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Visualization and Quantification of the Medial Surface Dynamics of an Excised Human Vocal Fold During Phonation
Visualization and Quantification of the Medial Surface Dynamics of an Excised Human Vocal Fold During Phonation Michael Doellinger and David A. Berry Los Angeles, California
Summary: The purpose of this investigation was to investigate physical mechanisms of vocal fold vibration during normal phonation through quantification of the medial surface dynamics of the fold. An excised hemilarynx setup was used. The dynamics of 30 microsutures mounted on the medial surface of a human vocal fold were analyzed across 18 phonatory conditions. The vibrations were recorded with a digital high-speed camera at a frequency of 4000 Hz. The positions of the sutures were extracted and converted to three-dimensional coordinates using a linear approximation technique. The data were reduced to principal eigenfuctions, which captured over 90% of the variance of the data, and suggested mechanisms of sustained vocal fold oscillation. The vibrations were imaged as the following phonatory conditions were manipulated: glottal airflow, an adductory force applied to the muscular process, and an elongation force applied to the thyroid cartilage. Over the range of variables studied, only the variation in glottal airflow yielded significant changes in subglottal pressure and fundamental frequency. All recordings showed high correlation for the distribution of the dynamics across the medial surface of the vocal fold. The distribution of the different displacement directions and velocities showed the highest variations around the superior region of the medial surface. Although the computed vibration patterns of the two largest empirical eigenfunctions were consistent with previous experimental observations, the relative prominence of the two eigenfunctions changed as a function of glottal airflow, impacting theories of vocal efficiency and vocal economy. Key Words: Empirical eigenfunctions—Hemi-larynx—High-speed imaging—Medial surface—Vocal folds.
Head & Neck Surgery, UCLA School of Medicine, 31-24 Rehab Center, 1000 Veteran Avenue, Los Angeles, CA, 900951794. E-mail: [email protected] Journal of Voice, Vol. 20, No. 3, pp. 401–413 0892-1997/$32.00 Ó 2006 The Voice Foundation doi:10.1016/j.jvoice.2005.08.003
Accepted for publication May 25, 2005. Supported by Grant R01 DC003072 from NIH/NIDCD. From the Laryngeal Dynamics Laboratory, Division of Head & Neck Surgery, UCLA School of Medicine, Los Angeles, California. Address correspondence and reprint requests to Dr. Michael Doellinger, The Laryngeal Dynamics Laboratory, Division of
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MICHAEL DOELLINGER AND DAVID A. BERRY INTRODUCTION
Measurement and analysis of vocal fold oscillation is necessary to evaluate and refine current theories of voice production. In recent years, many in vivo studies have been performed using digital high-speed imaging in combination with an endoscope to study vocal fold oscillation.1–5 These studies have helped to improve our understanding of normal and pathological voice production.6–8 However, because endoscopy only allows a superior view of the vocal folds, it was not possible to do a complete analysis of the medial surface dynamics of the vocal folds, where vocal fold opening and closing take place and where the sound is generated within the glottis.9 In contrast, direct imaging the medial surface would reveal the origin of the mucosal wave (eg, the mucosal upheaval) and its propagation along the medial surface of the folds. Different approaches have been used to analyze the medial surface dynamics of the vocal folds, including computational models10 and laboratory hemilarynx techniques that have used either canine or human excised larynges11–13 or in vivo canine larynges.14 Empirical eigenfunctions (EEFs) have become a common tool for reducing complex vocal fold vibrations to essential dynamics. Conceptually, EEFs may be viewed as the basic building blocks of many simple and complex vibration patterns. In previous computational studies, just a few EEFs captured a variety of periodic and aperiodic vocal fold vibrations.10,15 In other words, the principal difference between the vibration patterns was the entrainment (ie, same fundamental frequency) or lack of entrainment of the two largest EEFs.15 Laboratory investigations using excised canine11 or human larynges13 and in vivo canine larynges14 yielded similar results. In former theoretical15 and experimental studies,13 the largest EEF (EEF1) captured the alternating convergent–divergent shape of the glottis (lower and upper parts of the movement were 180 degrees out of phase), and the second largest EEF (EEF2) captured the in-phase lateral movement of the folds. The purpose of this work was to apply an excised hemilarynx technique to study the medial surface dynamics of the folds across a range of phonatory Journal of Voice, Vol. 20, No. 3, 2006
conditions, including variations in vocal fold adduction and elongation (as induced by external forces to the laryngeal cartilages) and variations in glottal airflow. Thus, variations in medial surface dynamics were investigated as a function of phonatory condition. METHOD An excised human larynx was obtained from the autopsy unit of the UCLA Medical Center. The larynx was obtained from a 76-year-old man who weighed approximately 85 kg. The larynx was quick-frozen with liquid nitrogen, stored in a 220 C freezer for 3 months, and slowly thawed the day before the experiment. This method of quick-freezing, storage at 220 C, and slow thawing was used because it has been shown to preserve the viscoelastic properties of the tissues.16 The hemilarynx methodology was recently described in detail elsewhere,13 as were the imaging methods and mathematical techniques for computing the physical coordinates of the vocal fold fleshpoints along the medial surface of the folds.17 Therefore, only a brief overview of these methods will be given. The creation of a hemi-larynx required the removal of one (ie, the right) vocal fold (Figure 1). To modify the degree of vocal fold adduction, a suture pierced the arytenoid cartilage at the muscular process, where varying weights (10, 20, or 50 g) were attached (Figure 1). Another suture with varying weights (10 or 20 g) was attached anteriorly at the thyroid cartilage, to elongate the vocal fold (Figure 1). The trachea was mounted over a stainless steel cylindrical tube with an inner diameter of 8 mm. A glass plate was attached at the top of the tube (Figure 1). A rubber glove was used to mount the hemi-larynx against this plate, so that the remaining vocal fold was pressed closely to the glass. Vacuum grease was applied between the anterior and the posterior regions of the larynx and the glass plate to prevent air leaks. To track the movements of the medial surface of the vocal fold, 35 surgical microsutures with a diameter of 0.034 mm were mounted (the size was chosen to be as small as possible to avoid any disturbance of the natural dynamics due to artificial mass distribution, but large enough to be imaged)
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FIGURE 1. Schematic of the experimental setup from a superior view. On the left side of the glass plate, the hemilarynx is shown, with external weights applied. On the other side of the glass plate, the prism and camera is shown.
(Figure 2). They were arranged at five vertical rows (C1–C5) with seven sutures per row (Figure 2). The lower five rows (L1–L5) were placed along the medial surface. The fifth row (L5) was placed near the vocal fold edge. The sixth (L6) and seventh rows were placed on the top of the vocal fold. As the seventh row was not visible over the entire glottal cycle, the dynamics of these sutures could not be reported. The vertical distance between the sutures was approximately 1.7 mm, and the horizontal distance was approximately 2 mm. To avoid any disturbance of the natural dynamics of the vocal fold, an experienced phonosurgeon positioned the sutures to penetrate only the mucosal epithelium and not the superficial layer.11,18 Vibrations of the vocal fold were induced by passing a constant airflow (200, 320, and 400 mL/s) up through the trachea and through the area between the glass plate and the vocal fold (ie, the hemi-glottis). The vibrations were imaged with a high-speed digital camera at 4000 frames/s and a pixel resolution of 512 x 512 (Figure 1). Three 150-W lamps served as light sources. The acoustical signal was simultaneously recorded at 44.1 kHz.
