August 2009
Volume 50, Issue 8
Free
Cornea  |   August 2009
A Link between Tear Instability and Hyperosmolarity in Dry Eye
Author Affiliations
  • Haixia Liu
    From the Indiana University School of Optometry, Bloomington, Indiana; the
  • Carolyn Begley
    From the Indiana University School of Optometry, Bloomington, Indiana; the
  • Minhua Chen
    From the Indiana University School of Optometry, Bloomington, Indiana; the
  • Arthur Bradley
    From the Indiana University School of Optometry, Bloomington, Indiana; the
  • Joseph Bonanno
    From the Indiana University School of Optometry, Bloomington, Indiana; the
  • Nancy A. McNamara
    Francis I. Proctor Foundation, University of California-San Francisco, San Francisco, California; the
  • J. Daniel Nelson
    Department of Ophthalmology, HealthPartners Medical Group and HealthPartners Research Foundation, Minneapolis, Minnesota; the
    Department of Ophthalmology, University of Minnesota, Minneapolis, Minnesota; and the
  • Trefford Simpson
    School of Optometry, University of Waterloo, Waterloo, Ontario, Canada.
Investigative Ophthalmology & Visual Science August 2009, Vol.50, 3671-3679. doi:https://doi.org/10.1167/iovs.08-2689
  • Views
  • PDF
  • Share
  • Tools
    • Alerts
      ×
      This feature is available to authenticated users only.
      Sign In or Create an Account ×
    • Get Citation

      Haixia Liu, Carolyn Begley, Minhua Chen, Arthur Bradley, Joseph Bonanno, Nancy A. McNamara, J. Daniel Nelson, Trefford Simpson; A Link between Tear Instability and Hyperosmolarity in Dry Eye. Invest. Ophthalmol. Vis. Sci. 2009;50(8):3671-3679. https://doi.org/10.1167/iovs.08-2689.

      Download citation file:


      © ARVO (1962-2015); The Authors (2016-present)

      ×
  • Supplements
Abstract

purpose. Tear film instability and tear hyperosmolarity are considered core mechanisms in the development of dry eye. The authors hypothesize that evaporation and instability produce transient shifts in tear hyperosmolarity that lead to chronic epithelial stress, inflammation, and symptoms of ocular irritation. The purpose of this study was to provide indirect evidence of short-term hyperosmolar conditions during tear instability and to test whether the corneal epithelium responds to transient hyperosmolar stress.

methods. Five subjects kept one eye open as long as possible, and overall discomfort and sensations associated with tear break-up were scaled. Later, the same subjects used the same scales to report discomfort sensations after instillation of NaCl and sucrose hyperosmolar drops (300–1000 mOsM/kg). A two-alternative, forced-choice experiment was used to obtain osmolarity thresholds. In the second experiment, primary cultured bovine corneal epithelial cells were transiently stressed with the same range of hyperosmolar culture medium, and proinflammatory mitogen-activated protein kinase (MAPKs) were measured by Western blot analysis.

results. Tear instability led to an average discomfort rating of 6.13 and sensations of burning and stinging. These sensations also occurred with hyperosmolar solutions (thresholds, 450–460 mOsM/kg) that required 800 to 900 mOsM/kg to generate the same discomfort levels reported during tear break-up. MAPK was activated at 600 mOsM/kg of transient hyperosmolar stress.

conclusions. These experiments provide a link between hyperosmolarity and tear instability, suggesting that hyperosmolar levels in the tear film may transiently spike during tear instability, resulting in corneal inflammation and triggering sensory neurons.

