Vocal Fold Dynamics for Frequency Change Harry Hollien, Gainesville, Florida Summary: This article provides a review of data drawn from a series of related experiments to demonstrate how frequency change (Df0) is accomplished in the modal register. The research cited involves studies of (1) laryngeal size, (2) vocal fold length, (3) vocal fold thickness, and (4) subglottic pressure; new data describe their effect on vocal fold mass. It was found that changes in these dimensions (1) explain how the shifts in frequency are accomplished, (2) establish the way vocal fold mass can be measured, and (3) strongly support the aerodynamic-myoelastic theory of phonation. Key Words: Vocal fold dynamics–Frequency change–Vocal folds–Fundamental frequency–Aerodynamic-myoelastic theory–Phonation–Laryngeal size–Vocal fold length–Vocal fold thickness–Subglottic pressure–Vocal fold mass–Modal register. INTRODUCTION Although a number of authors have addressed the issue of how the larynx—and especially the vocal folds—operate to vary fundamental frequency (F0) in speech and singing, only tentative explanations can be found. The present effort attempts to remedy this deficit. To do so, data that were collected over a period of some years are now being organized to support a model. They also will be used to assess certain aspects of the aerodynamic-myoelastic theory (ADMET) of phonation.1 A PERSPECTIVE The difficulty in developing a model of the desired type is that because there are many dimensions to ‘‘voice,’’ it would be impossible to include them all. For example, normal voice, vocal training (of all types), and voice disorders (due to disease, behaviors, and so forth) create several of the many complex continua that exist; so too do the different registers and ranges of voice as well as the extent and nature of vocal intensity and voice quality. Indeed, the complexity of phonation and its varying dimensions extends in many directions. Accordingly, and to provide a reasonably comprehensive framework for this project, certain limitations will be observed. Specifically, the focus will be on a ‘‘core’’ system rather than one of many dimensions. It will be limited to (1) the normal voice exclusive of any kind of specialty training—disorders, disease, or damage; (2) the adult voice, exclusive of those of children, youths, and the elderly; and (3) the modal register only2; no attempt will be made to include loft or falsetto on the high frequency end or vocal fry, pulse or the mixed voice associated with low frequencies. The primary reason for these limitations is that healthy adults phonating in the modal register create, by far, the most common type of phonation. Of even greater importance is that more research has been carried out in this area than on any of the other potential relationships. Finally, these limitations should assist in establishing a reasonable baseline for a model. Accepted for publication December 9, 2013. Much of the author’s research cited here was supported by grants from the National Institutes of Health. From the Institute for the Advanced Study of the Communicative Processes, University of Florida, Gainesville, Florida. Address correspondence and reprint requests to Harry Hollien, University of Florida, 229 SW 43rd Terrace, Gainesville, FL 32607. E-mail: [email protected]
Journal of Voice, Vol. -, No. -, pp. 1-11 0892-1997/$36.00 Ó 2014 The Voice Foundation http://dx.doi.org/10.1016/j.jvoice.2013.12.005
The presentation will be initiated with data on laryngeal size followed by consideration of vocal fold length, vocal fold thickness, and airflow/pressure variation. Many of the experiments relevant to the first three of these segments were carried out by the undersigned. Finally, it also should be noted that the research on which the cited processes/model will be based was conducted, almost exclusively, during the second half of the 20th century. Because of that time frame and because the present effort results from a coordinated program of related experiments, the material to follow will be drawn from data published during that period. LARYNGEAL SIZE First, information about laryngeal size, as related to sex and frequency range, should be useful in providing a perspective for the investigations to follow; that is, those on vocal fold length, thickness, and mass. In this regard, an investigation3 was carried out to provide just such information. Up until the initiation of that project, most attempts to quantitatively relate laryngeal dimensions to gender, age, voice level, and so forth had been based on either simple observations or by dissection of cadaver preparations.4–6 Although observations of males and females were found to suggest significant gender differences, little actual data had been provided to show if size variations within each sex also were anatomically ‘‘correlated’’ with voice. Moreover, even the data, which were available were vulnerable to the criticism that may be leveled at virtually all analyses of external measures or cadaver preparations, that is, that they do not adequately represent phonation in the first case or represent living tissue in the second. The approach used in this investigation was to study a population of live individuals by means of lateral soft-tissue X-rays. Four groups of six subjects each were selected from healthy volunteers aged 18–29 years. The groups were males with lowpitched voices (LM) (range: C2–D5); males with high-pitched voices (HM) (range: G2–F5); females with low-pitched voices (LF) (range: B2–A5); and females with high-pitched voices (HF) (range: G3–E6). Selection criteria7,8 required that subjects be free of speech or voice defects, had received no formal training in singing, and exhibited the ability to perform the phonatory tasks necessary for this, plus other related, experiments. Note also that the HM and LF subjects had similar frequency ranges. A standard lateral X-ray procedure was adapted to permit accurate laryngeal size measurements. The equipment used
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TABLE 1. Means of Four Measures (in mm) of Laryngeal Size, for Each of the Four Groups, With CDs Necessary for Significance at the 5% Level Subjects Measures
AP-1 AP-2 Vertical Area
34.1 24.2 36.7 715.6
30.4 21.2 31.7 606.0
26.6 16.5 26.9 405.0
25.7 15.1 20.8 301.0
2.12 1.86 2.19 60.62
Notes: There were six subjects in each group. Abbreviation: CD, critical differences.
