Logopedics Phoniatrics Vocology, 2014; 39: 50–55
ORIGINAL ARTICLE
Preliminary experiments to quantify liquid movement under mimetic vocal fold vibrational forces
INGO R. TITZE1,2, SARAH KLEMUK1 & XIAOYING LU1 1Department
of Communication Sciences and Disorders, The University of Iowa, Iowa City, IA, USA, and 2National Center for Voice and Speech, The University of Utah, Salt Lake City, UT, USA
Abstract Hydration of vocal fold tissues is essential for self-sustained oscillation. Normal regulatory processes of liquid transport to and from the vocal folds would be expected through the autonomic systems, but the possibility exists that liquid movement may occur locally due to vibrational pressures. Such movement may cause regions of lower or higher concentrations of liquid viscosity and therewith changes in phonation threshold pressure. Hyaluronic acid, a glycosaminoglycan that attracts large quantities of free water, may be a key molecule for transporting or localizing liquids. Some preliminary experiments are reported in which attempts were made to move low-concentration HA liquids with vibration. None of the experiments was conclusive, but collectively they lay some groundwork for future explorations. Key words: Fluid transport, hyaluronic acid, hydration, threshold pressure, vocal fold vibration
Introduction Movement of liquid within vocal fold tissues under vibration has been implicated as a precursor to localized edema and ultimately vocal injury (1,2). The hypothesis is that liquids are moved according to vibrational pressure gradients, creating local pockets of high and low hydration. This, in turn, may lead to non-uniform tissue viscosity and therewith changes in phonation threshold pressure. Hyaluronic acid (HA) is a water-binding molecule that serves as a lubricant in the extracellular matrices of tissues that are exposed to mechanical loads. It is a major component in the synovial fluids of joints as a lubricant (3). It is also found in the vitreous humor of the eye and in the umbilical cord. In vocal folds, HA has been identified as a primary interstitial fluid in the superficial layer of the lamina propria (4,5), which is subjected to large doses of vibration (6). The HA molecule has a strong affinity to bind free water at multiple sites (7), thereby being able to absorb more than 1,000 times its dry weight in solution. Hydrogen bonding of H2O to HA helps to retain low-viscosity liquid within extracellular spaces, increasing the fluid portion of the extracel-
lular matrix (ECM) volume. What is currently not clear is how liquid moves in the ECM under vibration. Can weak hydrogen bonds be broken by vibrational agitation so that free H2O can move through the ECM? If not, can there be independent movement of low-concentration HA relative to ECM movement? This report does not answer these questions. It provides only an overview of simple methods that have failed to quantify fluid transport, with the hope that better approaches will emerge. Sometimes, a report of several failures is the best step toward a successful study.
Viscosity of HA solutions A primary property of a lubricant is its viscosity, defined as the ratio of shear stress to shear strain rate. Generally, the size of the molecule and the nature of its binding to nearest neighbor molecules determine the viscosity. In most biological tissue, the viscosity decreases with temperature increase (molecular bonds are broken due to thermal agitation) and with frequency in oscillatory shear (molecular bonds are broken with rapid back-and-forth movement). The
Correspondence: Ingo R. Titze, PhD, National Center for Voice and Speech, 136 South Main Street, Suite 320, Salt Lake City, UT 84101-3306, USA. Fax: ⫹ 1 801-596-2013. E-mail: [email protected] (Received 21 March 2013 ; accepted 20 September 2013) ISSN 1401-5439 print/ISSN 1651-2022 online © 2014 Informa UK, Ltd. DOI: 10.3109/14015439.2013.848236
Liquid movement in vocal folds
51
Figure 1. Viscous modulus G″ for five Newtonian liquids.
