July 2016
Volume 57, Issue 9
Open Access
Articles  |   July 2016
Structural Changes Induced by a Corneal Shape-Changing Inlay, Deduced From Optical Coherence Tomography and Wavefront Measurements
Author Affiliations & Notes
  • Alan J. Lang
    Research and Development ReVision Optics, Inc., Lake Forest, California, United States
  • Keith Holliday
    Research and Development ReVision Optics, Inc., Lake Forest, California, United States
  • Arturo Chayet
    Codet Vision, Tijuana, Mexico
  • Enrique Barragán-Garza
    Laser Ocular Hidalgo, Monterrey, Mexico
  • Nikhita Kathuria
    Research and Development ReVision Optics, Inc., Lake Forest, California, United States
  • Correspondence: Alan Lang, ReVision Optics, Inc., 25651 Atlantic Ocean Boulevard, Suite A1, Lake Forest, CA 92630, USA; alang@revisionoptics.com
Investigative Ophthalmology & Visual Science July 2016, Vol.57, OCT154-OCT161. doi:10.1167/iovs.15-18858
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      Alan J. Lang, Keith Holliday, Arturo Chayet, Enrique Barragán-Garza, Nikhita Kathuria; Structural Changes Induced by a Corneal Shape-Changing Inlay, Deduced From Optical Coherence Tomography and Wavefront Measurements. Invest. Ophthalmol. Vis. Sci. 2016;57(9):OCT154-OCT161. doi: 10.1167/iovs.15-18858.

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

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Abstract

Purpose: Changes to the anterior stroma and epithelium induced by a meniscus-shaped corneal inlay are presented. The hypothesis that local curvature is a driver of epithelial remodeling is tested.

Methods: Records of 30 subjects enrolled in a prospective clinical investigation of the inlay, implanted in emmetropic presbyopic subjects, were analyzed. The change to the anterior corneal surface was measured using wavefront techniques. The epithelial thinning profile was measured using Fourier domain optical coherence tomography. The stromal change was calculated from the two measurements.

Results: The inlay's volume displaced the stroma anterior to the inlay, which was reflected in the change of Bowman's layer shape. The epithelium anterior to the inlay thinned by 18.4 ± 7.1 μm. Peripheral to the inlay's diameter (2 mm), circumferential epithelial thickening extended the change to the anterior corneal surface to approximately twice the inlay diameter. The central anterior corneal surface rose by 9.8 ± 3.4 μm, creating a progressive add power profile. The epithelial thinning was linearly related to the curvature of the alteration to the anterior surface height, consistent with a theoretical model.

Conclusions: When a meniscus-shaped corneal inlay is placed beneath a corneal flap, the flap's stroma takes on predominately the inlay's shape. The epithelium remodels within a zone approximately twice the inlay diameter, with an anterior corneal height change providing improved near and intermediate vision. The relationship between the epithelial, stromal, and anterior corneal surface changes confirms the hypothesis that epithelial changes are greatest in regions of greater local surface curvature.