FIGURE 1. Tracing of a lateral X-ray film showing the indices (F-GI-H) of general laryngeal size and the reference lines established for measuring A-P (A-C and B-C) and vertical (D-E) distances. was a Picker unit; padding and cork blocks were used to position the subject, and standard corrections were used to compensate for variations in enlargement. The size data were based on measurements of outlines of the walls of the laryngeal pharynx (Figure 1). Differences (Table 1) among the subject groups were statistically significant (re: analysis of variance) with all but two critical differences also significant. Thus, it was shown that individuals with low-pitched voices could be expected to have larger laryngeal tracts than individuals exhibiting higher pitch ranges. It also was shown that gender differences also constitute a powerful variable, that is, that males will have larger laryngeal structures than females although they may exhibit similar pitch ranges. VOCAL FOLD LENGTH The next step was to assess vocal fold length as a function of sex and modal pitch range. To do so, the present author9 first carried out relevant research on the same group of subjects studied in the preceding experiment. Subsequently, other groups, plus the same and other relationships, were addressed. First investigation of vocal fold length As stated, this experiment involved the population cited above. In this instance, however, subjects had their vocal folds photographed when they were abducting them and then when
phonating pitches were at low (10%), medium (25%), high (50%), and falsetto (85%) levels with respect to their total range. However, because falsetto is outside of the purview of this research, only the first three levels will be considered here. Until the time of this experiment, essentially no comprehensive investigations had been carried out directly on just how pitch (F0) changes were accomplished. Vocal fold length was a possibility with some authors suggesting that it was this dimension which was varied, whereas Negus6 countered that such changes were not possible. On the other hand, Moore10 and Farnsworth11 reported observing some sort of vocal fold lengthening-frequency relationships in their ultrahigh-speed motion pictures (see also Moore and von Leden12). Furthermore, both Irwin13 and Brackett14 had sometimes found similar, if somewhat varying, increases. Of course, individuals attempting research of this type faced a number of serious challenges. Among them were problems such as visualizing the vocal folds in their entire length, effectively photographing them and then measuring them with reasonable precision. At issue, especially, was variation in ‘‘lens-to-field distance’’, that is, the distance between the folds and the photographic film. This variable fluctuated both because of differences in an individual’s anatomic size and because the larynx was sometimes seen to rise with increases in pitch. Because the size of the photographic image is (in part) a function of these distances, it follows that measurements on laryngeal films could be subject to error, that is, if suitable corrections were not made. These problems were addressed9 by using updated systems, new measurement techniques, and by training the subjects to better expose their folds as they tolerated the attendant discomfort. The equipment consisted of a mounted laryngeal mirror, a parabolic ‘‘head’’ mirror (directing the light), a 500-W light source (with condensing lens and prism), and an Eastman Cine-Kodak 16-mm motion picture camera with a 4-in telephoto lens. A motion picture camera was used to permit selection of the optimum exposures for measurement. Control of subjects’ F0 was obtained by means of a reference tone at the required frequency level provided by an ordinary chromatic pitch pipe. Figure 2 provides a drawing of the image most often available. Of the possible measurements, those employed in this
Vocal Fold Dynamics for Df0
TABLE 2. Measurements of Vocal Fold Length for 16 Subjects During Abduction and Phonation in the Modal Register Fundamental Frequency Group
N Abducted Low Middle High
Low-pitched males High-pitched males Low-pitched females High-pitched females
4 4 4 4
19.5 14.5 11.3 10.0
10.3 9.9 7.6 6.5
11.3 10.3 8.2 6.9
15.2 12.9 10.6 8.5
Notes: All values are group means reported in millimeters.
