In vivo thickness dynamics measurement of tear film lipid and aqueous layers with optical coherence tomography and maximum-likelihood estimation

Jinxin Huang; Holly B. Hindman; Jannick P. Rolland

doi:10.1364/OL.41.001981

Dry eye disease (DED) is a common multi-factorial disease that affects the ocular surface. Symptoms of DED include discomfort, visual disturbance, and irritation. In severe cases, damage to and scarring of the ocular surface can cause permanent vision loss [1]. DED is recognized as one of the most frequent reasons for seeking eye care, and it seriously degrades the vision-related quality of life [2–4]. According to the Dry Eye Workshop [1], tear film instability has been established as a core mechanism of DED. Traditionally, this has been quantified as the temporal thinning of the tear film thickness leading to tear film breakup. The normal tear film consists of three layers: the lipid layer, the aqueous layer, and the mucin layer [5]. The aqueous and mucin components of the tear film are considered as one layer in this study because there is evidence to show that the mucin has a gradient of concentration, and there is no clear interface with the aqueous component [6].

Among different methods of measuring the tear film thickness in vivo [7–11], optical coherence tomography (OCT) was shown to be a promising approach due to its noninvasive nature and the recent advance of broadband light source techniques. A few methods based on spectral domain OCT were explored: indirect measurement of the tear film thickness with the application of a contact lens, and direct thickness measurements with an ultrahigh resolution OCT [12–14]. However, these OCT methods measure the total thickness of the tear film and cannot separate the lipid layer and the aqueous layer. We proposed an approach that is based on the combination of spectral domain OCT hardware and statistical decision theory [15–17] to simultaneously measure the thickness of both the lipid and aqueous layers of the tear film. The parameter space of the OCT hardware was investigated with a task-based assessment approach, and the customized instrumentation was previously detailed in [18]. The system was validated with a physical phantom of a dual-layer structure, which was implemented through the deposition of optical coatings to mimic the lipid and aqueous layers structure of the tear film [18]. In this Letter, we focus on the in vivo thickness and dynamics measurements of the tear film to show the feasibility of the proposed approach for a complete clinical study. For this purpose, a normal subject without DED was selected. The study was approved by the Research Subjects Review Board at the University of Rochester.

The structure of the tear film is schematically shown in Fig. 1. The lipid layer is about 20–150 nm thick; underneath the lipid lies the aqueous layer, which contributes the largest volume to the tear with a few microns in thickness. Since there is no clear interface between the aqueous layer and the mucin layer, we consider them as one layer with a rough interface on top of the corneal epithelium. The roughness of the interface between the aqueous and the corneal epithelium has been studied by King-Smith [19]. The refractive indices of the lipid layer, aqueous layer, and the corneal epithelium are known from prior studies [20–22], and the effect of dispersion is considered.

Fig. 1. Tear film model (the mucin component is considered as a rough interface between the aqueous layer and the corneal epithelium).

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In a spectral domain OCT, the direct output is a spectrum, which is a number array corresponding to the light intensity across the spectral band at the system detector (i.e., a line-scan camera in the spectral domain configuration). For a given tear film with lipid layer thickness $d_{l}$ and aqueous layer thickness $d_{a}$ , the corresponding spectrum collected at the detector is denoted as $N_{g | (d l, d a)} (x, Δ t)$ , where $x$ represents the pixel index number at the line-scan camera, and $Δ t$ is the integration time of the camera. During one exposure period of the line-scan camera, the acquisition of one spectrum $N_{g | (d l, d a)} (x, Δ t)$ is subject to the randomness from the Poisson noise of the photon counting process, source intensity noise of the broadband source, and the dark noise of the detector. The ensemble average of the output spectrum over the different noise is linked with the source spectrum $S (ω)$ by the following relation [15]:

〈 〈 〈 N_{g | (d_{l}, d_{a})} (x, Δ t) 〉 〉 〉 = \frac{R (x)}{e} Δ t \int_{ω_{x} - Δ ω_{x}}^{ω_{x}} S (ω) {| m (ω) |}^{2} d ω + N_{dark} (x, Δ t),

where

R (x)

is the responsivity of the detector,

e

is the charge of one electron,

ω_{x}

is the center angular frequency at the

x^{th}

pixel,

Δ ω_{x}

is the bandwidth of the angular frequency at the

x^{th}

pixel,

N_{dark} (x, Δ t)

is the dark noise, and

m (ω)

is the optical response of the interferometer. The brackets represent the ensemble average over the three sources of noise that are considered.

