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Mechanical stress in phonation
Journalof Voice
Vol. 8, No. 2, pp. 99-105 © 1994 Raven Press, Ltd., New York
Mechanical Stress in Phonation Ingo R.
Titze
Department of Speech Pathology and Audiology, National Center for Voice and Speech, University of Iowa, Iowa City, Iowa, and Recording and Research Center, Denver Center for the Performing Arts, Denver, Colorado, U.S.A.
Summary: Mechanical stress is always encountered in phonation. This includes tensile stress, shear stress, impact stress during collision, maximum active contractile stress in laryngeal muscles, inertial stress, and aerodynamic stress (pressure). Order of magnitude calculations reveal that tensile stress can reach the greatest value (near 1.0 MPa), contractile stress is next in size (near 100 kPa), and aerodynamic stress is relatively small (1-10 kPa). Inertial stress and impact stress are greater than aerodynamic stress, but less than contractile stress. Excessive collision and acceleration may be responsible for the greatest tissue damage, even though they do not account tbr the greatest stresses. This is because they act perpendicularly to the direction of tissue load-bearing fibers and are applied directly to mucosal tissue. Key Words: Stress--Strain-Injury--Vocal fold--Vibration--Damage--Vocal disorders.
This article was motivated by the lifelong investigations of voice disorders by Moore (1). Moore convinced this author, and many others in the field, that voice disorders and voice physiology are one and the same topic. One cannot understand normal vocal fold vibration with a disregard for abnormal vibration patterns. This is becoming increasingly more evident in light of modern views of nonlinear dynamics. Chaotic behavior is part of a normal selfoscillating vocal fold system, and "normal" vibration patterns can be seen when the vocal folds are visually impaired. Nowhere is this gray boundary between normal function and dysfunction more evident than in the assessment of mechanical stress in phonation. It is generally assumed that excessive mechanical stress can lead to organic disorders. But how much is excessive? Although repeated collision of the vocal folds is likely to be the primary cause of vocal nodules, we cannot produce much sound without colliding the vocal folds. So what is a tolerable
amount? We also believe that persistent "pressing" together of the arytenoid cartilages is a cause of contact ulcers, and rubbing vocal fold tissue with foreign objects (such as an endotracheal tube) is known to cause granulomas, but, again, we have no criteria for how much mechanical stress is abusive. Benign lesions are apparently a reaction to, and ultimately a fortification against, mechanical insult to vocal fold tissues. Little is known, however, about the kind of stress that routinely occurs during vocal fold vibration, and how that stress is distributed within the tissues. If the stress fields were known for various phonation types, perhaps some strategies for healthy, nonabusive voice production would become clearer. Specifically, it would be desirable to weigh phonation type and increases in vocal loudness against increases in tissue stress to obtain a cost/benefit ratio for certain vocal productions. The present study is an extension of the summary article on vocal strain written by Sonninen et al. (2), who summarized the types of mechanical loads and deformations found in the vocal folds. Twenty years later, we can shed only a little additional light on these critical questions: (a) What types of
Accepted March 31, 1993. Address correspondence and reprint requests to Dr. I. R. Titze at Department of Speech Pathology and Audiology, National Center for Voice and Speech, University of Iowa, Iowa City, IA 52242, U.S.A.
99
100
I . R . TITZE 16o-
stresses occur in vocal fold vibration, (b) How large are they under normal and maximal-effort phonation, and (c) Is there a likelihood that tissue damage will occur from a specific type of stress?
12o................................ .....
TYPES OF MECHANICAL STRESS AND RELATIVE MAGNITUDES
o
We begin by identifying the various types of mechanical stress encountered in vocal fold vibration, with an attempt to estimate their magnitudes. It should be understood that these estimates are order-of-magnitude. In many cases, experiments are yet to be done to verify the numbers. Tensile stress By far the greatest stress applied to vocal fold tissues is a tensile stress (Fig. 1). This is applied primarily to the longitudinal (anterior-posterior) fibers of the vocal ligament by the cricothyroid muscle. An estimate of the maximum tensile stress is obtained by assuming that collagenous and elastic fibers vibrate in a string-like fashion. Then tr = 4L2F2p
(1)
where tr is the tensile stress L is the length of the membranous vocal fold, F o is the fundamental frequency, and p is the tissue density (1,040 kg/m3). For a woman singing a high C (F o = 1,046 Hz) and a membranous length of 0.01 m, the stress is o- = 4(10 4)(1,046)2(1,040) ~ 500 kPa
(2)
For higher notes in the coloratura repertoire, frequencies up to 1,500 Hz are possible, for which the tensile stress would exceed 1.0 MPa. If the ligament cross-section is - 1 mm × 1 mm, then the tension is on the order of 1 N, or -¢2 lb. For typical speech fundamental frequencies, es-
Cross section S
I
~ F (cricothyroid force)
---I
Lo
~" AL ~ -
Tensile
stress
Tensile
strain = e = AL/Lo
Maximum active
80
40-
$1 S Passive ~ J
0
10
2~0
40
Strain (%)
FIG. 2. Maximum active contractile stress (dotted line) of the thyroarytenoid muscle of canine larynges. The total stress (solid line) is assumed to be the summation of the passive stress (dashed line) and maximum active stress (after ref. 3).
pecially for men, the tensile stress is much lower. At 100 Hz, for example, ~r is two orders of magnitude lower than at 1,000 Hz, giving a stress of - 5 kPa. Maximum active contractile stress in muscles The maximum active contractile stress in the thyroarytenoid (TA) and cricothyroid (CT) muscles of canines has been measured by Alipour-Haghighi et al. (3,4). Results are shown in Fig. 2 for the TA and in Fig. 3 for the CT. Note that these stresses vary with vocal fold length (strain), but have a range of values of -30-115 kPa. The TA muscle reaches a maximum active stress of 100 kPa at 20% elongation, whereas the pars recta of the CT reaches the same value at - 3 0 % elongation. One might ask how the CT can produce a stress of 1.0 MPa in the vocal ligament when its maximum contractile stress is only - 100 kPa. The answer lies in a transformation of cross-sectional area. The force applied to the ligament equals the force produced by the CT muscle, but because the ligament has a smaller cross-sectional area, the stress is magnified by a factor of 10 or so. Collision stress between vocal folds The collision stress between the vocal folds can be estimated from basic physical principles (Fig. 4). Assuming the mass of a tissue element at the medial surface to be
= cr = F / S
m = pAxAyAz
(3)
.