FIGURE 2. A tracing of the vocal folds and larynx as seen in laryngoscopic photographs. E is the epiglottis; F, the vocal folds; and T, the tubercles formed by the corniculate and arytenoid cartilages. Line A defines the most anterior extent of the vocal folds; and line B is considered to be the posterior boundary of the vibrating folds. project were of the maximum anteroposterior (A-P) extent of the vocal folds from (A) to a line tangent to the arytenoid tubercles (B). Correction procedures were established by obtaining the distance of the vocal folds to the laryngeal mirror primarily from the X-rays available for each subject (from the first study) and then photographing a millimeter grid at those levels. A table of corrections from their projected images (ie, of the grids) was developed and applied. Of the original group, only 16 subjects (ie, four from each group) were able to successfully complete this procedure. That is, some subjects could not always tilt their epiglottis far enough forward to expose the most anterior portion of the folds. Data from the acceptable views can be found in Table 2. First, it should be noted that vocal fold size varied among the groups. That is, average vocal fold length descended from low male to high male to low female and finally to high female. These (statistically significant) measurements were in agreement with those for general laryngeal size. In addition, the following relationships were noted. a) As F0 was raised, the vocal folds were systematically lengthened. b) The vocal folds were longer in the abducted position (ie, at rest or when the subject was breathing) than for any condition of phonation in the modal register. c) Low-pitched individuals exhibited generally longer vocal folds than those with higher pitch ranges; this relationship was found both between—and within—the sexes. Two additional experiments followed this one. They used yet more sophisticated techniques to assess both the validity and reliability of the data. Specifically, the issues addressed were as follows: (1) can the finding of vocal fold lengthening, in as-
sociation with rise in F0, be validated; (2) can the nature of these trends (ie, slopes, intergroup relationships, and so forth) be better specified; and (3) can the data indicating that they are shortened for phonation (relative to their length during abduction) be authenticated? This last finding (ie, the folds being shorter for phonation than when at rest) was somewhat unexpected. Indeed, it contradicted the long-held opinion that, for phonation, the vocal folds are adducted and stretched beyond the rest position.5,6,15 Of course, a small portion of the vocal folds do not vibrate as they lie between the tubercles. However, this relationship would not account for all of the difference. The second length investigation (men) In 1960, Hollien and Moore16 developed improved techniques for viewing the vocal folds and measuring them. They then studied six men, ranging in age from 27 to 53 years, who were able to expose the full A-P extent of their vocal folds while phonating F0s encompassing their modal range. Three subjects were classified as bass or baritone and three as tenors. All had histories essentially free of laryngeal pathology and/or formal singing training. The photographic exposures were made with an Arriflex 16 motion picture camera with a 6-in telephoto lens mounted on an extension bellows. The lighting system consisted of a 2000-W incandescent lamp (for color photography), a water cell cooler, and a focusing lens. During the experiment, each subject was requested to phonate at the musical tones of C, E, and A, within each octave, from the lowest to the highest tones sustainable in their modal register. Vocal pitch was controlled by having them match appropriate reference tones provided by an audio-generator coupled to a speaker system. They also were requested to produce all pitches at a ‘‘comfortable’’ loudness level. Because the challenge here was to obtain demonstrably accurate measurements of vocal fold length, the new procedure exploited certain features of the Arriflex 16 camera. That is, with a telephoto lens and extension bellows, it provided images of the folds at a very shallow depth of field. Thus, it was possible to bring the photographic image into very sharp (and shallow) focus and, then later, bring a millimeter grid to that same level, by means of a rack and pinion gear. Photographs of the grid were made and used to directly measure the length of the folds for that specific condition. Possible errors due to variation in the
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TABLE 3. Means of Vocal Fold Length (in mm) of Two Male Groups of N ¼ 3 Each Semitone Level E2 A2 C3 E3 A3 C4
82 110 131 165 220 262 Abduction
11.6 12.8 13.4 15.7 19.4 — 20.9
— 9.8 11.7 12.8 13.7 14.0 19.4
Notes: The baritones exhibited low-pitched voices and the tenors highpitched ranges.
distance from the vocal folds to the film were corrected by a single process. As with the first length investigation, measurements were made from the most anterior point of the folds (A) to a line drawn tangent to the anterior borders of the tubercles formed by the corniculate and arytenoid cartilages (B). These values thereby parallel those from both the first and subsequent investigations. Moreover, they delineated the length of the vibrating portion of the folds and were found to provide a consistency that was much superior to any of the other possible measures (Table 3). Again, the DF0 and subject trends were statistically significant. The findings were as follows: a) Excepting for a slight enlargement difference, the data and trends exhibited a close relationship to those from the preceding study. b) The length of vocal folds increased in concert with vocal pitch for the modal register. c) The vocal folds in abduction are always longer than for any phonatory condition in the modal register. d) The data clearly supported ADMET.
