Effects of Dehydration on the Viscoelastic Properties of Vocal Folds in Large Deformations

Summary

Dehydration may alter vocal fold viscoelastic properties, which may hamper phonation. The effects of water loss induced by an osmotic-pressure potential on vocal fold tissue viscoelastic properties were investigated. Porcine vocal folds were dehydrated by immersion in a hypertonic solution, and quasi-static and low-frequency dynamic traction tests were performed for elongations of up to 50%. Digital image correlation was used to determine local strains from surface deformations. The elastic modulus and the loss factor were then determined for normal and dehydrated tissues. An eight-chain hyperelastic model was used to describe the observed nonlinear stress-stretch behavior. Contrary to expectations, the mass history indicated that the tissue absorbed water during cyclic extension when submerged in a hypertonic solution. During loading history, the elastic modulus was increased for dehydrated tissues as a function of strain. The response of dehydrated tissues was much less affected when the load was releasing. This calls more attention to the modeling of vocal folds in micromechanics modeling. The internal hysteresis, which is often linked to phonation effort, increased significantly with water loss. The effects of dehydration on the viscoelastic properties of vocal fold tissue were quantified in a systematic way. The results will contribute to a better understanding of the basic biomechanics of voice production and ultimately will help establish objective dehydration and phonotrauma criteria.

1. Introduction

Voice production involves the self-sustained, flow-induced oscillations of the vocal folds. They are a layered structure of ligament, muscle and soft tissue, located within the larynx. Voice quality strongly depends on the viscoelastic properties of the vibrating mucosal tissue. The mechanical deformations of the vocal folds under load, as for many soft biological tissues, are governed at the microscopic level by interactions between extracellular matrix proteins and interstitial fluid. Frequent rehydration, supplied from the vocalis muscle and the epithelium, is required to maintain regular phonatory function. Local or systemic dehydration may lead to disordered vocalization¹. For example, maintaining adequate tension in the vocal fold is difficult in dehydrated vocal folds, particularly at high sound pitches¹. Dehydration may occur at the surface from convective mass transport or within the body from osmotic transport through the ligament⁷.

During phonation, the vocal folds are elongated by cricoarytenoid muscle contraction. A transverse mucosal wave is observed to propagate on the vocal folds surface, involving deformations of the multilayered lamina propria. The high-frequency vibrations of the lamina propria in the sagittal plane are small in amplitude relative to large-amplitude, quasi-static oscillations in the transverse plane. The hydration level is believed to significantly affect the stiffness and the viscosity of the vocal fold lamina propria (as stated below), and water mass transports are believed to occur over timescales that are much larger than the oscillation period. Therefore, the role of hydration on the viscoelastic properties of the vocal folds must be better understood in order to model their phonatory function.

The phonation threshold pressure (PTP) is defined as the minimum air pressure needed to initiate and maintain vocal fold self-oscillations. This metric has been used as an objective index to evaluate the effects of dehydration on voice quality. Finkelhor et al.² investigated the relationship between the PTP and the viscoelastic properties of vocal fold tissue. The PTP was measured using excised larynges submerged in three saline solutions of low, medium and high sodium-chloride concentrations. It was inferred that the mucosa viscosity decreased as the water content was increased. The influence of hydration level on voice quality was investigated by Verdolini et al.¹ using human subjects. The oral pressure for dry, hydrated and untreated larynges was measured during voiceless stop consonants at low, medium, and high pitches. The greatest oral pressure, as an estimate of PTP, was observed for dry conditions and high pitches.

