purpose. To analyze the relationship between tear volume and tear film lipid layer (TFLL) spread.

methods. Twenty-nine eyes from 22 subjects, including normal eyes and eyes with aqueous tear–deficient dry eye, were enrolled in this study. In all eyes, the radius of curvature (*R*: mm) of the central lower tear meniscus was measured with a video-meniscometer, and interference images from the TFLL were recorded with a video-interferometer. Interference images were captured as still images every 0.05 second, and the relationship between the acquisition time for each image after a blink and the averaged heights of the spreading TFLL in the upstroke of the blink were calculated.

results. In all cases, the time-dependent changes in TFLL spread could be described by the expression *H*(*t*) − *H*(0) = ρ[1 − exp(−*t*/λ)], where *H*(*t*) is the averaged height in millimeters at time *t*, *H*(0) is the averaged height at *t* = 0, ρ is a constant, *t* is time in seconds, and λ is the characteristic time in seconds. A statistically significant correlation was found between those changes and the initial upward velocity of the spreading TFLL [*H*′(0) = *dH*(0)/*dt*] and *R* (*r* = 0.573; *P* = 0.003).

conclusions. This study demonstrated that the time-dependent changes of TFLL spread are compatible with the Voigt model of viscoelasticity and that the initial velocity of TFLL spread after a blink decreased in proportion to the decrease of tear volume. There is potential interest in using this parameter to diagnose and evaluate the severity of aqueous tear deficiency.

^{ 1 }that can be imaged noninvasively by interferometry.

^{ 2 }

^{ 3 }

^{ 4 }We have reported elsewhere that graded interference patterns can be used as a parameter to screen dry eye and evaluate its severity.

^{ 5 }Other studies have shown that after a blink, the tear film lipid layer (TFLL) spreads over the aqueous layer in a reproducible manner

^{ 2 }

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }and that its dynamics can be observed using an interferometer. Such studies

^{ 10 }

^{ 11 }have noted that the time taken for the interference pattern to stabilize after a blink (defined as spreading time) is longer in aqueous-deficient dry eyes than in aqueous-sufficient normal eyes. Goto and Tseng

^{ 11 }noted that the spreading time was shortened in aqueous tear–deficient dry eyes after punctal occlusion and proposed that spreading is affected by aqueous tear volume. This semiquantitative method offers a novel direct approach to the study of lipid-layer kinetics. A related report has analyzed the kinetic behavior of particles embedded in the tear film, probably located at the level of the TFLL.

^{ 12 }

^{ 13 }

^{ 9 }

^{ 11 }

^{ 12 }This effect can be seen more clearly in eyes with aqueous tear deficiency because the speed of spreading is slower.

^{ 14 }

^{ 15 }(abnormal value, ≤5 mm/5 min), the measurement of fluorescein break-up time (BUT)

^{ 16 }(abnormal value, ≤5 seconds), and the grading of corneal staining with fluorescein

^{ 17 }and of ocular surface staining with rose Bengal.

^{ 18 }Abnormal scores for fluorescein were A1D1 and greater; A and D representing area and density, respectively, were graded from 0 to 1 (mild), 2 (moderate), and 3 (severe). An abnormal score for rose Bengal, based on the van Bijsterveld criteria, was ≥3.

^{ 19 }Healthy eyes in this study met the following criteria: normal Schirmer I test value, normal scores for fluorescein and rose Bengal staining, and normal BUT values. Exclusion criteria were meibomian gland dysfunction, punctal-plug occlusion or surgical punctal occlusion, previous corneal surgery, previous or current corneal disease (excluding aqueous tear–deficient dry eye), and hard or soft contact lens wear by the subject.

^{ 20 }

^{ 21 }

^{ 22 }

^{ 23 }

^{ 24 }

^{ 25 }Immediately after that, interference images from the TFLL were digitally recorded just after a blink with a video-interferometer (DR-1; Kowa, Tokyo, Japan).

^{ 5 }

^{ 25 }

*R*: mm) of the tear meniscus at the central lower eyelid was measured by video-meniscometry.

^{ 20 }

^{ 21 }

^{ 22 }

^{ 23 }

^{ 24 }

^{ 25 }With this, a real-time reflected image of a target consisting of a pair of horizontal, black-and-white stripes was captured digitally, and

*R*was calculated using the concave mirror formula.

^{ 20 }

^{ 21 }

^{ 22 }In our video-meniscometry, the

*R*of the lower tear meniscus is measured as the average of three consecutive measurements (Sugita J, et al.

*IOVS*2002;43 ARVO E-Abstract 95). In the model,

*R*is assumed to be constant over the duration of the interblink, as demonstrated by Palakuri et al.

^{ 26 }for the upper and lower tear meniscus using optical coherence tomography. However, it should be noted that Johnson et al.,

^{ 27 }using the video slit-lamp technique, reported an increase of

*R*at the end of the interblink period. The tear meniscus is reportedly responsible for 75% to 90% of the total tear volume,

^{ 28 }and the value of

*R*reportedly reflects the total tear volume over the ocular surface.