A variety of surgical techniques has attempted improvement of near and intermediate vision for presbyopic individuals. Currently, the most frequently utilized are monovision with either laser-assisted in situ keratomileusis (LASIK) or photorefractive keratectomy (PRK)1,2 or implantation of multifocal intraocular lenses with or without cataract.3 More recently, three different approaches made use of corneal inlays. The US Food and Drug Administration (FDA)-approved KAMRAInlay (Acufocus, Irvine, CA, USA) extends depth-of-focus from distance through near, by placing a pin-hole (1.6 mm diameter) in an annular disk of diameter 3.8 mm, at the center of the visual axis.4 The Flexivue Microlens (Presbia, Irvine, CA, USA) inlay is a donut-shaped, high-refractive-index lens that provides distance vision through its central zone (1.6 mm diameter) and the pupillary periphery outside the inlay, and near vision though the curved portion of the 3.2-mm-diameter inlay.5 The Flexivue Microlens is currently in an FDA clinical trial. 
The third corneal inlay, submitted to the FDA for premarket approval, is the Raindrop Near Vision Inlay (ReVision Optics, Inc., Lake Forest, CA, USA), whose shape and volume biomechanically elevates the cornea's anterior surface, creating a central zone with increased power within the pupil.68 The inlay's index of refraction is very close to that of the cornea. Thus the Raindrop inlay's shape does not induce intrinsic power. The Raindrop Near Vision Inlay has a meniscus-shape, is 2 mm in diameter, and is nominally 34 μm thick at the center and 14 μm thick at the edge. It is composed of a hydrogel material and is permeable to oxygen and glucose.9 
For the first time, we present the biomechanical stromal changes and epithelial remodeling induced by the volume of a corneal inlay and provide new insights regarding the mechanism of epithelial remodeling. 
Patients and Methods
Thirty sets of clinical records were selected from patients enrolled in a prospective clinical trial at two research sites in Mexico under the same protocol. Emmetropic subjects were implanted in the nondominant eye with the Raindrop Near Vision Inlay, designed to improve near and intermediate vision in presbyopic subjects. The protocol adhered to the tenets of the Declaration of Helsinki and was approved by the following institutional review boards: Universidad de Monterrey, Division de Ciencias de la Salud, Comité de Investigación y Ética, and Centro Oftalmologico de Tijuana S.A. de C.V. Comision de Investigación y Ética. Patients signed a written informed consent after explanation of the nature and possible consequences of the study. Patients were enrolled if the preoperative manifest spherical equivalent (MSE) was stable and between −0.5 and +1.0 diopters (D) (emmetropic), cylinder ≤ 0.75 D, spectacle add between and including +1.5 to +2.5 D (presbyopic), and best-corrected distance and near visual acuity equal to or better than 0.1 logMAR (20/25 Snellen), and subjects screened for preexisting corneal or other health issues.10 
The inlay is surgically placed at the center of the light-constricted pupil, under an 8-mm or greater diameter flap created by a femtosecond laser (IntraLase FS; Abbott Medical Optics, Santa Ana, CA, USA). More details concerning patient selection and the surgical procedure were previously reported in Barragán-Garza et al.10 
The intent of this analysis is to identify the epithelial and stromal changes induced by the inlay. The 6-month postoperative visit was selected because patient's visual acuity and refraction were stable.10 Patient records were reviewed and included if the following criteria were met: no clinically significant haze or superficial punctate keratitis (SPK) as judged by slit-lamp examination; the inlay radially located within 0.5 mm of the pupil center as determined by wavefront measurements; and preoperative and postoperative optical coherence tomography (OCT) scans available and of sufficient quality for analysis. One subject had SPK at the 6-month visit, which resolved at the 9-month exam without treatment. 
Visual acuity outcomes were measured with the Optec 6500 Vision Tester (Stereo Optical Co., Inc., Chicago, IL, USA). 
OCT Image Analysis
Fourier domain OCT scans were recorded using the RTVue−100 system (Optovue, Inc., Fremont, CA, USA), augmented with the adaptor lens (CAM-L mode) and software for corneal measurements. Six-millimeter-length cross-scans (one horizontal and one vertical) were recorded, attempting to center the cross at the center of the inlay at postoperative examinations and on the center of the pupil preoperatively. The best image, horizontal or vertical, was exported as a JPEG image file. The OCT image vertical (4.4 μm/pixel) and horizontal (6.5 μm/pixel) calibrations were determined by placing dimensional length bars on the OCT images using the measurement tool included in the Optovue software. The number of pixels along the each dimensional bar was determined in the exported OCT images, allowing calculation of the microns per pixel calibration. The manufacturer's optical instrument resolution is stated to be 5 μm, similar to the OCT image pixel size, suggesting that the exported images contain all information available. Figure 1 presents one patient's preoperative and postoperative OCT images. 
Figure 1
 
An example of the preoperative and postoperative (6 month) OCT images for one patient implanted with the inlay, with an overlay of the images showing the digitized preoperative surfaces in red and the postoperative surfaces in blue.
Figure 1
 