External validation It should be noted that other investigators independently demonstrated that the method used in this research, and the findings, were valid. Most relevant was Wendler’s work.17 He carried out a parallel experiment which authenticated both the procedure and data. The second ‘‘validation’’ involved lateral soft tissue X-ray experiments,18 carried out at the present author’s laboratory but by a research team led by a guest investigator. The results there also confirmed that vocal fold lengthening occurs as a function of rise in phonated F0. Finally, yet further confirmation regarding data validity and reliability was provided by other investigators.19–22 Third length investigation (women) To further validate the cited findings and provide parallel data for females, a replication was conducted on 10 adult women23 ranging in age from 18 to 32 years who were required to meet the same selection criteria as did the subjects in the previous two investigations. Moreover, to match the other studies, only data of the four women, each with the lowest and highest pitched voices were used in the present analyses. Finally, protocol for acquiring the images of the vocal folds, exactly followed those for the immediately preceding experiment on men (Figure 2). The results (refer to reference 23 for raw data) closely agreed with those previously found for women; so did the lengthening process. Accordingly, the data from all three studies can be found graphed in Figure 3. These curves, that is, those for the two each male/female groups–are ordered from LM (top) to HF (bottom). As is seen, most of the data points closely follow a straight line and the trends show a systematic increase of vocal fold length with rise in pitch. Also, please note that, as expected, the angle of the slopes increased with laryngeal/vocal fold size. To summarize: (1) systematic vocal fold lengthening occurs with rise in F0, (2) the folds are shorter for all modal register phonation than they are for abduction, (3) the lengthening process is the same both for sexes and for change in F0, and (4) the data supported ADMET.
FIGURE 3. Variation in vocal fold length (in mm) with change in vocal pitch. Relative frequency level values—in the modal register only—are calculated as percentages of the subject’s total pitch range above his lowest sustainable tone.
Vocal Fold Dynamics for Df0
Mechanics of lengthening Before proceeding, it would appear necessary to consider those operational mechanisms that support the above findings. The primary issue to be addressed is on how vocal fold lengthening is accomplished. On the surface anyway, this process appears to be a rather simple one. That is, once adduction is accomplished—primarily by contracting the thyroarytenoid (TA) muscles (especially the vocalis) in concert with the interarytenoids and the lateral cricothyroid (CT), frequency changes related to lengthening result from systematic contraction of the CT muscle. This latter position has been held for sometime and by most authors. Yet, it also has been found experimentally that the entire extent of the lengthening process cannot be achieved by CT activity alone. Specifically, data published by the undersigned and his associates24,25 indicate that, although the CT configurations tested provided for nearly all the (modal) length changes at the low and middle frequencies, they could account for only about 70%–80% of the lengthening which occurred at the upper part of the modal range. Accordingly, it is proposed that this additional shift could only be accomplished by contraction of the interarytenoid and posterior cricarytenoid muscles. Although such contractions have been reported by Gay et al,26 somewhat mixed data have been published by others.27–30 On the other hand, T. Shipp (1980) reported that he sometimes found activity of this nature at the upper frequencies but that it also can be missed due to the difficulty in accurately placing hook-wire electrodes downward into the posticus. Finally, the cited process was further validated by von Leden and Moore31,32 who demonstrated the nature of the anterior-posterior sliding movement of the arytenoids along the track provided by the cricoid. Thus, vocal fold lengthening appears to be accomplished primarily by the TA muscle operating in opposition to the CT as supplemented by a group of small muscles which can operate to shift the arytenoids in a posterior direction. Interpretation To reiterate, completion of the task to merge all the length data (two sets for males and two for females) permits the structuring of a partial model of vocal fold lengthening as related to frequency (F0) change. Specifically, it can be argued that change in F0 in the modal register is mediated by a lengthening of the vocal folds. Because the total mass of the vocal folds would not be expected to vary, this pattern—both logically and according to acoustic theory—should result in their being thinned. The next step, then, was to determine if this is actually what happens. RESEARCH ON VOCAL FOLD THICKNESS The next objective was to study the cross-sectional mass—or thickness—of the vocal folds as a function of DF0 in the modal register. Before 1954 when the first of these studies were initiated, only Griesman33 had used the tomographic procedure to systematically study laryngeal phenomena. He reviewed data of this type obtained from several singers while they were producing a variety of tones. His work suggested that trends might exist (especially with respect to F0) in the coronal crosssectional size of the vocal folds. Later, when others used this