^{ 23 }

^{ 5 }

^{ 10 }

^{ 11 }

^{ 24 }

^{ 25 }and is equipped with low- and high-magnification viewing modes that allow observation of 7-mm and 2-mm circular areas in the central cornea, respectively.

^{ 24 }In this study, the low-magnification mode was the primary mode selected to obtain information regarding the behavior of the precorneal TFLL.

*y*-direction at each pixel point along the horizontal

*x*-direction within the rectangular area. Images of the spreading TFLLs with ill-delineated upper borders and images with no spreading pattern, possibly because of extremely severe aqueous tear deficiency, were excluded. After calculating the averaged heights of the spreading lipid, the relationship between the acquisition time for the images after a blink and the calculated averaged heights of the spreading lipid were plotted. Curve-fitting to the plots satisfied an exponential equation in keeping with the simple rheological model of Voigt

^{ 29 }describing the behavior of a viscoelastic material (see Discussion).

*R*: mm), which was proportional to the total tear volume over the ocular surface,

^{ 23 }and the initial upward velocity of the lipid layer spread were analyzed. The Spearman correlation coefficient by rank test was performed, and

*P*≤ 0.05 was considered statistically significant.

*H*of lipid layer spread were found to conform to an exponential model of the form

*H*(

*t*) −

*H*(0) = ρ[1 − exp(−

*t*/λ)], where

*H*(

*t*) is the averaged heights in millimeters at time

*t*,

*H*(0) is the averaged heights at time

*t*= 0, ρ is a constant,

*t*is time in seconds, and λ is characteristic time in seconds.

*R*values calculated from the video-meniscometer–detected images (Fig. 5)from the central lower tear meniscus in three representative cases are given in Table 1 .

*R*and

*H*′(0) is shown in Figure 6 . There was a statistically significant correlation between

*R*and

*H*′(0) (

*r*= 0.573;

*P*= 0.003; Spearman correlation coefficient by rank test). The relationship between

*R*and the other parameters, including

*H*(0), ρ, and λ, was also analyzed. As a result, a similar and statistically significant correlation was found between

*R*and ρ (

*r*= 0.573;

*P*= 0.002), and a weak, statistically insignificant correlation was found between

*R*and

*H*(0) (

*r*= 0.318;

*P*= 0.095). However, there was no statistically significant correlation between

*R*and λ (

*r*= −0.241;

*P*= 0.194).

^{ 5 }

^{ 10 }

^{ 11 }

^{ 25 }at intervals of 0.05 second, allowing the dynamics of the TFLL spread to be analyzed quantitatively. The time dependence of the averaged height of the spreading TFLL, as determined from the captured images, was successfully fitted to an exponential formula of the form

*H*(

*t*) −

*H*(0) = ρ[1 − exp(−

*t*/λ)], where

*H*(

*t*) is the averaged height in millimeters at time

*t*,

*H*(0) is the averaged height at time

*t*= 0, ρ is a constant,

*t*is time in seconds, and λ is characteristic time in seconds. For the averaged height,

*H*is first measured when the TFLL first appears in the viewing window. True

*H*(0) is the point in time at which the TFLL front first crosses the lower boundary of the viewing window, so that

*H*(0) as recorded is not zero and has a positive value. The size of this depends on the rate of movement of the TFLL and is higher when the rate of TFLL movement is high rather than when it is low (Table 1) .

^{ 29 }The applied stress σ can be related to the shear γ through the sum of elastic and viscous forces such that

_{1}is suddenly applied at time

*t*= 0 and held constant thereafter, the linear differential equation can be solved to give

_{1}is related to the surface tension forces pulling the lipid layer upward and that the resultant shear (or observed linear displacement) of the lipid front

*H*(

*t*) corresponds to the shear parameter γ in the Voigt model. Hence, the resemblance between the exponential terms of the two expressions suggests a possible viscoelastic property of the tear film that will influence its spread. In relation to the above, Berger and Corrsin

^{ 12 }analyzed the movement of particles in the tear film after a blink, taking them to be components of the TFLL. On this basis they concluded that immediately after the blink, the TFLL was displaced, like a spring being stretched, and that the spring (the TFLL) was then allowed to return to its equilibrium position. This approach gives rise to an exponential equation similar to the Voigt model but may better reflect what happens. In addition, it seems that there is no lipid layer above the boundary seen in Figure 1 , but inspection of Figure 1indicates that a thin lipid layer is in fact present. To explain this, it has been proposed that TFLL spread consists of two events: first, that in the upstroke of the blink, a polar (largely phospholipid) layer spreads over the aqueous subphase; and second, that the nonpolar lipids (chiefly cholesterol and sterol esters, the greater part of the meibomian secretion) spread over the phospholipid layer.

^{ 30 }

^{ 31 }Therefore, it is reasonable to conclude that a finite surface tension gradient causes the upward velocity of the TFLL rather than a discontinuity of surface tension at the border, which would theoretically cause infinite velocity at that point.