A right-angle prism was placed at the glass plate, opposite the vocal fold, to simulate two camera views, which was a necessary condition to compute three-dimensional coordinates from a two-dimensional recording19 (Figure 1). For later calibration, a brass cube (53 mm3) was glued to the glass plate superior to the vocal fold.15,17 The tracking of suture positions and the computation of the physical coordinates was performed using a previously described linear transformation method.17 The rootmean-square linearization error20 was computed at 8.3%. The influence of this error on the resultant dynamics was negligible, especially because EEFs have been shown to be highly robust, despite substantial background noise.14,21 The three-dimensional coordinates were processed using EEFs. A detailed mathematical description and motivation of the EEF technique with regard to vocal fold dynamics can be found elsewhere11,15 and thus will not be given here. In this study, the only EEFs reported were those that captured a minimum of 2% of the statistical variance of the dynamics. Across all recordings, only the three to four largest EEFs fulfilled this requirement. Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 2. A recorded high-speed frame: The split view of the vocal fold is introduced by the glass prism. The six horizontal lines (L1–L6) and five columns (C1–C5) of vocal fold sutures are indicated.
RESULTS The imaged recordings were referred to as Rfm,t, where f represented the applied air flow (mL/s) (f 5 200, 320, and 400), m represented the weight applied (g) at the muscular process (m 5 10, 20, and 50), and t represented the weight applied (g) at the thyroid cartilage (t 5 10 and 20). Signals corresponding to each combination of applied airflow, muscular process pull, and thyroid cartilage pull were recorded and analyzed, yielding a total of 18 recordings. The investigated time interval was 100 ms (400 frames) or 12–14 oscillation cycles. The computed maximal displacement values in vertical, lateral, and longitudinal (ie, anterior to
posterior) directions, and maximal velocity values did not change significantly across the different phonatory conditions. The maximal values averaged over all recordings can be observed in Table 1. The subglottal pressure ranged between 2.17 kPa and 3.17 kPa. The acoustically measured fundamental frequencies were between 115 Hz and 140 Hz. Figure 3 shows the three-dimensional reconstruction of the mounted sutures and the linear interpolated vocal fold surface of recording R200 50,20. Each third recorded frame is shown. The sequence began at t 5 0, when the airflow started to open the glottis. Sutures along L5 laid still against the glass plate. The given axis captions correspond to a given origin (ie, left upper front corner of the calibration cube). In the first 1.5 ms, the medial surface separated from the glass plate (ie, glottis midline). Then, until t 5 5.25 ms, the lower medial part converged toward the glottal midline. Due to the closing glottis, at t 5 6.0 ms, the subglottal pressure increased and lifted the upper part of the vocal fold (L4–L6). At t 5 8.25 ms, sutures from L5 touched the glass plate and the oscillations cycle restarted. Figure 4A depicts the relationship between increasing applied airflow and subglottal pressure. From 200 mL/s to 320 mL/s airflow, the subglottal pressure increased at an average of 0.41 kPa 6 0.1 kPa. From 320 mL/s to 400 mL/s, the increase was 0.25 kPa 6 0.12 kPa. Within Figure 4B, the dependence of fundamental frequency on glottal flow is shown. The fundamental frequency was 123 Hz 6 4 for 200 mL/s, 135 Hz 6 3 for 320 mL/s, and 138 Hz 6 2 for 400 mL/s airflow. The applied force at the thyroid cartilage yielded overall an equal or light decrease in subglottal pressure 20.08 6 0.09 kPa
TABLE 1. Maximal Values Averaged Over All Recordings and Mean Correlations Over All Recordings Along the Five Vertical Suture Rows Max. Values Max. Max. Max. Max. Max. Max.
longitudinal displacement vertical displacement lateral displacement velocity acceleration deceleration
Abbreviation: Max, maximum. Journal of Voice, Vol. 20, No. 3, 2006
0.44 mm 1.29 mm 2.05 mm 1.34 mm/ms2 0.32 mm/ms2 20.36 mm/ms2
6 6 6 6 6 6
Correlation Values 0.07 0.08 0.17 0.19 0.06 0.07
0.65 0.91 0.94 0.87 0.77 0.71
6 6 6 6 6 6
0.15 0.07 0.04 0.10 0.13 0.10
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FIGURE 3. The reconstructed three-dimensional positions of the sutures. One glottal cycle is shown for recording R200 50,20. The cycle begins immediately before glottal opening.
(Figure 4C). The applied force at the muscular process had no unique influence on the subglottal pressure. In Figure 5, the distributions of maximal displacement and velocity values for all sutures averaged over all recordings are indicated. This averaging was justifiable, because the basic dynamics along the medial surface were similar over all recordings (ie, always the same areas showed high mobility or low mobility). Correlation values between the
recordings along each vertical suture column (and averaged over all five columns) are shown in Table 1. The values within Figure 5 were normalized to the computed maximal value within each recording (ie, the highest value for all sutures within each recording was 1). C corresponds to the vertical columns (anterior: C1 – posterior: C5) and L to the horizontal suture lines (L1–L6). L1 is the most inferior line, and L6 is the most superior line. In longitudinal direction, the highest displacements were at Journal of Voice, Vol. 20, No. 3, 2006
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MICHAEL DOELLINGER AND DAVID A. BERRY sutures (C3,L6) and (C5,L6). The smallest displacements were found at the sutures along L1 and (C3– C5,L5). The largest vertical displacements were found in the superior part of the vocal fold (L5 and L6). For the medial surface (L1–L4), an increase of the displacement from anterior (C1) to posterior (C5) can be observed. In contrast, the distribution of the vertical displacements on top of the vocal fold (L5 and L6) is clearly bell shaped. The largest lateral displacements could be found at the upper medial surface (L4) and along the suture row directly placed above the vocal fold edge (L5). The lateral displacements on the top of the vocal fold (L6) were significantly smaller. Along the medial surface (L1–L3), the lateral displacements increased from anterior to posterior. The highest velocity values were computed along L5. The values for L4 and L6 were a little smaller. The lowest velocities were computed at the most inferior suture line (L1). Similar to the vertical and lateral displacements, an increase of velocity from anterior (C1) to posterior (C5) could be observed along the lower medial surface (L1–L3). The suture movements of R320 10,10 for the recorded time period are shown in Figure 6. Within each subplot, the movements along the vertical columns (C1–C5) are exhibited. The axes are in millimeters and denote the distance to the chosen origin (ie, cube edge). Zero at the horizontal axis indicates the glass plate or glottis midline. In the inferior region (L1,L2), only small displacements occurred. There, the movements change from an elliptic (anterior) shape to a more linear movement (posterior). Along suture line L3, the movements were a flat ellipse, except that suture (C2,L3) had a horizontal figure-eight-like movement. Along line L4, the sutures followed elliptical trajectories. The peak within the cycle would indicate contact at the glass plate. In the most superior two suture rows, the cycles exhibited a more cone-like appearance. Suture (C1,L5) described the form of a horizontal eight. Overall, in the inferior part (L1-L3), from
= FIGURE 4. (A) Subglottal pressure as a function of glottal flow, (B) fundamental frequency as a function of glottal flow, and (C) subglottal pressure as a function of the elongation force applied to the thyroid cartilage. Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 5. Normalized maximal values of displacements in longitudinal, vertical, and lateral directions and the computed velocity for all 30 investigated sutures averaged over all 18 recordings.
anterior to posterior, a clear increase of amplitude of vibration could be observed. Within the upper two suture rows (L5 and L6), the distribution of the displacements from anterior to posterior was more bell shaped (ie, largest displacements at medial C3 and C4). As in the inferior part, the displacements at the posterior position (C5,L5–L6) are much higher than at the anterior (C1 and C2). The largest amplitudes of vibration were found along the medial suture column (C3). Hence, in Figure 7, one typical oscillation cycle for the medial column within recording R400 20,10 is shown, presenting each third recorded frame, which equaled 0.75 ms. The axis captions correspond to the chosen origin.