The mechanical stiffness of excised vocal folds, at the superficial layer, was locally measured by applying a normal point-force in the coronal plane (and having the indentation depth)³, and dry mucosa was found to be stiffer than hydrated tissues. In another study⁴, phonatory effort was estimated through various physiological and psychological observations to investigate the inverse relation between hydration level and PTP. Jiang et al.⁵ showed that surface rehydration of the vocal folds reduces the PTP as well as the minimum airflow required to sustain phonation. Hemler et al.⁶ studied the effects of the humidity of air flow over the surface of dissected human vocal folds. They observed increases in viscosity and stiffness following exposure to dry air, even when the tissue was systemically rehydrated from the ligament. The effects of dehydration and rehydration on the vocal linear viscoelastic properties were studied using shear rheometry at low frequencies, i.e., below 15 Hz⁷. Canine mucosal tissue samples were sequentially incubated in isotonic, hypertonic, and hypotonic solutions. Four- to seven-fold increases in stiffness and a frequency-dependent increase in viscosity were observed in dehydrated vocal folds.

Sivasankar et al.⁸ showed that dehydration through inhaled dry air or impairements in surface hydration is detrimental to phonation. The barrier functions of dehydrated vocal fold epithelia were estimated by recording the changes in their epithelial resistance, paracellular pathway morphology, and protein integrity⁹. Witt et al.¹⁰ also investigated the increase in phonation threshold flow rate following exposure to dry-air. The correlation between the degree of surface dehydration and the phonation threshold flow rate (PTF) was quantitatively estimated in an ex-vivo canine larynx model. An increase of 50% to 100% was observed in the PTF of vocal folds exposed to dry airflow. Hanson et al.¹¹ attempted to evaluate the physiological impact of dehydration by examining the recoverability of vocal folds, i.e., the capacity for water absorption up to the initial level. Their analysis was based on a bi-phasic model of the fluid-solid structure interactions¹¹. The rate of convective water transport in vocal folds was estimated during speech production using numerical simulations¹². A computational model was introduced to quantify the mass loss during inhalation. There is no model available for comparable studies of systemic water transport rates at the present time. The present study may help to fill this gap.

The purpose of the present study was to better quantify the relationship between the level of hydration and the viscoelastic properties of the vocal fold lamina propria through traction tests for strains up to 50%. Body dehydration was induced through immersion of the tissue in a hypertonic buffer solution. This procedure is believed to reduce the water content through changes in osmotic pressure. Porcine vocal fold tissue was used. Dissected vocal fold tissue samples were subjected to alternating mechanical traction tests and dehydration. The local strain on the tissue surface was measured using digital image correlation during tensile tests for the accurate estimation of the viscoelastic properties²².

The loading response was found to vary linearly with the axial stretch strains smaller than 15% (please see Figs. 7 and 8). At higher strains than 15%, the relationship between the applied force and the resulting elongation was nonlinear with a stiffening trend. Phenomenological models of the equilibrium stress-strain response of soft tissues were used in the past to interpret this type of result¹⁶, but these models do not yield any insights into possible structure-property relationships. In this work the experimental data were modeled using a microstructure-based model. The porcine vocal fold lamina propria has a composition similar to that of humans^17–18, and it has a similar mechanical structure composed of elastin and collagen. As a result, its mechanical behavior is also comparable to that seen in humans¹⁴. The three-dimensional organization of elastin and collagen in similar tissue was imaged by Miri et al.¹⁹ using multi-photon microscopy. In order to link structure and macroscopic properties the eight-chain model of Arruda and Boyce²⁰ was used. This statistically based model has been successfully applied in the past to soft tissues such as skin²¹. Hypothesizing structural similarities between the fibrous network of skin and that of vocal folds¹⁹, the eight-chain model was used to model the measured viscoelastic response. The model parameters were adjusted based on the response of the tissue to uni-axial tension forces. The results yield a possible interpretation of the basic physics of the material response on a microscopic scale, which were compared with multi-phase mechanical models of the vocal fold tissue (e.g., Zhang et al.¹³).