FIG. 1. Illustration of tensile stress and strain. Journal of Voice, Vol. 8, No. 2, 1994
3'0
where p is the tissue density given above and 2txAyAz is a small volume, then, from Newton's
MECHANICAL
STRESS
101
This velocity is reduced to zero during the collision interval, such that
Pars recta maximumactivestress
100 "
IN PHONATION
• pars obl]qua
Av = v -
(7)
0 = 2rrFoA
Substituting Eqs. 3, 5, and 7 into 4 yields ~
50
O3
o
o
t'o
2'0
3'0
40
If A y A z is taken to be the impact surface and Ax the depth of the vibrating tissue, then the collision stress is
Strain (%)
F ~r - AyA~ - 20"rrAFZpAx
FIG. 3. Maximum active contractile stress of two components of the CT muscle of canine larynges, The passive stress is also shown (after ref. 4).
second law, the average collision force over an impact interval At is (4)
F = mAv/At
where Av is the change in velocity during impact. Jiang and Titze (5) estimated the impact interval to be on the order of
r0 At-
10
(5)
where To is the fundamental period. The velocity change in Eq. 4 can be estimated by assuming sinusoidal motion with amplitude A and radian frequency o~ = 2¢rFo. The maximum velocity, which occurs near impact, is then v = oJA = 2 w F o A
(8)
F = 207rAF2pAxAyAz
pars obliqua Pars recta passive stress ~ = ~ O ~ p a esrtss s~~i~. v e
(9)
For an amplitude of vibration of 10 -3 m, a depth of vibration of 10 -3 m, and an Fo of 200 Hz, this stress is 2.6 kPa. Peak impact stresses on the order of 0.5-5.0 kPa were measured by Jiang and Titze (5) and are shown in Fig. 5 as a function of subglottal pressure. Similar increases in contact stress were obtained by Reed et al. (6) with a piezoelectric transducer placed between the vocal folds of a human subject. Values of Fo in Fig. 5 were <200 Hz. For frequencies approaching 1,000 Hz, one would expect much higher impact stresses if the amplitude and depth of vibration were to remain constant. Typically, however, both amplitude and depth of vibration decrease with F0, making the exact stress uncertain. One would expect that the impact stress could increase an order of magnitude, to - 5 0 kPa, for high F 0 and high subglottal pressure.
(6) 5.0"
Collision boundary
Tissue element of mass pAxAyAz
4.0
& 3.0, "5 2.0,
Q.
1.0,
J 11o Av
Impact stress = (pAx) ~ -
FIG. 4. Illustration of impact stress.
21o
31o
4.0
Subglottal pressure (kPa)
FIG. 5. Peak collision stress versus subglottal pressure in a canine hemilarynx (after ref. 5).
Journal of Voice, Vol. 8, No. 2, 1994
102
I.R.
Inertial stress The inertial stress is similar to the impact stress, except that acceleration and deceleration occur without collision. Assuming again that the tissue moves sinusoidally with amplitude A, i.e., x = Asintot
(1 1)
This stress is approximately half of the impact stress, on the order of 1-2 kPa for normal phonation. A e r o d y n a m i c stress
The mean aerodynamic driving stress is the mean intraglottal pressure, which has been estimated as
in the open phase (6). Here P,. is the input pressure to the vocal tract (supraglottal pressure), al is the glottal entry area, a2 is the glottal exit area, and P= is the subglottal pressure. The greatest pressure occurs for a highly convergent glottis, where az/al "~ 0, in which case Pg ~ P=" In high-effort phonation, P~ can be as high as 5-6 kPa, and occasionally reaches 10 kPa (8). This can be taken as the upper limit on aerodynamic stress. A r y t e n o i d contact stress
Maximum contact stress between the arytenoid cartilages has been estimated by Rethi (9) and Kakeshita (10) to be on the order of 50-100 kPa in animals who had the adductor muscles fully contracted. This range would tend to agree with the maximum active stresses measured in the CT and TA muscles of canines. Adduction stress for normal phonation is much lower than that, however, even for so-called "pressed voice." Values reported by Scherer et al. (11) were on the order of 1-5 kPa. Shear stress at anterior and posterior macula flava The shear stress in the ligament increases with the amplitude of vibration. If the ligament is pinned at the endpoints (anterior and posterior macula flava), then the shear stress -r can be written as "r = Ixsin0 Journal of Voice, Vol. 8, No. 2, 1994
where Ix is the shear modulus and 0 is the shear angle at the endpoints (Fig. 6). The shear angle can be expressed in terms of the vibrational amplitude and the membranous length of the vocal folds. Thus, if
(10)
then the maximum acceleration is to2A. The maximum inertial stress is mass (pAxAyAz) times acceleration (4~r2F~A) divided by the surface area (AyAz), which simplifies to cr = 47r2AF02pAx
TITZE
(13)
(14)
x = Asin~ry/L
is the displacement of a lowest-string mode in the anterior-posterior (y) direction, A is the amplitude (at the center) and L is the membranous length, then -rrA
dx
dy
y=O,L
L
- tan0 -~ sin0
(15)
For an amplitude of 0.2 mm and a length of 10 mm, sin 0 = 0.6. The shear modulus tx of the collagen fibers in the macula flavae is not known to this author, which makes it impossible to estimate the absolute value of the shear stress. All one can say is that it increases with amplitude of vibration and decreases with vocal fold length. The A / L ratio is a key variable for dynamic shear stress. Summary of relative magnitudes of stresses A summary chart of the relative magnitudes of the various mechanical stresses is given in Fig. 7. Estimates are made for conditions of normal phonation (clear bars) and maximum stress (crosshatched bars). Note the large maximum tensile stresses relative to all other stresses. Note also the relatively small aerodynamic stresses. Active contractile, arytenoid contact, impact, and inertial stresses are intermediate in size.