The suture positions along the vertical column were indicated with x. Their positions were interpolated using Splines, which minimize the flection within curves22 and were therefore applicable for tissue fitting. The glass plate is indicated by the gray vertical bar. The acoustical measured fundamental frequency was 138 Hz. The presented cycle begins (t 5 0 ms), when the subglottal pressure had increased, but the glottis remained closed. In other words, the tissue (sutures along L5) was still attached to the glass plate. The tissue around L3 and L4 was deformed away from the glass plate by the built-up air pressure. From t 5 0 ms to t 5 2.25 ms, the upper part was being pushed away Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 6. The lateral-vertical displacements of all sutures within recording R320 10,10 during the investigated time period of 100 ms.
from the glass plate (ie, the glottis opens) and the lower part already has started moving toward the glass plate. During the next three time steps, the upper part of the vocal fold relaxed and moved to a lower position. The medial part continued moving toward the glass plate and decreased the glottal area. At t 5 4.5 ms, the glottis was closed again and the subglottal pressure started to build up. The entire vocal fold started to lift and continued lifting until t 5 6.75 ms. Now the subglottal pressure started again to push back the tissue and the oscillation cycle repeated. In addition to computing the dynamics of the entire medial surface of the folds, the dynamics were also decomposed into their essential vibratory components. Hence, the two largest EEFs were investigated. The two largest eigenfunctions were entrained to the same fundamental frequency as measured acoustical signal. In Figure 8, the dependency of the percentage of statistical variance captured by EEF1 and EEF2 (the two largest EEFs) is exhibited, as a function of applied glottal airflow. In general, EEF1 captured less statistical variance in the dynamics as glottal airflow increased: 58.8% 6 1.3 (f 5 200 mL/s) over 56.5% 6 2.4 (f 5 320 mL/s) to 55.4% 6 2.0 (f 5 400 mL/s). In contrast, EEF2 generally captured more statistical variance with increasing glottal airflow: 31.8% 6 2.8 Journal of Voice, Vol. 20, No. 3, 2006
over 33.1% 6 2.2 to 34.3% 6 1.8. However, the behavior was not entirely consistent, because EEF2 decreased slightly within the recordings Rf20,10 and Rf50,10. As EEF2 captures the lateral, in-phase movement of the folds, which modulates the glottal airflow, these studies suggest that an increase in glottal airflow (or an increase in subglottal pressure) will result in increased vocal efficiency in converting airflow energy into acoustical energy. That is, it is generally understood that the airflow (or pressure) supplied by the lungs is the source of energy for the vibrating vocal folds. A certain amount of energy is used to generate EEF1 (responsible for alternately shaping a divergent/convergent glottis) and EEF2 (responsible for modulating the glottal airflow). EEF1 is a facilitator; for example, through glottal shaping it produces favorable pressure conditions for transferring energy from the airflow to the tissue, but it does not directly produce voice. As the mode that modulates the airflow, EEF2 does directly impact the strength of the acoustic signal, and a stronger EEF2 will result in a stronger acoustic intensity. If the amplitudes for EEF1 stay relatively constant, but the amplitudes of EEF2 increase, then a greater percentage of the energy from airflow from the lungs is being used to modulate the airflow and produce voice. Thus, as the
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FIGURE 7. The lateral-vertical movements of the vertical column C3 within recording R400 20,10 during one oscillation cycle.
ratio of EEF2 to EEF1 increases, the efficiency of the lungs in converting airflow energy into acoustic energy should increase. However, as the mode that opens and closes the folds increases (eg, EEF2), the potential impact stress of during collision might also increases. Thus, there may be potential tradeoffs between vocal efficiency and vocal collision force, which needs to be explored in determining an optimum combination of these modes.23 Finally, the directions of EEF1 and EEF2 along the vertical plane of the vocal fold were investigated. The vertical suture column C3 was chosen for this endeavor because this column contained the largest suture displacements. Across the
different settings, no systematic changes could be verified. Figure 9 shows the values for EEF1 and EEF2. Within the left subplots, the computed deflection angles were plotted corresponding to the orthogonal direction toward the glass plate (ie, glottis), with the x indicating their mean values. Within the right subplots, the mean values of the displacement directions along C3 are shown. For EEF1, the two most superior sutures exhibited a positive direction (around 30 ). The lower four sutures showed a negative angle between (236.3 and 223.1 ). For EEF2, the most superior suture showed a highly negative value (250.5 ). The following four sutures exhibited a light negative Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 8. The relative prominence of eigenfunctions EEF1 and EEF2 as a function of glottal flow.
averaged value between 218.3 and 28.9 . The most inferior suture showed a light positive mean value (2.8 ). DISCUSSION Vocal fold dynamics were investigated across different phonatory conditions. The dynamics were quantified and visualized across the entire medial surface of the folds and part of the superior surface (Figures 3 and 6). The dynamics were investigated as a function of various input parameters (ie, glottal airflow). Variation in adductory and elongation forces did not yield discernable differences in the investigated quantities (eg, displacements, velocities, EEFs, etc.) dynamics. However, dynamics across recordings were highly correlated, and areas of different behavior and vibrational amplitudes could be identified across the vocal fold surface. In the future, larger forces of elongation should be applied (eg, up to at least 100 g), which may reveal more significant differences between the phonatory conditions. In this study, vocal fold dynamics were visualized along the entire medial surface (L1–L4) and parts of the superior surface (L5,L6) of a vocal fold. For example, a threedimensional reconstructed oscillation cycle for R200 50,20 was presented in Figure 3 that was consistent with former theoretical studies.10,15,24,25 In this example, the vocal fold edge (L5) separated from the Journal of Voice, Vol. 20, No. 3, 2006
glass plate due to increasing subglottal pressure (t 5 0 ms), and the following displacement of the upper medial part with simultaneous approximation of the lower part could be observed (t 5 0.75 ms to t 5 5.25 ms). Also observed was the lifting of the vocal fold caused by the rising subglottal pressure, and the simultaneous deformation of the inferior surface until the glottis reopened (t 5 6 ms–8.25 ms). The elliptical shape of the tissue movement (Figure 6) confirmed earlier excised hemilarynx experiments,11 in vivo experiments,14 and computational studies.10,15 Moreover, two trajectories [(C1,L5)and (C2,L3)] exhibited a horizontal figure-eight vibration, a phenomenon also observed previously.15,26 Regarding the effects of airflow, adductory force, and elongation on displacements or velocity values, no clear interpretation could be made. One reason could be that the differences between the settings were too small to induce noticeable changes within the investigated quantities like displacements and velocities. However, the larynx investigated in this study began to show vibrational instabilities when the thyroid weight was increased to 50 g (flow 200 mL/s, muscular process 10 g) or when the airflow was increased to 500 mL/s (weights at thyroid cartilage and muscular process each 10 g). Although not the subject of this investigation, such vibrational instabilities will be the subject of a future report.