Dry eye, a common condition affecting millions, 1 2 3 is characterized by symptoms of ocular discomfort, dryness, irritation, and visual disturbance. 4 5 The 2007 DEWS (Dry Eye Workshop) report considered tear instability and hyperosmolarity to be core mechanisms of dry eye, suggesting that tear instability leads to hyperosmolar conditions and inflammation, resulting in dry eye symptoms of ocular irritation. 6 However, conditions within the thin tear film over the corneal surface are difficult to measure. Thus, the underlying connection between tear instability and hyperosmolarity, which is considered central to the dry eye condition, remains theoretical. 7 8  
Tear osmolarity is currently measured from the lower meniscus and ranges from approximately 300 to 310 mOsM/kg in normal eyes. 9 10 The current cutoff for a dry eye diagnosis is 316 mOsM/kg, 11 although tear hyperosmolarity in individual patients with dry eye may reach as high as 360 mOsM/kg. 12 However, most animal and in vitro studies of hyperosmolarity in dry eye require long-term exposure to higher levels (400–600 mOsM/kg) to demonstrate an inflammatory response of the ocular surface via activation of the mitogen-activated protein kinase (MAPK) pathway and cytokine production. 13 14 Therefore, the minor increase in chronic levels of lower meniscus tear osmolarity measured from patients with dry eye may be insufficient to generate the inflammatory response hypothesized to underlie the corneal damage/sensations associated with dry eye. 
However, tear film osmolarity measured from the lower meniscus may not fully reflect the rapid spatial and temporal changes that occur over the corneal surface during the interblink interval. The corneal compartment of the tear film is separated from the menisci by “black lines” 15 16 and can be subject to rapid thinning due to evaporation and tear break-up, 17 18 especially among patients with dry eye 19 or when blinking is slowed during tasks requiring concentration. 20 Thus, the osmolarity of the corneal tear film compartment may change rapidly during the interblink interval. 15 In support of this idea, subjects in previous studies in our laboratory used the descriptors burning and stinging to describe sensations during periods of tear break-up, which supports the hypothesis that hyperosmolarity increases in the tear film with increasing tear instability. 21 However, the amount of change required to produce these sensations is unknown, as is the response of the corneal epithelium to very transient shifts in hyperosmolarity. 
Thus, although current theories predict transient increases in corneal tear film hyperosmolarity during tear instability, 6 the amount of the increase and its possible effects on the underlying epithelium and nerves have not been investigated. Therefore, we designed this study to estimate the levels of hyperosmolarity in the unstable corneal tear film by comparing the corneal psychophysical response to instilled hyperosmolar drops and irritative sensations during tear instability (experiment 1). We then determined whether transient exposure to these levels of hyperosmolarity induces a proinflammatory response from the in vitro corneal epithelium (experiment 2). 
Methods
Experiment 1: Sensory Response to Instability and Hyperosmolar Solutions
Five subjects with no history of ocular disease were selected for the study. All subjects had participated in previous psychophysical experiments or agreed to be trained to detect small differences in corneal sensation before beginning the study. Informed consent was obtained from all participants. The study was approved by the Indiana University Human Subject Committee and was conducted in accordance with the tenets of the Declaration of Helsinki. 
Sensory Response to Tear Instability.
We used staring tear break-up dynamics (S-TBUD), a method previously developed in our laboratory, to study the rate and repeatability of tear break-up (TBU) in normal and dry eye subjects. 19 21 Briefly, 2 μL of 2% sodium fluorescein was instilled into the experimental eye (chosen randomly) and the subjects were asked to keep the eye open as long as possible, until they felt the need to blink. The trial was monitored by a video slit lamp camera at 8× magnification, and the other eye was held shut by the subject. Subjects filled out the Dry Eye Questionnaire (DEQ) before the S-TBUD to measure the symptoms. 22  
At the end of each S-TBUD trial, the subject was asked to report the overall intensity of discomfort experienced during the trial on a scale of 0 (no discomfort) to 10 (extreme discomfort) and to grade the level of five sensations on visual analog scales (VAS) adapted from Acosta et al. 23 We selected the VAS descriptors of burning, stinging, irritation, pricking, and cooling based on data from our previous S-TBUD studies. 21 This procedure was repeated three times with 5-minute intervals between testing. 
As described previously, 19 21 we quantified the dry area growth rate (DAGR) for tear break-up from S-TBUD trials by extracting video frames and calculating the percentage of the area of break-up (AB) within the exposed corneal surface for each. 19 21 The maximum blink interval (MBI), which was the length of time that the subject kept the eye open during the trial, and tear break-up time (TBUT) were also measured from videos by an observer unaware of the subject or trial. 
Sensory Response to Hyperosmolar Solutions.
In this experiment, we determined the threshold for detection and the suprathreshold sensory response to hyperosmolar solutions by psychophysical methods. We used the same five subjects as in the previous experiment to ensure that scaling of sensations was consistent. All subjects were trained to distinguish small differences in solution osmolarity before beginning the project. 
Both NaCl and sucrose isosmolar and hyperosmolar solutions were tested. Although NaCl could be expected to contribute significantly to tear film osmolarity, sodium ions can also interact with ion channels 24 and nociceptive nerve endings, 25 while sucrose should not. Sucrose was used as a control to determine whether the sensory response we measured was due to the effect of hyperosmolarity or Na+ or Cl ions. 
Isosmolar and hyperosmolar solutions were prepared by adding sucrose or NaCl to phosphate-buffered saline (PBS), and the osmolarity was adjusted by measurement with a vapor pressure osmometer (Vapro; Wescor, Inc., Logan, UT). A sterile pipette was used to instill 40 μL of test solution onto the upper cornea while the lid was slightly lifted by the experimenter and the subject was looking down. The drop was allowed to flow down and bathe the cornea before the subject blinked, so that the subject could assess the level of corneal discomfort from the drop. 
The threshold for detection of hyperosmolar NaCl and sucrose solutions was determined using a two-alternative, forced-choice (2AFC) paradigm. Two drops were instilled, one into each eye. One eye received an isosmolar reference drop (300 mOsM/kg) and the other a test drop, ranging from 400 to 600 mOsM/kg. This range was established by a pilot experiment, which showed that >600 mOsM/kg could be easily detected by subjects, whereas <400 mOsM/kg was undetectable. Test drops were given in 25 mOsM/kg steps, with each level of osmolarity tested 15 times, for a total of 135 sets per type of hyperosmolar solution or 270 repetitions in total. The eyes and the order of solutions were chosen at random. The two drops were instilled one after another (within 10 seconds), and subjects were asked to choose which eye felt more discomfort. There was a minimum 10-minute period between instillation of pairs of drops, which was established as an effective washout period by a separate set of pilot experiments. The percentage of trials in which the eye receiving the hyperosmolar solution felt more discomfort was plotted for each level of osmolarity. To obtain the detection threshold for hyperosmolar solutions, data were fitted with Quick’s version of the Weibull function, 26 which was used to interpolate the sensory threshold for hyperosmolarity (osmolarity necessary for 75% correct performance). 27 28  
To determine the suprathreshold ocular sensations caused by hyperosmolar drops of NaCl and sucrose, we tested 300 to 1000 mOsM/kg solutions in 100-mOsM/kg steps, with each level of osmolarity tested three times, for a total of 24 test drops per type of solution. We stopped at an upper limit of 1000 mOsM/kg because preliminary testing showed high levels of discomfort over that level. In these experiments, only one eye was tested at a time, alternating between left and right. The order of solutions was randomized, with at least 10 minutes between drops. After each drop, the subject reported the overall intensity of discomfort and scaled the five different sensations on the VAS, as described in the preceding TBU experiment. All data were fit by the following Steven’s law power function 29 :  
\[{\psi}(I){=}{\kappa}I^{{\alpha}}\]
where I is the stimulus magnitude, ψ(I) is the psychophysical function encompassing the subject’s sensation in response to the stimulus, α is the exponent dependent on the type of stimulation, and κ is a proportionality constant that is determined by the type of stimulation and the units used. 
Experiment 2: Corneal Epithelial Response to Hyperosmolar Solutions
In the second portion of the study, we determined whether the in vitro corneal epithelium responds to short-term hyperosmolar stress (using levels of osmolarity suggested from experiment 1) by activating the MAPK pathway. 
Corneal Epithelial Cell Culture.
