July 2005
Volume 46, Issue 7
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Cornea  |   July 2005
Thinning Rate of the Precorneal and Prelens Tear Films
Author Affiliations
  • Jason J. Nichols
    From The College of Optometry, Ohio State University, Columbus, Ohio.
  • G. Lynn Mitchell
    From The College of Optometry, Ohio State University, Columbus, Ohio.
  • P. Ewen King-Smith
    From The College of Optometry, Ohio State University, Columbus, Ohio.
Investigative Ophthalmology & Visual Science July 2005, Vol.46, 2353-2361. doi:10.1167/iovs.05-0094
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      Jason J. Nichols, G. Lynn Mitchell, P. Ewen King-Smith; Thinning Rate of the Precorneal and Prelens Tear Films. Invest. Ophthalmol. Vis. Sci. 2005;46(7):2353-2361. doi: 10.1167/iovs.05-0094.

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      © 2016 Association for Research in Vision and Ophthalmology.

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Abstract

purpose. To apply interferometry as an in vivo measure of tear film thinning between blinks.

methods. Wavelength-dependent interference was used to measure the tear film thinning rates in 20 normal contact lens wearers, and spectra were captured at a rate of 4.5 per second for 20 seconds. Four recordings of precorneal tear film (PCTF) thinning were made, followed by 1 hour of hydrogel lens wear and then four recordings of prelens tear film (PLTF) thinning. Subjects were asked to blink 1 second after the beginning of the recording and then hold their eyes open for an additional 19 seconds, followed by 2 minutes of rest between recordings.

results. The average thinning rate of the PLTF was greater than that of the PCTF and average initial tear film thickness of the PLTF was less than that of the PCTF. For both these reasons, the “tear thinning time” (time to reach 0 thickness) was typically shorter for the PLTF than for the PCTF. Histograms of PCTF and PLTF thinning rates showed a narrow peak corresponding to slow thinning of approximately 1 μm/min, but also many examples of rapid thinning of approximately 10 μm/min, with greater variability. Both the initial thickness and thinning rate of the PLTF correlated with corresponding values for the PCTF, although many more rapidly changing values were associated with the PLTF. Plots of rapid thinning of PCTF and PLTF were both linear and were not accompanied by any significant increase in thickness of corneal epithelium or contact lens, respectively.

conclusions. Tear film thinning can be analyzed in terms of flow in three spatial directions: (1) outward (evaporation), (2) inward (into the epithelium or contact lens), and (3) parallel to the tear film surface. The results indicate that the second mechanism may be unimportant. Studies have shown a range of tear film evaporation rates from 0.24 to 1.45 μm/min, whereas, when the lipid layer is washed away from the tear film, the thinning rate, due to evaporation, would be approximately 7μm/min. Thus, slow thinning rates may be due to tear film evaporation, whereas rapid rates (which are often greater than 7 μm/min) presumably include other mechanisms such as dewetting, Marangoni flow (i.e., surface tension gradients), and pressure–gradient flow.