^{ 12 }also reported that the spreading velocity of particles on the tear film is adequately described by a logarithmic function. Because the particles they observed appeared to be located in the lipid film, their report may be taken to reflect the velocity of the spreading TFLL.

*H*(

*t*) −

*H*(0) = ρ[1 − exp(−

*t*/λ)]. Differentiation of this with respect to time gives

*H*′(

*t*) = ρ/λ × exp(−

*t*/λ). The velocity of particles observed by Owens and Phillips

^{ 12 }can also be described in exponential form as (velocity) =

*k*

_{1}× exp(−

*k*

_{2}

*t*), where

*k*

_{1}and

*k*

_{2}are constants. It can then readily be seen that this leads to a positional formula (position) = const.[1 − exp(−

*k*

_{2}

*t*)] similar to ours and that the particle motion follows the same form as our TFLL spread. This strengthens the suggestion of Owens and Phillips

^{ 12 }that the particles are embedded in and move with the lipid layer, though the sizes of these particles suggest that they may also project into the aqueous layer. Although this might help to explain our observed connection between TFLL spreading rate and tear volume, we did not notice such particles in the image samples of the TFLL images we studied.

*R*and the other parameters, including

*H*(0), ρ, and λ, showed a strong and statistically significant relationship between

*R*and ρ. However, there was no statistically significant correlation between

*R*and λ, yet there was a weak, though statistically insignificant, correlation in the relationship between

*R*and

*H*(0). It can theoretically be expected that the time constant, λ, correlates with the meniscus radius,

*R*, and that one might expect equilibrium to occur more quickly when the tear film is thicker (greater meniscus radius), yet no correlation was found in the cases we studied. However, the correlation with statistical significance similar to that between

*R*and

*H*′(0) was found between

*R*and ρ. This is reasonable, taking the Voigt model (equation 2)into consideration, because λ in our empiric equation corresponds to τ (i.e., η/κ of equation 2 , where both η and κ are material, intrinsic properties of the TFLL and are unrelated to

*R*). Moreover, considering

*H*′(0) = ρ/λ and the significant correlation between

*H*′(0) and

*R*obtained from our result, a significant correlation between

*R*and ρ is also reasonably expected, where ρ is concerned with the equilibrium value for lipid spread and implies how high the lipid layer can spread along the

*y*-direction; a lower height for lipid layer spread can be expected when the tear film is thinner (lower meniscus radius) because a thicker aqueous layer would be expected to allow the lipid layer to be carried higher.

^{ 11 }of the speed of lipid layer spreading indicated that the time required for the lipid layer to stabilize after a blink was longer than normal in aqueous tear–deficient dry eyes but was shortened after punctal occlusion. This implied a normalization of the speed of spreading by the restoration of tear volume. However, the diagnosis of dry eye in that study was made by a Schirmer-based fluorescein clearance test, and tear volume was not estimated.

^{ 23 }Furthermore, the formula given by Creech et al.

^{ 32 }suggests that the precorneal aqueous layer thickness is proportional to the meniscus radius. Our present study has shown a positive relationship between meniscus radius and initial velocity of the TFLL spread, which strongly supports the concept that this parameter is influenced by tear volume, particularly tear film thickness. Thus, it is likely that the slowed initial velocity of the TFLL spread in our patients with aqueous-deficient dry eye was related to reduced tear film thickness.

^{ 12 }Their analysis could be roughly described as a viscoelastic model in which the elastic component is provided by the TFLL, whereas the viscous component is attributed to the whole thickness of the tears, particularly the aqueous layer. They assume that surface tension is inversely related to the concentration of a surfactant (presumably related to lipid layer thickness); when the tear surface is stretched, the surfactant concentration is reduced and the surface tension increases. Thus, the lipid layer behaves like an elastic membrane whose tension increases when it is stretched. Moreover, according to their model, the force-per-unit area on the lipid layer is

*dT/dx*= μ ·

*v/h*, where

*T*is the surface tension,

*x*is the vertical position on the cornea, μ is the viscosity of the (aqueous) tear film,

*v*is the upward velocity of the lipid layer, and

*h*is the thickness of the (aqueous) tears. Rearranged,

*v*= (

*h*/μ) ·

*dT/dx*, and upward velocity is thus proportional to tear film thickness.

^{ 33 }

^{ 34 }it will be of interest to study the relationship between TFLL spread and dry eye symptoms.

^{ 10 }Therefore, it could prove difficult to diagnose aqueous-deficient dry eye by such a method in the presence of MGD. In addition, analysis of the spreading using graphic software was time consuming. New image-processing computer algorithms and analytical techniques are in development and should permit analysis of all interference patterns automatically in the near future.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

Case | H(0) (mm) | ρ (mm) | λ (s) | R (mm) | H′(0) (mm/s) |
---|---|---|---|---|---|

1 | 0.08 | 1.54 | 0.68 | 0.09 | 2.25 |

2 | 0.02 | 4.00 | 0.79 | 0.14 | 5.04 |

3 | 2.96 | 2.85 | 0.14 | 0.45 | 20.52 |

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

**Figure 7.**

**Figure 7.**