Bovine eyes were obtained from a local abattoir. Corneal epithelial–stromal patches were excised and soaked in 1× dispase solution for 1 hour to loosen the epithelial–stromal junction. The epithelial layers were then carefully peeled off and soaked in 0.25% trypsin to separate the cells. The cell suspension was cultured in Dulbecco’s modified Eagle’s medium/nutrient mixture F-12 (DMEM/F12; Invitrogen-Gibco, Grand Island, NY) containing 5 ng/mL EGF, 5 μg/mL insulin, 50 μg/mL gentamicin, 1.25 μg/mL amphotericin B, and 6% fetal bovine serum (FBS), at 37°C under 5% CO2 and 95% humidity. The medium was renewed every 2 to 3 days until the cells were confluent. The cells were then subcultured into 35-mm Petri dishes, under the same culture conditions. The epithelial phenotype of these cultured cells was confirmed by epithelial morphology and immunofluorescent staining with cytokeratin antibodies (AE-5). 
Hyperosmolarity Exposure.
Confluent cultures were washed three times with PBS and switched to a serum-free medium (DMEM-F12 without FBS) for 24 hours. The cultures were then treated with 700-mOsM/kg DMEM-F12 solution (osmolarity was adjusted by adding sucrose or NaCl) for 10 and 30 seconds and 2, 5, 10, 15, and 30 minutes, and washed with cold PBS three times. A 10-second exposure time period was the shortest that could be reliably delivered in our experimental setup. 
We also varied the level of osmolarity, within the range suggested by the results in experiment 1. Confluent cultures were treated with 300, 400, 500, 600, 700, 800, 1000, and 1200 mOsM/kg DMEM-F12 solutions (osmolarity was adjusted by adding sucrose or NaCl) for 30 seconds. The 30-second time period was chosen because the time course experiments suggested it produced a marked activation of at least some MAPK pathways. 
Western Blot.
Adherent cells were lysed in a nondenaturing cell lysis buffer (Cell Signaling Technology, Beverly, MA) containing 20 mM Tris-HCl (pH 7.5), 150 mM NaCl, 1 mM Na2EDTA, 1 mM EDTA, 1% Triton, 2.5 mM sodium pyrophosphate, 1 mM β-glycerophosphate, 1 mM Na3VO4, 1 μg/mL leupeptin, 1 mM PMSF, and protease inhibitor cocktail. The cells were scraped and transferred to microcentrifuge tubes, and sonicated for 10–15 seconds. The cell extracts were centrifuged at 14,000g for 10 minutes at 4°C, and the supernatants were stored at 80°C before use. The total protein concentrations of the conditioned media and cell extracts were determined by a bicinchoninic acid (BCA) protein assay (Pierce Biotechnology, Rockford, IL). 
Cell extract samples with equal amount of protein in each lane were mixed with 6× SDS reducing sample buffer and boiled for 5 minutes before loading. The proteins were separated by SDS polyacrylamide gel electrophoresis (PAGE) and transferred to NC membranes for 1 hour, which were blocked with 5% nonfat milk in TBST (50 mM Tris [pH 7.5], 0.9% NaCl, and 0.1% Tween-20) for 1 hour at room temperature, and then incubated overnight at 4°C with a rabbit antibody against JNK (1:1000), p-JNK (1:1000), ERK (1:1000), p-ERK (1:1000), P38 (1:1000), or p-P38 (1:1000). The membranes were washed with TBST three times and then incubated for 1 hour at RT with horseradish-peroxidase–conjugated goat anti-rabbit IgG (1:2000 dilution). After the membranes were washed four times, the signals were detected with an enhanced chemiluminescence reagent (ECL; Pierce Biotechnology). Data were analyzed using gel analysis software (Un-scan-it; Silk Scientific, Orem, UT). 
Cell-Viability Staining.
To determine whether cell viability was affected by hyperosmolar stress under these conditions, we stressed the cells with the highest level of hyperosmolarity and longest time used in this experiment (1200 mOsM/kg hyperosmolar DMEM/F12 for 30 seconds or 700 mOsM/kg hyperosmolar DMEM/F12 for 30 minutes) and then washed the cells with DMEM/F12 three times. Each control or experimental culture was triplicated in a 96-well plate. 
Cell cultures then underwent live/dead staining with a calcein and ethidium homodimer live/dead viability/cytotoxicity kit (Molecular Probes, Eugene, OR) according to the manufacturer’s instructions. The percentages of live and dead cells were calculated according to the green and red fluorescence intensity in each cell culture using a microplate reader (Fluorostar Galaxy; BMG Labtechnology, Inc., Durham, NC). 
Results
Experiment 1: Sensory Response to TBU and Hyperosmolar Solutions
The average age of the five subjects was 31.4 ± 11.9 years (range, 21–52), and two subjects were men. According to the DEQ, the subjects reported a range of relatively mild dry eye symptoms, from none to rare or infrequent symptoms of discomfort, dryness, grittiness, tired eyes, burning, and grittiness. Only one male subject had been diagnosed with mild dry eye, but none was using drops for dry eye. The Schirmer I test results (without anesthetic) in all five subjects averaged 17 ± 3 mm (range, 14–22) and TBUT averaged 11 ± 10 seconds (range, 4–25 seconds). 
Sensory Response to TBU.
All subjects showed areas of TBU or tear thinning at the end of each S-TBUD trial, but the AB and MBI varied greatly among subjects. Table 1shows average results from the three trials of each subject. Three subjects (3, 4, and 5) showed relatively rapid TBU in a short period (high DAGR) that approached dry eye subjects in a previous study. 19 The other two subjects were able to keep their eyes open longer and showed slow thinning of the tear film. 
TBU and sensation levels reported from individual trials of two subjects are shown in Figure 1 . Figure 1ashows the final fluorescein image, just before the blink, from trial 3 of subject 4. Figure 1bshows the DAGR graph for the trial, with associated sensations in Figure 1c . This subject, who reported mild to moderate dry eye symptoms on the DEQ and was diagnosed with dry eye, indicated high levels of discomfort, irritation, burning, and stinging, with lower levels of pricking and cooling during the trial. Figure 1dshows a similar data set from a subject with more stable tear film, longer MBI, and less TBU. The final fluorescein image showed slow evaporation of the tear film, especially inferiorly, within which there was a small area of actual break-up. This subject graded overall discomfort lower than the other subject, along with lower values for irritation, burning, stinging, and pricking. A cooling sensation was negligible in both subjects. 
Figure 2shows the aggregate sensation data for all subjects. As in Figure 1 , the 0 to 10 grades for overall discomfort and the continuous VAS scale marked from 0 to 10 (irritation, stinging, burning, pricking, and cooling) are plotted together with the same y-axis. Each data point represents an average of the three trials for each subject and the bar shows the mean. The grade of overall discomfort averaged at 6.1 ± 1.1 in all five subjects, with a range of 5.0 to 7.5. There was no significant difference between reported levels of irritation, stinging, burning, and pricking, but cooling was significantly less than the others (ANOVA with post hoc, P < 0.05). 
Sensory Response to Hyperosmolar Solutions.
Figures 3a and 3bshow the individual psychometric functions in all five subjects and from the 2AFC hyperosmolarity detection task. The average detection threshold for sucrose was 460 ± 16 mOsM/kg (range, 442–476 mOsM/kg), which was slightly higher than the NaCl threshold of 454 ± 14 mOsM/kg (range, 438–474 mOsM/kg). The difference between the thresholds was not significant (P = 0.12, paired t-test). 
Average overall discomfort scores associated with different levels of suprathreshold sucrose and NaCl hyperosmolar solutions are shown in Figure 4 . The average grade of overall discomfort increased monotonically as the osmolarity stimulus increased, reaching significance at 600 mOsM/kg for sucrose and 500 mOsM/kg for NaCl (ANOVA with post hoc, P < 0.05). Generally, for the same osmolarity, subjects reported a slightly higher overall discomfort with NaCl than with sucrose, but the difference was not statistically significant (P = 0.066, repeated-measures ANOVA). Best fit power curves for discomfort data yielded similar exponents (α) for NaCl and sucrose (0.8857 and 0.8848, respectively). Values for the scalar constant (κ) were also similar between the two solutions (0.025 and 0.021, respectively). Within the ranges tested, the responses to increasingly hyperosmolar sucrose solutions showed an almost linear relationship to dosage, whereas responses to NaCl appeared to begin to level off at approximately 900 mOsM/kg. 
Figure 5shows the VAS scores of irritation, burning, stinging, pricking, and cooling sensations for NaCl (Fig. 5a)and sucrose (Fig. 5b)hyperosmolar solutions. Each data point represents the average response from all five subjects for each sensation, and aggregate data were fitted with power functions. 29 Power-fitting formulas for each sensation and best fit correlations are listed in Table 2 . Exponents of power fitting ranged from 0.9514 to 1.0160 for NaCl and 0.9184 to 1.4000 for sucrose, reflecting the almost linear relation between the stimulus and reported sensation within the range tested. Correlations between the stimulus and VAS sensation were very high and were statistically significant (P < 0.0001, ANOVA). As Figure 5shows, three of the response curves (irritation, burning and stinging) were so similar that they overlapped each other for both NaCl and sucrose. Pricking was reported at slightly lower levels, and cooling was reported least. 
Estimation of the Level of Hyperosmolarity during Tear Instability.
The overall purpose of the first experiment in the study was to estimate the levels of hyperosmolarity that may occur during tear instability by making comparisons between discomfort experienced during S-TBUD trials and exposure to hyperosmolar solutions. Figure 4shows that the average grade of discomfort during the S-TBUD testing was 6.1, which was also generated by an osmolarity of 809 mOsM/kg for NaCl and 914 mOsM/kg for sucrose. The full range of discomfort scores for all trials of S-TBUD testing was 5.0 to 7.5, which corresponds to an estimated range of 696 to 972 mOsM/kg of hyperosmolarity due to NaCl and 785 to 1125 mOsM/kg for sucrose. Table 2lists similar TBU discomfort comparisons for each individual sensation on VAS scales. 