5 technique, they did so to either study voice pathology34,35 or events which were related to singing.36–38 Nevertheless, their observations were not inconsistent with Griesman’s. The first vocal fold thickness experiment The objective of this effort39 was to determine if the vocal fold dimensions of size, area, and thickness would systematically vary with changes in F0. This investigation used the same 24 subjects who populated those on laryngeal size and the initial one on vocal fold length. The procedure used here was laminagraphic X-ray (previously referred to as ‘‘planigraphic’’ and now as ‘‘tomographic’’). The unit used was a Keleket Selectoplane laminagraphic X-ray unit. Subjects were placed supine on the X-ray table with a head immobilizer and sponge rubber padding positioned to ensure proper placement (and comfort). A marker system permitted the vocal folds (1) to be located accurately and (2) to have the X-rays made on a plane, which passed approximately through the midpoint of their A-P length. Exposures also were taken at either 1 cm (women) or 2 cm (men) both anterior and posterior to the midpoint plane. Subjects were required to phonate at the same three F0s as they did in the first vocal fold length study (ie, at 10%, 25%, and 50% of their total range). However, in this case, vocal intensity also was controlled. The procedure required all subjects to produce three samples of each of their experimental frequencies at a ‘‘comfortable’’ level. These levels were measured and the mean calculated. A voice level monitor with two neon reference lights was then used to provide intensity cues to the subject during the experiment. That is, one of the neon lights would glow when the subject reached a vocal intensity within 2 dB of that desired, both lights would glow if the criterion level was exceeded by 2 dB or more. Once the subject was in position, with the proper X-ray settings and his or her output established, laminagrams were made at each of the F0 levels. Measurements were made only on film resulting from phonation as the photos created by the nonphonation or rest conditions (ie, when the vocal folds were abducted) did not outline them. That is, they usually were not distinguishable from the lateral laryngeal walls. On the other hand, an example of the experimental material may be seen in Figure 4. Of the measurements (Figure 5), the two most relevant to this review were (1) the area of mesial vocal fold projection into the airway and (2) mean vocal fold thickness. Area is shown as the shaded portion on the figure and mean thickness was obtained by dividing area by the distance to D-E parallel to (C). These lines (ie, D-E) are the standard reference line used to close the area of the folds laterally; please note that they were shown not to vary significantly from condition to condition for any subject. All reported values were obtained by taking the individual measurement for each fold and averaging them to provide a single value; this procedure is common to all the following studies. The findings of this investigation (all were statistically significant) were that individuals exhibiting low pitch ranges/levels had larger, more massive vocal folds than did individuals with higher ones—so did male size exceed that for females. Second, as the F0 of an individual’s voice was raised, the vocal folds were reduced in cross-sectional area and became thinner.
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FIGURE 4. An example of a coronal cross-section laminagraph showing the laryngeal area and the vocal folds during phonation. What was not expected was the relatively high correlation between vocal fold thickness and absolute F0 of phonation (Figure 6). As can be seen, the thickness of the vocal folds appears to be reasonably similar at each F0 no matter if the subject was male or female or had a high-pitched or low-pitched voice. Thus, it appears that the per-unit-mass of the folds relates to the frequency produced no matter how massive (or not) these structures are naturally.40 However, this finding was pursued further and for two reasons. The first was to assess its validity and the second to determine if this change constitutes a symbiotic relationship with the lengthening patterns cited above. Indeed, if lengthening and thickness combine to provide a common structure for specific frequencies, they also provide (1) evidence of the validity of ADMET and (2) a basis for the calculation of vocal fold mass.
FIGURE 5. Tracing of a laminagram of the vocal folds showing the reference lines used for the cross-sectional area and thickness measurements.
The second thickness study As stated, the goals for the second experiment41 were primarily to test the hypothesis that the thickness of the vocal folds correlates directly with the (modal) F0 produced and does so moreor-less irrespective of laryngeal size or gender. Subjects for this investigation were three males and three females ranging in age from 19 to 33 years. The usual selection criteria were applied and each subject’s pitch range was then obtained by standard procedure.7 To create a group as heterogeneous as possible, subjects were chosen so that low-, medium-, and high-pitched voices were represented within each sex. The equipment used was virtually identical to that which supported the first experiment—with but one exception. In this instance, Auer film packs, which featured multiple X-ray plates, were used. This procedure allowed five coronal planes (5 mm
apart) to be made simultaneously along the A-P dimension of the vocal folds. It was by this means that measurements could be made along (nearly) the entire A-P length of the folds. Subjects were required to phonate six pitches within their modal register; they were 123, 147, 165, 220, 262, and 294 Hz for men; 220, 262, 294, 349, 392, and 440 Hz for women. Of course, no phonation in falsetto was included. Subjects were placed supine on the laminagraph table. Sponge rubber padding, a head immobilizer, and a chest strap were used to ensure maintenance of appropriate positioning—and do so with a minimum of subject discomfort. Each subject was placed so that the central ray of the equipment would pass through his or her larynx at the vocal fold’s midpoint. Both determination of the center A-P plane and those along the A-P distance were validated by the use of the cited Auer multi-film pack.