Study of the thinning of the precorneal tear film (PCTF) or prelens tear film (PLTF) between blinks has the potential to elucidate many physiological and clinical aspects of the tear film. The mechanism of thinning of the tear film can be analyzed into three components, as shown in Figure 1for a vertical section of the cornea: (1) water passing outward into the surrounding air (i.e., evaporation); (2) water flowing across the inner surface of the tear film (i.e., in or out of the corneal epithelium or contact lens; the barrier function of the corneal epithelium and permeability of the contact lens, as well as any osmotic gradient between tear film and corneal epithelium, would be important factors in this flow); (3) thinning (or thickening) may be caused by flow of tears parallel to the surfaces of the tear film. For example, consider a small square area (e.g., 1 × 1 mm) of the tear film. If there is more outflow of tears along some edges of the square than there is inflow along the other edges (as indicated in Fig. 1 ), the tear film (on average) thins within that area. Thickness changes of this sort may be caused by gradients of surface tension in the tear film (Marangoni flow 1 ) or by curvature of the tear film surface (e.g., near a tear meniscus 2 ) which generates pressure-gradients in the tear film. 
A final result of tear film thinning—the sum of these three processes—can be tear film breakup and dry spot formation over either the cornea or contact lens. In the case of the cornea, time until breakup after a blink is an important clinical test of dry eye conditions. 3 4 In addition, this breakup may cause ocular surface damage 5 and therefore contribute to the etiology of dry eye. In the case of the contact lens, breakup may cause deposition of lipids and other tear components on the lens surface, hence affecting its wettability and comfort. 6  
Evaporation (or outward flow of the tear fluid) is probably the most recognized mechanism of tear film thinning, and investigators have reported tear film evaporation rates ranging from 0.24 to 1.45 μm/min. 7 8 9 10 11 However, if the PCTF thickness is approximately 3 μm and it thins at approximately 1 μm/min, it would take approximately 3 minutes for the PCTF to evaporate, causing a dry spot to form. This is approximately 5 to 15 times greater than estimates of noninvasive tear breakup time and dry spot formation reported in the literature. 12 13 14 15 16 17 Thus, although evaporation seems to be an important factor in tear film breakup, it is too slow to offer a complete explanation of tear film thinning. 
Benedetto et al. 18 used fluorescence to study changes in tear film thickness between blinks. They found that, over the superior cornea, the tear film thickened for about 1 second after a blink, whereas a corresponding thinning of the tear film was found over inferior cornea. When equilibrium thickness (fluorescence) was reached, the superior tear film was thicker than the inferior. These thickness changes were ascribed to the upward drift of the lipid layer of the tear film that occurs over a similar period after a blink. 1 19 It should be noted that in dry eye conditions, this upward drift can continue for many seconds, thus increasing the potential contribution of this drift to tear film breakup. 20 A limitation of the method of Benedetto et al. 18 is that it is insensitive to the first two mechanisms of thinning mentioned earlier. For example, evaporation of the tear film does not reduce the total amount of fluorescein in the tear film and so does not reduce fluorescence. Thus, there is a need for new noninvasive methods of studying tear thinning between blinks, particularly during the later interblink period after the initial upward drift of the tear film. 
Recent developments in methods of measuring tear film thickness should enable better measurements of tear film thinning between blinks. Methods of measuring the complete thickness of the PCTF and the PLTF have recently been reviewed. 21 Because invasive methods may alter the thickness of the tear film, the preferred methods are noninvasive and are generally based on optical interference principles (e.g., thickness-, angle- and wavelength-dependent fringes, reviewed by King-Smith et al. 22 ). The first interferometric measurements of the PLTF were made with thickness-dependent fringes. 23 24 25 However, this method is difficult to apply to measuring the complete thickness of the PCTF, because the corresponding interference fringes are weak and masked by the higher-contrast image from the superficial lipid layer. 26 Danjo et al. 27 was the first to apply another interferometric method, wavelength-dependent fringes (WDFs) or spectral oscillations to measuring the PCTF thickness. This method has the advantages of high resolution (permitting direct measurement of thin layers such as the PCTF and PLTF) and good signal-to-noise ratio and has been used in our laboratory for measuring PCTF and PLTF thickness, 28 29 30 as well as that of other layers, such as the epithelial and corneal layers, 28 and postlens tear film and contact lens thickness. 29 30 31 Recent measurements made with optical coherence tomography, although less precise and less direct than those made with WDFs, have been reasonably consistent with our reported measurements of PCTF and PLTF thickness of approximately 2 to 3 μm. 32 Based on these considerations, the present study of PCTF and PLTF thinning was based on the WDF method. The purpose of this report is to describe the thinning of both the PCTF and PLTF and the relation between these measures. 
Methods
Interferometry
The details of our interferometric methods, including the optical system and the validity and reliability of the technique, have been described in general and as they relate to measuring tear film thinning. 30 33 However, some general principles of our method of measuring the tear film are presented herein. In general, some wavelengths show reflections from the front and back surfaces of the tear film that are in phase, yielding a maximum of reflectance, whereas other wavelengths show reflections that are out of phase, yielding a minimum of reflectance. These maxima and minima alternate in the spectrum, giving rise to spectral oscillations. The thickness of any layer is given by the frequency of the corresponding oscillations on a plot of reflectance as a function of 2n/λ where n is the refractive index of tears and λ is wavelength in a vacuum. 28 Because the thickness of any layer is indicated by its frequency, the Fourier analysis of the reflectance spectrum shows corresponding peaks due to various layers. The reflectance spectrum (562–1030 nm) is recorded on a charge-coupled device (CCD) camera that samples the spectral image from a spectrograph. For these measures, spectra were captured at a rate of 4.5 per second for a period of 20 seconds (providing 90 spectra in total). The measurement area was nominally 33 × 35 μm (in practice, probably larger due to aberrations, defocus, and eye movements). PCTF thickness measurements were considered valid if the nominal reflectance from the cornea exceeded 0.5% (thus avoiding blinks), the contrast of spectral oscillations (at 800 nm) exceeded 0.2%, and the thickness exceeded 1 μm. PLTF thickness measurements were considered valid if the nominal reflectance exceeded 0.5%, the contrast of spectral oscillations exceeded 1%, and the thickness exceeded 0.5 μm. Epithelial and contact lens thicknesses were determined by methods described in previous studies. 28 30 The mean temperature and humidity were 26°C and 49%, respectively. Refractive indexes (at 589 nm) of the tears, epithelium, and contact lens were assumed to be 1.337, 1.401, and 1.405, respectively, and correction was made for dispersion. 30 34 35  