An example of the preoperative and postoperative (6 month) OCT images for one patient implanted with the inlay, with an overlay of the images showing the digitized preoperative surfaces in red and the postoperative surfaces in blue.
A custom MATLAB (MathWorks, Natick, MA, USA) software program was written to assist the operator in digitizing the anterior and posterior corneal surfaces, the position of Bowman's layer, and the anterior and posterior inlay surfaces. Figure 1 includes an overlay of the postoperative and preoperative OCT images, showing the preoperative digitized surfaces in red and the postoperative digitized surfaces in blue. The software fits a best-fit sphere to the posterior corneal surface over approximately a 5 mm diameter, centered on the inlay in the postoperative examinations. Normals to these surface are determined. Along these normals, thicknesses between various corneal features were measured (e.g., the anterior corneal surface and the location of Bowman's layer were used to measure the epithelial thickness). The epithelial thickness profile was determined every 0.05 mm horizontally across the cornea, preoperatively centered on pupil and postoperatively centered on the inlay. In these measurements, the epithelial thickness includes the tear film layer, and the posterior aspect of the epithelial thickness is the upper boundary of Bowman's layer (Fig. 1). 
Wavefront Measurements for Anterior Surface Change
In Figure 1, one observes pixel saturation (bright white pixel intensity extending over adjacent pixels) on the anterior corneal surface, above the inlay. This occurs in nearly every image, because the operator is centering on the inlay. Because of this pixel saturation and the vertical 4.4-μm pixel size, the change to the anterior corneal surface in Figure 1 is difficult to accurately measure. Rather, we determined the anterior corneal surface height change from wavefront measurements, using the iTrace aberrometer (Tracey Technologies, Houston, TX, USA). The presence of the inlay alters the anterior corneal surface and increases the total length of the eye by height Δh. Wavefront measurements quantify the optical path length (OPL), which is the physical length × the index of refraction. Postoperatively, this additional corneal height adds Δh × nc to the wavefront OPL, where nc is the corneal index of refraction (1.376). We assume that the only change to the total eye wavefront was this alteration of the anterior corneal surface. This is reasonable because the subjects are presbyopic, and the Tracey instrument stimulus is set at infinity. The comparison of the postoperative wavefront OPL with the preoperative wavefront OPL must be done at the same physical point in space, which is Δh anterior to the preoperative corneal surface. Thus, the preoperative contribution to the wavefront OPL is Δh, located in air. The anterior surface height change profile [Δh(r)] is calculated from the wavefront difference profile [ΔW(r)], the latter reflecting the change in OPL: Δh(f) = ΔW(r)/(nc − 1). The inlay's thickness does not contribute wavefront OPL, because the inlay's index of refraction is equal to that of the cornea. Following measurement, the Zernike files were exported and read by another custom MATLAB software program. After calculating the postoperative − preoperative wavefront 3D difference map, the center of the inlay effect was located and recorded with respect to the center of the pupil. Surrounding inlay center, 16 radial profiles were interpolated and averaged to yield the mean radial inlay effect height profile. 
Epithelial and Stromal Analysis
As indicated in Figure 2, placement of the inlay on the flap bed raises the stroma anterior to the inlay. This alters the shape of the Bowman's layer profile [ΔBowShape(r)]. Initially, the epithelium is raised, but epithelial remodeling or “flow” reduces the rise, coming to equilibrium and a final change to the anterior corneal surface [ΔAntCornShape(r)]. Geometrically in Figure 2  where EpiThickpost(r) and EpiThickpre(r) are, respectively, the postoperative and preoperative epithelial thickness profiles. Based on separate analysis, the thickness of Bowman's layer remained unchanged with implantation of the inlay, to within the resolution of the OCT measurement. In Equation 1, the change to the anterior corneal surface was more accurately derived from the wavefront measurements, and the preoperative and postoperative epithelial thickness profiles were derived from the OCT measurements. The change in the Bowman's layer shape was calculated using Equation 1. In principal, the change in the Bowman's layer shape can be derived from OCT measurements. However, alignment with the preoperative Bowman's layer location or selection of a postoperative reference location beyond the inlay effect zone is problematic, especially given the limitations of the pixel size (e.g., 4.4 μm/6.5 μm). In separate unpublished analysis, we confirmed that direct measurement of the change in Bowman's layer location by various methods is consistent with the approach in Equation 1.  
Figure 2
 