Vocal Fold Dynamics for Df0
FIGURE 6. Thickness of the vocal folds as a function of frequency change. The measures of thickness were obtained by dividing vocal fold area by their lateral dimension. Frequency level values were obtained by converting the F0 of phonation to semitones above the reference frequency of 16.35 Hz.
Once the subject was in position and all proper settings/ outputs determined, a trial was run. The procedure was continued until all the experimental conditions were satisfied. The measurements were made as per the first thickness study, excepting that (1) they were made from photographs of the Xray plates and (2) multiple measurements were made for each condition. The obtained findings confirmed the high correlation between vocal fold thickness and F0 (Figure 7). Indeed, a correlation coefficient of 0.91 was obtained. This robust relationship is considered to be even more remarkable when the extremely heterogeneous population studied in this instance is considered. Indeed, the very small variation in the frequency-thickness relationship was somewhat unexpected. Moreover, it should also be noted that vocal fold thickness was found to vary but little over much of its A-P length. To expand the available database (so matches could be made with subjects from the vocal length studies), yet another experiment was carried out.42 The purposes of this investigation were to (1) further test the hypotheses cited above, (2) study the obtained curves in more detail, and (3) study other relationships. Thus, data for 10 additional subjects (phonating in the modal register) could be added to the 30 individuals populating the first two studies. Because the patterns here correlated highly with the first two data sets, it appeared that enough subjects were available to permit combining the length and thickness measures.
FIGURE 7. Thickness of the vocal folds as a function of absolute frequency level. Measures of thickness were made as seen in Figure 5. In this case, however, a number of overlapping frequency-thickness relationships were studied.
Evaluation of potential error sources However, before doing so, certain concerns had to be addressed. That is, misgivings had been expressed that the effects of gravity might distort the laryngeal structures when subjects were placed in the supine position (rather than vertically) for research of this nature. Second, it had not yet been fully demonstrated that the vocal folds exhibited the same thickness throughout their entire A-P dimension. Third, concern also had been articulated relative to the possibility that variation of vocal fold thickening at lower frequencies and thinning at higher ones might possibly be due (at least in part) to the complexity of their movement rather than just to their lengthening and thinning. In this regard, it must be remembered that each tomograph took a full second to complete. Hence, each picture consists of many complete vibratory cycles. If it were true that the lack of stiffness at the low frequencies resulted from the folds moving in a complex manner but in a much simpler pattern for the higher ones, they would appear larger at the lower tones than for the higher. The first concern was resolved43,44 when identical levels for vocal fold cross-sectional size and voice pitch were found for subjects studied in both in the vertical and supine positions under what were otherwise identical conditions. Accordingly, it was judged that valid research of this type can be carried out with subjects supine. The second issue, thickness versus A-P length, was addressed by additional procedures using the Auer multiple-plate cassettes. First, a random sample (25%) of all experimental conditions had previously been carried out. Now analyses of 30% of the photos from the multi-palate procedures were added to that
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FIGURE 8. An illustrative series of stroboscopic laminagrams showing the vibratory action of the vocal folds in coronal cross-section. As seen, the vocal folds are closed in the first photograph; they then open, progress through a full vibratory cycle, and ultimately move toward closure, which can be seen in the last (lower right) photograph. corpus. Although these X-rays covered the entire A-P length in only 84% of the cases, little-to-no variation (ie, 2.6%) was found among any of the measurements. Hence, the answer to the second concern is that it appears that vocal fold thickness varies but little along their entire A-P dimension. Stroboscopic laminagraphy To reiterate, the third concern was triggered by the fact that each laminagraphic image of the vocal folds was created by X-raying a large number of vibratory cycles. Thus, it was suggested that variation in movement patterns might create the illusion of size differences. A stroboscopic laminagraph45,46 (STROL) was developed as a response to this rather serious problem. This system provided a series of coronal views of the vocal folds (usually N ¼ 10) when they are at each of several phases distributed equally throughout the vibratory cycle. Although each picture is a composite of several short exposures obtained from a number of vibratory cycles, they occur only when the folds are in exactly the same position. Thus, in practice, the folds are seen in 10 different positions throughout a vibratory cycle and accurate measurements of area and