Experiment 2: Epithelial Response to Hyperosmolar Solutions
Time Course Experiments.
Figure 6shows a representative blot of the time course of MAPK activation by 700 mOsM/kg sucrose (Fig. 6a)and NaCl (Fig. 6b)hyperosmolar conditions, with the ratios of p-MAPK/MAPK graphed at the bottom of the figure. The sucrose hyperosmolar stress activated both JNK2 and p38 phosphorylation after as little as 10 seconds of exposure, and NaCl after 30 seconds of exposure. The phosphorylation level increased as the exposure time increased. JNK1 showed a time-dependent phosphorylation increase, but there was no difference between control and short-term exposure. There was no significant change observed in ERK. 
Level of Osmolarity Experiments.
Figure 7shows a representative result of MAPK activation after 30 seconds’ exposure to varying hyperosmolar solutions of sucrose (Fig. 7a)or NaCl (Fig. 7b)with the ratios of p-MAPK/MAPK graphed at the bottom of the figure. The same experiments were repeated three times with similar results. Phosphorylation of p38 occurred at 500 to 600 mOsM/kg and at 700 mOsM/kg for JNK2. The level of phosphorylation did not increase with further increases in osmolarity. No changes in pERK were detected. 
Cell Viability Staining.
Figure 8shows the percentage of live and dead cells from control and treated cultures. None of the cells treated with hyperosmolar solutions showed a significant increase in the percentage of dead cells compared with live controls. 
Discussion
We used a novel combination of very different techniques, ranging from psychophysics to cell biology, to establish a causal connection between tear instability and hyperosmolarity, considered fundamental causes of the dry eye condition. 6 To achieve this goal, our unique study design measured the responses of the two main corneal cell types affected by changing tear osmolarity, epithelial cells, and underlying sensory neurons. Taken together, the results of this study imply that tear film osmolarity is likely to spike transiently during periods of tear instability, thus stimulating corneal nerves and the ocular surface epithelium and resulting in sensations of discomfort and proinflammatory signaling. 
Corneal nerves are theoretically able to sense three basic types of stimuli: mechanical, chemical, and temperature. These stimuli are qualitatively described as producing sharp pain, irritation, burning, stinging, warming, and cooling. 30 31 In this and previous studies in our laboratory, subjects chose high levels of burning and stinging to describe sensations associated with TBU and thinning during S-TBUD trials, 19 21 which suggests a chemical stimulus 31 32 during tear instability. Although hyperosmolarity is the most likely candidate, 6 7 8 increases in tear pH due to decreases in [CO2] during eye opening 33 could provide another chemical stimulus. The major stabilizer of tear film pH is the bicarbonate buffer system, which exists as a gradient of CO2 levels from the anterior chamber to 0 in air. Thus, rapid changes in tear film thickness during tear instability would not be expected to markedly influence tear film pH, although some tear film proteins may also contribute to pH. 34 The sensation of irritation is less specific to stimulus type and could be associated with a mechanical, chemical, or high-temperature stimulus. 23 A cooling sensation was reported by some subjects and may occur when evaporation associated with tear thinning leads to stimulation of cold receptors. 31 35  
Thus, these results strongly suggest that transient increases in tear film hyperosmolarity during tear instability caused the sensations noted by subjects during the S-TBUD trials. Even though sucrose is physiologically unrealistic, we included it in the investigation to serve as a control for the effect of hyperosmolarity. The absence of significant differences between NaCl and sucrose solutions suggests that the sensory response to these solutions is due to hyperosmolarity, rather than to the chemical effect of Na+ or Cl ions. However, suprathreshold responses to NaCl began to level off at 800 mOsM/kg, which may indicate saturation produced by Na+ ions interacting with nerve terminals. 36 If we had expanded our range of testing above 1000 mOsM/kg, it is possible that a marked saturation effect would have emerged. 
Threshold levels for detection of hyperosmolar solutions in this experiment, approximately 450 mOsM/kg, were well above the highest levels measured from the lower meniscus, reportedly 360 mOsM/kg. 12 Thus, the symptom of burning, often reported by patients with dry eye, 22 may be caused by levels of hyperosmolarity substantially above threshold in the dry eye tear film. In addition, the tear film osmolarity over the corneal surface is likely to be grossly underestimated by measurement from the lower meniscus, as this fluid is a mix of newly secreted tears and older tears wiped from the ocular surface by the upper lid during the blink. 15  
The psychophysics portion of this experiment was based on the concept that corneal nerves are able to sense changes in osmolarity in the corneal compartment of the tear film. Indeed, the range of detection thresholds among subjects was surprisingly small, considering the differences in age and sex among subjects, suggesting that thresholds were highly characteristic of the human cornea. 
Our results from psychophysical experiments suggest that corneal sensory neurons respond to increased tear film hyperosmolarity, ranging upward from thresholds near 450 mOsM/kg. Previous studies have demonstrated that corneal epithelial cells respond to these levels of hyperosmolarity with inflammation and apoptosis. 13 14 In this experiment, we showed that exposure times as brief as 10 to 30 seconds of 700 mOsM/kg NaCl were adequate to activate the MAPK pathway, specifically JNK and p-38. ERK was not activated in our experiments, but less robust ERK expression with hyperosmolar stress has also been found in other cell types. 37 Thus, our results provide strong support for the hypothesis that the corneal epithelium reacts to very short-term hyperosmolar stress that may occur within areas of TBU or thinning. Although we did not measure resultant cytokine release or apoptosis, others have shown that these downstream events are likely with hyperosmolar activation of the MAPK pathway in corneal epithelium. 13 14 We did not test for apoptosis in this study, and so cell cultures that appeared viable by live/dead assay staining may have included apoptotic cells. 
We used an unusual study design, combining very different psychophysical and cell biology techniques to test our hypothesis concerning the effects of fluctuations of hyperosmolarity on the corneal surface. Our data demonstrate surprising agreement between the two cell types likely to be affected by these fluctuations: corneal epithelial cells and sensory neurons. Both cell types responded at approximately 600 to 700 mOsM/kg, neurons with a pain response and epithelial cells with a proinflammatory signal. Because the purpose of corneal neurons is to protect the epithelial tissue from damage or injury, these results suggest that hyperosmolar stress at that level is potentially injurious to the epithelium and thus is protected by the pain response. The common symptom of burning and stinging among patients with dry eye 38 also implies that tear film fluctuations over 450 mOsM/kg commonly occur. 
Events within areas of TBU and thinning over the corneal surface are unknown. Within areas of tear thinning, it is often assumed that tear film hyperosmolarity increases, 6 7 but TBU remains a poorly understood phenomenon. Most agree that the aqueous component of the tear film is absent within areas of break-up, 39 40 leaving the underlying bound mucin layer exposed. However, the mucin layer is highly hydrated and should be isosmotic with the tear film and cornea. It is possible that the retreating aqueous layer and subsequent exposure of the bound mucin layer during TBU also leads to local hyperosmotic conditions. We plan to study this phenomenon further in future studies by real-time tracking of corneal sensations and the emergence of TBU or thinning. 
Our results suggest that the ocular surface may frequently be exposed to hyperosmolar conditions when local tear film thinning or break-up occur. Blinking and reflex secretion of tears 41 42 43 are natural processes that should tend to mitigate prolonged local hyperosmotic conditions. The ocular surface is a mucous membrane that requires proper wetting for good vision and cellular function, 44 thus protective signaling of stress and damage is critical. Fluctuating hyperosmolarity may provide this signal, most likely triggering a blink, which should act to rewet the surface and restore isosmotic conditions. 6  
Tear deficiency 6 or slowing of the blink during a concentrating task 45 46 may result in local or global spikes in hyperosmolarity of the tear film, which stress the corneal epithelium and underlying nerves. The resultant inflammation and irritation of underlying nociceptors may account for the symptoms of ocular irritation noted among patients with dry eye. 47 Our results also suggest that, while transient spikes in hyperosmolarity are stressful to corneal surface cells, the outcome may not necessarily be cellular death. This may provide one explanation for the often cited poor correlation between dry eye symptoms and clinically demonstrable cellular tissue damage. 48 49  
 