Figure 7.

a. Axial stress vs. axial strain of porcine vocal folds (m = 5) subjected to quasi-static loading in the normal solution. ( round 1; round 2; round 3)

b. Axial stress vs. axial strain of porcine vocal folds (m = 5) subjected to quasi-static loading in the hypertonic solution. ( round 1; round 2; round 3)

Figure 8.

a. Axial stress vs. axial strain of porcine vocal folds (m = 5) subjected to dynamic loading (1 Hz) in the normal solution. ( round 1; round 2; round 3)

b. Axial stress vs. axial strain of porcine vocal folds (m = 5) subjected to dynamic loading (1 Hz) in the hypertonic solution. ( round 1; round 2; round 3)

2. Methods

2.1 Sample preparation

Healthy porcine larynges (m = 10) were obtained from a local abattoir immediately post mortem. They were immersed in a 0.9% saline solution and transported to the laboratory for testing. Within a few hours, the sample dissection was initiated by removing connective soft tissues around the larynx. A mid-sagittal cut was made in the anterior section. Two hemi-larynges were separated in a way that the thyroid cartilage was preserved at the anterior commissure (Fig.1a). Following removal of the ventricular (i.e., superior¹⁴) vocal folds using a small scalpel, the true (i.e., inferior¹⁴) vocal folds were then separated from the sub-glottal wall (Fig.1a). Small portions of the arytenoid and thyroid cartilages, with 5–8 mm width and 3–5 mm thickness, were kept to facilitate gripping of the vocal folds during axial-tension tests (Fig.1b). The vocalis muscle was smoothly excised out from the vocal fold lamina propria. Care was taken not to damage the lamina propria to ensure loading uniformity. A portion of muscle was left in the neighborhood of ending cartilages, as shown in Fig.1b. The dissection of all samples was done within 3–4 hours postmortem.

Figure 1.

a) Porcine hemilarynx and a vocal fold sample prepared for mechanical tensile test. b) Vocal fold lamina propria (LP).

2.2 Test protocols

A three-step traction-test procedure was used as follows. Traction tests were performed using an EnduraTEC tester (ElectroForce (ELF) 3200, Bose Inc., Eden Prairie, MN), equipped with a digital camera (Flea2, Point Grey Research Inc., Richmond, BC) to capture the surface deformation. The second-axis output signal of the ELF machine, used in simple uniaxial mode, was used to trigger the camera in order to synchronize displacement, force and images. A schematic of the test apparatus is shown in Fig. 2. The apparatus was set for a displacement-control mode. The displacement actuator is able to impose a displacement range of 12 mm. The applied displacement is also compensated by a PID feedback from the displacement sensor. PID stands for proportional, integral and derivative.

Figure 2.

a) Schematic of the experimental apparatus for mechanical tensile test (two cameras are shown for the case of three-dimensional imaging). b) Picture of the apparatus for axial testing of porcine vocal folds. One camera was used for imaging the planar deformation field. Note that the tissue sample was submerged in the normal solution (PBS) for the first round and in the hypertonic solution (30% NaCl) during the second and third rounds.

The thickness of the samples was measured at four different locations using a caliper (Mitutoyo, Tokyo, Japan) with a precision of 1 µm. A speckle pattern was applied onto the surface, as described in the following subsection. The sample was installed between two grips via four black silk (3.0 metric) sutures on each end (Figs. 1b and 2a). Because the current method uses non-contact optical measurements, the results are not affected by the sutures. The parts attached to the tissue only transmit the extension loading. The sample was submerged in a normal phosphate buffer solution (PBS) at 37°C ± 0.5°C such that a thin layer of fluid covered the upper surface (i.e., the epithelium). A fiber-optic light source (Cole-Parmer Instrument Co, Montreal, QC) was also used to illuminate the sample (Fig. 2).

Dehydration protocol was applied as follows. While submerging in PBS, the sample was subjected to a quasi-static cyclic ramp loading at a rate of 0.1 mm/s followed by a 1-Hz sinusoidal loading, as a first round. The bath solution was then replaced by a hypertonic solution (30% NaCl). The tissue was kept in the hypertonic solution over a period of 30 minutes. The temperature was held constant at 37°C ± 0.5°C. A similar loading history was then applied with the sample immersed in the same hypertonic solution for a second round of traction tests. One last round was carried out following a 30-minute submersion in the same hypertonic solution. The three-round procedure was then performed on another set of samples bathed in the normal solution (PBS) to supply baseline data (i.e., normal protocol).