A diagram showing the change in anterior corneal surface shape (ΔAntCornShape), the change in epithelial thickness (EpiThickpost − EpiThickpre), and the change in Bowman's layer shape (ΔBowShape), induced by the inlay.
Figure 2
 
A diagram showing the change in anterior corneal surface shape (ΔAntCornShape), the change in epithelial thickness (EpiThickpost − EpiThickpre), and the change in Bowman's layer shape (ΔBowShape), induced by the inlay.
Equation 1 makes the assumption that the inlay does not alter the stroma posterior to the inlay. In the OCT images, the inlay does not appear to sit into the posterior stroma (Fig. 1). Additionally, visual overlay of the preoperative and postoperative posterior corneal surfaces, with attention to finding the best match of the preoperative posterior surface shape with that of the postoperative posterior surface shape, centered on the inlay location, showed no indication of the inlay systematically flattening the posterior corneal surface below the inlay (Fig. 1). Although a formal numerical analysis might have been possible, the repetition of the above observations across other subjects led us to assume that the stroma below the inlay was unchanged. 
The operative flap thickness was estimated from the OCT and the wavefront measurements, averaging profiles over ±0.4 mm from the inlay center, and using a similar geometry    
Results
Clinical Outcomes
For these 30 patients at the 6-month visit, the uncorrected near (40 cm) visual acuity improved by four lines (P < 0.01), from 0.46 ± 0.08 logMAR (20/58) preoperatively to 0.03 ± 0.08 logMAR (20/22) postoperatively. Uncorrected intermediate (80 cm) visual acuity improved by two lines (P < 0.01), from 0.32 ± 0.09 logMAR (20/41) preoperatively to 0.10 ± 0.06 logMAR (20/25) postoperatively. Uncorrected distance visual acuity in the treated eye lost two lines (P < 0.01), from 0.01 ± 0.12 logMAR (20/21) preoperatively to 0.17 ± 0.15 logMAR (20/30) postoperatively. However, the loss in best-corrected distance visual acuity was not clinically significant (−0.03 ± 0.05 logMAR) but was statistically significant (P = 0.01). Likewise, the change in binocular uncorrected distance visual acuity was not clinically significant (0.03 ± 0.12 logMAR) or statistically significant (P = 0.21). Thus, both eyes contribute to uncorrected distance vision, with the untreated eye providing the highest spatial frequencies (highest visual acuity). The treated eye significantly improved near and intermediate visual abilities. The 1-year clinical outcomes of patients enrolled in the emmetropic protocol are discussed in detail in Barragán-Garza et al.10 
Anterior Corneal Surface Change
The mean (N = 30) change to the anterior corneal surface (ΔAntCornShape), induced by the inlay's volume, is presented in Figure 3. The average central height increased by 9.8 ± 3.4 μm, with progressively less change at larger radii, and returned to the unaltered preoperative corneal surface at a 2.5 mm radius from the inlay center. Thus, the inlay's effect zone is approximately twice the inlay's physical diameter. The axial add power profile11 was calculated from this anterior surface change and is shown in Figure 3. About 5 D of refractive add power was induced at the center of the pupil, falling below 0.25 D at the 4 mm diameter, providing the mechanism for the improved uncorrected near and intermediate visual acuity discussed above.6 
Figure 3
 
The mean change (N = 30) of the anterior corneal surface height, derived from wavefront measurements (solid line). Error bars denote 1 SD. The axial power, induced by this anterior surface change (dashed line).
Figure 3
 
The mean change (N = 30) of the anterior corneal surface height, derived from wavefront measurements (solid line). Error bars denote 1 SD. The axial power, induced by this anterior surface change (dashed line).
Figure 4 correlates the change in central anterior corneal surface height with the preoperative corneal and epithelial thicknesses. The latter two are averages of the profiles within ±0.4 mm of the center of the scan. Although the anterior corneal surface height change varies among patients, it is not a function of the preoperative corneal or epithelial thickness. Additionally, no correlation was found between the change in the central anterior corneal surface height and either preoperative corneal power or patient age. 
Figure 4
 