Anteriorboundary
7///S,
I~O~
Vocalligament
i Shear stress =/.tsinO FIG. 6. Illustration of shear stress in the vocal ligament.
M E C H A N I C A L STR E SS I N P H O N A T I O N
~"
~', //i
100-
~,~
Max
Normal
//1
S~ //1
Tensile '~ Aryienoid stress Contractile contact muscle stress stress
Impact stress
lnertial stress
Aerodynamic
FIG. 7. Summary of the relative magnitudes of various mechanical stresses in vocal fold tissues.
DAMAGE CRITERIA Damage to vocal fold tissue may occur from any of the mechanical stresses described. Based on the relative size of the tensile stress in relation to other stresses, one would reason that the vocal ligament would be at the highest risk of damage, particularly at high pitches. Excessive tension would appear to rupture the tissue fibers. If the vocal ligament has comparable strength to other ligaments in the body, however, it is well protected against this type of rupture. The following discussion will clarify this point. Rupture due to tensile stress As an analogy with other body tissues, consider the anterior cruciate ligament of the knee, which has been studied extensively by Noyes and Grood (12). This ligament is larger than the vocal ligament. The authors report an average length of 27 mm and an average cross-sectional area of 44 mm 2. This is approximately twice the length of the vocal ligament and approximately 10 times the cross-section. Nevertheless, because stress and strain are essentially independent of sample size, the comparison is useful. Figure 8 shows the mechanical response of the anterior cruciate ligament under tensile stress. Strain was applied at a rate of 100% per second. The attempt was to simulate conditions in sports, where extension, flexion, and torsion occur quite rapidly. Tissue age was a parameter in the study. One group of subjects was in the 16-26-year age bracket, whereas another was in the 48-86-year bracket. Note that the older group displayed a lower maxi-
103
mum stress (13.3 MPa as compared with 37.8 MPa for the younger group). Furthermore, this maximum stress occurred at a lower strain (30 instead of 44%). Thus, not only could the younger ligament support more tensile stress, but it could support this stress at a greater elongation. Failure of the ligament occurred differently in the two age groups. For the younger group, collagen fibers were ruptured throughout the length of the ligament. This caused the stress to decrease rapidly as shown. For the older group, failure was primarily due to bone avulsion. This took place more gradually and is probably the cause of earlier failure with increased strain. It is important to contemplate the overall stress magnitude that this k n e e ligament can support. In the "linear" range, stresses can be 10-20 MPa. This is 40-80 times the stress we estimated for a soprano singing a high C. If the vocal fold ligament is made up of the same type and density of collagen fibers as this knee ligament, one would conclude that there is little chance of failure of the vocal ligament by excessive CT contraction. The vocal ligament probably serves to protect other tissues in the vocal fold from rupture. If we can assume that 30% is a strain limit on the vocal folds, which tends to agree with the estimates of van den Berg (13), then the mucosa and the TA muscle will not be elongated to their yield points. Figures 9 and 10 show stress-strain curves for the canine TA muscle and vocal fold cover, respectively. These curves were obtained by cyclic stretch-release methods at a rate of 1 Hz (similar to 50Max stress
40-
~
20-
(~
M~,x stress -
,~aJLure
10"
",,. ~, ,, "
0
•
~
10
•
Linear i
20
,
limit i
30
,
i
40
,
i
50
6'0
70
Strain (%)
FIG. 8. Stress-strain curve for the anterior cruciate ligament in humans (after ref. 12). Solid line is for the younger specimen (16-26 years) and dashed line for the older specimen (48-86 years). Journal of Voice, Vol. 8, No. 2, 1994
104
I . R . TITZE 30-
The primary symptom of a vascular disorder is "white finger," which is basically the symptom of reduced circulation. Circulation is impeded by rapid acceleration and deceleration of the tissue. Estimates of maximum acceleration of vocal fold tissues within the vibratory cycle were implicit in Eq. 1,
20"
N lO-
o
(16)
a = toZA = 4~rZF~A
o
1'o
2'0
a'0
40
Strain (%)
FIG. 9. Stress-strain curve for the thyroarytenoid muscle of canines during cyclic stretch and release.
the rate of the knee ligament elongation). Note that 30-40% elongation was possible without tissue damage. Thus, the presence of a vocal ligament would tend to keep strains in the "safe" range for muscle and mucosal tissue. Excessive vibration In his H a n d b o o k o f H u m a n Vibration, Griffin
(14) lists five disorders associated with handtransmitted vibration: (a) vascular disorders, (b) bone and joint disorders, (c) peripheral neurologic disorders, (d) muscle disorders, and (e) other (e.g., central nervous system). These disorders are usually associated with tool use. They may not apply at all to vocal fold vibration, but it is worthwhile to make a few comparisons. Parameters for consideration are vibrational magnitude, frequency, and duration.
