and symmetric convergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.32 cm for the transglottal pressure of 5 cm H20

Case II

The pressure distributions of the 15 degree oblique divergent glottis of +10o (Case II) are

displayed with data of the +10o degree divergent symmetric glottis. The pressure distributions of

-10o convergent and +20o divergent vocal fold walls of the 15 degree oblique divergent glottis is compared to the flow wall and non-flow wall data of the +10o degree divergent symmetric

glottis. Symmetric data are limited to the transglottal pressure below 15 cm H20 for all diameters

except the largest diameter, 0.32 which only include the three transglottal pressure drops 1, 3,

and 5 cm H20.

153

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.5

1.5

2.5 Pressure Drop (cm H20) (cm Drop Pressure 3

3.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Pressure Drop (cm H20) (cm Drop Pressure 5

Figure B15. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.005 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 154

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Pressure Drop (cm H20) (cm Drop Pressure 10

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2

4 6 8 10 12 14 Pressure Drop (cm H20) (cm Drop Pressure 16 18

Figure B16. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.005 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 155

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.5

1.5

2.5

3 Pressure Drop (cm H20) (cm Drop Pressure 3.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B17. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.01 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 156

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B18. Case II comparison of the pressure distributions for an oblique and symmetric

divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.01 cm

for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 157

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B19. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.02 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 158

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B20. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.02 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 159

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B21. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.04 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 160

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B22. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.04 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 161

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B23. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.08 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 162

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B24. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.08 cm for the transglottal pressures of 10 (top) and 15 (bottom) cm H20 163

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Figure B25. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.16 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 (oblique divergent non-flow side;

oblique convergent flow side) 164

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Figure B26. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.16 cm transglottal pressure of 10 cm H20 (oblique divergent non-flow side; convergent flow side)

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Figure B27. Case II comparison of the pressure distributions for an oblique and symmetric

divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.16 cm

transglottal pressure of 3 cm H20 (oblique divergent flow side; convergent non-flow side) 165

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

5 Pressure Drop (cm H20) (cm Drop Pressure 6

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

10 Pressure Drop (cm H20) (cm Drop Pressure 12

Figure B28. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.16 cm for the transglottal pressures of 5 (top) and 10 (bottom) cm H20 (oblique divergent flow side;

oblique convergent non-flow side)

166

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4

6 8 10 12 14

Pressure Drop (cm H20) (cm Drop Pressure 16 18 20

Figure B29. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.16 cm transglottal pressure of 15 cm H20 (oblique divergent flow side; convergent non-flow side)

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.25

0.5

0.75

Pressure Drop (cm H20) (cm Drop Pressure 1.25

1.5

Figure B30. Case II comparison of the pressure distributions for an oblique and symmetric

divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.32 cm

transglottal pressure of 1 cm H20 (oblique divergent non-flow side; convergent flow side) 167

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

6 Pressure Drop (cm H20) (cm Drop Pressure 7

Figure B31. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.32 cm for the transglottal pressures of 3 (top) and 5 (bottom) cm H20 (oblique divergent non-flow side;

convergent flow side)

168

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.25

0.5

0.75

Pressure Drop (cm H20) (cm Drop Pressure 1.25

1.5

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5

1 1.5 2 2.5 3 3.5 Pressure Drop (cm H20) (cm Drop Pressure 4 4.5

Figure B32. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.32 cm for the transglottal pressures of 1 (top) and 3 (bottom) cm H20 (oblique divergent flow side;

convergent non-flow side) 169

Axial Distance (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

6 Pressure Drop (cm H20) (cm Drop Pressure 7

Figure B33. Case II comparison of the pressure distributions for an oblique and symmetric divergent glottis with an included angle of 10 degrees a minimal nominal diameter of 0.32 cm for the transglottal pressure of 5 cm H20 (oblique divergent flow side; convergent non-flow side).