latter phenomenon is known as shear-thinning and has been observed in vocal fold tissues (8,9). However, low-concentration liquid HA (less than 1% HA after having absorbed H2O in the amount of 99% of its dry weight) does not exhibit shear thinning. It basically behaves like a Newtonian fluid, at least below 100 Hz. Figure 1 shows measurements made in our laboratory of the viscous shear moduli of HA solutions (0.05%, 0.1%, and 0.2%) in comparison to low-viscosity and high-viscosity Newtonian fluids (H2O and highly viscous silicon oil). The viscous modulus is defined as G″ ⫽ ωh, where h is the viscosity. The viscosity is constant if G″ rises in 1:1 proportion with frequency, as Figure 1 shows for all five liquids. Note that the viscosities of the lowconcentration HA liquids are 10–100 times greater than those of pure water. The viscosity of vibrating tissue in the vocal folds determines, in part, the phonation threshold pressure (10). Vocal folds with a high viscosity require a higher lung pressure for self-sustained oscillation than less viscous vocal folds. Thus ‘ease of phonation’ has been tied to reduction of viscosity in vocal fold tissues. Prolonged duration of vocal fold vibration without adequate rest periods appears to raise the phonation threshold pressure (11,12). A current hypothesis is that fluids are re-distributed in the tissue by mechanical forces (repeated acceleration and deceleration) during vibration. If there are only short rest periods in phonation, there may not be sufficient time to return to an equilibrium distribution in the tissues.
perature, and their weakly bound H2O was allowed to evaporate over a period of 120 min. A 0.0% solution (pure water) served as a control. Measurements of the mass of the wet paper were made every 10 minutes for the 2 hours. Figure 2 shows the results. The mean evaporation rate was 3.08 mg/min for pure water, 2.75 mg/min for 0.5% HA, and 2.5 mg/min for 1% HA. The latent heat of vaporization (or condensation) at 20°C is 2,454 J/g (13). With these preliminary data, we can assume that the binding energy of H2O to HA is the fractional difference in evaporation energy, or ⎛ 0.33 mg min ⎞ Eb ⫽ ⎜ (2454) J g = 263 J g 0.5%HA ⎝ 3.08 mg min ⎟⎠
⎛ 0.58 mg min ⎞ ⫽⎜ (2454) J g ⫽ 462 J g 1.0%HA ⎝ 3.08 mg min ⎟⎠
(1)
(2)
Binding energy estimated from an evaporation test Low-concentration HA solutions (0.5% and 1%) were deposited on dry absorption paper at room tem-
Figure 2. Evaporative mass loss of pure water and two HA solutions in a stationary, ambient environment.
52
I. R. Titze et al.
The binding energies in Equations 1 and 2 give an important order-of-magnitude estimation for how easily H2O molecules can be dissociated from HA. It requires several hundred J/g. In the event that H2O cannot be freed by mechanical or thermal agitation, the water molecules could possibly exchange bonds with neighbors, and thus H2O could propagate along the HA, or other macromolecules, in the vocal folds. It is convenient to express the binding energy in J/mole. With an H2O density of 18 g/mole, the binding energy is about 4.7 kJ/mole for 0.5% HA and 8.3 kJ/mole for 1.0% HA. Typical dipole–dipole (noncovalent) binding energy is reported to be in the range of 2.5–21 kJ/mole (14). Thus, if low-concentration HA–H2O bonds can be characterized as dipole–dipole (Van der Waals) bonds, our evaporation experiments suggest that they are relatively weak. The objective of our next preliminary study was to determine if vibrational forces typical in vocal fold vibration are strong enough to dissociate H2O from an HA solution.
Kinetic energy increase from vibration It was hypothesized that the kinetic energy of tissue particles in the vocal folds during vibration, or the energy of collision between the vocal folds, is sufficient to break some hydrogen bonds and allow H2O to move freely. In the vocal folds, typical amplitudes of vibration of tissue particles are on the order of 1 mm. Average male speaking fundamental frequencies are 125 Hz, and average female speaking fundamental frequencies are 190 Hz. Taking the average of these, an experimental target fundamental frequency becomes F0 ⫽ (125 ⫹ 190)/2 ⫽ 157.5 Hz
(3)
The angular frequency ω ⫽ 2π F0 is therefore about 1000 rad/s. The peak velocity for sinusoidal tissue motion is ωA, where A is the vibrational amplitude, yielding a kinetic energy (per unit volume of tissue) of Ek ⫽ 1/2 r(Aw)2
the tissue. In addition, low-concentration HA may move en masse through vocal fold tissue pores. We now present a few initial attempts to redistribute H2O and HA solutions with vibrational forces.