Compared to the phantom validation, a leading challenge of in vivo tear film thickness measurements lies in the involuntary eye movements, which cannot be controlled. There are three types of involuntary eye motion: drift, microsaccades, and tremor [23]. Drift is a slow random motion of the eye away from a fixation point; microsaccades are small rapid eye movements; and tremor occurs along a single preferred axis in any individual. The eye movements caused by involuntary motion can be on the order of a few microns within the integration time of the camera in the worst scenario. The motion along the optical axis direction is particularly problematic, because it causes blurring effects on the interference signal of the tear film with respect to a fixed reference mirror. To manage this challenge, a common path configuration was tailored for the in vivo application by utilizing the interface of the air and the lipid layer as a reference. Although the common path configuration was used in the data acquisition, the reference arm with a fixed mirror is still of great importance for this application. The fixed reference mirror provides guidance in the alignment process by showing where the eye is along the optical axis direction and to make sure the corneal surface is located at the focus of the illumination beam. To investigate the efficiency of the common path configuration, a physical phantom was mounted on a motorized stage and two sets of spectra were acquired. One set was taken with a still stage, and the other was taken with a moving stage to mimic the eye motion along the optical axis direction. Both datasets were processed and the thickness estimates had the same precision.

With a common path configuration, the total response of the interferometer $m (ω)$ is from the sample being tested. Assuming a normal incidence of the light beam on the corneal surface and a uniform thickness of the tear film within the beam spot (20 μm diameter, FWHM), the optical response from the tear film is formulated as

m_{s} (ω) = \frac{1}{2} (\begin{array}{l} r_{1} + r_{2} (1 - r_{1}^{2}) \cdot \exp (i 2 n_{l} \frac{ω}{c} d_{l}) / (1 + r_{1} r_{2} \cdot \exp (i 2 n_{l} \frac{ω}{c} d_{l})) \\ + r_{3} (1 - r_{1}^{2}) (1 - r_{2}^{2}) \cdot \exp (i 2 n_{l} \frac{ω}{c} d_{l} + i 2 n_{a} \frac{ω}{c} d_{a}) \end{array}) \cdot \exp (i 2 n_{0} \frac{ω}{c} l_{s}),

where

n_{0}

,

n_{l}

,

n_{a}

, and

n_{c}

are the refractive indices of the air, lipid, aqueous, and corneal epithelium;

c

is the speed of light;

l_{s}

is the length of the sample arm;

r_{1}

and

r_{2}

are the amplitude reflectances at the air-lipid and lipid-aqueous interfaces, respectively, and they follow the Fresnel reflection;

r_{3}

is the amplitude reflectance at the aqueous-cornea interface and is formulated as [19]

r_{3} = \frac{n_{a} - n_{c}}{n_{a} + n_{c}} \cdot \exp (- 2 σ^{2} n_{a}^{2} \frac{ω^{2}}{c^{2}}),

where

σ

is the standard deviation of the surface height of the aqueous-cornea interface and characterizes the roughness of the interface.

Another challenge of in vivo tear film thickness measurements comes from the curvature of the corneal surface (i.e., radius of curvature of about 7.8 mm on average). With a telecentric scanning scheme, which is widely used in OCT and was adopted in the current system, the light beam scans perpendicular to a flat surface and does not follow the curvature of the cornea. In fact, only the light incident at the apex of the cornea meets the normal incidence assumption, which is assumed in the development of the maximum-likelihood estimator in order to be able to accurately measure the lipid layer thickness. Thus, in this study, to show the feasibility of the proposed approach for in vivo measurement of both the lipid and aqueous layers thickness, spectra were acquired at the apex of the cornea.