Clinical Study
All patients recruited for the study were required to review and sign informed consent documents, that had been approved by the Biomedical Institutional Review Board of The Ohio State University, according to the tenets of the Declaration of Helsinki. Twenty experienced contact-lens–wearing subjects (mean age, 31.8 ± 8.6, four men) participated in the study. Each subject was free of ocular disease (including dry eye), and each was a current contact lens wearer. Subjects were asked not to wear contact lenses on the day of the experiment and to report for testing wearing their spectacles. Subjects first completed four PCTF thinning measures, wherein they were asked to blink 1 second into the experiment, while the thinning measure continued for an additional 19 seconds. Between each thinning measure, subjects rested for a period of 2 minutes. All measures of tear film thinning were taken on the right eye. After completion of the PCTF thinning measures, subjects were asked to apply etafilcon A contact lenses to both eyes (Acuvue 1-Day, Vistakon; Johnson and Johnson, Jacksonville, FL; power, −0.50 D; base curve, 8.5 mm), which were worn for 1 hour to allow for lens settling. 29 Four measures to determine PLTF thinning were then taken in a manner identical to that described for the measures of PCTF thinning. After completion of this, the fit of the lenses was verified using standard clinical techniques, including the assessment of movement, centration, and coverage. 
Outcomes assessed from the interferometric spectra when measures were taken without a contact lens included PCTF thickness over time (i.e., the PCTF thinning rate) and epithelial thickness over time (i.e., epithelial thickness during tear film thinning). Outcomes assessed from the interferometric spectra when measures were taken with a contact lens on the eye included PLTF thickness over time (i.e., the PLTF thinning rate), and contact lens thickness over time. 
Analyses and Statistical Procedures
Regression lines were fitted to thickness-versus-time data starting 2 seconds after the blink for each recording, to determine PCTF and PLTF thinning rates (thus avoiding transients sometimes observed immediately after the blink—e.g., Fig. 3A ). Regression line fits were terminated either at the end of the 20-second recording, or when the thickness became too thin for valid measurements, or if and when a second blink occurred in the 20-second recording. Regression lines were considered valid if they could be fitted over a period of at least 1 second. For both PCTF and PLTF, probability density functions (PDFs) of rates of thickness change (see Fig. 9 ) were estimated by a maximum-likelihood method on computer (SigmaPlot; SPSS, Chicago, IL). 
Mixed modeling was used to test for differences in tear film thinning rates and initial thicknesses. Within-subject factors included layer (i.e., PCTF versus PLTF) and experimental trial (i.e., experimental trials 1 through 4). In general, mixed modeling regression is appropriate when there are repeated measurements obtained from the same subject. As opposed to repeated-measures analysis of variance, mixed modeling allows the user to specify forms of the variance–covariance matrix and, if desired, to treat factors in the model as random effects. The best fit of the variance–covariance matrix is determined by assessing Aikike’s information criterion (AIC), with smaller values indicating a better fit. For our purposes, we tested the three most frequently occurring matrix structures: compound unstructured, and autoregressive symmetries. As with other parametric modeling methods, there was an assumption of normally distributed residuals (errors), which was checked visually in all models. 
Results
Figure 2shows representative changes in PCTF thickness as a function of time after a blink. Figure 2Ashows relatively slow thinning—the slope of the regression line is −0.94 μm/min. Figure 2Bshows a considerably faster rate—a slope of −7.43 μm/min. Figure 2Cis unusual, in that thickening of the PCTF is observed—a slope of +3.13 μm/min. Only 6 of 80 recordings of the PCTF showed thickening, as in this example; four of these six occurred in one subject. All 80 recordings of the PCTF provided estimates of rates of thickness change, which are summarized in Table 1
Figure 3shows some corresponding results for the PLTF. Figure 3Ashows relatively slow thinning—a slope of −1.40 μm/min. Note the initial transient in tear film thickness, which is sometimes observed after a blink. For this reason, the first 2 seconds after a blink were excluded from the regression line fit. Figure 3Bshows more rapid thinning—a slope of −7.42 μm/min. Whereas the PLTF thickness was measurable up to ∼11.5 seconds, the regression line has been extrapolated to indicate that 0 thickness would be reached at a time of approximately 15 seconds (i.e., 14 seconds after the blink). Estimates of rates of thickness change were obtained in 76 of 80 recordings of the PLTF, which are summarized in Table 1
As shown in Table 1 , the mean (±SD) thinning rate of the PCTF was 3.79 ± 4.20 μm/min, whereas it was 6.79 ± 4.32 μm/min for the PLTF. Mixed modeling regression for thinning rate of the combined PCTF/PLTF data set showed a significant effect of layer (PCTF versus PLTF, F = 28.17, P < 0.0001) no significant effect of trial number (trials 1–4, F = 1.52, P = 0.22) and no significant interaction effect (layer × trial; F = 0.84, P = 0.48). Table 1also shows the mean (±SD) initial thickness of the PCTF was 3.98 ± 1.06 μm/min, whereas it was 2.54 ± 1.16 μm/min for the PLTF. The corresponding analysis for initial thickness (2 seconds after a blink) again showed a significant effect of layer (F = 60.89, P < 0.0001), a significant effect of trial number (F = 3.64, P = 0.03), but no significant interaction effect (F = 2.23, P = 0.12). Post hoc comparisons (Tukey method) between trials found a significant difference (P = 0.01) only between trials 1 and 4 of the PLTF (corresponding thicknesses, 2.21 and 2.87 μm). It is thus possible that initial thickness may have increased somewhat with trial number, perhaps due to some reflex tearing. 