For a fundamental frequency of 200 Hz and a vibrational amplitude of 0.001 m, there is a peak acceleration of 1,600 m/s 2, with a root mean squared value of 1,100 m/s 2. If such a vibration were to occur continuously for 30 min, it would fall well into the unacceptable region of exposure according to International Standards Organization (ISO) standards (ref. 14, p. 647). As shown in Fig. 11, accelerations of even one-tenth this value would be unacceptable (see data point in relation to the line of safety). Phonation is never continuous, of course, for 30 rain. This makes the dosage criterion difficult to assess, but it cannot be ruled out that excessive vibration could lead to some vascular disorders in the larynx. Impact stress
Assessment of safe limits of impact stress is also difficult. We do not have well-controlled experiments that show the tissue damage as a direct result of collision. The studies by Gray et al. (15) and Gray and Titze (16) are beginnings. Continuous phonation was maintained (by an artificial air supply) for several hours at high intensity in anesthetized canines. Electron-microscopic examination showed 10000
4O 1000, E
30 ¸
UnbaccePt e4A~~ep~le vimagni ratiotunabl des
100-
& 20 ¸
10-
_/
vibration
8 1
10.
0 0
i
,
i
lO
,
20
3'0
Strain (%)
4'0
so ;.
FIG. 10. S t r e s s - s t r a i n curve for the vocal fold cover of canines during cyclic stretch and release.
Journal of Voice, Vol. 8, No. 2, 1994
o
1'o
16o
lC;OO 10000
Frequency (Hz)
FIG. 11. 1SO standard for hand-transmitted vibration (after ref. 14). Data point suggests that vocal fold vibration could exceed the m a x i m u m r e c o m m e n d e d dose.
M E C H A N I C A L STRESS I N P H O N A T I O N
destruction of surface microvillae, of squamous epithelial cells, and of the basement membrane zone. Future investigations should quantify this type of destruction in terms of measured impact stress. It would also be extremely valuable to know the time course and degree of the healing process.
105
that aerodynamic stresses of themselves do not pose a damage risk. Acknowledgment: This study was supported by grant no. P60 DC00976 from the National Institute on Deafness and Other Communication Disorders. I thank Julie Lemke for manuscript preparation and Mark Peters for graphic support.
CONCLUSION The largest mechanical stresses in vocal fold vibration are the tensile stresses required for pitch increase. Estimates are that they may reach values on the order of 1 MPa. This would be excessive for epithelial or muscular tissue, but seems to be normal for ligamental tissue. We assume, therefore, that a well-developed and healthy vocal ligament provides a "safety-valve" for other, perhaps more injury-prone, tissues in the vocal folds. The ligament limits elongation and assumes most of the tensile stress at high pitches. The ligament cannot protect as well against vocal fold collision, however, where the stress is transverse to the fibers. Here the softer tissues of the lamina propria are exposed and do absorb most of the impact stress. Some evidence of destruction has been reported, and the fact that vocal fold nodules occur bilaterally at the point of maximum impact stress (5) attest to this. The possibility that safe limits of tissue acceleration are exceeded in prolonged phonation needs further exploration. Exposure durations are shorter than what is typically reported for hand-transmitted vibration with power tools, but acceleration magnitudes are comparably larger. This leaves the integrated dosage uncertain. Finally, shear stresses and aerodynamic stresses were discussed briefly, but no damage estimates could be made in this preliminary study. Aerodynamic stresses are very small in comparison to tensile stresses and maximum contractile stresses of the laryngeal muscles, which leads one to speculate
REFERENCES 1. Moore P. Organic voice disorders. Englewood Cliffs, New Jersey: Prentice-Hall, 1991. 2. Sonninen A, Damst6 PH, Jol J, Fokkens J. On vocal strain. Folia Phoniatr (Basel) 1972;24:321-36. 3. Alipour-Haghighi F, Titze IR, Perlman A. Tetanic contraction in vocal fold muscle. J Speech Hear Res 1989;32:22631. 4. Alipour-Haghighi F, Titze IR, Perlman A. Tetanic response of the cricothyroid muscle. Ann Otol Rhinol Laryngol 1991; 100:626-31. 5. Jiang JJ, Titze IR. Measurement of vocal fold intraglottal pressure and impact stress. J Voice 1994;8:132-44. 6. Reed CG, Doherty ET, Shipp T. Direct measurement of vocal fold medial forces. ASHA 1992;34:131(A). 7. Titze IR. The physics of small-amplitude oscillation of the vocal folds. J Acoust Soc A m 1988;83:1536-52. 8. Schutte H. The efficiency o f voice production. Groningen: Kemper, 1980. 9. Rethi L. Die stimmbandspannung, experimentell gepr~ft. Sitzgsber Akadem Wissenschaft Wien Math Naturwissenshaft Kl III 1897;106:244. 10. Kakeshita T. Uber eine neue methode zur messung der beim stimubrandverschluss winkende krafte. I Mitt Pflugers Arek far die Gesamunte Physiol 1927;215:19. 11. Scherer RC, Cooper DS, Alipour-Haghighi F, Titze IR. Contact pressure between the vocal processes of an excised bovine larynx. In: Titze J, Scherer R, eds. Vocal fold physiology: biomechanics, acoustics, and phonatory control. Denver: Denver Center for the Performing Arts, 1985:292-303. 12. Noyes FR, Grood ES. The strength of the anterior cruciate ligament in humans and rhesus monkeys. J Bone Joint Surg A m 1976;58:1074-82. 13. van den Berg J. Myoelastic-aerodynamic theory of voice production. J Speech Hear Res 1958;1:227-44. 14. Griffin MJ. Handbook o f human vibration. New York: Academic Press, 1990. 15. Gray SD, Titze IR, Lusk RP. Electron microscopy of hyperphonated vocal cords. J Voice 1987;1:109-15. 16. Gray S, Titze IR. Histologic investigation of hyper-phonated canine vocal cords. Ann Otol Rhinol Laryngol 1988;97: 381-8.