Attempts to move H2O and HA with vibrational forces A Bohlin Gemini 120 rheometer was used to vibrate HA liquid solutions in a shear mode at a frequency of around 100 Hz. Dry powder HA was obtained from Wuhan Yuancheng Technology Development Co., Ltd (Wuhan, Hubei, P.R. China). Its chemical composition was fermented, pharmacy-grade sodium hyaluronate with a molecular weight of 1,760 kDa (1 kDa ⫽ 1.66 ⫻ 10-24 kg) and a pH of 6.7. In a first experiment, the HA was hydrated with heavy water (D2O). The experimental set-up is shown in Figure 3. An agarose gel was prepared with distilled water (H2O) as an absorbing medium at the bottom of a petri dish in a titanium cup. This gel is known to accept free water interstitially. HA was pipetted onto the agarose gel. Each layer of material was 1 mm thick. The top plate was lowered onto the HA liquid layer and rotated in a controlled strain mode (strain ⫽ 0.2). The angular displacement of the top plate was of the form q ⫽ q0 sin wt
(5)
where θ0 is the maximum rotation angle and ω is the applied angular frequency. The peak vibrational energy of any particle near the rotating top plate at a radius r was Ek ⫽ 1/2 r(rq)2 ⫽ 1/2 r(rwq0)2
(6)
The peak torsional strain in the rheometer was
γ⫽
r θ0 d
(7)
(4)
For a density ρ ⫽ 0.4 kg/mole of a core unit molecule of HA, an amplitude A ⫽ 0.001 m, and ω ⫽ 1000 rad/s, the kinetic energy produced is on the order of 0.2 J/mole. This is several orders of magnitude smaller than the required energy to break weak hydrogen bonds reported above. Specifically, it is four orders of magnitude smaller than the HA–H2O bond estimated from our evaporation experiments. The preliminary conclusion is, therefore, that vibrational forces will not free H2O from HA, but H2O molecules could possibly trade bonds with nearest neighbors, thereby ‘propagating’ bound water through
Figure 3. Rheometer appliance to drive HA solution into an agarose gel.
Liquid movement in vocal folds where d is the vertical thickness of the HA layer. Substituting for θ0 in Equation 6, the peak kinetic energy per unit volume was Ek ⫽ 1/2 r(wgd )2
(8)
For a machine-controlled strain of 0.2, an angular frequency of 1,000 rad/s, and layer thickness of 0.001 m (measured to ⫾ 0.00001 m accuracy by the machine after calibration), the peak energy was 20 J/m3, or 20 Pa of vibrational shear stress, as determined by the machine. This is a small vibrational shear stress in light of the approximately 1,000 Pa stress experienced in vocal fold vibration and collision (15), but the rheometer could not be driven to higher stress for this material at this frequency. The duration of vibration ranged from 1–10 min. A control case (no vibration) was included to determine the amount of no-stress diffusion of H2O into the gel. After vibration, the HA liquid was removed from the cup, and the agarose gel was ultra-centrifuged to collect the mixture of pure water with deuterium. Attempts to quantify the amount of D2O driven into the gel failed because the portion of deuterium in the pure water was within the noise level of the detecting technique. A new attempt to quantify liquid movement under vibrational pressure was to introduce a dye into the HA solution (Coomassie Brilliant Blue, Bio-Rad, Hercules, CA, USA) and to track the movement of dye particles into the gel. The dye had a molecular weight of 1.334 MDa. It was mixed (0.025%) with a
53
4.5% concentration of HA. The gel thickness was increased to 10 mm so that a dye density gradient could be established. The frequency of vibration was 40 Hz (the highest frequency possible for this set-up), and the duration of vibration was 3–15 minutes. The group of three graphs in Figure 4 shows dye brightness (0 ⫽ black, 255 ⫽ white) as a function of vertical distance from the HA–agarose interface after three different time periods of vibration. Dashed lines are for diffusion only and solid lines for diffusion⫹ vibration. Lower brightness indicates more dye penetration. Although no statistical significance was reachable with these few measurements, the trend is toward greater dye penetration with vibration than simply by diffusion. A next step would have been to repeat the experiment many times and vary the vibrational frequency and energy, but a fundamental question remained unanswered. Even though this preliminary experiment showed that dye tends to move under vibrational pressure, we could not conclude that water or low-concentration HA moves at the same rate as the dye, given its difference in molecular size and weight. Until this question is answered, further experimentation with dye was terminated. An important factor in liquid movement in the vocal folds may be the pore size of extracellular matrix solid component, i.e. the spaces that are available between collagen, elastin, and other structural proteins for liquids to slide through. Following this hypothesis about pore size, we conducted a preliminary experiment with membranes of different pore
Figure 4. Brightness of dye in agarose gel following diffusion alone (dashed lines) and diffusion with vibration of dye-filled 4.5% HA (solid lines).