To align the eye with the optical system, a customized chinrest was mounted on translational stages that allow a freedom of movement in three dimensions. With the translational stages, the eye of a human subject can be roughly aligned with respect to the OCT system. The interference signal from the tear film and the reference mirror is used to guide the alignment along the axial direction; once the eye is aligned along the axial direction, the reference mirror is blocked and the lateral alignment is done through a dual-axis galvanometer-based optical scanning mirror. The galvanometer-based scanning mirror steers the light beam and performs a rapid coarse scan on the corneal surface in a 3 by 3 mm area, with a 30 by 30 points sampling grid. A spectrum is acquired at each sampling point, and the energy of the collected spectrum is quantified, which is then registered with the sampling grid to form an energy distribution map. An example of the energy maps is shown in Fig. 2(a). The apex of the corneal surface is assumed to be around the point that has the maximum energy. Since the sampling grid of 100 μm is five times larger compared to the beam spot size of 20 μm (FWHM, diameter), a finer search on the corneal surface is needed. From the energy map shown in Fig. 2(a), the coordinates of the point with the maximum energy are extracted automatically and are then sent as feedbacks to the galvanometer-based scanner. The scanner immediately steers the light beam to the area around the maximum energy point [i.e., the area in the red box of Fig. 2(a)] and performs another rapid scan with a much finer step, in a 300 by 300 μm area with a 30 by 30 points grid. The energy map of the finer scanning is shown in Fig. 2(b), which is a $10 \times$ zoomed-in version of the red box area in Fig. 2(a), and the point with the maximum energy is centered. The maximum energy point on the finer map is assumed to be located at the apex of the corneal surface and its spectrum is extracted as $N g (x, Δ t)$ .

Fig. 2. Energy maps of (a) a coarse scanning over a 3 by 3 mm area and (b) a $10 \times$ zoom in of the red box area in (a).

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To estimate the thickness of both the lipid and aqueous layers of the tear film, a maximum-likelihood estimation is performed. The maximum-likelihood estimator calculates the probability that the measured spectrum $N g (x, Δ t)$ is generated by different lipid and aqueous thickness pairs and is given by

P (N_{g} | d_{l}, d_{a}) = \frac{1}{{(2 π)}^{\frac{M}{2}} \prod_{x} {[K_{N_{g | (d_{l}, d_{a})}} (x, Δ t)]}^{\frac{1}{2}}} \times \exp [- \frac{1}{2} \sum_{x} \frac{{(N_{g} (x, Δ t) - 〈 〈 〈 N_{g | (d_{l}, d_{a})} (x, Δ t) 〉 〉 〉)}^{2}}{K_{N_{g | (d_{l}, d_{a})}} (x, Δ t)}],

where

K_{N g | (d l, d a)} (x, Δ t)

is the variance of the output at the

x^{th}

pixel for a given thickness pair

(d_{l}, d_{a})

and is a second order polynomial of the ensemble mean [16], and

M

is the number of pixels in the line-scan camera. The ensemble mean for a given thickness pair is calculated using Eqs. (1)–(3). The source spectrum is calibrated by using the convex side of a plano-convex lens (Thorlabs, LA1540), which has a known dispersion property and has a radius of curvature of 7.7 mm.

The estimator makes an estimate by maximizing the conditional-likelihood in Eq. (4), which is equivalent to finding the minimum of the negative conditional log-likelihood:

({\hat{d}}_{l}, {\hat{d}}_{a}) = \begin{matrix} \arg \min \\ d_{l}, d_{a} \end{matrix} (- \log (P (N_{g} | d_{l}, d_{a}))) .

As an example to illustrate the principle, one estimation process of a spectrum acquired from a human subject is visualized in Fig. 3. Figure 3(a) is the calculated negative conditional log-likelihood of the measured spectrum being generated by different thickness pairs of lipid and aqueous layer thickness. The false color in the figure represents the conditional-likelihood. Figure 3(b) and (3c) are the profile of the cross sections along the maximum-likelihood point. The estimates for the lipid layer and aqueous layer are 55 nm and 2.17 μm, respectively.