Table 1.
 
Dry Eye Symptoms Measured in Each Subject
Table 1.
 
Dry Eye Symptoms Measured in Each Subject
Subject
1 2 3 4 5
AB, % 8.11 ± 6.08 0.73 ± 0.35 28.62 ± 16.31 9.03 ± 3.89 19.89 ± 5.30
MBI, s 90.22 ± 18.05 34.55 ± 10.71 14.46 ± 4.72 10.81 ± 10.64 13.11 ± 2.65
AB/MBI (DAGR) 0.0010 ± 0.0007 0.0002 ± 0.0001 0.0190 ± 0.0059 0.0153 ± 0.0116 0.0152 ± 0.0028
TBUT, s 25.00 ± 21.79 18.33 ± 6.66 4.33 ± 0.58 4.00 ± 0.00 4.17 ± 0.76
Figure 1.
 
Example S-TBUD trials from two different subjects. The final fluorescein image just before the blink with the MBI in the bottom right corner (a, d), the percentage area of break-up (AB) versus time (DAGR) (b, e), and the sensations reported by subjects in the trial (c, f).
Figure 1.
 
Example S-TBUD trials from two different subjects. The final fluorescein image just before the blink with the MBI in the bottom right corner (a, d), the percentage area of break-up (AB) versus time (DAGR) (b, e), and the sensations reported by subjects in the trial (c, f).
Figure 2.
 
Sensations reported by each subject during S-TBUD trials (average of three trials). Black bar: mean of all five subjects.
Figure 2.
 