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FIGURE 9. On the left subplot, the angle of deflection of EEF1 and EEF2 along the vertical suture column C3 toward the glass plate for all recordings is shown. In the right subplot, the corresponding mean values of the angles at each suture location are indicated by arrows.
The dependence of subglottal pressure and fundamental frequency on glottal flow was observed, and it was consistent with prior observations.27,28 In contrast to earlier theoretical and experimental studies, the distribution of displacement and velocity values along the entire medial and parts of the upper surface were calculated. Relatively high longitudinal displacements (L4 and L6) were found in areas with large vertical and lateral displacements
(Figure 5). The results indicated the highest lateral displacements in the region around the vocal fold edge and below (eg, L4 and L5). In contrast, the largest vertical displacements were at the superior region of the vocal fold (eg, L5 and L6). These results were consistent with earlier experimental observations in which only one vertical suture row was mounted on the medial surface.11 Furthermore, some significant differences between the investigated Journal of Voice, Vol. 20, No. 3, 2006
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sutures could be found. For example, the values for displacements and velocity for the lower vocal fold part increased from anterior to posterior, the upper sutures traversed a more bell-shaped trajectory (as opposed to an elliptical trajectory), and the highest values of displacement occurred around C3 and C4 (Figure 5). In general, the dynamics along the superior surface of the fold was more symmetric (in an anterior–posterior sense) than in the inferior region of the medial surface. However, the displacement and velocity values on the superior surface (L4–L6) were also larger posteriorly than anteriorly, which may be an important consideration in future modeling of the self-oscillating vocal folds10 or in fitting mathematical models to vocal fold oscillations.3 The different magnitudes of displacement and velocity along vertical and horizontal directions also suggest similar differentiations in modeling mucosal wave propagation.29,30 The investigation of the EEFs was consistent with recent empirical work.13,17 Only three to four EEFs were necessary to capture essential dynamics (eg, eigenfunctions were not considered unless they captured at least 2% of the statistical variance of the data) and to explain 93.6% 6 1.5 of total variance in the data. The percentage of variance captured by EEF1 and EEF2 was consistent with previous experimental excised13 and in vivo12 hemilarynx studies. EEF1 captured 52–61% of the statistical variance,13 and EEF2 captured 27–37% of the variance. As in previous studies, EEF1 was primarily responsible for producing an alternating divergent–convergent shape in the glottis, a rotational vibration pattern that included both horizontal and vertical motion. This can be observed in Figure 9, where the mean directions of EEF1 and EEF2 for the different sutures are indicated. The deflection angles for EEF1 exhibit a much larger absolute value at the medial surface. The lower four sutures exhibit an angle of !223 . The two upper sutures an angle of O26 . This confirmed earlier theoretical assumptions10 and earlier case studies,13,17 indicating that EEF1 was primarily more responsible for producing the alternating divergent–convergent shape of the glottis. The directions for the lower five sutures within EEF2 were approximately orthogonal to the glass plate, indicating that EEF2 primarily governed the lateral movement of the Journal of Voice, Vol. 20, No. 3, 2006
vocal fold (responsible for modulating the glottal airflow and producing the acoustic signal). The high mean value (250.5 ) for the suture on top to the vocal folds has its origin in the more circle-like (Figure 6) movement of that suture. The relative prominence of EEF1 and EEF2 decreased and increased, respectively, as a function of increasing glottal flow (Figure 8) or subglottal pressure. As EEF2 reflects more the lateral movement, an increase of EEF2 was the natural consequence of increased airflow. The relative prominence of these two EEFs as a function of subglottal pressure may impact future theories of vocal efficiency and vocal economy, and it will be the subject of future investigations. The presented work revealed new insight into the medial surface dynamics of the vocal folds. These studies suggest that vocal fold motion is more elliptical along the medial surface but more bell-shaped along the superior surface. Similarly, along the superior surface, the displacements and velocities of individual fleshpoints are greater posteriorly and anteriorly (Figure 5). Through use of the hemilarynx methodology, it was possible to quantify and visualize the entire medial surface of a fold, as well as a portion of the superior surface, across the entire glottal cycle (Figures 3 and 6), with high temporal resolution (4000 frames/s). Future studies will need to explore a larger range of adductory and elongation forces to see their influence on the resultant dynamics. In future work, the hemilarynx methodology will also be used to explore vibrational instabilities, and to test hypotheses regarding mechanisms of irregular vocal fold vibration that have been suggested by computational models.15 REFERENCES 1. Svec JG, Schutte HK. Videokymography: high-speed line scanning of vocal fold vibration. J Voice. 1996;10:201–205. 2. Hong KH, Kim HK, Niimi S. Laryngeal gestures during stop production using high-speed digital images. J Voice. 2002;16:207–214. 3. Doellinger M, Braunschweig T, Lohscheller J, Eysholdt U, Hoppe U. Normal voice production: computation of driving parameters from endoscopic digital high speed images. Methods Inf Med. 2003;42:271–276. 4. Hoppe U, Rosanowski F, Doellinger M, Lohscheller J, Schuster M, Eysholdt U. Glissando: Laryngeal motorics and acoustics. J Voice. 2003;17:370–376.
EXCISED HUMAN VOCAL FOLD 5. Granqvist S, Hertegard S, Larsson H, Sundberg J. Simultaneous analysis of vocal fold vibration and transglottal airflow: exploring a new experimental setup. J Voice. 2003; 17:319–330. 6. Cutler JL, Cleveland T. The clinical usefulness of laryngeal videostroboscopy and the role of high-speed cinematography in laryngeal evaluation. Curr Opin Otolaryngol Head Neck Surg. 2002;10:462–466. 7. Eysholdt U, Rosanowski F, Hoppe U. Vocal fold vibration irregularities caused by different types of laryngeal asymmetry. Eur Arch Otorhinolaryngol. 2003;260:412–417. 8. Hertegard S, Larsson H, Wittenberg T. High-speed imaging: applications and development. Logoped Phoniatr Vocol. 2003;28:133–139. 9. Titze IR. Principles of Voice Production. Englewood Cliffs, NJ: Prentice Hall; 1994. 10. Alipour F, Berry DA, Titze IR. A finite-element model of vocal-fold vibration. J Acoust Soc Am. 2000;108:3003– 3012. 11. Berry DA, Montequin DW, Tayama N. High-speed digital imaging of the medial surface of the vocal folds. J Acoust Soc Am. 2001;110:2539–2547. 12. Doellinger M, Berke GS, Berry DA. Quantitative measurements of the medial surface of the vocal folds in an in vivo canine model. In: Slifka J, Manuel S, Matthies M, eds. From Sound to Sense: 501 Years of Discoveries in Speech Communication. Cambridge, MA: MIT; 2004:C127–C132. 13. Doellinger M, Tayama N, Berry DA. Empirical eigenfunctions and medial surface dynamics of a human vocal fold. Methods Inf Med. 2005;44:384–391. 14. Doellinger M, Berry DA, Berke GS. Medial surface dynamics of an in vivo canine vocal fold during phonation. J Acoust Soc Am. 2005;117:3174–3183. 15. Berry DA, Herzel H, Titze IR, Krischer K. Interpretation of biomechanical simulations of normal and chaotic vocal fold oscillations with empirical eigenfunctions. J Acoust Soc Am. 1994;95:3595–3604. 16. Chan RW, Titze IR. Effect of postmortem changes and freezing on viscoelastic properties of vocal fold tissues. Ann Biomed Eng. 2003;31:482–491. 17. Doellinger M, Berry DA. Computation of the three-dimensional medial surface dynamics of the vocal folds. J Biomech. 2006;39:369–374.