Fig. 3. (a) Negative conditional log-likelihood of one measured spectrum is generated by different thickness pairs of lipid and aqueous layer thickness; (b) conditional log-likelihood along the red line in (a) and the lipid layer thickness estimate; (c) conditional log-likelihood along the green line in (a) and the aqueous layer thickness estimate.

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With blinks, the tear film is redistributed over the ocular surface. Tear film thickness and distribution can fluctuate over a blink cycle–affected by evaporation, surface tension, gravity, and breakup effects [24]. Simultaneous measurement of both the lipid and the aqueous tear layers can advance the understanding of the contributions of different tear layers to tear film instability observed in DED, which could lead to new and targeted therapies in the management of DED. To investigate if both the dynamics of the lipid and aqueous layers of the tear film can be simultaneously measured by the proposed approach, a normal subject was aligned with the OCT system. In this study, the light power delivered at the eye was 0.15 mW, which is at least 50 times below the maximum permissible exposure as specified by the American National Standards Institute. Data was acquired on the right eye, and the acquisition started once the subject had a complete blink. The subject was asked to keep the eye open for 10 s in the data acquisition process. Following the automatic alignment process explained in Fig. 2, the system captured four 30 by 30 fine-sampling grids per second. From each sampling grid, the spectrum of the point at the corneal apex is extracted as an input to the maximum-likelihood estimator.

To report on the repeatability and typical variations in the measurements from one subject, three dynamics curves are reported that were acquired one week apart. The measurements were carried out in a laboratory environment with a temperature of $22 \pm 1 ° C$ and relative humidity in the range of 40–50%. The simultaneously measured thickness dynamics of both the lipid layer and the aqueous layer are shown in Fig. 4. The three dynamics measurements from one subject have an average standard deviation of 8 nm for the lipid layer and 0.44 μm for the aqueous layer. The dynamics trends of the three observations are consistent. The dynamics curves of the lipid layer show that right after a complete blink, the lipid layer gets thicker rapidly; the thickening rate ranges from 5 to $18 nm / s$ with an average of $10 nm / s$ , and it stabilizes after an average of 2.5 s. The aqueous layer gets thinner gradually with an average thinning rate of $0.29 μm / s$ . The thickening of the lipid layer may be explained by the rapid upward drift of the lipid right after a blink, as observed by King-Smith with an imaging interferometry approach [25]. After the lipid layer reaches stability, the thickness is similar to prior findings from interferometry [26]. The thinning of the aqueous layer is also consistent with the results from previous reports [13,14,27].

Fig. 4. Repeated measurements of the tear film dynamics of both the lipid and aqueous layers over the corneal apex of one subject over a three week period. Each color represents a measurement, and the measurements were taken one week apart.

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In conclusion, the thickness dynamics of the lipid and aqueous layers have been successfully measured in vivo; the proposed approach is shown to be feasible to investigate the tear film dynamics. In vivo studies in a pool of at least 25 normal and 25 DED subjects will be carried out to begin characterizing the tear layers dynamics in both healthy and dry eye subjects, as well as understanding the variations between subjects. Further development of the technique will integrate a scanning scheme that will allow normal incidence of the scanning beam along the corneal surface, enabling measurements of thickness maps.

Funding

II VI Foundation Block-Gift Program (GR506127); University of Rochester PumpPrimer Grant (OP212541); Research to Prevent Blindness Unrestricted Grant.

Acknowledgment

This research benefited from stimulating discussions with James Aquavella and Patrice Tankam as well as technical support from Di Xu and Amy Entin. Finally, we deeply thank Mare Perevich for her assistance with the Institutional Review Board approval process.

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In vivo thickness dynamics measurement of tear film lipid and aqueous layers with optical coherence tomography and maximum-likelihood estimation

Abstract

Funding

Acknowledgment

REFERENCES

Cited By

Figures (4)

Equations (5)

Optics Letters