2.3 Digital image correlation

Surface deflections were quantified using digital image correlation (DIC) to determine the local strain field¹⁵. Tissue dyes (Thermo Fisher Scientific, Ontario, ON) were used to create a random speckle pattern on the surface of the tissue. A bright dye was applied to make a uniform background and then the black dye was spread out randomly (Fig. 1a). The tissue sample was submerged in the solution with the superior surface of the sample near the fluid surface to minimize optical distortion. The commercially available software package Vic-Snap (Correlated Solutions Inc., Colombia, SC) was used for the kinematic analysis of the recorded images. The displacement field was obtained from analysis of deformed and undeformed images. The strain field was then calculated using a finite-difference approximation of the displacement gradients.

The DIC procedures are as follows. One reference image of the nominal undeformed body is chosen over the area of interest. The randomized speckle pattern over the area creates a unique grayscale distribution over the region analyzed. Since multiple pixels may have the same grayscale values, a subset of pixels with a predetermined size is chosen and the intensity distribution within that region is calculated. The images are divided into equal subsets, with each subset identified by a unique pattern. The speckle pattern should be random. The size of the speckle dots must be smaller than that of the chosen subsets. The motion of any specific point between two pixels affects the average intensities of both pixels. Neither has the same value as in the previous image. An interpolation field is then created. A computer algorithm is used to estimate the grayscale values of points between pixels. The subsequent position of each subset is obtained from the best correlation in the surrounding subsets.

2.4 Constitutive model

A constitutive law is required to simulate the relation between stress components and the strain field. The eight-chain model was obtained from the entropy changes of long-chain elements in polymers²⁰. It has been shown to be efficient in modeling the mechanical extension of soft tissues²¹. As a hyperelastic model it can be introduced with the strain energy potential W. For the case of incompressible material, the eight-chain model has the following form of strain energy potential function²¹

$$W={\mathit{\text{n k}}}_B\theta \sqrt{N}[{\lambda }_c\beta -\sqrt{N}\text{ ln}(\text{sinh}(\beta )/\beta )],$$ (1)

where k_B = 1.3807 × 10⁻²³ Nm/K is Boltzman’s constant, and θ = 310K represents the absolute temperature. ln(β) is the natural logarithm and sinh(β) is the hyperbolic sinusoidal function. The term β is defined as

$$\beta =L^{-1}({\lambda }_c/\sqrt{N}),$$ (2)

where λ_c is the chain stretch, i.e.,

$${\lambda }_c={({\lambda }_1^2+{\lambda }_2^2+{\lambda }_3^2)}^{1/2}/\sqrt{3}$$ (3)

and L⁻¹(β) is the inverse Langevin function²⁰. λ_i’s (i = 1, 2, 3) represent the material stretches along the global coordinates, i.e., longitudinal, transverse and thickness directions. The material parameters are N, which is the number of rigid links of a specific length, and n, which is the network molecular chain density. Hence, high/low N and n values imply, respectively, long/short and strong/weak collagen fibrils. From Eq. (1) the true stress-stretch relation for the case of axial tension experiment may be expressed in terms of two unknown parameters, N and n, as:

$${\sigma }_1=\frac{{\mathit{\text{n k}}}_B\theta \sqrt{N}}{3}{L}^{-1}(\frac{{\lambda }_1^2+2/{\lambda }_1^2}{\sqrt{N}})\frac{{\lambda }_1^2-1/{\lambda }_1}{{\lambda }_1^2+2/{\lambda }_1^2}$$ (4)

For more details on this formulation, the reader is referred to Bischoff et al.²¹. From the axial force F obtained from the ELF machine and the longitudinal stretch λ₁ (≡1 + ε), calculated by DIC, the following force-stretch relation is deduced

$$F=\frac{1}{3}{\mathit{\text{h w n k}}}_B\theta \sqrt{N}{L}^{-1}(\frac{{\lambda }_1^2+2/{\lambda }_1^2}{\sqrt{N}})\frac{{\lambda }_1-1/{\lambda }_1^2}{{\lambda }_1^2+2/{\lambda }_1^2},$$ (5)

where h and w denote, respectively, the effective thickness and width of each sample (Fig. 2). The optimal combination of these parameters was established based on a least-square error regression procedure. All experimental data were parameterized using Eq. (5). The root square of the mean squared error was between 0.04 and 0.12 for most of the cases.