Journal of Voice, Vol. 8, No. 2, 1994
Vol. 8, No. 2, pp. 99-105 © 1994 Raven Press, Ltd., New York
Mechanical Stress in Phonation Ingo R.
Titze
Department of Speech Pathology and Audiology, National Center for Voice and Speech, University of Iowa, Iowa City, Iowa, and Recording and Research Center, Denver Center for the Performing Arts, Denver, Colorado, U.S.A.
Summary: Mechanical stress is always encountered in phonation. This includes tensile stress, shear stress, impact stress during collision, maximum active contractile stress in laryngeal muscles, inertial stress, and aerodynamic stress (pressure). Order of magnitude calculations reveal that tensile stress can reach the greatest value (near 1.0 MPa), contractile stress is next in size (near 100 kPa), and aerodynamic stress is relatively small (1-10 kPa). Inertial stress and impact stress are greater than aerodynamic stress, but less than contractile stress. Excessive collision and acceleration may be responsible for the greatest tissue damage, even though they do not account tbr the greatest stresses. This is because they act perpendicularly to the direction of tissue load-bearing fibers and are applied directly to mucosal tissue. Key Words: Stress--Strain-Injury--Vocal fold--Vibration--Damage--Vocal disorders.
This article was motivated by the lifelong investigations of voice disorders by Moore (1). Moore convinced this author, and many others in the field, that voice disorders and voice physiology are one and the same topic. One cannot understand normal vocal fold vibration with a disregard for abnormal vibration patterns. This is becoming increasingly more evident in light of modern views of nonlinear dynamics. Chaotic behavior is part of a normal selfoscillating vocal fold system, and "normal" vibration patterns can be seen when the vocal folds are visually impaired. Nowhere is this gray boundary between normal function and dysfunction more evident than in the assessment of mechanical stress in phonation. It is generally assumed that excessive mechanical stress can lead to organic disorders. But how much is excessive? Although repeated collision of the vocal folds is likely to be the primary cause of vocal nodules, we cannot produce much sound without colliding the vocal folds. So what is a tolerable
amount? We also believe that persistent "pressing" together of the arytenoid cartilages is a cause of contact ulcers, and rubbing vocal fold tissue with foreign objects (such as an endotracheal tube) is known to cause granulomas, but, again, we have no criteria for how much mechanical stress is abusive. Benign lesions are apparently a reaction to, and ultimately a fortification against, mechanical insult to vocal fold tissues. Little is known, however, about the kind of stress that routinely occurs during vocal fold vibration, and how that stress is distributed within the tissues. If the stress fields were known for various phonation types, perhaps some strategies for healthy, nonabusive voice production would become clearer. Specifically, it would be desirable to weigh phonation type and increases in vocal loudness against increases in tissue stress to obtain a cost/benefit ratio for certain vocal productions. The present study is an extension of the summary article on vocal strain written by Sonninen et al. (2), who summarized the types of mechanical loads and deformations found in the vocal folds. Twenty years later, we can shed only a little additional light on these critical questions: (a) What types of
Accepted March 31, 1993. Address correspondence and reprint requests to Dr. I. R. Titze at Department of Speech Pathology and Audiology, National Center for Voice and Speech, University of Iowa, Iowa City, IA 52242, U.S.A.
99
100
I . R . TITZE 16o-
stresses occur in vocal fold vibration, (b) How large are they under normal and maximal-effort phonation, and (c) Is there a likelihood that tissue damage will occur from a specific type of stress?
12o................................ .....
TYPES OF MECHANICAL STRESS AND RELATIVE MAGNITUDES
o
We begin by identifying the various types of mechanical stress encountered in vocal fold vibration, with an attempt to estimate their magnitudes. It should be understood that these estimates are order-of-magnitude. In many cases, experiments are yet to be done to verify the numbers. Tensile stress By far the greatest stress applied to vocal fold tissues is a tensile stress (Fig. 1). This is applied primarily to the longitudinal (anterior-posterior) fibers of the vocal ligament by the cricothyroid muscle. An estimate of the maximum tensile stress is obtained by assuming that collagenous and elastic fibers vibrate in a string-like fashion. Then tr = 4L2F2p
(1)
where tr is the tensile stress L is the length of the membranous vocal fold, F o is the fundamental frequency, and p is the tissue density (1,040 kg/m3). For a woman singing a high C (F o = 1,046 Hz) and a membranous length of 0.01 m, the stress is o- = 4(10 4)(1,046)2(1,040) ~ 500 kPa
(2)
For higher notes in the coloratura repertoire, frequencies up to 1,500 Hz are possible, for which the tensile stress would exceed 1.0 MPa. If the ligament cross-section is - 1 mm × 1 mm, then the tension is on the order of 1 N, or -¢2 lb. For typical speech fundamental frequencies, es-
Cross section S
I
~ F (cricothyroid force)
---I
Lo
~" AL ~ -
Tensile
stress
Tensile
strain = e = AL/Lo
Maximum active
80
40-
$1 S Passive ~ J
0
10
2~0
40
Strain (%)
FIG. 2. Maximum active contractile stress (dotted line) of the thyroarytenoid muscle of canine larynges. The total stress (solid line) is assumed to be the summation of the passive stress (dashed line) and maximum active stress (after ref. 3).
pecially for men, the tensile stress is much lower. At 100 Hz, for example, ~r is two orders of magnitude lower than at 1,000 Hz, giving a stress of - 5 kPa. Maximum active contractile stress in muscles The maximum active contractile stress in the thyroarytenoid (TA) and cricothyroid (CT) muscles of canines has been measured by Alipour-Haghighi et al. (3,4). Results are shown in Fig. 2 for the TA and in Fig. 3 for the CT. Note that these stresses vary with vocal fold length (strain), but have a range of values of -30-115 kPa. The TA muscle reaches a maximum active stress of 100 kPa at 20% elongation, whereas the pars recta of the CT reaches the same value at - 3 0 % elongation. One might ask how the CT can produce a stress of 1.0 MPa in the vocal ligament when its maximum contractile stress is only - 100 kPa. The answer lies in a transformation of cross-sectional area. The force applied to the ligament equals the force produced by the CT muscle, but because the ligament has a smaller cross-sectional area, the stress is magnified by a factor of 10 or so. Collision stress between vocal folds The collision stress between the vocal folds can be estimated from basic physical principles (Fig. 4). Assuming the mass of a tissue element at the medial surface to be
= cr = F / S
m = pAxAyAz
(3)
.