Sensations reported by each subject during S-TBUD trials (average of three trials). Black bar: mean of all five subjects.
Figure 3.
 
Detection threshold for NaCl (a) and sucrose (b). Each curve represents a Weibull fitting of one individual subject’s data. Dashed lines: the average threshold (75% correct).
Figure 3.
 
Detection threshold for NaCl (a) and sucrose (b). Each curve represents a Weibull fitting of one individual subject’s data. Dashed lines: the average threshold (75% correct).
Figure 4.
 
Overall discomfort grade for suprathreshold NaCl and sucrose hyperosmolar solutions. Dashed lines: the osmolarity corresponding to TBU.
Figure 4.
 
Overall discomfort grade for suprathreshold NaCl and sucrose hyperosmolar solutions. Dashed lines: the osmolarity corresponding to TBU.
Figure 5.
 
Average VAS score for the five suprathreshold sensations of NaCl (a) and sucrose (b) in all subjects. Error bars, SD.
Figure 5.
 
Average VAS score for the five suprathreshold sensations of NaCl (a) and sucrose (b) in all subjects. Error bars, SD.
Table 2.
 
The Power-Fitting Formulas, Correlation, and Corresponding TBU Discomfort Comparison Osmolarities for Dry Eye Sensations
Table 2.
 
The Power-Fitting Formulas, Correlation, and Corresponding TBU Discomfort Comparison Osmolarities for Dry Eye Sensations
NaCl Sucrose
Power-Fitting Formula r TBU Comparison (mOsM/kg) Power-Fitting Formula r TBU Comparison (mOsM/kg)
Irritation y = 0.01345*x 0.9745 0.984 775 (670–966) y = 0.01577*x 0.9184 0.99 882 (747–1133)
Stinging y = 0.01154*x 0.9940 0.980 809 (559–989) y = 0.00878*x 1.0030 0.98 931 (624–1054)
Burning y = 0.01499*x 0.9514 0.964 753 (612–1009) y = 0.00748*x 1.0310 0.99 855 (693–1138)
Pricking y = 0.00725*x 1.0160 0.968 854 (578–1261) y = 0.00222*x 1.1790 0.99 931 (638–1315)
Cooling y = 0.00430*x 0.9864 0.938 810 (357–1519) y = 0.00018*x 1.4000 0.99 1080 (466–1742)
Figure 6.
 
Western blot analysis of MAPK phosphorylation after exposure to 700 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress for 10 and 30 seconds and 2, 5, 10, 15, and 30 minutes. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2.
Figure 6.
 
Western blot analysis of MAPK phosphorylation after exposure to 700 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress for 10 and 30 seconds and 2, 5, 10, 15, and 30 minutes. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2.
Figure 7.
 
Western blot analysis of MAPK phosphorylation after 30 seconds’ exposure to 300, 400, 500, 600, 700, 800, 1000, and 1200 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2
Figure 7.
 
Western blot analysis of MAPK phosphorylation after 30 seconds’ exposure to 300, 400, 500, 600, 700, 800, 1000, and 1200 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2
Figure 8.
 
Cell viability after 700 mOsM/kg exposure for 30 minutes or 1200 mOsM/kg exposure for 30 seconds. The percentage of live and dead cells was calculated based on the fluorescein intensity of calcein and EthD-1.
Figure 8.
 