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18. Hirano M. Structure and vibratory behavior of the vocal folds. In: Sawashima M, Franklin S, eds. Dynamic Aspects of Speech Production. Tokyo, Japan: University of Tokyo; 1977:13–30. 19. Abdel-Abziz Y, Karara H. Direct linear transformation from comparator coordinates into object space coordinates in close-range photogrammetry. Proceedings of the Symposium on Close-Range Photogrammetry. American Society of Photogrammetry, Falls Church, VA. 1971: 1–18. 20. Choo AMT, Oxland TR. Improved RSA accuracy with DLT and balanced calibration marker distributions with an assessment of initial-calibration. J Biomech. 2003;36: 259–264. 21. Breuer KS, Sirovich L. The use of the Karhunen-Loeve procedure for the calculation of linear eigenfunctions. J Comput Phys. 1991;96:277–296. 22. Farin G. Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide (Computer Science and Scientific Computing). New York: Academic Press; 1996. 23. Berry DA, Verdolini K, Montequin DW, Chan RW, Titze IR. A quantitative output-cost ratio in voice production. J Speech Lang Hear Res. 2001;44:29–37. 24. Berry DA, Clark MJ, Montequin DW, Titze IR. Characterization of the medial surface of the vocal folds. Ann Otol Rhinol Laryngol. 2001;110:470–477. 25. Berry DA, Titze IR. Normal modes in a continuum model of vocal fold tissues. J Acoust Soc Am. 1996;100:3345– 3354. 26. Baer T. Investigation of phonation using excised larynges [doctoral thesis]. Cambridge, MA: Massachusetts Institute of Technology; 1975. 27. Alipour F, Scherer RC, Finnegan EM. Pressure flow relationship during phonation. J Voice. 1997;11:187–194. 28. Alipour F, Montequin DW, Tayama N. Aerodynamic profiles of a hemilarynx with vocal tract. Ann Otol Rhinol Laryngol. 2001;110:550–555. 29. Titze IR. Parameterization of the glottal area, glottal flow, and vocal fold contact area. J Acoust Soc Am. 1984;75: 570–580. 30. Titze IR. A four parameter model of the glottis and vocal contact area. Speech Commun. 1989;8:191–201.
Journal of Voice, Vol. 20, No. 3, 2006
Summary: The purpose of this investigation was to investigate physical mechanisms of vocal fold vibration during normal phonation through quantification of the medial surface dynamics of the fold. An excised hemilarynx setup was used. The dynamics of 30 microsutures mounted on the medial surface of a human vocal fold were analyzed across 18 phonatory conditions. The vibrations were recorded with a digital high-speed camera at a frequency of 4000 Hz. The positions of the sutures were extracted and converted to three-dimensional coordinates using a linear approximation technique. The data were reduced to principal eigenfuctions, which captured over 90% of the variance of the data, and suggested mechanisms of sustained vocal fold oscillation. The vibrations were imaged as the following phonatory conditions were manipulated: glottal airflow, an adductory force applied to the muscular process, and an elongation force applied to the thyroid cartilage. Over the range of variables studied, only the variation in glottal airflow yielded significant changes in subglottal pressure and fundamental frequency. All recordings showed high correlation for the distribution of the dynamics across the medial surface of the vocal fold. The distribution of the different displacement directions and velocities showed the highest variations around the superior region of the medial surface. Although the computed vibration patterns of the two largest empirical eigenfunctions were consistent with previous experimental observations, the relative prominence of the two eigenfunctions changed as a function of glottal airflow, impacting theories of vocal efficiency and vocal economy. Key Words: Empirical eigenfunctions—Hemi-larynx—High-speed imaging—Medial surface—Vocal folds.
Head & Neck Surgery, UCLA School of Medicine, 31-24 Rehab Center, 1000 Veteran Avenue, Los Angeles, CA, 900951794. E-mail: [email protected] Journal of Voice, Vol. 20, No. 3, pp. 401–413 0892-1997/$32.00 Ó 2006 The Voice Foundation doi:10.1016/j.jvoice.2005.08.003
Accepted for publication May 25, 2005. Supported by Grant R01 DC003072 from NIH/NIDCD. From the Laryngeal Dynamics Laboratory, Division of Head & Neck Surgery, UCLA School of Medicine, Los Angeles, California. Address correspondence and reprint requests to Dr. Michael Doellinger, The Laryngeal Dynamics Laboratory, Division of
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Measurement and analysis of vocal fold oscillation is necessary to evaluate and refine current theories of voice production. In recent years, many in vivo studies have been performed using digital high-speed imaging in combination with an endoscope to study vocal fold oscillation.1–5 These studies have helped to improve our understanding of normal and pathological voice production.6–8 However, because endoscopy only allows a superior view of the vocal folds, it was not possible to do a complete analysis of the medial surface dynamics of the vocal folds, where vocal fold opening and closing take place and where the sound is generated within the glottis.9 In contrast, direct imaging the medial surface would reveal the origin of the mucosal wave (eg, the mucosal upheaval) and its propagation along the medial surface of the folds. Different approaches have been used to analyze the medial surface dynamics of the vocal folds, including computational models10 and laboratory hemilarynx techniques that have used either canine or human excised larynges11–13 or in vivo canine larynges.14 Empirical eigenfunctions (EEFs) have become a common tool for reducing complex vocal fold vibrations to essential dynamics. Conceptually, EEFs may be viewed as the basic building blocks of many simple and complex vibration patterns. In previous computational studies, just a few EEFs captured a variety of periodic and aperiodic vocal fold vibrations.10,15 In other words, the principal difference between the vibration patterns was the entrainment (ie, same fundamental frequency) or lack of entrainment of the two largest EEFs.15 Laboratory investigations using excised canine11 or human larynges13 and in vivo canine larynges14 yielded similar results. In former theoretical15 and experimental studies,13 the largest EEF (EEF1) captured the alternating convergent–divergent shape of the glottis (lower and upper parts of the movement were 180 degrees out of phase), and the second largest EEF (EEF2) captured the in-phase lateral movement of the folds. The purpose of this work was to apply an excised hemilarynx technique to study the medial surface dynamics of the folds across a range of phonatory Journal of Voice, Vol. 20, No. 3, 2006
conditions, including variations in vocal fold adduction and elongation (as induced by external forces to the laryngeal cartilages) and variations in glottal airflow. Thus, variations in medial surface dynamics were investigated as a function of phonatory condition. METHOD An excised human larynx was obtained from the autopsy unit of the UCLA Medical Center. The larynx was obtained from a 76-year-old man who weighed approximately 85 kg. The larynx was quick-frozen with liquid nitrogen, stored in a 220 C freezer for 3 months, and slowly thawed the day before the experiment. This method of quick-freezing, storage at 220 C, and slow thawing was used because it has been shown to preserve the viscoelastic properties of the tissues.16 The hemilarynx methodology was recently described in detail elsewhere,13 as were the imaging methods and mathematical techniques for computing the physical coordinates of the vocal fold fleshpoints along the medial surface of the folds.17 Therefore, only a brief overview of these methods will be given. The creation of a hemi-larynx required the removal of one (ie, the right) vocal fold (Figure 1). To modify the degree of vocal fold adduction, a suture pierced the arytenoid cartilage at the muscular process, where varying weights (10, 20, or 50 g) were attached (Figure 1). Another suture with varying weights (10 or 20 g) was attached anteriorly at the thyroid cartilage, to elongate the vocal fold (Figure 1). The trachea was mounted over a stainless steel cylindrical tube with an inner diameter of 8 mm. A glass plate was attached at the top of the tube (Figure 1). A rubber glove was used to mount the hemi-larynx against this plate, so that the remaining vocal fold was pressed closely to the glass. Vacuum grease was applied between the anterior and the posterior regions of the larynx and the glass plate to prevent air leaks. To track the movements of the medial surface of the vocal fold, 35 surgical microsutures with a diameter of 0.034 mm were mounted (the size was chosen to be as small as possible to avoid any disturbance of the natural dynamics due to artificial mass distribution, but large enough to be imaged)
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FIGURE 1. Schematic of the experimental setup from a superior view. On the left side of the glass plate, the hemilarynx is shown, with external weights applied. On the other side of the glass plate, the prism and camera is shown.