FIG. 1. Illustration of tensile stress and strain. Journal of Voice, Vol. 8, No. 2, 1994
3'0
where p is the tissue density given above and 2txAyAz is a small volume, then, from Newton's
MECHANICAL
STRESS
101
This velocity is reduced to zero during the collision interval, such that
Pars recta maximumactivestress
100 "
IN PHONATION
• pars obl]qua
Av = v -
(7)
0 = 2rrFoA
Substituting Eqs. 3, 5, and 7 into 4 yields ~
50
O3
o
o
t'o
2'0
3'0
40
If A y A z is taken to be the impact surface and Ax the depth of the vibrating tissue, then the collision stress is
Strain (%)
F ~r - AyA~ - 20"rrAFZpAx
FIG. 3. Maximum active contractile stress of two components of the CT muscle of canine larynges, The passive stress is also shown (after ref. 4).
second law, the average collision force over an impact interval At is (4)
F = mAv/At
where Av is the change in velocity during impact. Jiang and Titze (5) estimated the impact interval to be on the order of
r0 At-
10
(5)
where To is the fundamental period. The velocity change in Eq. 4 can be estimated by assuming sinusoidal motion with amplitude A and radian frequency o~ = 2¢rFo. The maximum velocity, which occurs near impact, is then v = oJA = 2 w F o A
(8)
F = 207rAF2pAxAyAz
pars obliqua Pars recta passive stress ~ = ~ O ~ p a esrtss s~~i~. v e
(9)
For an amplitude of vibration of 10 -3 m, a depth of vibration of 10 -3 m, and an Fo of 200 Hz, this stress is 2.6 kPa. Peak impact stresses on the order of 0.5-5.0 kPa were measured by Jiang and Titze (5) and are shown in Fig. 5 as a function of subglottal pressure. Similar increases in contact stress were obtained by Reed et al. (6) with a piezoelectric transducer placed between the vocal folds of a human subject. Values of Fo in Fig. 5 were <200 Hz. For frequencies approaching 1,000 Hz, one would expect much higher impact stresses if the amplitude and depth of vibration were to remain constant. Typically, however, both amplitude and depth of vibration decrease with F0, making the exact stress uncertain. One would expect that the impact stress could increase an order of magnitude, to - 5 0 kPa, for high F 0 and high subglottal pressure.
(6) 5.0"
Collision boundary
Tissue element of mass pAxAyAz
4.0
& 3.0, "5 2.0,
Q.
1.0,
J 11o Av
Impact stress = (pAx) ~ -
FIG. 4. Illustration of impact stress.
21o
31o
4.0
Subglottal pressure (kPa)
FIG. 5. Peak collision stress versus subglottal pressure in a canine hemilarynx (after ref. 5).
Journal of Voice, Vol. 8, No. 2, 1994
102
I.R.
Inertial stress The inertial stress is similar to the impact stress, except that acceleration and deceleration occur without collision. Assuming again that the tissue moves sinusoidally with amplitude A, i.e., x = Asintot
(1 1)
This stress is approximately half of the impact stress, on the order of 1-2 kPa for normal phonation. A e r o d y n a m i c stress
The mean aerodynamic driving stress is the mean intraglottal pressure, which has been estimated as
in the open phase (6). Here P,. is the input pressure to the vocal tract (supraglottal pressure), al is the glottal entry area, a2 is the glottal exit area, and P= is the subglottal pressure. The greatest pressure occurs for a highly convergent glottis, where az/al "~ 0, in which case Pg ~ P=" In high-effort phonation, P~ can be as high as 5-6 kPa, and occasionally reaches 10 kPa (8). This can be taken as the upper limit on aerodynamic stress. A r y t e n o i d contact stress
Maximum contact stress between the arytenoid cartilages has been estimated by Rethi (9) and Kakeshita (10) to be on the order of 50-100 kPa in animals who had the adductor muscles fully contracted. This range would tend to agree with the maximum active stresses measured in the CT and TA muscles of canines. Adduction stress for normal phonation is much lower than that, however, even for so-called "pressed voice." Values reported by Scherer et al. (11) were on the order of 1-5 kPa. Shear stress at anterior and posterior macula flava The shear stress in the ligament increases with the amplitude of vibration. If the ligament is pinned at the endpoints (anterior and posterior macula flava), then the shear stress -r can be written as "r = Ixsin0 Journal of Voice, Vol. 8, No. 2, 1994
where Ix is the shear modulus and 0 is the shear angle at the endpoints (Fig. 6). The shear angle can be expressed in terms of the vibrational amplitude and the membranous length of the vocal folds. Thus, if
(10)
then the maximum acceleration is to2A. The maximum inertial stress is mass (pAxAyAz) times acceleration (4~r2F~A) divided by the surface area (AyAz), which simplifies to cr = 47r2AF02pAx
TITZE
(13)
(14)
x = Asin~ry/L
is the displacement of a lowest-string mode in the anterior-posterior (y) direction, A is the amplitude (at the center) and L is the membranous length, then -rrA
dx
dy
y=O,L
L
- tan0 -~ sin0
(15)
For an amplitude of 0.2 mm and a length of 10 mm, sin 0 = 0.6. The shear modulus tx of the collagen fibers in the macula flavae is not known to this author, which makes it impossible to estimate the absolute value of the shear stress. All one can say is that it increases with amplitude of vibration and decreases with vocal fold length. The A / L ratio is a key variable for dynamic shear stress. Summary of relative magnitudes of stresses A summary chart of the relative magnitudes of the various mechanical stresses is given in Fig. 7. Estimates are made for conditions of normal phonation (clear bars) and maximum stress (crosshatched bars). Note the large maximum tensile stresses relative to all other stresses. Note also the relatively small aerodynamic stresses. Active contractile, arytenoid contact, impact, and inertial stresses are intermediate in size.