3. Results and Discussions

3.1 Mass history

The loss of interstitial fluid induced by osmotic-pressure potential was presumed to cause no variation in the molecular composition of the matrix protein⁷. Between initial and final weights of those samples that were subjected to the dehydration protocol, no significant difference was observed. Hence, another two sets of porcine vocal folds (m = 4) were subjected to both protocols for the estimation of water loss. The cartilage at the anterior and posterior ends significantly contributed to the overall weight. To eliminate possible bias from the cartilage, the arytenoid and thyroid cartilages were extracted during the sample preparation. A central area of approximately 15 mm×4 mm (please see the dash-dot region in Fig. 1b) was preserved. Weighing was performed before and after each round of the traction test experiments. The samples were weighed using an electronic balance (Thermo Fisher Scientific, Ontario, ON). The overall results, normalized with the initial weight M = 0.2416±0.0292g for hypertonic protocol and M = 0.1974±0.0657g for normal protocol, are shown in Fig. 3. Upon extension, the tissue appears to have absorbed water in the first round of traction tests. A notable mass loss (ΔM = 0.0562±0.0032g from step “2” to step “3”) occurred during the first 30-minute submersion in the hypertonic solution. Contrary to what was expected, the tissue then absorbed water during the two rounds of traction tests.

Figure 3.

Normalized mass history of porcine vocal folds for two different protocols: normal solution ■ (m= 4), and hypertonic solution ◆ (m= 4). (Note: the time period for the extension tests was approximately 20 minutes)

A hypothetical justification for the dehydration (from step 2 to step 3 in Fig. 3) and the mechanical extension (from step 3 to step 4 in Fig. 3) is illustrated in Fig. 4, based on postulated biophysical mechanisms that were originally proposed for articular cartilages. Concentration here refers to the abundance of solute particles (like chloride sodium molecules) per volume of the solution. Arbitrary constants were introduced for better understanding of the sketch. The osmotic pressure is basically the pressure difference across a permeable interface separating two solutions of different concentrations. At time t=0 (step 2 of Fig. 3), the osmotic pressure forces the water out of the tissue at a high flow rate. The hydrostatic pressure, force exerted by fluid molecules on an immersed body, at this point in time should be identical on both sides of the interface because the tissue was kept in a buffer solution before submersion. After a short time, at t=t₁, a large hydrostatic pressure gradient is formed across the interface. Water may then be expelled from the tissue with a significantly reduced flow rate. After a certain time, at t=t₂, equilibrium is reached between the osmotic and hydrostatic pressures. Thus, the rate of water transport into and out of the tissue should be equal.

Figure 4.

Postulated mechanisms of water loss/absorption in the tissue submerged in the hypertonic solution (i.e., 30% NaCl) and subjected to mechanical test at time t (0 < t₁ < t₂ < t₃ < t₄). Parameters c_t and c_b denote the solute concentrations of the tissue and bath, respectively. C, C′, C″ are real-valued constants. p and p_osm indicate hydrostatic and osmotic pressures, respectively.

The explanations of Fig. 4 are followed here. At a later time at t=t₃ (step 3 of Fig. 3), the tissue is extended along the axial direction. The hydrostatic pressure inside the tissue is increased because of global force equilibrium. Solute particles such as chloride sodium migrate into the tissue because the membrane is penetrable. This denaturalizes and reverses the osmotic-pressure potential. The new potential is stronger than the hydrostatic pressure compared to the case of the normal solution. When the tensile force is removed, at t=t₄, equilibrium is reached across the interface. The state of equilibrium has changed since some particles have migrated into the tissue. The final water content (step 4 of Fig. 3) is thus larger than that of the equilibrium condition before loading (step 3 of Fig. 3). Further studies are needed to confirm this proposed hypothetical mechanism.