(Figure 2). They were arranged at five vertical rows (C1–C5) with seven sutures per row (Figure 2). The lower five rows (L1–L5) were placed along the medial surface. The fifth row (L5) was placed near the vocal fold edge. The sixth (L6) and seventh rows were placed on the top of the vocal fold. As the seventh row was not visible over the entire glottal cycle, the dynamics of these sutures could not be reported. The vertical distance between the sutures was approximately 1.7 mm, and the horizontal distance was approximately 2 mm. To avoid any disturbance of the natural dynamics of the vocal fold, an experienced phonosurgeon positioned the sutures to penetrate only the mucosal epithelium and not the superficial layer.11,18 Vibrations of the vocal fold were induced by passing a constant airflow (200, 320, and 400 mL/s) up through the trachea and through the area between the glass plate and the vocal fold (ie, the hemi-glottis). The vibrations were imaged with a high-speed digital camera at 4000 frames/s and a pixel resolution of 512 x 512 (Figure 1). Three 150-W lamps served as light sources. The acoustical signal was simultaneously recorded at 44.1 kHz.
A right-angle prism was placed at the glass plate, opposite the vocal fold, to simulate two camera views, which was a necessary condition to compute three-dimensional coordinates from a two-dimensional recording19 (Figure 1). For later calibration, a brass cube (53 mm3) was glued to the glass plate superior to the vocal fold.15,17 The tracking of suture positions and the computation of the physical coordinates was performed using a previously described linear transformation method.17 The rootmean-square linearization error20 was computed at 8.3%. The influence of this error on the resultant dynamics was negligible, especially because EEFs have been shown to be highly robust, despite substantial background noise.14,21 The three-dimensional coordinates were processed using EEFs. A detailed mathematical description and motivation of the EEF technique with regard to vocal fold dynamics can be found elsewhere11,15 and thus will not be given here. In this study, the only EEFs reported were those that captured a minimum of 2% of the statistical variance of the dynamics. Across all recordings, only the three to four largest EEFs fulfilled this requirement. Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 2. A recorded high-speed frame: The split view of the vocal fold is introduced by the glass prism. The six horizontal lines (L1–L6) and five columns (C1–C5) of vocal fold sutures are indicated.
RESULTS The imaged recordings were referred to as Rfm,t, where f represented the applied air flow (mL/s) (f 5 200, 320, and 400), m represented the weight applied (g) at the muscular process (m 5 10, 20, and 50), and t represented the weight applied (g) at the thyroid cartilage (t 5 10 and 20). Signals corresponding to each combination of applied airflow, muscular process pull, and thyroid cartilage pull were recorded and analyzed, yielding a total of 18 recordings. The investigated time interval was 100 ms (400 frames) or 12–14 oscillation cycles. The computed maximal displacement values in vertical, lateral, and longitudinal (ie, anterior to
posterior) directions, and maximal velocity values did not change significantly across the different phonatory conditions. The maximal values averaged over all recordings can be observed in Table 1. The subglottal pressure ranged between 2.17 kPa and 3.17 kPa. The acoustically measured fundamental frequencies were between 115 Hz and 140 Hz. Figure 3 shows the three-dimensional reconstruction of the mounted sutures and the linear interpolated vocal fold surface of recording R200 50,20. Each third recorded frame is shown. The sequence began at t 5 0, when the airflow started to open the glottis. Sutures along L5 laid still against the glass plate. The given axis captions correspond to a given origin (ie, left upper front corner of the calibration cube). In the first 1.5 ms, the medial surface separated from the glass plate (ie, glottis midline). Then, until t 5 5.25 ms, the lower medial part converged toward the glottal midline. Due to the closing glottis, at t 5 6.0 ms, the subglottal pressure increased and lifted the upper part of the vocal fold (L4–L6). At t 5 8.25 ms, sutures from L5 touched the glass plate and the oscillations cycle restarted. Figure 4A depicts the relationship between increasing applied airflow and subglottal pressure. From 200 mL/s to 320 mL/s airflow, the subglottal pressure increased at an average of 0.41 kPa 6 0.1 kPa. From 320 mL/s to 400 mL/s, the increase was 0.25 kPa 6 0.12 kPa. Within Figure 4B, the dependence of fundamental frequency on glottal flow is shown. The fundamental frequency was 123 Hz 6 4 for 200 mL/s, 135 Hz 6 3 for 320 mL/s, and 138 Hz 6 2 for 400 mL/s airflow. The applied force at the thyroid cartilage yielded overall an equal or light decrease in subglottal pressure 20.08 6 0.09 kPa
TABLE 1. Maximal Values Averaged Over All Recordings and Mean Correlations Over All Recordings Along the Five Vertical Suture Rows Max. Values Max. Max. Max. Max. Max. Max.
longitudinal displacement vertical displacement lateral displacement velocity acceleration deceleration
Abbreviation: Max, maximum. Journal of Voice, Vol. 20, No. 3, 2006
0.44 mm 1.29 mm 2.05 mm 1.34 mm/ms2 0.32 mm/ms2 20.36 mm/ms2
6 6 6 6 6 6
Correlation Values 0.07 0.08 0.17 0.19 0.06 0.07
0.65 0.91 0.94 0.87 0.77 0.71
6 6 6 6 6 6
0.15 0.07 0.04 0.10 0.13 0.10
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FIGURE 3. The reconstructed three-dimensional positions of the sutures. One glottal cycle is shown for recording R200 50,20. The cycle begins immediately before glottal opening.