Anteriorboundary
7///S,
I~O~
Vocalligament
i Shear stress =/.tsinO FIG. 6. Illustration of shear stress in the vocal ligament.
M E C H A N I C A L STR E SS I N P H O N A T I O N
~"
~', //i
100-
~,~
Max
Normal
//1
S~ //1
Tensile '~ Aryienoid stress Contractile contact muscle stress stress
Impact stress
lnertial stress
Aerodynamic
FIG. 7. Summary of the relative magnitudes of various mechanical stresses in vocal fold tissues.
DAMAGE CRITERIA Damage to vocal fold tissue may occur from any of the mechanical stresses described. Based on the relative size of the tensile stress in relation to other stresses, one would reason that the vocal ligament would be at the highest risk of damage, particularly at high pitches. Excessive tension would appear to rupture the tissue fibers. If the vocal ligament has comparable strength to other ligaments in the body, however, it is well protected against this type of rupture. The following discussion will clarify this point. Rupture due to tensile stress As an analogy with other body tissues, consider the anterior cruciate ligament of the knee, which has been studied extensively by Noyes and Grood (12). This ligament is larger than the vocal ligament. The authors report an average length of 27 mm and an average cross-sectional area of 44 mm 2. This is approximately twice the length of the vocal ligament and approximately 10 times the cross-section. Nevertheless, because stress and strain are essentially independent of sample size, the comparison is useful. Figure 8 shows the mechanical response of the anterior cruciate ligament under tensile stress. Strain was applied at a rate of 100% per second. The attempt was to simulate conditions in sports, where extension, flexion, and torsion occur quite rapidly. Tissue age was a parameter in the study. One group of subjects was in the 16-26-year age bracket, whereas another was in the 48-86-year bracket. Note that the older group displayed a lower maxi-
103
mum stress (13.3 MPa as compared with 37.8 MPa for the younger group). Furthermore, this maximum stress occurred at a lower strain (30 instead of 44%). Thus, not only could the younger ligament support more tensile stress, but it could support this stress at a greater elongation. Failure of the ligament occurred differently in the two age groups. For the younger group, collagen fibers were ruptured throughout the length of the ligament. This caused the stress to decrease rapidly as shown. For the older group, failure was primarily due to bone avulsion. This took place more gradually and is probably the cause of earlier failure with increased strain. It is important to contemplate the overall stress magnitude that this k n e e ligament can support. In the "linear" range, stresses can be 10-20 MPa. This is 40-80 times the stress we estimated for a soprano singing a high C. If the vocal fold ligament is made up of the same type and density of collagen fibers as this knee ligament, one would conclude that there is little chance of failure of the vocal ligament by excessive CT contraction. The vocal ligament probably serves to protect other tissues in the vocal fold from rupture. If we can assume that 30% is a strain limit on the vocal folds, which tends to agree with the estimates of van den Berg (13), then the mucosa and the TA muscle will not be elongated to their yield points. Figures 9 and 10 show stress-strain curves for the canine TA muscle and vocal fold cover, respectively. These curves were obtained by cyclic stretch-release methods at a rate of 1 Hz (similar to 50Max stress
40-
~
20-
(~
M~,x stress -
,~aJLure
10"
",,. ~, ,, "
0
•
~
10
•
Linear i
20
,
limit i
30
,
i
40
,
i
50
6'0
70
Strain (%)
FIG. 8. Stress-strain curve for the anterior cruciate ligament in humans (after ref. 12). Solid line is for the younger specimen (16-26 years) and dashed line for the older specimen (48-86 years). Journal of Voice, Vol. 8, No. 2, 1994
104
I . R . TITZE 30-
The primary symptom of a vascular disorder is "white finger," which is basically the symptom of reduced circulation. Circulation is impeded by rapid acceleration and deceleration of the tissue. Estimates of maximum acceleration of vocal fold tissues within the vibratory cycle were implicit in Eq. 1,
20"
N lO-
o
(16)
a = toZA = 4~rZF~A
o
1'o
2'0
a'0
40
Strain (%)
FIG. 9. Stress-strain curve for the thyroarytenoid muscle of canines during cyclic stretch and release.
the rate of the knee ligament elongation). Note that 30-40% elongation was possible without tissue damage. Thus, the presence of a vocal ligament would tend to keep strains in the "safe" range for muscle and mucosal tissue. Excessive vibration In his H a n d b o o k o f H u m a n Vibration, Griffin
(14) lists five disorders associated with handtransmitted vibration: (a) vascular disorders, (b) bone and joint disorders, (c) peripheral neurologic disorders, (d) muscle disorders, and (e) other (e.g., central nervous system). These disorders are usually associated with tool use. They may not apply at all to vocal fold vibration, but it is worthwhile to make a few comparisons. Parameters for consideration are vibrational magnitude, frequency, and duration.