The linearity of thinning is analyzed in Figure 4 . Figure 4Ashows thickness averaged at each time point for 15 PCTF recordings (in 10 subjects), with a thinning rate of more than 3 μm/min with measurements over the full 20-second period (0 on the time scale corresponds to 2 seconds after any of the blinks). Figure 4Bshows equivalent plots for an average of 10 PLTF recordings (in five subjects). In both cases, the linear regressions were good fits to the data. For both PCTF and PLTF, linear fits were slightly better than the fit based on an exponential decay. A second-order (quadratic) fit (not shown) was little better than a linear fit, deviating by only 0.03 μm at most over the measurement period of more than 16 seconds, for both PCTF and PLTF. 
In Figure 5 , the rate of thickness change is plotted as a function of initial thickness measured 2 seconds after the blink. Although there is an indication that the rate of PCTF thinning increased with increasing PCTF initial thickness, there was no significant correlation. 
It may be noted that many of the thinning rates were relatively slow and tightly clustered in a narrow range of approximately 0 to 2 μm/min (particularly for the PCTF, Fig. 5A ). The data showing more rapid thinning (greater than ∼2 μm/min) are more broadly distributed. This difference will be considered further later in the article (Fig. 9) . It may also be noted, from Figure 5A , that the thinning rate of the PCTF seemed more variable when the initial thickness was relatively large. This finding applies to both the individual data and subject averages. For example, in the 13 subjects with average initial thickness greater than 3.4 μm, the SD of the thinning rate was 4.64 μm/min, whereas in the 7 subjects with thickness less than 3.4 μm, the corresponding SD was 0.84 μm/min. This difference in SD between the two groups based on initial thickness is statistically significant (F = 30.6, P = 0.0002) and would still be significant after allowing for multiple possible comparisons (there are 19 distinct ways in which data for the 20 subjects could have been divided into “thick” and “thin” groups). However, this dependency of variance of thinning rate on initial thickness does not seem to apply to the PLTF (Fig. 5B)
If the initial tear film thickness is t (in micrometers), and the thinning rate is r (in micrometers/minute), then the tear film would theoretically thin to 0 thickness in t/r minutes; as the “initial thickness” is actually measured 2 seconds after the blink, 0 thickness would be reached in a tear thinning time of  
\[60t/r{+}2\]
seconds after the blink. (The thinning plot and extrapolated regression line of Fig. 3Billustrate this calculation). In Figure 6 , the tear thinning time is plotted as a function of initial thickness. As shown, in some cases, the tear thinning time was less than 15 seconds for the PCTF and <10 seconds of the PLTF. (Note that estimates of tear thinning time depend on linear extrapolation of fitted regression lines; thus, the shorter tear thinning times, which require less extrapolation, are probably more reliable than the longer times.) 
In Figure 7 , the average rate of PLTF thickness change for each subject is shown as a function of the corresponding PCTF rate. The thinning rate of the PLTF was faster than that of the PCTF in 18 of the 20 subjects. The PLTF thinning rate correlated significantly with that of the PCTF (n = 20, r 2 = 0.32, P = 0.009). 
Figure 8plots the average initial PLTF thickness (2 seconds after the blink) for each subject as a function of the corresponding PCTF thickness. The dashed line indicates equality of thickness. The PLTF is thinner than the PCTF in 19 of 20 subjects. The solid line is the regression line fit to the data. PLTF initial thickness correlated significantly with PCTF initial thickness (n = 20, r 2 = 0.50, P < 0.001). 
As noted earlier, the data in Figure 5indicate that thinning rates of both the PCTF and the PLTF are often in a rather narrow range of approximately 0 to 2 μm/min, with a considerably broader distribution of more rapid thinning rates. Figures 9A and 9Bshow histograms of thinning rates for the PCTF and PLTF, respectively. These histograms are obviously asymmetrical, with narrow peaks corresponding to slow thinning of approximately 1 μm/min but with many instances of much more rapid thinning. PDFs were fitted to these histograms by maximizing likelihood (L) defined by  
\[L{=}{{\prod}_{i{=}1}^{N}}\ p(r_{i}),\]
where r i is the rate of thickness change for the ith of N recordings (N = 80 for the PCTF, 76 of the PLTF), and p(r i) is the PDF equation to be fitted to the histogram. The following two PDFs were fitted: first, a bimodal PDF, being the sum of two Gaussian functions  
\[p(r){=}(f_{1}/\sqrt{2{\pi}}{\sigma}_{1})e^{{-}(r{-}r_{1})^{2}/2{\sigma}_{1}^{2}}{+}{[}(1{-}f_{1})/\sqrt{2{\pi}}{\sigma}_{2}{]}e^{{-}(r{-}r_{2})^{2}/2{\sigma}_{2}^{2}},\]
where r is rate of thickness change, and the parameters f 1, σ1, r 1, σ2, and r 2 were adjusted to maximize the likelihood. The second type of fit was a skewed PDF with a single peak (at r = r 0) of the form  
\[p(r){=}(f/\sqrt{2{\pi}}{\sigma})e^{{-}(r{-}r_{0})^{2}/2{\sigma}^{2}}{+}{[}(1{-}f)k/(ae^{b(r{-}r_{0})}{+}be^{{-}a(r{-}r_{0})}){]},\]
where the parameters f, σ, r 0 , a, and b were adjusted to maximize likelihood. The parameter k was adjusted so that, for any values of a and b  
\[{{\int}_{{-}{\infty}}^{{\infty}}}k/(ae^{b(r{-}r_{0})}{+}be^{{-}a(r{-}r_{0})})dr{=}1.\]
Both fits involve the same number (n = 5) of adjustable parameters, all of which have considerable impact on the final fit. For the PCTF, the skewed PDF of equation gave a maximum likelihood approximately eight times greater than that for the bimodal PDF of equation 3 , and the former PDF is given by the curve in Figure 9A . The peak of this PDF, r 0, corresponding to slow thinning, occurred at a thinning rate of 0.79 μm/min; rapid thinning corresponds to the long tail on the left of the PDF. For the PLTF, the bimodal PDF of equation 3gave a maximum likelihood approximately 4000 times greater than that for the skewed PDF of equation 4 , and the former PDF is given by the curve in Figure 9B . The peaks of the two Gaussian functions correspond to a slow thinning rate (r 1) of 1.25 μm/min and a rapid thinning rate (r 2) of 9.19 μm/min. The probability of slow thinning (f 1 in equation 3 ) was 0.30. (In considering the relative likelihood of bimodal and skewed PDFs, it should be noted that the rate of thickness change data, r i in equation 2 , are not all independent data but are obtained from four recordings from each of 20 subjects. This tends to overestimate the likelihood ratios. Also, the likelihood-ratio estimates, of course, depend on the exact form of the assumed PDF equations.) 