A typical plot of the axial force recorded by the load cell versus the displacement out of the tensile test machine arm is shown in Fig. 5. In this experiment the peak displacement value was 11 mm. Force (or stress) relaxation is observed because the force magnitude for a given displacement decreases between successive cycles. Hysteresis loops are observed over each period. The hysteretic area and the elastic constant are both significantly larger in the first cycle than in subsequent cycles. Such a trend is also observed in the case of engineering rubber materials, for example. A few initial cycles are often applied to pre-condition the tissue (e.g. Alipour et al.¹⁴) to avoid subsequent relaxation. This procedure may cause the loss of possibly valuable information because the relaxation process may reveal interesting details of the microstructure of the material. In contrast with rubber, however, a similar but less pronounced strain softening relaxation was observed in the second and third rounds of the tension tests. The hierarchical organization of the tissue may change during submersion, which may change the entropy. Or the water change may have contributed changes in tissue viscoelasticity because the solid network already absorbed water during submersion. It has been reported that tissue hydration reduces viscosity¹⁰. Nevertheless, a significant hysteresis area is observed in the first three cycles. Hence, entropy variations may have possibly contributed more than water content. Beyond the third cycle, the mechanical response appears to reach a steady state and consequently water content should be, on average, constant.

Figure 5.

Traction force vs. arm displacement for five successive load cycles of ramp displacement at 0.1 mm/s. ( 1^st cycle; 2^nd cycle; 3^rd cycle; 4^th cycle; 5^th cycle).

3.2 Strain field

Optical measurements based on DIC were made to evaluate the planar strain field. The EnduracTEC tester provides in-plane Green’s strain tensor through the optical tracking of four dots (four corners of a square). Silicon rubber samples were subjected to axial traction tests using both the four-dot optical measurement and DIC. Reasonable agreement was observed for the axial strain values. Generally the strain obtained from the displacement of the arm (Fig. 2) is not accurate because of local deformations at the tissue-suture connections and the inhomogeneity of the strain field. This was verified through comparisons between the strain-displacement correlations of a physical rubber model and porcine vocal folds. At large strains, significant differences were observed. Optimal parameters such as the aperture and exposure time of the camera were obtained by trial and errors in preliminary studies.

In-plane strain components were calculated using Vic-2D (Correlated Solutions Inc., Colombia, SC). A subset size of 25×25 pixels was selected over the area of interest, which includes almost the entire surface of the vocal fold. For large elongations, the software analyzed each image by tracking the points in previous images. The data near the boundaries was ignored due to edge effects. Areas that were out of focus caused significant errors. A circular area with a 3-mm diameter was thus selected to calculate the average axial strain magnitude. This process was followed to ensure consistency across samples.

The strain distributions of one sample are shown in Fig. 6. The reference image shows the initial state. A pre-stress of less than 10% of the maximum stress was applied to uncurl the un-deformed tissue. Contours of axial strain, shown in Fig. 6, illustrate the inhomogeneity of the strain field and, consequently, of the mechanical stress during deformation. In the area of interest, the axial strain ranges from 21.8% to 28.9% for deformation image 1, and from 37.6% to 64.4% for deformation image 2. The strain reaches a local maximum value along a line that connects two sutures. A region of significant shear strain was observed, which violates the assumption of pure axial strain normally made in uniaxial tension tests. This stresses the importance of local strain measurements for the accurate determination of the axial strain. Area-averaging over the selected region may be used to filter shear strain variations as needed.

Figure 6.

Reference image and two subsequent deformed images with superimposed axial-strain contours of one vocal fold sample subjected to the ramp loading (0.1 mm/s). a) Reference image. b) Deformed image for 5-mm extension. c) Deformed image for 11-mm extension.