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I. R. Titze et al.
Figure 5. Rheometer appliance for study with porous membrane.
size to produce a barrier to liquid movement. As shown in Figure 5, a porous membrane was inserted between the HA solution and the bottom of the cup, which was perforated with holes so that liquid could escape into a sponge-like receiving material under the cup (not shown). The top plate was also perforated so that HA under the plate could be replenished. Pore size was quantified in μm. Figure 6 shows the amount of fluid penetration through the pores (in grams) as a function of pore size in a 5-min period. A critical pore size was 0.4 μm for our HA solutions. For a control case, there was no oscillatory driving pressure. Penetration was by gravity and capillary action. When vibrational pressure was added, any additional fluid movement through the pores was not conclusively determined. For a duration of 2–10 s of vibration, there appeared to be an increase of about 50% in fluid transfer, but with longer durations the amount decreased. One explanation may be that the pores began to clog with HA deposits along the pore walls. Another explanation might be that HA traps H2O to form a flexible bubble, confined by an outer ‘mesh’ that grows with release of H2O binding over time, thus terminating fluid transfer after a few seconds.
Figure 6. Liquid transport through membrane pores in 5 min.
Conclusions A few preliminary experiments showed that exposures of HA solutions to vibrational energies typical in vocal fold vibration are not likely to break H2O–HA bonds to free H2O molecules. Thus, free water entering from the blood stream may not remain abundant in vocal fold tissues that contain HA or other waterbinding molecules. However, low-concentration HA fragments may be able to move in a porous substrate with pore sizes greater than about 0.4 μm. Vibrational stresses appear to be strong enough to cause some of this liquid movement. The viscosity of low-concentration HA appears to be fairly frequency-independent at low sonic frequencies, but rises in proportion to concentration. Thus, the concentration of HA appears to be a possible regulatory mechanism for tissue viscosity in vocal folds. In turn, viscosity determines frictional losses and phonation threshold pressure in vocal fold vibration, given that both quantities are proportional to tissue viscosity (10). The question of whether liquid gradients (nonuniform distribution of liquids) can be created by vibrational pressure gradients has not been resolved by these preliminary experiments. In fact, an argument could be made that the presence of HA in vocal folds is for the purpose of preventing such liquid gradients. A biphasic condition in which liquid moves independently of the solid motion of fibers may therefore signal a pathological condition of either an insufficient amount of HA to bind the free H2O, or an excess of low-concentration HA that migrates easily through enlarged extracellular matrix pores. Declaration of interest: The authors have no conflicts of interest to report. This work was supported by grant no. 5R01 DC 010275-02 from the National Institute on Deafness and Other Communication Disorders.
Liquid movement in vocal folds References 1. Jiang JJ, Ng J, Hanson D. The effects of rehydration on phonation in excised canine larynges. J Voice. 1999;13: 51–9. 2. Tao C, Jiang JJ, Zhang Y. A fluid-saturated poroelastic model of the vocal folds with hydrated tissue. J Biomechanics. 2008;42:744–80. 3. Volpi N, Schiller J, Stern R, Soltés L. Role, metabolism, chemical modifications and applications of hyaluronan. Curr Med Chem. 2009;16:1718–45. 4. Gray SD, Titze IR, Chan RW, Hammond TH. Vocal fold proteoglycans and their influence on biomechanics. Laryngoscope. 1999;109:845–54. 5. Chan RW, Gray SD, Titze IR. The importance of hyaluronic acid in vocal fold biomechanics. Otolaryngol Head Neck Surg. 2001;124:607–14. 6. Hunter EJ, Titze IR. Variation of intensity, fundamental frequency, and voicing for teachers in occupational versus non-occupational settings. J Speech Language Hear Res. 2010;53:862–75. 7. Laurent TC, Laurent UBG, Fraser JRE. Functions of hyaluronan. Ann Rheum Dis. 1995;54:429–32.