(Figure 4C). The applied force at the muscular process had no unique influence on the subglottal pressure. In Figure 5, the distributions of maximal displacement and velocity values for all sutures averaged over all recordings are indicated. This averaging was justifiable, because the basic dynamics along the medial surface were similar over all recordings (ie, always the same areas showed high mobility or low mobility). Correlation values between the
recordings along each vertical suture column (and averaged over all five columns) are shown in Table 1. The values within Figure 5 were normalized to the computed maximal value within each recording (ie, the highest value for all sutures within each recording was 1). C corresponds to the vertical columns (anterior: C1 – posterior: C5) and L to the horizontal suture lines (L1–L6). L1 is the most inferior line, and L6 is the most superior line. In longitudinal direction, the highest displacements were at Journal of Voice, Vol. 20, No. 3, 2006
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MICHAEL DOELLINGER AND DAVID A. BERRY sutures (C3,L6) and (C5,L6). The smallest displacements were found at the sutures along L1 and (C3– C5,L5). The largest vertical displacements were found in the superior part of the vocal fold (L5 and L6). For the medial surface (L1–L4), an increase of the displacement from anterior (C1) to posterior (C5) can be observed. In contrast, the distribution of the vertical displacements on top of the vocal fold (L5 and L6) is clearly bell shaped. The largest lateral displacements could be found at the upper medial surface (L4) and along the suture row directly placed above the vocal fold edge (L5). The lateral displacements on the top of the vocal fold (L6) were significantly smaller. Along the medial surface (L1–L3), the lateral displacements increased from anterior to posterior. The highest velocity values were computed along L5. The values for L4 and L6 were a little smaller. The lowest velocities were computed at the most inferior suture line (L1). Similar to the vertical and lateral displacements, an increase of velocity from anterior (C1) to posterior (C5) could be observed along the lower medial surface (L1–L3). The suture movements of R320 10,10 for the recorded time period are shown in Figure 6. Within each subplot, the movements along the vertical columns (C1–C5) are exhibited. The axes are in millimeters and denote the distance to the chosen origin (ie, cube edge). Zero at the horizontal axis indicates the glass plate or glottis midline. In the inferior region (L1,L2), only small displacements occurred. There, the movements change from an elliptic (anterior) shape to a more linear movement (posterior). Along suture line L3, the movements were a flat ellipse, except that suture (C2,L3) had a horizontal figure-eight-like movement. Along line L4, the sutures followed elliptical trajectories. The peak within the cycle would indicate contact at the glass plate. In the most superior two suture rows, the cycles exhibited a more cone-like appearance. Suture (C1,L5) described the form of a horizontal eight. Overall, in the inferior part (L1-L3), from
= FIGURE 4. (A) Subglottal pressure as a function of glottal flow, (B) fundamental frequency as a function of glottal flow, and (C) subglottal pressure as a function of the elongation force applied to the thyroid cartilage. Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 5. Normalized maximal values of displacements in longitudinal, vertical, and lateral directions and the computed velocity for all 30 investigated sutures averaged over all 18 recordings.
anterior to posterior, a clear increase of amplitude of vibration could be observed. Within the upper two suture rows (L5 and L6), the distribution of the displacements from anterior to posterior was more bell shaped (ie, largest displacements at medial C3 and C4). As in the inferior part, the displacements at the posterior position (C5,L5–L6) are much higher than at the anterior (C1 and C2). The largest amplitudes of vibration were found along the medial suture column (C3). Hence, in Figure 7, one typical oscillation cycle for the medial column within recording R400 20,10 is shown, presenting each third recorded frame, which equaled 0.75 ms. The axis captions correspond to the chosen origin.
The suture positions along the vertical column were indicated with x. Their positions were interpolated using Splines, which minimize the flection within curves22 and were therefore applicable for tissue fitting. The glass plate is indicated by the gray vertical bar. The acoustical measured fundamental frequency was 138 Hz. The presented cycle begins (t 5 0 ms), when the subglottal pressure had increased, but the glottis remained closed. In other words, the tissue (sutures along L5) was still attached to the glass plate. The tissue around L3 and L4 was deformed away from the glass plate by the built-up air pressure. From t 5 0 ms to t 5 2.25 ms, the upper part was being pushed away Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 6. The lateral-vertical displacements of all sutures within recording R320 10,10 during the investigated time period of 100 ms.
from the glass plate (ie, the glottis opens) and the lower part already has started moving toward the glass plate. During the next three time steps, the upper part of the vocal fold relaxed and moved to a lower position. The medial part continued moving toward the glass plate and decreased the glottal area. At t 5 4.5 ms, the glottis was closed again and the subglottal pressure started to build up. The entire vocal fold started to lift and continued lifting until t 5 6.75 ms. Now the subglottal pressure started again to push back the tissue and the oscillation cycle repeated. In addition to computing the dynamics of the entire medial surface of the folds, the dynamics were also decomposed into their essential vibratory components. Hence, the two largest EEFs were investigated. The two largest eigenfunctions were entrained to the same fundamental frequency as measured acoustical signal. In Figure 8, the dependency of the percentage of statistical variance captured by EEF1 and EEF2 (the two largest EEFs) is exhibited, as a function of applied glottal airflow. In general, EEF1 captured less statistical variance in the dynamics as glottal airflow increased: 58.8% 6 1.3 (f 5 200 mL/s) over 56.5% 6 2.4 (f 5 320 mL/s) to 55.4% 6 2.0 (f 5 400 mL/s). In contrast, EEF2 generally captured more statistical variance with increasing glottal airflow: 31.8% 6 2.8 Journal of Voice, Vol. 20, No. 3, 2006
over 33.1% 6 2.2 to 34.3% 6 1.8. However, the behavior was not entirely consistent, because EEF2 decreased slightly within the recordings Rf20,10 and Rf50,10. As EEF2 captures the lateral, in-phase movement of the folds, which modulates the glottal airflow, these studies suggest that an increase in glottal airflow (or an increase in subglottal pressure) will result in increased vocal efficiency in converting airflow energy into acoustical energy. That is, it is generally understood that the airflow (or pressure) supplied by the lungs is the source of energy for the vibrating vocal folds. A certain amount of energy is used to generate EEF1 (responsible for alternately shaping a divergent/convergent glottis) and EEF2 (responsible for modulating the glottal airflow). EEF1 is a facilitator; for example, through glottal shaping it produces favorable pressure conditions for transferring energy from the airflow to the tissue, but it does not directly produce voice. As the mode that modulates the airflow, EEF2 does directly impact the strength of the acoustic signal, and a stronger EEF2 will result in a stronger acoustic intensity. If the amplitudes for EEF1 stay relatively constant, but the amplitudes of EEF2 increase, then a greater percentage of the energy from airflow from the lungs is being used to modulate the airflow and produce voice. Thus, as the
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FIGURE 7. The lateral-vertical movements of the vertical column C3 within recording R400 20,10 during one oscillation cycle.
ratio of EEF2 to EEF1 increases, the efficiency of the lungs in converting airflow energy into acoustic energy should increase. However, as the mode that opens and closes the folds increases (eg, EEF2), the potential impact stress of during collision might also increases. Thus, there may be potential tradeoffs between vocal efficiency and vocal collision force, which needs to be explored in determining an optimum combination of these modes.23 Finally, the directions of EEF1 and EEF2 along the vertical plane of the vocal fold were investigated. The vertical suture column C3 was chosen for this endeavor because this column contained the largest suture displacements. Across the
different settings, no systematic changes could be verified. Figure 9 shows the values for EEF1 and EEF2. Within the left subplots, the computed deflection angles were plotted corresponding to the orthogonal direction toward the glass plate (ie, glottis), with the x indicating their mean values. Within the right subplots, the mean values of the displacement directions along C3 are shown. For EEF1, the two most superior sutures exhibited a positive direction (around 30 ). The lower four sutures showed a negative angle between (236.3 and 223.1 ). For EEF2, the most superior suture showed a highly negative value (250.5 ). The following four sutures exhibited a light negative Journal of Voice, Vol. 20, No. 3, 2006
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FIGURE 8. The relative prominence of eigenfunctions EEF1 and EEF2 as a function of glottal flow.