For a fundamental frequency of 200 Hz and a vibrational amplitude of 0.001 m, there is a peak acceleration of 1,600 m/s 2, with a root mean squared value of 1,100 m/s 2. If such a vibration were to occur continuously for 30 min, it would fall well into the unacceptable region of exposure according to International Standards Organization (ISO) standards (ref. 14, p. 647). As shown in Fig. 11, accelerations of even one-tenth this value would be unacceptable (see data point in relation to the line of safety). Phonation is never continuous, of course, for 30 rain. This makes the dosage criterion difficult to assess, but it cannot be ruled out that excessive vibration could lead to some vascular disorders in the larynx. Impact stress
Assessment of safe limits of impact stress is also difficult. We do not have well-controlled experiments that show the tissue damage as a direct result of collision. The studies by Gray et al. (15) and Gray and Titze (16) are beginnings. Continuous phonation was maintained (by an artificial air supply) for several hours at high intensity in anesthetized canines. Electron-microscopic examination showed 10000
4O 1000, E
30 ¸
UnbaccePt e4A~~ep~le vimagni ratiotunabl des
100-
& 20 ¸
10-
_/
vibration
8 1
10.
0 0
i
,
i
lO
,
20
3'0
Strain (%)
4'0
so ;.
FIG. 10. S t r e s s - s t r a i n curve for the vocal fold cover of canines during cyclic stretch and release.
Journal of Voice, Vol. 8, No. 2, 1994
o
1'o
16o
lC;OO 10000
Frequency (Hz)
FIG. 11. 1SO standard for hand-transmitted vibration (after ref. 14). Data point suggests that vocal fold vibration could exceed the m a x i m u m r e c o m m e n d e d dose.
M E C H A N I C A L STRESS I N P H O N A T I O N
destruction of surface microvillae, of squamous epithelial cells, and of the basement membrane zone. Future investigations should quantify this type of destruction in terms of measured impact stress. It would also be extremely valuable to know the time course and degree of the healing process.
105
that aerodynamic stresses of themselves do not pose a damage risk. Acknowledgment: This study was supported by grant no. P60 DC00976 from the National Institute on Deafness and Other Communication Disorders. I thank Julie Lemke for manuscript preparation and Mark Peters for graphic support.
CONCLUSION The largest mechanical stresses in vocal fold vibration are the tensile stresses required for pitch increase. Estimates are that they may reach values on the order of 1 MPa. This would be excessive for epithelial or muscular tissue, but seems to be normal for ligamental tissue. We assume, therefore, that a well-developed and healthy vocal ligament provides a "safety-valve" for other, perhaps more injury-prone, tissues in the vocal folds. The ligament limits elongation and assumes most of the tensile stress at high pitches. The ligament cannot protect as well against vocal fold collision, however, where the stress is transverse to the fibers. Here the softer tissues of the lamina propria are exposed and do absorb most of the impact stress. Some evidence of destruction has been reported, and the fact that vocal fold nodules occur bilaterally at the point of maximum impact stress (5) attest to this. The possibility that safe limits of tissue acceleration are exceeded in prolonged phonation needs further exploration. Exposure durations are shorter than what is typically reported for hand-transmitted vibration with power tools, but acceleration magnitudes are comparably larger. This leaves the integrated dosage uncertain. Finally, shear stresses and aerodynamic stresses were discussed briefly, but no damage estimates could be made in this preliminary study. Aerodynamic stresses are very small in comparison to tensile stresses and maximum contractile stresses of the laryngeal muscles, which leads one to speculate
REFERENCES 1. Moore P. Organic voice disorders. Englewood Cliffs, New Jersey: Prentice-Hall, 1991. 2. Sonninen A, Damst6 PH, Jol J, Fokkens J. On vocal strain. Folia Phoniatr (Basel) 1972;24:321-36. 3. Alipour-Haghighi F, Titze IR, Perlman A. Tetanic contraction in vocal fold muscle. J Speech Hear Res 1989;32:22631. 4. Alipour-Haghighi F, Titze IR, Perlman A. Tetanic response of the cricothyroid muscle. Ann Otol Rhinol Laryngol 1991; 100:626-31. 5. Jiang JJ, Titze IR. Measurement of vocal fold intraglottal pressure and impact stress. J Voice 1994;8:132-44. 6. Reed CG, Doherty ET, Shipp T. Direct measurement of vocal fold medial forces. ASHA 1992;34:131(A). 7. Titze IR. The physics of small-amplitude oscillation of the vocal folds. J Acoust Soc A m 1988;83:1536-52. 8. Schutte H. The efficiency o f voice production. Groningen: Kemper, 1980. 9. Rethi L. Die stimmbandspannung, experimentell gepr~ft. Sitzgsber Akadem Wissenschaft Wien Math Naturwissenshaft Kl III 1897;106:244. 10. Kakeshita T. Uber eine neue methode zur messung der beim stimubrandverschluss winkende krafte. I Mitt Pflugers Arek far die Gesamunte Physiol 1927;215:19. 11. Scherer RC, Cooper DS, Alipour-Haghighi F, Titze IR. Contact pressure between the vocal processes of an excised bovine larynx. In: Titze J, Scherer R, eds. Vocal fold physiology: biomechanics, acoustics, and phonatory control. Denver: Denver Center for the Performing Arts, 1985:292-303. 12. Noyes FR, Grood ES. The strength of the anterior cruciate ligament in humans and rhesus monkeys. J Bone Joint Surg A m 1976;58:1074-82. 13. van den Berg J. Myoelastic-aerodynamic theory of voice production. J Speech Hear Res 1958;1:227-44. 14. Griffin MJ. Handbook o f human vibration. New York: Academic Press, 1990. 15. Gray SD, Titze IR, Lusk RP. Electron microscopy of hyperphonated vocal cords. J Voice 1987;1:109-15. 16. Gray S, Titze IR. Histologic investigation of hyper-phonated canine vocal cords. Ann Otol Rhinol Laryngol 1988;97: 381-8.
Journal of Voice, Vol. 8, No. 2, 1994