Cell viability after 700 mOsM/kg exposure for 30 minutes or 1200 mOsM/kg exposure for 30 seconds. The percentage of live and dead cells was calculated based on the fluorescein intensity of calcein and EthD-1.
SchaumbergDA, SullivanDA, BuringJE, DanaMR. Prevalence of dry eye syndrome among US women. Am J Ophthalmol. 2003;136:318–326. [CrossRef] [PubMed]
MossSE, KleinR, KleinBE. Prevalence of and risk factors for dry eye syndrome. Arch Ophthalmol. 2000;118:1264–1268. [CrossRef] [PubMed]
ChiaEM, MitchellP, RochtchinaE, LeeAJ, MarounR, WangJJ. Prevalence and associations of dry eye syndrome in an older population: the Blue Mountains Eye Study. Clin Exp Ophthalmol. 2003;31:229–232. [CrossRef]
BegleyCG, ChalmersRL, MitchellGL, et al. Characterization of ocular surface symptoms from optometric practices in North America. Cornea. 2001;20:610–618. [CrossRef] [PubMed]
ScheinOD, TielschJM, MunozB, Bandeen-RocheK, WestS. Relation between signs and symptoms of dry eye in the elderly: a population-based perspective. Ophthalmology. 1997;104:1395–1401. [CrossRef] [PubMed]
LempMA, BaudouinC, BaumJ, et al. The definition and classification of dry eye disease: Report of the Definition and Classification Subcommittee of the International Dry Eye WorkShop (2007). Ocul Surf. 2007;5:75–92. [CrossRef] [PubMed]
FoulksGN. The correlation between the tear film lipid layer and dry eye disease. Surv Ophthalmol. 2007;52:369–374. [CrossRef] [PubMed]
BaudouinC. A new approach for better comprehension of diseases of the ocular surface (in French). J Fr Ophtalmol. 2007;30:239–246. [CrossRef] [PubMed]
GilbardJP, FarrisRL, SantamariaJ, 2nd. Osmolarity of tear microvolumes in keratoconjunctivitis sicca. Arch Ophthalmol. 1978;96:677–681. [CrossRef] [PubMed]
NelsonJD, WrightJC. Tear film osmolality determination: an evaluation of potential errors in measurement. Curr Eye Res. 1986;5:677–681. [CrossRef] [PubMed]
TomlinsonA, KhanalS, RamaeshK, DiaperC, McFadyenA. Tear film osmolarity: determination of a referent for dry eye diagnosis. Invest Ophthalmol Vis Sci. 2006;47:4309–4315. [CrossRef] [PubMed]
GilbardJP, FarrisRL. Tear osmolarity and ocular surface disease in keratoconjunctivitis sicca. Arch Ophthalmol. 1979;97:1642–1646. [CrossRef] [PubMed]
LuoL, LiDQ, PflugfelderSC. Hyperosmolarity-induced apoptosis in human corneal epithelial cells is mediated by cytochrome c and MAPK pathways. Cornea. 2007;26:452–460. [CrossRef] [PubMed]
LiDQ, LuoL, ChenZ, KimHS, SongXJ, PflugfelderSC. JNK and ERK MAP kinases mediate induction of IL-1beta, TNF-alpha and IL-8 following hyperosmolar stress in human limbal epithelial cells. Exp Eye Res. 2006;82:588–596. [CrossRef] [PubMed]
BronAJ, TiffanyJM, YokoiN, GouveiaSM. Using osmolarity to diagnose dry eye: a compartmental hypothesis and review of our assumptions. Adv Exp Med Biol. 2002;506:1087–1095. [PubMed]
MillerKL, PolseKA, RadkeCJ. Black-line formation and the “perched” human tear film. Curr Eye Res. 2002;25:155–162. [CrossRef] [PubMed]
NicholsJJ, MitchellGL, King-SmithPE. Thinning rate of the precorneal and prelens tear films. Invest Ophthalmol Vis Sci. 2005;46:2353–2361. [CrossRef] [PubMed]
CraigJP, TomlinsonA. Importance of the lipid layer in human tear film stability and evaporation. Optom Vis Sci. 1997;74:8–13. [CrossRef] [PubMed]
LiuH, BegleyCG, ChalmersR, WilsonG, SrinivasSP, WilkinsonJA. Temporal progression and spatial repeatability of tear break-up. Optom Vis Sci. 2006;83:723–730. [CrossRef] [PubMed]
HimebaughN, BegleyC, BradleyA, WilkinsonJ. Blinking and tear break-up during four visual tasks. Optom Vis Sci. .Published online January 19, 2009.
BegleyCG, HimebaughN, RennerD, et al. Tear break-up dynamics: a technique for quantifying tear film instability. Optom Vis Sci. 2006;83:15–21. [CrossRef] [PubMed]
BegleyCG, CafferyB, ChalmersRL, MitchellGL. Use of the dry eye questionnaire to measure symptoms of ocular irritation in patients with aqueous tear deficient dry eye. Cornea. 2002;21:664–670. [CrossRef] [PubMed]
AcostaMC, BelmonteC, GallarJ. Sensory experiences in humans and single-unit activity in cats evoked by polymodal stimulation of the cornea. J Physiol. 2001;534:511–525. [CrossRef] [PubMed]
LevinMH, KimJK, HuJ, VerkmanAS. Potential difference measurements of ocular surface Na+ absorption analyzed using an electrokinetic model. Invest Ophthalmol Vis Sci. 2006;47:306–316. [CrossRef] [PubMed]
SteenKH, WegnerH, ReehPW. The pH response of rat cutaneous nociceptors correlates with extracellular [Na+] and is increased under amiloride. Eur J Neurosci. 1999;11:2783–2792. [CrossRef] [PubMed]
QuickRF, Jr. A vector-magnitude model of contrast detection. Kybernetik. 1974;16:65–67. [CrossRef] [PubMed]
WichmannFA, HillNJ. The psychometric function: I. fitting, sampling, and goodness of fit. Percept Psychophys. 2001;63:1293–1313. [CrossRef] [PubMed]
SwansonWH, BirchEE. Extracting thresholds from noisy psychophysical data. Percept Psychophys. 1992;51:409–422. [CrossRef] [PubMed]
StevensSS. Neural events and the psychophysical law. Science. 1970;170:1043–1050. [CrossRef] [PubMed]
BelmonteC, Garcia-HirschfeldJ, GallarJ. Neurobiology of ocular pain. Prog Retin Eye Res. 1997;16:117–156. [CrossRef]
AcostaMC, TanME, BelmonteC, GallarJ. Sensations evoked by selective mechanical, chemical, and thermal stimulation of the conjunctiva and cornea. Invest Ophthalmol Vis Sci. 2001;42:2063–2067. [PubMed]
FengY, SimpsonTL. Nociceptive sensation and sensitivity evoked from human cornea and conjunctiva stimulated by CO2. Invest Ophthalmol Vis Sci. 2003;44:529–532. [CrossRef] [PubMed]
FischerFH, WiederholtM. Human precorneal tear film pH measured by microelectrodes. Graefes Arch Clin Exp Ophthalmol. 1982;218:168–170. [CrossRef] [PubMed]
ColesWH, JarosPA. Dynamics of ocular surface pH. Br J Ophthalmol. 1984;68:549–552. [CrossRef] [PubMed]
CraigJP, SinghI, TomlinsonA, MorganPB, EfronN. The role of tear physiology in ocular surface temperature. Eye. 2000;14:635–641. [CrossRef] [PubMed]
NikodemovaM, GreerMA, StrbakV. Hypo-osmolarity stimulates and high sodium concentration inhibits thyrotropin-releasing hormone secretion from rat hypothalamus. Neuroscience. 1999;88:1299–1306. [CrossRef] [PubMed]
DuzgunSA, RasqueH, KitoH, et al. Mitogen-activated protein phosphorylation in endothelial cells exposed to hyperosmolar conditions. J Cell Biochem. 2000;76:567–571. [CrossRef] [PubMed]
BegleyCG, ChalmersRL, AbetzL, et al. The relationship between habitual patient-reported symptoms and clinical signs among patients with dry eye of varying severity. Invest Ophthalmol Vis Sci. 2003;44:4753–4761. [CrossRef] [PubMed]
FattI. Observations of tear film break up on model eyes. CLAO J. 1991;17:267–281. [PubMed]
HollyFJ. Formation and stability of the tear film. Int Ophthalmol Clin. 1973;13:73–96. [CrossRef] [PubMed]
LavezzoMM, SchelliniSA, PadovaniCR, HiraiFE. Eye blink in newborn and preschool-age children. Acta Ophthalmol. 2008;86:275–278. [CrossRef] [PubMed]
LawrensonJG, BirhahR, MurphyPJ. Tear-film lipid layer morphology and corneal sensation in the development of blinking in neonates and infants. J Anat. 2005;206:265–270. [CrossRef] [PubMed]
HarrisonWW, BegleyCG, LiuH, ChenM, GarciaM, SmithJA. Menisci and fullness of the blink in dry eye. Optom Vis Sci. 2008;85:706–714. [CrossRef] [PubMed]
TiffanyJM. The normal tear film. Dev Ophthalmol. 2008;41:1–20. [PubMed]
AcostaMC, GallarJ, BelmonteC. The influence of eye solutions on blinking and ocular comfort at rest and during work at video display terminals. Exp Eye Res. 1999;68:663–669. [CrossRef] [PubMed]
NakamoriK, OdawaraM, NakajimaT, MizutaniT, TsubotaK. Blinking is controlled primarily by ocular surface conditions. Am J Ophthalmol. 1997;124:24–30. [CrossRef] [PubMed]
BelmonteC, AcostaMC, GallarJ. Neural basis of sensation in intact and injured corneas. Exp Eye Res. 2004;78:513–525. [CrossRef] [PubMed]
NicholsKK, NicholsJJ, MphM, MitchellGL. The lack of association between signs and symptoms in patients with dry eye disease. Cornea. 2004;23:762–770. [CrossRef] [PubMed]
SmithJA, AlbeitzJ, BegleyC, et al. The epidemiology of dry eye disease: Report of the Epidemiology Subcommittee of the International Dry Eye WorkShop (2007). Ocul Surf. 2007;5:93–107. [CrossRef] [PubMed]
Figure 1.
 