The strain history in successive cycles was investigated. For a quasi-static loading, the strain values were consistently repetitive. For dynamic sinusoidal loading, however, the strain increased slightly over successive cycles. Averaged peak values for the fourth and fifth cycles of each round are reported. An exciting trend was also observed when the strain histories for three rounds were compared. During the second and third rounds, while the samples were submerged in a hypertonic solution, the strain magnitude did not vanish completely when the displacement was zero. This residual stress may be related to water loss in the vocal fold tissue (Fig. 3), which may have shrunk the tissue and consequently increased the stress contribution in the extracellular matrix because of a reduction in the tissue cross section.

3.3 Effects of dehydration on vocal fold stiffness and viscosity

Overall stresses, calculated by Eq. (4), versus strain values for all cases are presented in Figs. 6 and 7. The associated model parameters that were used to generate those figures are reported in Table 1. Low-amplitude shear strains associated with the linear viscoelastic properties of dehydrated vocal folds were reported by Chan and Tayama⁷. These data were compared to the initial shear modulus, μ_o, calculated using the eight-chain model in the present study and the results are shown in Table 1. A nearly four-fold increase in shear modulus with dehydration was observed, which is consistent with the lower range of the data of Chan and Tayama⁷. The average Young’s modulus of six porcine vocal folds, with standard deviation, was reported¹⁴ to be 16.3±2.9 kPa, a much lower magnitude than obtained in the present study (40.5±15.7 kPa from “10” samples). The discrepancy may be attributed to the fact that strain estimates based on arm displacement, as opposed to optical-based local strain measurements, tend to cause an underestimation of Young’s modulus²².

Table 1.

Eight-chain model parameters and initial shear modulus for two different protocols: normal solution (m = 5), and hypertonic solution (m = 5). R#i stand for the i^th round of traction test.

Normal solution					Hypertonic solution
Load	R	N	n (1/m3) ×10 23	µo (kPa)	Load	R	N	n (1/m3) ×10 23	µo (kPa)
Quasi-static	1	1.18 ± 0.07	8.48 ± 1.77	17.4 ± 5.83	Quasi-static	1	1.28 ± 0.03	14.2 ± 7.88	18.2 ± 9.98
	2	1.18 ± 0.08	8.19 ± 2.02	17.4 ± 5.87		2	1.12 ± 0.04	21.6 ± 10.3	60.3 ± 29.6
	3	1.17 ± 0.07	7.81 ± 2.88	16.7 ± 6.42		3	1.12 ± 0.03	20.1 ± 8.49	58.7 ± 25.7
Dynamic (1 Hz)	1	1.31 ± 0.26	14.6 ± 6.55	23.8 ± 14.4	Dynamic (1 Hz)	1	1.31 ± 0.12	23.3 ± 15.7	25.7 ± 13.6
	2	1.30 ± 0.25	13.4 ± 7.11	22.8 ± 15.3		2	1.10 ± 0.06	37.3 ± 25.7	99.3 ± 49.2
	3	1.30 ± 0.27	13.8 ± 7.32	24.7 ± 17.9		3	1.10 ± 0.07	36.6 ± 27.3	96.5 ± 51.9

The tangent modulus, i.e., the slope of the stress-strain curve, is a measure of mechanical stiffness. For large strains, it was greatly increased in dehydrated tissues. The free-length parameter of the fibers, N, decreased with dehydration. This suggests a shortening of the effective length of the collagen fibers. When the liquid is expelled from the tissue and the salt molecules are drawn in, the fibers may become more entangled. This may create additional physical (and possibly chemical) crosslinks between fibers. The accompanying rise in the network-density parameter of the fibers, n, suggests a denser distribution of protein networks. This is consistent with the reduction of volume expected following water loss. A comparison between the second round and the third round reveals that dehydrated tissue may not tolerate additional modification, even if the water content is different. The irreversibility⁷ of the dehydration process occurred in the current protocol.

The nonlinear trend of the stress-strain curves, for different rounds in Figs. 7 and 8, are the same for various strain levels. The tangent modulus, or the stiffness, for dynamic loading is higher than that for quasi-static loading. As seen above, higher stiffness is a result of water removal. It can be concluded that water plays less of a role for dynamic loading than for quasi-static loading. This may explain in part the need for hydration following continuous and long high-pitch phonation⁴, when the vocal folds are extended over a long time period. Another factor is of course surface dehydration. The data are amenable to interpretation by light of mixture theories to model the vocal fold tissue under nonlinear loading (e.g., Hanson et al.¹¹). The data reported here may be useful as a baseline for model verifications.