The possibility that rapid thinning of the PCTF could be caused by passage of tear fluid into the epithelium was studied as follows. (It should be noted that only a fraction of the recordings gave satisfactory measurements of epithelial thickness—that is, measurements at most time points with low variability.) First, four PCTF recordings (from three subjects) were selected because they had rapid PCTF thinning (>3 μm/min) with measurements over the full 20-second period, and good recordings of epithelial thickness. Solid curves in Figures 10A and 10Bshow averaged thickness data for PCTF and epithelium, respectively. Vertical magnification is the same in these two figures. Dotted curves are fitted regression lines over the period starting at least 2 seconds after any of the blinks. Rates of change in thickness in the PCTF and epithelium were −8.74 and −0.28 μm/min, respectively. These results indicate that rapid thinning of the PCTF is not caused by passage of tear fluid into the epithelium. 
A corresponding analysis of the PLTF and contact lens is shown in Figure 11 , where data for five suitable recordings (from three subjects) have been averaged. (The PLTF average shows a transient thickening after the blink with a similar time course to that in Figure 3A , but of opposite polarity). Over the period of the regression lines, the rates of change in thickness of the PLTF and contact lens were −6.46 and −0.37 μm/min, respectively. These results indicate that rapid thinning of the PLTF is not caused by passage of tear fluid into the contact lens. 
Discussion
The results show several similarities between the observed thinning of the PCTF and PLTF. Figures 2 3 5 and 9show that both PCTF and PLTF have variable rates of thinning, with some that are relatively slow (up to approximately 2 μm/min) but others that are considerably more rapid (up to approximately 20 μm/min). Figure 4shows that, excepting the transient changes in the 2 seconds after a blink, both PCTF and PLTF give nearly linear plots of tear film thickness versus time—that is, nearly constant thinning rates. Figure 7shows that the thinning rate of the PLTF correlated significantly with that for the PCTF, indicating that some common mechanisms are involved. Likewise, Figure 8shows that the initial thickness (2 seconds after the blink) of the PLTF correlated significantly with that of the PCTF. This correlation presumably indicates that both PCTF and PLTF thicknesses involve some factors common to each subject (e.g., tear meniscus radius, surface tension, viscosity, eyelid velocity 2 ). 
The results also show several significant differences between the thinning of the PCTF and PLTF. Figure 8and Table 1show that, in these studies, the average PLTF initial thickness is significantly less, by approximately 1.4 μm, than that of the PCTF. Figure 7and Table 1show that the average PLTF thinning rate is significantly faster, by about a factor of 1.8, than that of the PCTF. Both the smaller initial thickness of the PLTF and its more rapid thinning rate contribute to a faster tear thinning time—equation 1 and Figure 6 . Substituting the mean data from Table 1 , typical tear thinning times for PCTF and PLTF are 65 seconds and 24 seconds, respectively. 
The histogram of thinning rates for the PCTF in Figure 9Awere fit better by a skewed PDF (equation 4)than by a bimodal PDF (equation 3) , whereas the reverse was true of the histogram for PLTF rates in Figure 9B . A bimodal PDF, such as that fitted for the PLTF (Fig. 9B)suggests that at least two different mechanisms of tear film thinning are involved, with perhaps one acting in cases of slow thinning, and another acting (perhaps in addition to the first) in cases of rapid thinning. A skewed PDF, such as that fitted to the PCTF (Fig. 9A)could be interpreted in terms of a single mechanism with a skewed distribution of thinning rates, but may also correspond to variable contributions from more than one mechanism. An additional observation is that slow thinning rates, corresponding to the narrow peaks of the two PDFs in Figure 9 , were greater for the PLTF (1.25 μm/min), than for the PCTF (0.79 μm/min). Figure 9also shows that there are relatively more cases of rapid thinning (e.g., approximately 10 μm/min) of the PLTF than of the PCTF. 
Slow thinning of the PCTF and PLTF may be caused by evaporation (Fig. 1 , arrow 1). Previous studies have reported a range of PCTF evaporation rates from 0.24 to 1.45 μm/min. 7 8 9 10 11 The mean of 0.79 μm/min for the slow mode of PCTF thinning, derived from the PDF of Figure 9A , is reasonably consistent with these evaporation rates. The corresponding mean for PLTF thinning is 1.25 μm/min and so is somewhat greater than that of the PCTF. Hamano et al. 7 and Thai et al. 36 have suggested that the PLTF evaporates approximately 30% to 35% faster than the PCTF, and so their data are reasonably consistent with our proposal that slow thinning is due to evaporation, and the PLTF thus evaporates faster than the PCTF. 
Mishima and Maurice 37 showed that when the lipid layer is washed away from the tear film, the thinning rate due to evaporation would be approximately 7 μm/min. Accordingly, it is likely that the observed rapid thinning rates are not entirely due to evaporation, as they are often greater than 7 μm/min; evaporation should, of course, make a contribution to this thinning, and it is possible that evaporation rate is greater for rapid thinning than for slow thinning. Cases of thickening of the PCTF (Figs. 2C 5 and 9)cannot, of course, be explained by evaporation. Mechanisms other than evaporation should therefore be considered in rapid tear film thinning measures especially as they relate to the other two components of tear film thinning: tear film flow into the cornea or contact lens (Fig. 1 , arrow 2) and flow of the tear fluid parallel to the tear film surface (Fig. 1 , arrows 3). As Figures 10 and 11show, it seems unlikely that much fluid passes into or out of the corneal epithelium or a contact lens during the interblink period. Thus, mechanisms associated with the third component of tear film thinning (i.e., flow parallel to the tear film surface) should be considered. 
For the PLTF, wettability is known to be important for tear film stability, so it seems probable that poor wettability may make an important contribution to rapid thinning. 38 39 40 41 42 43 44 The finding that tear thinning rates of the PLTF are significantly greater than those of the PCTF (see Fig. 7 ; Table 1 ) may relate to the fact that contact lenses are less wettable than the corneal epithelium. A wettable surface is one that would maintain a stable, uniform liquid film, resisting the formation of dry spots. Typically, determinations of wettability are conducted by in vitro measures of contact angle, but these measures are limited in that they are not possible in the eye with a dynamic, natural tear film. Early observations with highly hydrophobic silicone-based lenses showed that indeed these surfaces are not wettable by aqueous-type tears due to the low surface energy of the material. 38 Although the surface energy of a hydrophilic lens is much higher, these lenses still have a tendency to dewet when on the eye. This dewetting of hydrogels may be related to the chemical nature of the polymer, the deposition of substances such as lipids on the lens surface, and the tear film itself (as the tear film contains various surfactants). In any of these situations, a dry spot on the lens surface is the energetically favorable situation. Measures of tear film breakup time over a lens (whether invasive with fluorescein or noninvasive without fluorescein) provide somewhat crude, subjective estimates of tear film thinning (and potentially, wettability). Noninvasive optical studies, including the methods used in the present study, could provide quantitative in vivo measures of wettability of hydrogel lenses. 
