The tear film that covers the anterior corneal surface has a dynamic behavior. It is well established that immediately after a blink, the tear film undergoes formation (build up) that is followed by a phase of relative tear film stability.1 However, if the eye is left open for a sufficiently long period of time, the tear film will deteriorate. Tear film break-ups will normally appear within a minute from the last blink, but they can also appear much sooner, for example, for those diagnosed with a dry eye syndrome.2
The phase of tear film build-up is closely associated with the spread of the lipid layer.3,4 Earlier, modeling work of Brown and Dervichian5 suggested a two-step build-up phase in which, in response to a blink, the precorneal tear film is first pulled by the upper eyelid because of the capillary action after which the lipid layer is spread subsequently thickening and stabilizing the overall tear film. Another modeling approach suggests that the first step of build-up could be associated with the movement of the polar meibomian lipids while the second step with the slower spread of the nonpolar lipids.4 Recently, more complex models of interactions between polar and nonpolar lipids have been proposed.6,7 Nevertheless, evidence of two-step tear film behavior during the build-up phase can be noted in examination of the anterior eye with a slit lamp, but there have been no reports yet available on quantifying each of the two considered sub-phases. Depending on the measuring technique, estimates of the overall tear film build-up phase time,TBLD, vary from less than a second8–10 to several seconds.1,11,12
Tear film stability phase follows the build-up and is characterized by relative stability of the tear film surface kinetics. During natural blinking, it is expected that this phase is immediately followed by the next blink and that there is no subsequent deterioration of tear film.7 During prolonged interblink intervals or during forced opening of the eye, the stability of tear film may decrease but this may still not lead to break-ups. This phase has been termed the tear film thinning phase.3,13 Finally, the quality of tear film, which could be assessed using subjective or objective measures, can deteriorate to such an extent that a break-up is claimed. This point marks the tear film break-up time, TBUT, a vital clinical parameter in the diagnosis of dry eye syndrome.
Hence, the tear film surface kinetics can be characterized by up to five distinctive phases as it is schematically shown in Fig. 1. In a general case, these five phases include: (i) initial fast tear film build-up phase, (ii) further slower tear film build-up phase, (iii) tear film stability phase, (iv) tear film thinning phase, and (v) after a detected break-up, subsequent tear film deterioration phase.
To date, there have been no measuring techniques available that could clearly identify all considered phases of tear film surface kinetics in one interblink interval.
Lateral shearing interferometry (LSI) has been used to objectively and quantitatively assess the tear film surface quality (TFSQ) in a noninvasive manner.14,15 When compared with other noninvasive methods, the modified LSI technique15 showed to be the most sensitive way of recording tear film surface irregularities.10 However, at the same time, the technique has been hindered by the naturally occurring eye movements resulting in significant measurement noise.14
The assessment of the TFSQ in LSI is essentially based on the spatial average of localized weighted first-order frequency estimates of the interference fringes, called the M2 measure.15 The measurement noise in LSI results mainly from natural eye movements. Longitudinal eye movements related to cardiopulmonary signals can also interfere because they modulate the M2 measure. Recently, we have developed a new estimation technique for extracting the first-order frequency from the interference fringes that combines the consistent spectral estimation techniques with morphological image processing techniques.16 The technique is more robust to changes in interference fringes caused by natural eye movements resulting in TFSQ estimates that are less noisy.
Our aim was to improve our current LSI technique by providing it with a set of robust parameter estimation techniques so that all considered above phases of tear film surface kinetics could be estimated.
A large number of measurements have been performed on a group of normal subjects10 and subjects diagnosed with dry eye. Of particular interest, here are the measurements in which the subjects were asked to blink and keep their eyes open as long as they could, so that all five phases of tear film surface kinetics could be estimated from the TFSQ-time series. The study was approved by the university research ethics committee, and all subjects gave informed consent before participation and were treated in accordance with the Declaration of Helsinki.
The first step in the TFSQ estimation procedure is to approximate the time series with a smooth regular function such as a polynomial.15 Adhering to the principle of parsimony to achieve a more robust estimator and to take care of the dynamics of TFSQ in terms of adequately estimating its derivative,17 Mallows'18 CP information criterion has been used to estimate the optimal order of the polynomial. In Mallows' criterion, we have increased the penalty function by weighting it by a factor of eight rather than the traditionally used factor of two.