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8. Chan RW, Titze IR. Viscoelastic shear properties of human vocal fold mucosa: measurement methodology and empirical results. J Acoust Soc Am. 1999;106 (4 Pt 1): 2008–21. 9. Klemuk SA, Titze IR. Viscoelastic properties of three biomaterials at low audio frequencies. Laryngoscope. 2004; 114:1597–603. 10. Titze IR. The physics of small-amplitude oscillation of the vocal folds. J Acoust Soc Am. 1988;83:1536–52. 11. Solomon NP, DiMattia MS. Effects of a vocally fatiguing task and systemic hydration on phonation threshold pressure. J Voice. 2000;14:341–62. 12. Chang A, Karnell MP. Perceived phonatory effort and phonation threshold pressure across a prolonged voice loading task: a study of vocal fatigue. J Voice. 2004;18:454. 13. Moran MJ, Shapiro HN. Fundamentals of engineering thermodynamics. 3rd ed. New York: John Wiley & Sons; 1996. 14. Lodish H, Berk A, Zipursky SL, Matsudaira P, Baltimore D, Darnell J. Noncovalent bonds. Section 2.2. In: Molecular cell biology. 4th ed. New York: W. H. Freeman; 2000. Available from: http://www.ncbi.nlm.nih.gov/books/NBK21726/. 15. Jiang JJ, Titze IR. Measurement of vocal fold intraglottal pressure and impact stress. J Voice. 1994;8:132–44.
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ORIGINAL ARTICLE
Preliminary experiments to quantify liquid movement under mimetic vocal fold vibrational forces
INGO R. TITZE1,2, SARAH KLEMUK1 & XIAOYING LU1 1Department
of Communication Sciences and Disorders, The University of Iowa, Iowa City, IA, USA, and 2National Center for Voice and Speech, The University of Utah, Salt Lake City, UT, USA
Abstract Hydration of vocal fold tissues is essential for self-sustained oscillation. Normal regulatory processes of liquid transport to and from the vocal folds would be expected through the autonomic systems, but the possibility exists that liquid movement may occur locally due to vibrational pressures. Such movement may cause regions of lower or higher concentrations of liquid viscosity and therewith changes in phonation threshold pressure. Hyaluronic acid, a glycosaminoglycan that attracts large quantities of free water, may be a key molecule for transporting or localizing liquids. Some preliminary experiments are reported in which attempts were made to move low-concentration HA liquids with vibration. None of the experiments was conclusive, but collectively they lay some groundwork for future explorations. Key words: Fluid transport, hyaluronic acid, hydration, threshold pressure, vocal fold vibration
Introduction Movement of liquid within vocal fold tissues under vibration has been implicated as a precursor to localized edema and ultimately vocal injury (1,2). The hypothesis is that liquids are moved according to vibrational pressure gradients, creating local pockets of high and low hydration. This, in turn, may lead to non-uniform tissue viscosity and therewith changes in phonation threshold pressure. Hyaluronic acid (HA) is a water-binding molecule that serves as a lubricant in the extracellular matrices of tissues that are exposed to mechanical loads. It is a major component in the synovial fluids of joints as a lubricant (3). It is also found in the vitreous humor of the eye and in the umbilical cord. In vocal folds, HA has been identified as a primary interstitial fluid in the superficial layer of the lamina propria (4,5), which is subjected to large doses of vibration (6). The HA molecule has a strong affinity to bind free water at multiple sites (7), thereby being able to absorb more than 1,000 times its dry weight in solution. Hydrogen bonding of H2O to HA helps to retain low-viscosity liquid within extracellular spaces, increasing the fluid portion of the extracel-
lular matrix (ECM) volume. What is currently not clear is how liquid moves in the ECM under vibration. Can weak hydrogen bonds be broken by vibrational agitation so that free H2O can move through the ECM? If not, can there be independent movement of low-concentration HA relative to ECM movement? This report does not answer these questions. It provides only an overview of simple methods that have failed to quantify fluid transport, with the hope that better approaches will emerge. Sometimes, a report of several failures is the best step toward a successful study.