Although wettability may be important for rapid thinning of the PLTF, other factors should be considered, for both the PCTF and PLTF. Surface tension generates a pressure in the tear film that depends on the curvature of the outer surface of the tear film. Spatial variation of curvature can thus cause “pressure–gradient” tear flow and tear thinning. For example, the concave tear meniscus near the lids or the edge of a contact lens, generates negative pressure, sucking fluid from the nearby tear film. 45 For the PCTF, this typically generates a very thin region next to the meniscus (the “dark line”) that prevents any further significant flow. The PCTF is therefore sometimes described as a “perched” tear film. 46 Another example of pressure–gradient flow is a bump (or ridge) on the epithelial surface that could generate a corresponding bump on the outer PCTF surface immediately after a blink. This convexity would generate an increased pressure in the tear film over the bump and hence a divergent flow away from the bump, causing thinning. 21 Although this mechanism could be at least partly responsible for some cases of rapid thinning, it should be expected that, at other positions (e.g., near the edge of the bump), there would be relatively concave regions that would tend to cause thickening of the tear film, so that the average effect of this type of thinning would be small. Thus, it seems that pressure–gradient flow cannot explain the relatively high average rate of thinning observed for rapid thinning at the center of the cornea. In addition, pressure–gradient flow over a bump would be expected to occur relatively rapidly at first and then more slowly as the tear film thins and there is more viscous resistance to tear flow 21 . The fact that tear thinning is rather linear (Fig. 4)is also evidence that pressure–gradient flow is not the only mechanism involved in rapid thinning. 
Another possible cause of tear film thinning is Marangoni flow due to surface tension gradients. 1 For example, in Figure 1 , imagine that there is a surface tension gradient at the top of the figure that is greater than that at the bottom. The difference would cause more outflow of tear fluid at the top than inflow at the bottom (as indicated in Fig. 1 ), and hence thinning of the tear film. Marangoni flow should be distinguished from pressure–gradient flow. Although they both involve surface tension, Marangoni flow can occur when the outer surface of the tears is perfectly spherical, so that pressure–gradients are very small (for a spherical tear surface, the ratio of pressure–gradient flow to Marangoni flow is of the order of the ratio of tear film thickness to corneal radius). Marangoni flow is thought to be responsible for the upward drift of the PCTF for approximately 1 second after a blink 1 19 . At least in dry eye conditions, this drift can go on for considerably more than 1 second, 20 and so Marangoni flow could be responsible for the rapid thinning observed in this study. Doane has noted that the PLTF seems to be dragged toward the lids, as the lids cover the edge of the contact lens. 44 Marangoni flow may help to explain this observation, with a higher surface tension near the lids than at the center of the lens. These surface tension gradients might be explained by the deposition of lipids on the surface of contact lenses and a resultant alteration in the lipid layer of the tear film. The possible contribution of Marangoni flow to breakup of the PCTF has been discussed recently. 47  
Figure 5Ashowed that the variance of thinning rates of the PCTF increases with the tear film’s initial thickness. This may be expected for both pressure–gradient and Marangoni flow. For pressure–gradient flow, the total flux (tear thickness × mean velocity) of tear flow, for a given pressure gradient, is proportional to h 3, where h is tear film thickness. For Marangoni flow, flux, for a given surface tension gradient, is proportional to h 2. 21 Thus, if pressure–gradient flow and/or Marangoni flow contribute to PCTF thinning, one might expect that variance of thinning rate would increase with PCTF thickness and that is what we observed. One might also expect the PCTF thinning rate would increase with PCTF thickness. The regression line in Figure 5Ashows such a trend, even though the slope is not significant. It seems more difficult to explain these observations in terms of evaporation. For the PLTF (Fig. 5B) , there is no obvious relation between either thinning rate or variance of thinning rate and PLTF thickness. This difference from the findings for the PCTF may be related to the contribution of dewetting to PLTF thinning. In this regard, it should be remembered, despite the evidence of differences in thinning mechanisms between the PCTF and PLTF, that the correlation between thinning rates shown in Figure 7indicates that there are also some common factors in PCTF and PLTF thinning. 
The possible relation of the current studies to tear film breakup in front of the cornea or contact lens is illustrated in Figure 6 . In some cases, the tear thinning time can be less than 15 seconds for the PCTF and less than 10 seconds of the PLTF. These values are comparable to noninvasive breakup times. 12 13 14 15 16 17 It should be noted that tear film breakup can occur anywhere on the cornea, whereas the tear thinning times in Figure 6correspond to a single point at the center of the cornea. Thus, tear breakup times, which correspond to the earliest breakup observed at any position, would presumably tend to match the smallest tear thinning times in Figure 6 . It thus seems probable that the current tear thinning studies are relevant to predictions of tear film breakup times. 
The thinning of the tear film is a complex process that involves mechanisms such as evaporation, dewetting, pressure–gradient flow, and Marangoni flow. The interferometric method discussed in this article has the advantage that quantitative estimates of tear film thinning can be obtained. However, interferometric imaging systems, such as those based on thickness-dependent fringes could provide additional information about the spatial distribution of tear film thinning. 26 36 44 Such studies should help to elucidate the role of different mechanisms in tear film thinning and breakup, especially as these ideas relate to dry eye disease. 
 