The second step of the procedure consists of detecting the break-up. Group data statistics10 from measurements of TFSQ in 18 normal subjects during natural blinking has been used. Similar to many medical diagnosis detection scenarios, to improve the probability of detection, only one standard deviation from the group average TFSQ has been set as the detection threshold. The time, at which the optimally estimated polynomial trend to data exceeded the detection threshold, was chosen as an estimate of the tear film break-up time TBUT (Fig. 1). This is achieved by detrending the polynomial (subtracting the detection threshold value from the lowest polynomial coefficient), estimating its roots, and analyzing the slopes around all valid real roots. In cases, where the polynomial trend did not exceed the predetermined threshold, the end of recording (corresponding to the subsequent blink) could be taken as an estimate of TBUT.
In the third step, the TFSQ data from the beginning of the time series to the estimated TBUT is fitted in a least squares sense with a quad-linear model, in which each phase of the TFSQ time series is fitted with a linear function—the most parsimonious model. This quad-linear model is constructed in a manner in which a subsequent linear function is constrained by the estimator of the preceding linear function describing the earlier phase of tear film. This is performed using an iterative nonlinear constrained least-squares approach in a nested four-loop algorithm. The intercept of the second and the third linear trends is taken as an estimator of the tear film build-up time, TBLD, provided that the slope of the third line (that of the stability phase) lies in a predetermined range. Finally, the remaining of the TFSQ time series (i.e., beyond TBUT) may be fitted with another linear trend constrained on the estimator of the tear film thinning phase trend in the same manner as this is performed in the quad-linear model. We choose a multilinear fit to TFSQ time series for two reasons. Firstly, from the principle of parsimony, we want to apply the simplest possible model. Secondly, to determine the transition points between different phases, a model was sought in which those points were clearly defined.
In some cases, it is not possible to identify all five considered phases of tear film surface kinetics. For example, when measuring TFSQ in healthy eyes, there may not be much difference between the tear film stability phase and that of tear film thinning. In dry eye subjects, however, the tear film stability phase could be much shorter or may not be distinguished at all. To take into account such situations in the modeling, it is necessary to test in each sequence whether a quad-linear fit is warranted. This can been achieved by performing a log likelihood ratio test of the Pearson's correlation coefficients for a quad linear and a trilinear fit in a similar way as it was done in our earlier work with a test between linear and bilinear fit.10
We show several representative examples of estimating tear film surface kinetics in measurements in which the subjects were asked to blink and keep their eyes open as long as they could. Fig. 2A shows an example of a measurement from a 28-year-old-male subject with healthy tear film. After the initial fast tear film build-up phase, the estimated TFSQ does not exceed the detection threshold and only the first three phases of tear film surface kinetics can be observed. Of particular interest is the long tear film stability phase. Fig. 2B shows an example of a measurement from a 68-year-old-male subject with a dry eye and lipid anomaly, in which all five phases of tear film surface kinetics are clearly observed. Representative frames corresponding to those five phases are shown in Fig. 3. Fig. 2C shows an example of a measurement from a 66-year-old-female subject with a dry eye and aqueous deficiency. The estimated TFSQ lies above the detection threshold during the whole measurement period. Nevertheless, there are still four distinct phases of tear film surface kinetics that can be observed. Finally, Fig. 2D shows an example of a measurement from a 20-year-old-female subject with healthy tear film where no tear film stability phase has been identified. In this case, the trilinear rather than quad linear approximation to the data showed a better fit. This indicates that in some cases tear film build-up could be immediately followed by tear film thinning.
To ascertain the goodness-of-fit for the four examples provided, we first compared the bilinear fit with the two-stage build-up phase to those of exponential, double exponential, and power law functions. Similarly, we compared the trilinear fit from Fig. 2A with those functions. The results in terms of sum of squared errors, root mean square error, and Pearson's correlation coefficient (r2) are given in Tables 1 and 2, for the bilinear and trilinear fit, respectively. The bilinear fit gave the best results among the considered models for three of four traces of TFSQ (indicated by bold font) and gave second best performance to the double exponential model for one TFSQ trace in which the initial phase of build-up was particularly short (normal subject with unstable tear film).