Viscosity of HA solutions A primary property of a lubricant is its viscosity, defined as the ratio of shear stress to shear strain rate. Generally, the size of the molecule and the nature of its binding to nearest neighbor molecules determine the viscosity. In most biological tissue, the viscosity decreases with temperature increase (molecular bonds are broken due to thermal agitation) and with frequency in oscillatory shear (molecular bonds are broken with rapid back-and-forth movement). The
Correspondence: Ingo R. Titze, PhD, National Center for Voice and Speech, 136 South Main Street, Suite 320, Salt Lake City, UT 84101-3306, USA. Fax: ⫹ 1 801-596-2013. E-mail: [email protected] (Received 21 March 2013 ; accepted 20 September 2013) ISSN 1401-5439 print/ISSN 1651-2022 online © 2014 Informa UK, Ltd. DOI: 10.3109/14015439.2013.848236
Liquid movement in vocal folds
51
Figure 1. Viscous modulus G″ for five Newtonian liquids.
latter phenomenon is known as shear-thinning and has been observed in vocal fold tissues (8,9). However, low-concentration liquid HA (less than 1% HA after having absorbed H2O in the amount of 99% of its dry weight) does not exhibit shear thinning. It basically behaves like a Newtonian fluid, at least below 100 Hz. Figure 1 shows measurements made in our laboratory of the viscous shear moduli of HA solutions (0.05%, 0.1%, and 0.2%) in comparison to low-viscosity and high-viscosity Newtonian fluids (H2O and highly viscous silicon oil). The viscous modulus is defined as G″ ⫽ ωh, where h is the viscosity. The viscosity is constant if G″ rises in 1:1 proportion with frequency, as Figure 1 shows for all five liquids. Note that the viscosities of the lowconcentration HA liquids are 10–100 times greater than those of pure water. The viscosity of vibrating tissue in the vocal folds determines, in part, the phonation threshold pressure (10). Vocal folds with a high viscosity require a higher lung pressure for self-sustained oscillation than less viscous vocal folds. Thus ‘ease of phonation’ has been tied to reduction of viscosity in vocal fold tissues. Prolonged duration of vocal fold vibration without adequate rest periods appears to raise the phonation threshold pressure (11,12). A current hypothesis is that fluids are re-distributed in the tissue by mechanical forces (repeated acceleration and deceleration) during vibration. If there are only short rest periods in phonation, there may not be sufficient time to return to an equilibrium distribution in the tissues.
perature, and their weakly bound H2O was allowed to evaporate over a period of 120 min. A 0.0% solution (pure water) served as a control. Measurements of the mass of the wet paper were made every 10 minutes for the 2 hours. Figure 2 shows the results. The mean evaporation rate was 3.08 mg/min for pure water, 2.75 mg/min for 0.5% HA, and 2.5 mg/min for 1% HA. The latent heat of vaporization (or condensation) at 20°C is 2,454 J/g (13). With these preliminary data, we can assume that the binding energy of H2O to HA is the fractional difference in evaporation energy, or ⎛ 0.33 mg min ⎞ Eb ⫽ ⎜ (2454) J g = 263 J g 0.5%HA ⎝ 3.08 mg min ⎟⎠
⎛ 0.58 mg min ⎞ ⫽⎜ (2454) J g ⫽ 462 J g 1.0%HA ⎝ 3.08 mg min ⎟⎠
(1)
(2)
Binding energy estimated from an evaporation test Low-concentration HA solutions (0.5% and 1%) were deposited on dry absorption paper at room tem-
Figure 2. Evaporative mass loss of pure water and two HA solutions in a stationary, ambient environment.
52
I. R. Titze et al.
The binding energies in Equations 1 and 2 give an important order-of-magnitude estimation for how easily H2O molecules can be dissociated from HA. It requires several hundred J/g. In the event that H2O cannot be freed by mechanical or thermal agitation, the water molecules could possibly exchange bonds with neighbors, and thus H2O could propagate along the HA, or other macromolecules, in the vocal folds. It is convenient to express the binding energy in J/mole. With an H2O density of 18 g/mole, the binding energy is about 4.7 kJ/mole for 0.5% HA and 8.3 kJ/mole for 1.0% HA. Typical dipole–dipole (noncovalent) binding energy is reported to be in the range of 2.5–21 kJ/mole (14). Thus, if low-concentration HA–H2O bonds can be characterized as dipole–dipole (Van der Waals) bonds, our evaporation experiments suggest that they are relatively weak. The objective of our next preliminary study was to determine if vibrational forces typical in vocal fold vibration are strong enough to dissociate H2O from an HA solution.