thickness can be performed on them. As would be expected, this technique also is capable of providing motion pictures of the vibrating vocal folds in the coronal cross section47 (a video is available). However, in this review, the measurements provided by STROL will be used only to validate the accuracy of the metrics of vocal fold thickness obtained from ordinary laminagraphy. Basically, STROL uses an X-ray, which is both powered and controlled by a Keleket Novematic 500 console. To do so, that unit features an internal pulse-forming network, which converts an experimental subject’s sustained phonational output (ie, his or her F0 when produced at a fixed frequency) into sharp pulses. These pulses are amplified and used to drive the X-ray tube. The X-rays produced by these circuits pass through the subject and
impinge on an image intensifier. A 35 mm Nikon camera, which is placed facing the intensifier screen, takes a 0.5 second exposure during each swing of the yoke and advances one frame at the end of the swing. Thus, the X-ray is flashed at the same rate as the subject’s phonated F0 during each laminagraphic swing with its phase advanced 36 at the end of each arc. With the 10 steps in each complete trial, a full 360 phase shift sequence is accomplished to produce the 10 photographs found in Figure 8. Seen there are the 10 sequential positions of the vocal folds progressing from their closed position through a complete vibratory cycle and, then, back to closure. Measurements of vocal fold thickness were made for subjects producing seven frequencies48; the clearest image at, or near, closure was selected for this purpose. These data provided even tighter curves (but ones of the same magnitude) than did those seen graphed in Figures 6 and 7. Indeed, the actual thickness and the slope of their thinning (as a function of increased F0) almost exactly merged with data that was obtained from ordinary laminagrams. Hence, the third concern was met and the data specifying a reduction in vocal fold per-unit mass (ie, thickness) as a function of DF0 could be considered valid. Subglottic air pressure Before proceeding, a fourth dimension must be considered. It is to determine if the relationships established by the experiments reviewed above are consistent with the predicted aerodynamic reality. After all, it now appears clear that the vocal folds are first contracted for phonation by moving them to the midline by means of the TA muscle system operating in opposition to the other (intrinsic) laryngeal muscles. As attempts are made to increase absolute frequency, the TA contracts yet further with the CT and posticus (and related muscles) also further contracting in opposition. The end result is a continual thinning of the folds. In turn, they stiffen (as they thin) and impedance to airflow is increased. Theoretically, airflow itself might not
Vocal Fold Dynamics for Df0
TABLE 4. Total Vocal Fold Mass Measurements (in mm) for 12 Subjects From Two Categories (Low- and High-Pitched Males) Frequency (Hz) 82 110 131 156 165 185 220 262 Mean
570 554 525 — 551 577 574 — 558
— 375 336 320 360 — 316 348 342
Notes: Values were calculated by multiplying each subject’s vocal fold length by vocal fold thickness. All cells are the means for at least four subjects.
increase markedly but, it would be expected that subglottic pressure would do so. That is, it would if the conditions specified by ADMET are to be met. It was not necessary for the present author to conduct the necessary airflow/pressure experiments because relevant research already had been reported. First, these studies provided little, if any, data indicating systematic airflow-frequency relationships for the modal register, that is, except (perhaps) for small increases at the very top of the frequency continuum.28,49,50 On the other hand—and as postulated—these authors plus Ladefoged51 provided data specifying that, except for very low modal register frequencies, subglottic pressure (Ps) increased systematically with rise in F0. This relationship serves to complement those established above and provides data about operations that are necessary for vocal fold vibration in the modal register. They also provide the final link for the development of a model. Incidentally, these findings are further confirmed by data on vocal fold tilting as this dimension increases in concert with rise in F0.52 That is, if Ps is increased at the higher frequencies in the modal range (where the vocal folds are thinner), compensatory activity would be expected with the folds pushed upward as they opened at the start of the vibrating cycle. In turn, it is expected that this motion would be muted somewhat for the lower frequencies where the folds are thicker. In any event, those were the patterns reported; they are consistent with the other data presented. Vocal fold mass It now appears that the measurements of the vocal folds (ie, as reviewed in the above text) permit calculation of reasonably good estimates of vocal fold mass. That is, if the thickness (T) of the folds is known, and their length (L) can be determined, mass will be the sum of the first value multiplied by the second (ie, M ¼ L 3 T). Moreover, if these two metrics can be calculated for a number of frequencies throughout the extent of the modal register, actions that might cause changes in mass—if they were to occur—can be identified.