Most previous studies have focused on the effects of dehydration on tissue viscosity, particularly at the level of the superficial layer (e.g., Witt et al.¹⁰). While vocal folds may undergo surface dehydration for in-situ tests, body dehydration, used in the present study, yields information that may be a better representation of the bulk behavior of the tissue. Note that average data for stretching-releasing (loading-unloading) were not reported because the maximum stretches were different for various samples. This was due to the tests being performed in a displacement-control mode. The complete data is reported in Table 2. To calculate the mechanical loss factor ζ, stretching and releasing curves were fitted with a polynomial of degree 5, and then the loop integral (i.e., the dissipated energy) was divided by the area under the stretching curve (i.e., the extension energy).

Table 2.

Energy loss magnitudes for porcine vocal folds for two different protocols: normal solution (m = 5), and hypertonic solution (m = 5). R#i stand for the i^th round of traction test. The parameter ε_max is the upper limit for the average axial strain in the tissue.

Normal solution					Hypertonic solution
Sample	εmax(%)	Energy loss (ζ)			Sample	εmax(%)	Energy loss (ζ)
		R#1	R#2	R#3			R#1	R#2	R#3
1	47.9	0.064	0.047	0.041	1	58.5	0.059	0.414	0.401
2	66.8	0.096	0.101	0.099	2	62.8	0.075	0.387	0.378
3	45.9	0.027	0.022	0.013	3	67.9	0.091	0.571	0.545
4	48.8	0.054	0.058	0.043	4	60.3	0.065	0.293	0.283
5	52.6	0.057	0.067	0.076	5	44.1	0.056	0.401	0.392

The loss factor, ζ, is inversely correlated with the propensity for self-sustained oscillations. Phonation normally occurs when mechanical energy losses within the vocal fold lamina propria are small. The loss factor in dehydrated tissue samples is greater than 30%. In contrast the loss factor of hydrated tissue was found to be smaller than 10%. Thus a 20% decrease in water mass, estimated from the data of Fig. 3 and the tissue porosity of 80%, led to a five-to-seven fold increase in loss factor. Similar stress-strain curves were observed for the five dehydrated samples. The load-releasing history in dehydrated tissues is very similar to that of normal tissues. It may be concluded that dehydration mainly affects the stretching response of the vocal fold tissue, when it is longitudinally, and extracellular water may not contribute to the resistance of the tissue during load release.

The contribution of the fluid phase must be accounted for to properly model the viscoelastic response of vocal fold tissue. Any accurate model should capture the releasing response of the tissue when the factors associated with water are removed. The stretching response must be matched with the results for 20% water loss, e.g. five-to-seven fold increase of ζ at high strains. Considering stretch-dependent viscosity as a function of tissue porosity would be one possible way to capture such trends in mathematical models. Hence, the results of this study may provide a framework for the modeling of the viscoelastic response of the vocal folds for large deformations.

4. Conclusions

The viscoelastic response of dehydrated vocal fold tissues for large extensions was investigated. A uniaxial tension test set-up, equipped with a digital camera, was used to impose quasi-static and dynamic cyclical mechanical loading on porcine vocal folds, while a hypertonic solution was used to expel water from the tissue. A record of the mass history revealed significant mass changes during loading. The tissue was found to absorb water when initially submerged in hypertonic solution and subjected to mechanical extension. The tangent modulus of dehydrated tissue was significantly increased relative to that of hydrated tissue and varied with the strain magnitude. The eight-chain model previously used in statistical mechanics was used to interpret stress-strain results based on the free length and the network density of the fibers. In addition, large hysteresis areas for dehydrated tissues indicated a rise in internal viscosity, reaching values of 50% in some cases. This may substantiate the reported increase in phonation effort. This study may be useful for the clinical assessment of body dehydration.