Kinetic energy increase from vibration It was hypothesized that the kinetic energy of tissue particles in the vocal folds during vibration, or the energy of collision between the vocal folds, is sufficient to break some hydrogen bonds and allow H2O to move freely. In the vocal folds, typical amplitudes of vibration of tissue particles are on the order of 1 mm. Average male speaking fundamental frequencies are 125 Hz, and average female speaking fundamental frequencies are 190 Hz. Taking the average of these, an experimental target fundamental frequency becomes F0 ⫽ (125 ⫹ 190)/2 ⫽ 157.5 Hz
(3)
The angular frequency ω ⫽ 2π F0 is therefore about 1000 rad/s. The peak velocity for sinusoidal tissue motion is ωA, where A is the vibrational amplitude, yielding a kinetic energy (per unit volume of tissue) of Ek ⫽ 1/2 r(Aw)2
the tissue. In addition, low-concentration HA may move en masse through vocal fold tissue pores. We now present a few initial attempts to redistribute H2O and HA solutions with vibrational forces.
Attempts to move H2O and HA with vibrational forces A Bohlin Gemini 120 rheometer was used to vibrate HA liquid solutions in a shear mode at a frequency of around 100 Hz. Dry powder HA was obtained from Wuhan Yuancheng Technology Development Co., Ltd (Wuhan, Hubei, P.R. China). Its chemical composition was fermented, pharmacy-grade sodium hyaluronate with a molecular weight of 1,760 kDa (1 kDa ⫽ 1.66 ⫻ 10-24 kg) and a pH of 6.7. In a first experiment, the HA was hydrated with heavy water (D2O). The experimental set-up is shown in Figure 3. An agarose gel was prepared with distilled water (H2O) as an absorbing medium at the bottom of a petri dish in a titanium cup. This gel is known to accept free water interstitially. HA was pipetted onto the agarose gel. Each layer of material was 1 mm thick. The top plate was lowered onto the HA liquid layer and rotated in a controlled strain mode (strain ⫽ 0.2). The angular displacement of the top plate was of the form q ⫽ q0 sin wt
(5)
where θ0 is the maximum rotation angle and ω is the applied angular frequency. The peak vibrational energy of any particle near the rotating top plate at a radius r was Ek ⫽ 1/2 r(rq)2 ⫽ 1/2 r(rwq0)2
(6)
The peak torsional strain in the rheometer was
γ⫽
r θ0 d
(7)
(4)
For a density ρ ⫽ 0.4 kg/mole of a core unit molecule of HA, an amplitude A ⫽ 0.001 m, and ω ⫽ 1000 rad/s, the kinetic energy produced is on the order of 0.2 J/mole. This is several orders of magnitude smaller than the required energy to break weak hydrogen bonds reported above. Specifically, it is four orders of magnitude smaller than the HA–H2O bond estimated from our evaporation experiments. The preliminary conclusion is, therefore, that vibrational forces will not free H2O from HA, but H2O molecules could possibly trade bonds with nearest neighbors, thereby ‘propagating’ bound water through
Figure 3. Rheometer appliance to drive HA solution into an agarose gel.