Interferometry is a sensitive method to analyze surface topography. The interferograms recorded in the lateral shearing setup present the interference between two wavefronts reflected from the lipid layer—air interface. Depending on the regularity of the external layer of tear film, regular or deformed high-contrast fringes are recorded. The applied numerical measure of the fringes' regularity shows differences in the tear film surface in time. Up to five phases of tear film surface kinetics can be distinguished but of particular interest are the first two phases of the tear film build-up process, where the tear film surface becomes more regular and the TFSQ measure decreases. At first, fast changes in TFSQ are observed immediately after arising of the upper eyelid and spreading of the new tear film layer. This is then followed by slower changes in the TFSQ that are most likely linked to the spread of the lipid layer. The upward lipid layer motion phenomenon has been analyzed and described earlier by logarithmic8 and exponential functions3 that reveal the retardant movement of external layer of tears. Possible explanations of the fast and the lag phases of the tear film build-up have been given by Benedetto et al.7 and most recently by McCulley and Shine.6 They suggest a two-step process in which the spread of the aqueous layer with polar lipids is followed by slower spread of the nonpolar lipid layer. These ideas somehow agree with Brown and Dervichian's model,5 which demonstrates the behavior of two layers: polar and nonpolar, which are pulled by a model eyelid wiper. The polar aqueous layer movement is followed by the slower motion of oil (nonpolar layer) spread over the aqueous layer, dragging along the additional water. The coating model of Wong et al.19 also supports our results. In this model, the thick oily layer deposited in the lower meniscus does not immediately follow the tear film dragged by the upper eyelid and continues to spread upward for about a second. In LSI, we might observe the fast pulling phase of the nonpolar lipids immediately after the blink and next the restrain and distribution of nonpolar lipids over the ocular surface. According to Benedetto et al.,7 all motion in the tear film stops after ∼2 to 3 s and this has been confirmed in our measurements with lateral sharing interferometry for majority of subjects. However, other studies indicate that the slow upward movement of lipids or changes in the tear film topography could last up to 10 s.12 This has also been confirmed in our measurements in some subjects who demonstrated longer phase of tear film build-up.
In most of the subjects, subsequently after build-up, tear film creates regular fringes achieving a relatively stable phase in which no significant changes in the fringes' regularity are noticed. The first fast phase of the tear film build-up requires good quality of captured frames. If it was so, the build-up time phase was observed in every case. Depending on the slope of the following three lines in our quad-linear model, we can distinguish the second slower build-up phase, the stability phase, and the tear film thinning phase. In some cases, the tear film thinning phase followed the build-up time and the tear film stability phase was not distinguished. This could occur if the stability phase was short. In those cases, a tri-linear model was found to better fit the TFSQ time series. It is worth noting that for normal eyes the tear film stability phase or the thinning phase are long and very often did not reach the detection threshold before the blink or the end of the recording.
The two last phases of tear film surface kinetics correspond to the tear film thinning process, which is caused mainly by evaporation3 and leads to tear film break-up. The break-up is claimed if the estimated TFSQ exceeds a predefined threshold. If eye is still open, we can observe progressive deterioration and drying of the ocular surface. In some dry eye subjects, the estimated TFSQ lies, in its entirety, above the detection threshold. Nevertheless, phases of the tear film kinetics can be still distinguished, but the tear film is never perfectly regular as it is indicated by the value of the TFSQ.
In the majority of LSI sequences, one can observe the two-stage build-up phase. In fact, in natural blinking conditions, 99% of measurements contain the build-up phase.10 In addition, in suppressed blinking conditions—cases considered here—there was always the third and often the fifth (after the estimated break-up) phase indentified. In some cases, it was hard to distinguish phase II from phase III or phase III from phase IV. A clear complete five-phase trace (Fig. 2B) was observed occasionally.
Summarizing, unlike other currently used noninvasive techniques for TFSQ assessment, the LSI technique provides means for complete temporal characterization of tear film surface kinetics and the opportunity for the analysis of the two-step tear film build-up process.
D. Robert Iskander
QUT School of Optometry
Victoria Park Road
Kelvin Grove, Queensland 4059
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Keywords:© 2010 American Academy of Optometry
tear film kinetics; tear film build-up; tear film break-up; parameter estimation