Example S-TBUD trials from two different subjects. The final fluorescein image just before the blink with the MBI in the bottom right corner (a, d), the percentage area of break-up (AB) versus time (DAGR) (b, e), and the sensations reported by subjects in the trial (c, f).
Figure 1.
 
Example S-TBUD trials from two different subjects. The final fluorescein image just before the blink with the MBI in the bottom right corner (a, d), the percentage area of break-up (AB) versus time (DAGR) (b, e), and the sensations reported by subjects in the trial (c, f).
Figure 2.
 
Sensations reported by each subject during S-TBUD trials (average of three trials). Black bar: mean of all five subjects.
Figure 2.
 
Sensations reported by each subject during S-TBUD trials (average of three trials). Black bar: mean of all five subjects.
Figure 3.
 
Detection threshold for NaCl (a) and sucrose (b). Each curve represents a Weibull fitting of one individual subject’s data. Dashed lines: the average threshold (75% correct).
Figure 3.
 
Detection threshold for NaCl (a) and sucrose (b). Each curve represents a Weibull fitting of one individual subject’s data. Dashed lines: the average threshold (75% correct).
Figure 4.
 
Overall discomfort grade for suprathreshold NaCl and sucrose hyperosmolar solutions. Dashed lines: the osmolarity corresponding to TBU.
Figure 4.
 
Overall discomfort grade for suprathreshold NaCl and sucrose hyperosmolar solutions. Dashed lines: the osmolarity corresponding to TBU.
Figure 5.
 
Average VAS score for the five suprathreshold sensations of NaCl (a) and sucrose (b) in all subjects. Error bars, SD.
Figure 5.
 
Average VAS score for the five suprathreshold sensations of NaCl (a) and sucrose (b) in all subjects. Error bars, SD.
Figure 6.
 
Western blot analysis of MAPK phosphorylation after exposure to 700 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress for 10 and 30 seconds and 2, 5, 10, 15, and 30 minutes. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2.
Figure 6.
 
Western blot analysis of MAPK phosphorylation after exposure to 700 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress for 10 and 30 seconds and 2, 5, 10, 15, and 30 minutes. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2.
Figure 7.
 
Western blot analysis of MAPK phosphorylation after 30 seconds’ exposure to 300, 400, 500, 600, 700, 800, 1000, and 1200 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2
Figure 7.
 
Western blot analysis of MAPK phosphorylation after 30 seconds’ exposure to 300, 400, 500, 600, 700, 800, 1000, and 1200 mOsM/kg sucrose (left) and NaCl (right) hyperosmotic stress. Data are the ratio of phosphorylated MAPK to total MAPK for JNK, p38, and ERK-1 and -2
Figure 8.
 
Cell viability after 700 mOsM/kg exposure for 30 minutes or 1200 mOsM/kg exposure for 30 seconds. The percentage of live and dead cells was calculated based on the fluorescein intensity of calcein and EthD-1.
Figure 8.
 
Cell viability after 700 mOsM/kg exposure for 30 minutes or 1200 mOsM/kg exposure for 30 seconds. The percentage of live and dead cells was calculated based on the fluorescein intensity of calcein and EthD-1.
Table 1.
 
Dry Eye Symptoms Measured in Each Subject
Table 1.
 
Dry Eye Symptoms Measured in Each Subject
Subject
1 2 3 4 5
AB, % 8.11 ± 6.08 0.73 ± 0.35 28.62 ± 16.31 9.03 ± 3.89 19.89 ± 5.30
MBI, s 90.22 ± 18.05 34.55 ± 10.71 14.46 ± 4.72 10.81 ± 10.64 13.11 ± 2.65
AB/MBI (DAGR) 0.0010 ± 0.0007 0.0002 ± 0.0001 0.0190 ± 0.0059 0.0153 ± 0.0116 0.0152 ± 0.0028
TBUT, s 25.00 ± 21.79 18.33 ± 6.66 4.33 ± 0.58 4.00 ± 0.00 4.17 ± 0.76
Table 2.
 
The Power-Fitting Formulas, Correlation, and Corresponding TBU Discomfort Comparison Osmolarities for Dry Eye Sensations
Table 2.
 
The Power-Fitting Formulas, Correlation, and Corresponding TBU Discomfort Comparison Osmolarities for Dry Eye Sensations
NaCl Sucrose
Power-Fitting Formula r TBU Comparison (mOsM/kg) Power-Fitting Formula r TBU Comparison (mOsM/kg)
Irritation y = 0.01345*x 0.9745 0.984 775 (670–966) y = 0.01577*x 0.9184 0.99 882 (747–1133)
Stinging y = 0.01154*x 0.9940 0.980 809 (559–989) y = 0.00878*x 1.0030 0.98 931 (624–1054)
Burning y = 0.01499*x 0.9514 0.964 753 (612–1009) y = 0.00748*x 1.0310 0.99 855 (693–1138)
Pricking y = 0.00725*x 1.0160 0.968 854 (578–1261) y = 0.00222*x 1.1790 0.99 931 (638–1315)
Cooling y = 0.00430*x 0.9864 0.938 810 (357–1519) y = 0.00018*x 1.4000 0.99 1080 (466–1742)
×
×

This PDF is available to Subscribers Only

Sign in or purchase a subscription to access this content. ×

You must be signed into an individual account to use this feature.

×