Liquid movement in vocal folds where d is the vertical thickness of the HA layer. Substituting for θ0 in Equation 6, the peak kinetic energy per unit volume was Ek ⫽ 1/2 r(wgd )2
(8)
For a machine-controlled strain of 0.2, an angular frequency of 1,000 rad/s, and layer thickness of 0.001 m (measured to ⫾ 0.00001 m accuracy by the machine after calibration), the peak energy was 20 J/m3, or 20 Pa of vibrational shear stress, as determined by the machine. This is a small vibrational shear stress in light of the approximately 1,000 Pa stress experienced in vocal fold vibration and collision (15), but the rheometer could not be driven to higher stress for this material at this frequency. The duration of vibration ranged from 1–10 min. A control case (no vibration) was included to determine the amount of no-stress diffusion of H2O into the gel. After vibration, the HA liquid was removed from the cup, and the agarose gel was ultra-centrifuged to collect the mixture of pure water with deuterium. Attempts to quantify the amount of D2O driven into the gel failed because the portion of deuterium in the pure water was within the noise level of the detecting technique. A new attempt to quantify liquid movement under vibrational pressure was to introduce a dye into the HA solution (Coomassie Brilliant Blue, Bio-Rad, Hercules, CA, USA) and to track the movement of dye particles into the gel. The dye had a molecular weight of 1.334 MDa. It was mixed (0.025%) with a
53
4.5% concentration of HA. The gel thickness was increased to 10 mm so that a dye density gradient could be established. The frequency of vibration was 40 Hz (the highest frequency possible for this set-up), and the duration of vibration was 3–15 minutes. The group of three graphs in Figure 4 shows dye brightness (0 ⫽ black, 255 ⫽ white) as a function of vertical distance from the HA–agarose interface after three different time periods of vibration. Dashed lines are for diffusion only and solid lines for diffusion⫹ vibration. Lower brightness indicates more dye penetration. Although no statistical significance was reachable with these few measurements, the trend is toward greater dye penetration with vibration than simply by diffusion. A next step would have been to repeat the experiment many times and vary the vibrational frequency and energy, but a fundamental question remained unanswered. Even though this preliminary experiment showed that dye tends to move under vibrational pressure, we could not conclude that water or low-concentration HA moves at the same rate as the dye, given its difference in molecular size and weight. Until this question is answered, further experimentation with dye was terminated. An important factor in liquid movement in the vocal folds may be the pore size of extracellular matrix solid component, i.e. the spaces that are available between collagen, elastin, and other structural proteins for liquids to slide through. Following this hypothesis about pore size, we conducted a preliminary experiment with membranes of different pore
Figure 4. Brightness of dye in agarose gel following diffusion alone (dashed lines) and diffusion with vibration of dye-filled 4.5% HA (solid lines).
54
I. R. Titze et al.
Figure 5. Rheometer appliance for study with porous membrane.
size to produce a barrier to liquid movement. As shown in Figure 5, a porous membrane was inserted between the HA solution and the bottom of the cup, which was perforated with holes so that liquid could escape into a sponge-like receiving material under the cup (not shown). The top plate was also perforated so that HA under the plate could be replenished. Pore size was quantified in μm. Figure 6 shows the amount of fluid penetration through the pores (in grams) as a function of pore size in a 5-min period. A critical pore size was 0.4 μm for our HA solutions. For a control case, there was no oscillatory driving pressure. Penetration was by gravity and capillary action. When vibrational pressure was added, any additional fluid movement through the pores was not conclusively determined. For a duration of 2–10 s of vibration, there appeared to be an increase of about 50% in fluid transfer, but with longer durations the amount decreased. One explanation may be that the pores began to clog with HA deposits along the pore walls. Another explanation might be that HA traps H2O to form a flexible bubble, confined by an outer ‘mesh’ that grows with release of H2O binding over time, thus terminating fluid transfer after a few seconds.
Figure 6. Liquid transport through membrane pores in 5 min.
Conclusions A few preliminary experiments showed that exposures of HA solutions to vibrational energies typical in vocal fold vibration are not likely to break H2O–HA bonds to free H2O molecules. Thus, free water entering from the blood stream may not remain abundant in vocal fold tissues that contain HA or other waterbinding molecules. However, low-concentration HA fragments may be able to move in a porous substrate with pore sizes greater than about 0.4 μm. Vibrational stresses appear to be strong enough to cause some of this liquid movement. The viscosity of low-concentration HA appears to be fairly frequency-independent at low sonic frequencies, but rises in proportion to concentration. Thus, the concentration of HA appears to be a possible regulatory mechanism for tissue viscosity in vocal folds. In turn, viscosity determines frictional losses and phonation threshold pressure in vocal fold vibration, given that both quantities are proportional to tissue viscosity (10). The question of whether liquid gradients (nonuniform distribution of liquids) can be created by vibrational pressure gradients has not been resolved by these preliminary experiments. In fact, an argument could be made that the presence of HA in vocal folds is for the purpose of preventing such liquid gradients. A biphasic condition in which liquid moves independently of the solid motion of fibers may therefore signal a pathological condition of either an insufficient amount of HA to bind the free H2O, or an excess of low-concentration HA that migrates easily through enlarged extracellular matrix pores. Declaration of interest: The authors have no conflicts of interest to report. This work was supported by grant no. 5R01 DC 010275-02 from the National Institute on Deafness and Other Communication Disorders.
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