averaged value between 218.3 and 28.9 . The most inferior suture showed a light positive mean value (2.8 ). DISCUSSION Vocal fold dynamics were investigated across different phonatory conditions. The dynamics were quantified and visualized across the entire medial surface of the folds and part of the superior surface (Figures 3 and 6). The dynamics were investigated as a function of various input parameters (ie, glottal airflow). Variation in adductory and elongation forces did not yield discernable differences in the investigated quantities (eg, displacements, velocities, EEFs, etc.) dynamics. However, dynamics across recordings were highly correlated, and areas of different behavior and vibrational amplitudes could be identified across the vocal fold surface. In the future, larger forces of elongation should be applied (eg, up to at least 100 g), which may reveal more significant differences between the phonatory conditions. In this study, vocal fold dynamics were visualized along the entire medial surface (L1–L4) and parts of the superior surface (L5,L6) of a vocal fold. For example, a threedimensional reconstructed oscillation cycle for R200 50,20 was presented in Figure 3 that was consistent with former theoretical studies.10,15,24,25 In this example, the vocal fold edge (L5) separated from the Journal of Voice, Vol. 20, No. 3, 2006
glass plate due to increasing subglottal pressure (t 5 0 ms), and the following displacement of the upper medial part with simultaneous approximation of the lower part could be observed (t 5 0.75 ms to t 5 5.25 ms). Also observed was the lifting of the vocal fold caused by the rising subglottal pressure, and the simultaneous deformation of the inferior surface until the glottis reopened (t 5 6 ms–8.25 ms). The elliptical shape of the tissue movement (Figure 6) confirmed earlier excised hemilarynx experiments,11 in vivo experiments,14 and computational studies.10,15 Moreover, two trajectories [(C1,L5)and (C2,L3)] exhibited a horizontal figure-eight vibration, a phenomenon also observed previously.15,26 Regarding the effects of airflow, adductory force, and elongation on displacements or velocity values, no clear interpretation could be made. One reason could be that the differences between the settings were too small to induce noticeable changes within the investigated quantities like displacements and velocities. However, the larynx investigated in this study began to show vibrational instabilities when the thyroid weight was increased to 50 g (flow 200 mL/s, muscular process 10 g) or when the airflow was increased to 500 mL/s (weights at thyroid cartilage and muscular process each 10 g). Although not the subject of this investigation, such vibrational instabilities will be the subject of a future report.
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FIGURE 9. On the left subplot, the angle of deflection of EEF1 and EEF2 along the vertical suture column C3 toward the glass plate for all recordings is shown. In the right subplot, the corresponding mean values of the angles at each suture location are indicated by arrows.
The dependence of subglottal pressure and fundamental frequency on glottal flow was observed, and it was consistent with prior observations.27,28 In contrast to earlier theoretical and experimental studies, the distribution of displacement and velocity values along the entire medial and parts of the upper surface were calculated. Relatively high longitudinal displacements (L4 and L6) were found in areas with large vertical and lateral displacements
(Figure 5). The results indicated the highest lateral displacements in the region around the vocal fold edge and below (eg, L4 and L5). In contrast, the largest vertical displacements were at the superior region of the vocal fold (eg, L5 and L6). These results were consistent with earlier experimental observations in which only one vertical suture row was mounted on the medial surface.11 Furthermore, some significant differences between the investigated Journal of Voice, Vol. 20, No. 3, 2006
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sutures could be found. For example, the values for displacements and velocity for the lower vocal fold part increased from anterior to posterior, the upper sutures traversed a more bell-shaped trajectory (as opposed to an elliptical trajectory), and the highest values of displacement occurred around C3 and C4 (Figure 5). In general, the dynamics along the superior surface of the fold was more symmetric (in an anterior–posterior sense) than in the inferior region of the medial surface. However, the displacement and velocity values on the superior surface (L4–L6) were also larger posteriorly than anteriorly, which may be an important consideration in future modeling of the self-oscillating vocal folds10 or in fitting mathematical models to vocal fold oscillations.3 The different magnitudes of displacement and velocity along vertical and horizontal directions also suggest similar differentiations in modeling mucosal wave propagation.29,30 The investigation of the EEFs was consistent with recent empirical work.13,17 Only three to four EEFs were necessary to capture essential dynamics (eg, eigenfunctions were not considered unless they captured at least 2% of the statistical variance of the data) and to explain 93.6% 6 1.5 of total variance in the data. The percentage of variance captured by EEF1 and EEF2 was consistent with previous experimental excised13 and in vivo12 hemilarynx studies. EEF1 captured 52–61% of the statistical variance,13 and EEF2 captured 27–37% of the variance. As in previous studies, EEF1 was primarily responsible for producing an alternating divergent–convergent shape in the glottis, a rotational vibration pattern that included both horizontal and vertical motion. This can be observed in Figure 9, where the mean directions of EEF1 and EEF2 for the different sutures are indicated. The deflection angles for EEF1 exhibit a much larger absolute value at the medial surface. The lower four sutures exhibit an angle of !223 . The two upper sutures an angle of O26 . This confirmed earlier theoretical assumptions10 and earlier case studies,13,17 indicating that EEF1 was primarily more responsible for producing the alternating divergent–convergent shape of the glottis. The directions for the lower five sutures within EEF2 were approximately orthogonal to the glass plate, indicating that EEF2 primarily governed the lateral movement of the Journal of Voice, Vol. 20, No. 3, 2006
vocal fold (responsible for modulating the glottal airflow and producing the acoustic signal). The high mean value (250.5 ) for the suture on top to the vocal folds has its origin in the more circle-like (Figure 6) movement of that suture. The relative prominence of EEF1 and EEF2 decreased and increased, respectively, as a function of increasing glottal flow (Figure 8) or subglottal pressure. As EEF2 reflects more the lateral movement, an increase of EEF2 was the natural consequence of increased airflow. The relative prominence of these two EEFs as a function of subglottal pressure may impact future theories of vocal efficiency and vocal economy, and it will be the subject of future investigations. The presented work revealed new insight into the medial surface dynamics of the vocal folds. These studies suggest that vocal fold motion is more elliptical along the medial surface but more bell-shaped along the superior surface. Similarly, along the superior surface, the displacements and velocities of individual fleshpoints are greater posteriorly and anteriorly (Figure 5). Through use of the hemilarynx methodology, it was possible to quantify and visualize the entire medial surface of a fold, as well as a portion of the superior surface, across the entire glottal cycle (Figures 3 and 6), with high temporal resolution (4000 frames/s). Future studies will need to explore a larger range of adductory and elongation forces to see their influence on the resultant dynamics. In future work, the hemilarynx methodology will also be used to explore vibrational instabilities, and to test hypotheses regarding mechanisms of irregular vocal fold vibration that have been suggested by computational models.15 REFERENCES 1. Svec JG, Schutte HK. Videokymography: high-speed line scanning of vocal fold vibration. J Voice. 1996;10:201–205. 2. Hong KH, Kim HK, Niimi S. Laryngeal gestures during stop production using high-speed digital images. J Voice. 2002;16:207–214. 3. Doellinger M, Braunschweig T, Lohscheller J, Eysholdt U, Hoppe U. Normal voice production: computation of driving parameters from endoscopic digital high speed images. Methods Inf Med. 2003;42:271–276. 4. Hoppe U, Rosanowski F, Doellinger M, Lohscheller J, Schuster M, Eysholdt U. Glissando: Laryngeal motorics and acoustics. J Voice. 2003;17:370–376.
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