Figure 1.
 
Three directions of tear flow that can cause tear film thinning. Arrow 1: flow across the outer tear surface, or evaporation. Arrow 2: flow into (or out of) the underlying epithelium or contact lens. Arrows 3: flow in the plane of the tear film. If the outward flow (top arrow) is greater than the inward flow (bottom arrow), the tear film tends to thin.
Figure 1.
 
Three directions of tear flow that can cause tear film thinning. Arrow 1: flow across the outer tear surface, or evaporation. Arrow 2: flow into (or out of) the underlying epithelium or contact lens. Arrows 3: flow in the plane of the tear film. If the outward flow (top arrow) is greater than the inward flow (bottom arrow), the tear film tends to thin.
Figure 2.
 
Examples of changes in precorneal tear film (PCTF) thickness as a function of time after a blink. Dashed line: measured reflectance (at 800 nm), and the dip in this line indicates the timing of the blink. Solid line: PCTF thickness. Dotted line: regression line fitted starting 2 seconds after the blink. (A) Slow and (B) rapid thinning; (C) thickening.
Figure 2.
 
Examples of changes in precorneal tear film (PCTF) thickness as a function of time after a blink. Dashed line: measured reflectance (at 800 nm), and the dip in this line indicates the timing of the blink. Solid line: PCTF thickness. Dotted line: regression line fitted starting 2 seconds after the blink. (A) Slow and (B) rapid thinning; (C) thickening.
Table 1.
 
Average Initial Thickness, 2 Seconds after a Blink, and Rate of Change of Thicknesses
Table 1.
 
Average Initial Thickness, 2 Seconds after a Blink, and Rate of Change of Thicknesses
Measure Layer Mean SD between Subjects SD within Subjects
Initial thickness PCTF 3.98 μm 1.06 μm 1.00 μm
Initial thickness PLTF 2.54 μm 1.16 μm 0.58 μm
Rate PCTF −3.79 μm/min 4.20 μm/min 3.38 μm/min
Rate PLTF −6.97 μm/min 4.32 μm/min 3.24 μm/min
Figure 3.
 
Examples of changes in prelens tear film (PLTF) thickness as a function of time after a blink. See Figure 2for details. (A) Slow and (B) rapid thinning.
Figure 3.
 
Examples of changes in prelens tear film (PLTF) thickness as a function of time after a blink. See Figure 2for details. (A) Slow and (B) rapid thinning.
Figure 4.
 
Linearity of tear film thinning. (A) Solid line: average for 15 PCTF recordings in 10 subjects, with a thinning rate over 3 μm/min with measurements over the full 20-second period. The time scale started at least 2 seconds after any of the blinks. Dotted line: linear regression fit; dashed line: an exponential decay fit. (B) Average of 10 PLTF recordings.
Figure 4.
 
Linearity of tear film thinning. (A) Solid line: average for 15 PCTF recordings in 10 subjects, with a thinning rate over 3 μm/min with measurements over the full 20-second period. The time scale started at least 2 seconds after any of the blinks. Dotted line: linear regression fit; dashed line: an exponential decay fit. (B) Average of 10 PLTF recordings.
Figure 5.
 
Rate of change in thickness plotted as a function of initial thickness (2 seconds after a blink). (•) Individual measurements; (▵) averages for each subject; (○) overall means. Solid lines: regression lines through the subject averages; dashed lines: no thinning.
Figure 5.
 
Rate of change in thickness plotted as a function of initial thickness (2 seconds after a blink). (•) Individual measurements; (▵) averages for each subject; (○) overall means. Solid lines: regression lines through the subject averages; dashed lines: no thinning.
Figure 6.
 
Thinning times (from equation 1 ) plotted as a function of initial thickness (2 seconds after the blink).
Figure 6.
 
Thinning times (from equation 1 ) plotted as a function of initial thickness (2 seconds after the blink).
Figure 7.
 
Rate of thickness change for the PCTF, plotted as a function of the corresponding rate for the PLTF. (▵): averages for each subject. Solid line: regression line through the subject averages; dashed line: equality of PLTF and PCTF rates.
Figure 7.
 
Rate of thickness change for the PCTF, plotted as a function of the corresponding rate for the PLTF. (▵): averages for each subject. Solid line: regression line through the subject averages; dashed line: equality of PLTF and PCTF rates.
Figure 8.
 
Initial thickness (2 seconds after the blink) for the PCTF, plotted as a function of the corresponding thickness of the PLTF. Symbols and lines are as described in Figure 7 .
Figure 8.
 
Initial thickness (2 seconds after the blink) for the PCTF, plotted as a function of the corresponding thickness of the PLTF. Symbols and lines are as described in Figure 7 .
Figure 9.
 
Histograms of thinning rates. The histogram of (A) PCTF data has been fitted by the skewed PDF of equation 4 , and that of (B) PLTF data has been fitted by the bimodal PDF of equation 3 .
Figure 9.
 
Histograms of thinning rates. The histogram of (A) PCTF data has been fitted by the skewed PDF of equation 4 , and that of (B) PLTF data has been fitted by the bimodal PDF of equation 3 .
Figure 10.
 
(A) PCTF thickness averaged for four recordings of rapid thinning, in which epithelial and PCTF thicknesses were measured for the full 20-second recording period. (B) Corresponding average of epithelial thickness.
Figure 10.
 
(A) PCTF thickness averaged for four recordings of rapid thinning, in which epithelial and PCTF thicknesses were measured for the full 20-second recording period. (B) Corresponding average of epithelial thickness.
Figure 11.
 
(A) PCTF thickness averaged for five recordings of rapid thinning, in which contact lens and PLTF thickness were measured for the full 20 second recording period. (B) Corresponding average of contact lens thickness.
Figure 11.
 
(A) PCTF thickness averaged for five recordings of rapid thinning, in which contact lens and PLTF thickness were measured for the full 20 second recording period. (B) Corresponding average of contact lens thickness.
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Figure 1.
 