TABLE 5. Total Vocal Fold Mass Measurements (in mm) for 14 Subjects From Two Categories (Low- and High-Pitched Females) Frequency (Hz) 151 165 208 220 226 262 311 330 349 440 523 Mean
220 225 221 222 — 219 — 210 233 233 207 221
— 141 — 128 156 136 138 117 — 145 137 137
Notes: Values were calculated by multiplying each subject’s vocal fold length by vocal fold thickness. All cells are the means for, at least, four subjects.
More to the point, the characteristics of vocal fold mass were established by the experiments described in this report. That is, data on mass were first calculated for the eight males and eight females who populated the initial length and thickness experiments. Since only four subjects were common to the subsequent procedures, an independent evaluation was carried out on four groups of matched subjects—ie, two groups each, for males (LM and HM) and for females (LF and HF). The matching process was accomplished by first creating a pool of all males who met the pitch range (low, high) criteria; a parallel one was assembled for females. The final population was then obtained by matching each subject (relative to age, size, pitch range, and so forth) from the vocal fold lengthening studies to the person most like him/her from the thickness studies. Two sets of three male pairs (N ¼ 6) and four female pairs (N ¼ 8) proved suitable. Hence, the final groups consisted of 14 men and 16 women drawn from three sources. The frequency-mass data for males can be found in Table 4. Note that only minor variation of total vocal fold mass occurs at the data points along the frequency continuum. As can be seen, this relationship held for the individuals who populated both the length and thickness experiments as well as those (ie, the matched pairs) from the studies involving more advanced protocol. Indeed, both procedures resulted in nearly identical mass calculations. That is, not only were the total mass values found to be internally similar throughout the frequency ranges for the matched pairs, they proved to be of almost the same dimensions as those for the initial groups. Consideration of the table also will reveal that only small variations occur among the mean values. It also can be observed that vocal fold mass was greater for the men with the lower pitch ranges. The data for the women can be found in Table 5. Examination will reveal that the patterns cited for men also held for them. That is (1) all women exhibit smaller vocal folds than do men, (2) there is an internal difference between low-pitched
10 and high-pitched women, (3) the data are comparable for both matched pairs of women and those who were common to both procedures and, most important, (4) vocal fold mass varied little over the entire range of frequencies studied. Finally, it can be noted that these are the first direct compilations of vocal fold mass measurements to have been reported. Conclusions based on these data appear obvious. Vocal fold mass does not vary (or, at least, varies but little) as a function of DF0 if it is produced within the modal register. Specifically, the variation around the means for the four groups was LM ¼ 16.9 mm, HM ¼ 19.1 mm, LF ¼ 8.5 mm, and HF ¼ 10.0 mm. Accordingly, it can be argued that these modest variations in vocal fold mass are due, most probably, to the difficultly in making measurements as precise as would be desirable. Indeed, the nature of the anatomic images—and the physiological movements—studied plus the procedures used in measuring them, probably can account for most of the variation encountered. A MODEL The model resulting from the cited corpus of experiments turns out to be relatively straightforward. It can be articulated as follows. Frequency change in the modal register is accomplished by a systematic thinning of the vocal folds with the thickness directly related to the actual F0 phonated. Operations of this type are consistent with those principles of acoustics, which dictate how the larynx functions as an audio oscillator. Furthermore, they appear to hold irrespective of the overall size or sex of the individual who is phonating or the size of their vocal folds. In turn, the dynamics of vocal fold thinning are mediated by their continual, but orderly, lengthening. The mechanism that supports the cited processes is also fairly evident. That is, the vibratory portion of the folds is adducted and shortened, but then stretched, to systematically reduce cross-sectional area. They perform this operation without violating total vocal fold mass, which remains constant. In turn, these relationships are controlled primarily by the action of the CT muscle complex operating in opposition to the TA group—an action is supplemented by the contraction of certain intrinsic laryngeal muscles (especially the posticus) plus several of the external ones. Finally, these changes are made in concert with the systematic variation of subglottal pressure as provided by the respiratory system. It is hoped that the hypotheses proposed here will be further tested. In the interim, the data presented—and the conclusions drawn—can be used to refine certain aspects of the ADMET of phonation in humans. Most important, however, they serve to strongly support that theory. Finally, it is also possible that the model can be used as a starting point for the study of related types and classes of vocal fold activity. REFERENCES 1. van den Berg JW. Myoelastic-aerodynamic theory of voice production. J Speech Hear Res. 1958;1:227–244. 2. Hollien H. On vocal registers. J Phonetics. 1974;2:125–143.
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