Three directions of tear flow that can cause tear film thinning. Arrow 1: flow across the outer tear surface, or evaporation. Arrow 2: flow into (or out of) the underlying epithelium or contact lens. Arrows 3: flow in the plane of the tear film. If the outward flow (top arrow) is greater than the inward flow (bottom arrow), the tear film tends to thin.
Figure 1.
 
Three directions of tear flow that can cause tear film thinning. Arrow 1: flow across the outer tear surface, or evaporation. Arrow 2: flow into (or out of) the underlying epithelium or contact lens. Arrows 3: flow in the plane of the tear film. If the outward flow (top arrow) is greater than the inward flow (bottom arrow), the tear film tends to thin.
Figure 2.
 
Examples of changes in precorneal tear film (PCTF) thickness as a function of time after a blink. Dashed line: measured reflectance (at 800 nm), and the dip in this line indicates the timing of the blink. Solid line: PCTF thickness. Dotted line: regression line fitted starting 2 seconds after the blink. (A) Slow and (B) rapid thinning; (C) thickening.
Figure 2.
 
Examples of changes in precorneal tear film (PCTF) thickness as a function of time after a blink. Dashed line: measured reflectance (at 800 nm), and the dip in this line indicates the timing of the blink. Solid line: PCTF thickness. Dotted line: regression line fitted starting 2 seconds after the blink. (A) Slow and (B) rapid thinning; (C) thickening.
Figure 3.
 
Examples of changes in prelens tear film (PLTF) thickness as a function of time after a blink. See Figure 2for details. (A) Slow and (B) rapid thinning.
Figure 3.
 
Examples of changes in prelens tear film (PLTF) thickness as a function of time after a blink. See Figure 2for details. (A) Slow and (B) rapid thinning.
Figure 4.
 
Linearity of tear film thinning. (A) Solid line: average for 15 PCTF recordings in 10 subjects, with a thinning rate over 3 μm/min with measurements over the full 20-second period. The time scale started at least 2 seconds after any of the blinks. Dotted line: linear regression fit; dashed line: an exponential decay fit. (B) Average of 10 PLTF recordings.
Figure 4.
 
Linearity of tear film thinning. (A) Solid line: average for 15 PCTF recordings in 10 subjects, with a thinning rate over 3 μm/min with measurements over the full 20-second period. The time scale started at least 2 seconds after any of the blinks. Dotted line: linear regression fit; dashed line: an exponential decay fit. (B) Average of 10 PLTF recordings.
Figure 5.
 
Rate of change in thickness plotted as a function of initial thickness (2 seconds after a blink). (•) Individual measurements; (▵) averages for each subject; (○) overall means. Solid lines: regression lines through the subject averages; dashed lines: no thinning.
Figure 5.
 
Rate of change in thickness plotted as a function of initial thickness (2 seconds after a blink). (•) Individual measurements; (▵) averages for each subject; (○) overall means. Solid lines: regression lines through the subject averages; dashed lines: no thinning.
Figure 6.
 
Thinning times (from equation 1 ) plotted as a function of initial thickness (2 seconds after the blink).
Figure 6.
 
Thinning times (from equation 1 ) plotted as a function of initial thickness (2 seconds after the blink).
Figure 7.
 
Rate of thickness change for the PCTF, plotted as a function of the corresponding rate for the PLTF. (▵): averages for each subject. Solid line: regression line through the subject averages; dashed line: equality of PLTF and PCTF rates.
Figure 7.
 
Rate of thickness change for the PCTF, plotted as a function of the corresponding rate for the PLTF. (▵): averages for each subject. Solid line: regression line through the subject averages; dashed line: equality of PLTF and PCTF rates.
Figure 8.
 
Initial thickness (2 seconds after the blink) for the PCTF, plotted as a function of the corresponding thickness of the PLTF. Symbols and lines are as described in Figure 7 .
Figure 8.
 
Initial thickness (2 seconds after the blink) for the PCTF, plotted as a function of the corresponding thickness of the PLTF. Symbols and lines are as described in Figure 7 .
Figure 9.
 
Histograms of thinning rates. The histogram of (A) PCTF data has been fitted by the skewed PDF of equation 4 , and that of (B) PLTF data has been fitted by the bimodal PDF of equation 3 .
Figure 9.
 
Histograms of thinning rates. The histogram of (A) PCTF data has been fitted by the skewed PDF of equation 4 , and that of (B) PLTF data has been fitted by the bimodal PDF of equation 3 .
Figure 10.
 
(A) PCTF thickness averaged for four recordings of rapid thinning, in which epithelial and PCTF thicknesses were measured for the full 20-second recording period. (B) Corresponding average of epithelial thickness.
Figure 10.
 
(A) PCTF thickness averaged for four recordings of rapid thinning, in which epithelial and PCTF thicknesses were measured for the full 20-second recording period. (B) Corresponding average of epithelial thickness.
Figure 11.
 
(A) PCTF thickness averaged for five recordings of rapid thinning, in which contact lens and PLTF thickness were measured for the full 20 second recording period. (B) Corresponding average of contact lens thickness.
Figure 11.
 
(A) PCTF thickness averaged for five recordings of rapid thinning, in which contact lens and PLTF thickness were measured for the full 20 second recording period. (B) Corresponding average of contact lens thickness.
Table 1.
 
Average Initial Thickness, 2 Seconds after a Blink, and Rate of Change of Thicknesses
Table 1.
 
Average Initial Thickness, 2 Seconds after a Blink, and Rate of Change of Thicknesses
Measure Layer Mean SD between Subjects SD within Subjects
Initial thickness PCTF 3.98 μm 1.06 μm 1.00 μm
Initial thickness PLTF 2.54 μm 1.16 μm 0.58 μm
Rate PCTF −3.79 μm/min 4.20 μm/min 3.38 μm/min
Rate PLTF −6.97 μm/min 4.32 μm/min 3.24 μm/min
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