Correlation of the change in central anterior corneal surface height at the 6-month visit with the preoperative corneal and preoperative epithelial thicknesses.
Figure 4
 
Correlation of the change in central anterior corneal surface height at the 6-month visit with the preoperative corneal and preoperative epithelial thicknesses.
Epithelial Thickness Profile Remodeling
Preoperatively, the centrally averaged (±0.4 mm from pupil center) epithelial thickness was 52.1 ± 5.9 μm; postoperatively, it was 33.7 ± 4.4 μm. The epithelial thinning profile was calculated as the postoperative epithelial thickness profile − the centrally averaged preoperative epithelial thickness, and the mean (N = 30) change is presented in Figure 5. In the presence of the inlay, the epithelium thins by 18.4 ± 7.1 μm within ±0.4 mm of the inlay center. The epithelial thickness returns to the preoperative thickness just outside the inlay diameter. There is a hint of an epithelial thickening peripheral to the inlay diameter (2 mm), which is also suggested in the overlay image in Figure 1. Most OCT images suggest a similar peripheral thickening. However, the mean peripheral change is less than 2 μm, which is less than the measurement error; 1 SD is approximately 6 μm (Fig. 5). 
Figure 5
 
The mean change in epithelial thickness derived from OCT measurements. Error bars denote 1 SD.
Figure 5
 
The mean change in epithelial thickness derived from OCT measurements. Error bars denote 1 SD.
Figure 6 correlates the central epithelial thinning (average of ±0.4 mm from center of inlay) with the preoperative central corneal thickness and the postoperative anterior corneal surface height change. The epithelial thinning varies among patients, but is not a function of the preoperative corneal thicknesses. Interestingly, the postoperative change to the anterior corneal surface is also independent of the epithelial thinning. Also, epithelial thinning was not correlated with either preoperative age (R2 < 0.01) or preoperative corneal power (R2 = 0.01). 
Figure 6
 
Correlation of the central epithelial thinning at the 6-month visit with the preoperative corneal thickness and the postoperative central anterior corneal surface height change.
Figure 6
 
Correlation of the central epithelial thinning at the 6-month visit with the preoperative corneal thickness and the postoperative central anterior corneal surface height change.
Curvature as a Driver of Epithelial Remodeling
The mathematical first-order flow model of epithelial remodeling proposed by Huang et al.12 states that the epithelial thickness changes more in regions where the curvature of the stromal shape is greatest. In our case, the stromal shape altered by the inlay is reflected in the change to Bowman's layer shape (ΔBowShape) (Fig. 1). The change in Bowman's layer shape is the driver of the epithelial thickness change. As the remodeling comes to equilibrium, the model of Huang et al.12 predicts that the epithelial thinning should be proportional to the curvature of the alteration to the anterior corneal surface (Equation 13 in Huang et al.12). In our notation  where s2 is the proportionality constant in the model of Huang et al.12 The value of s is interpreted by the model of Huang et al.12 as “the radius over which smoothing occurs” (i.e., a smoothing constant).  
To test this theoretical linearity using our independent wavefront and OCT measurements, the mean anterior corneal surface height change in Figure 3 was fit to an eighth-order symmetric radial polynomial (Fig. 7), and the second-order derivative was calculated analytically at each radial location (e.g., Equation 3). Figure 8 plots the mean epithelial thinning (from Fig. 5) as a function of the “curvature” of the anterior corneal surface height change at each corresponding radius. Note that the left and right segments of the cross-sectional profile in Figure 5 were averaged around r = 0, the center of the inlay, to yield a single representative radial epithelial thinning profile. Two regions of linearity are found in Figure 8. Where the epithelial thinning is greatest at the center of the inlay effect (r = 0 mm to r = 0.6 mm in Fig. 5), from the measured slope, the equivalent Huang smoothing constant was calculated to be 0.48 mm. Over the more peripheral radial zone (r = 0.7 mm to r = 1.2 mm in Fig. 5), the equivalent Huang smoothing constant was calculated to be 1.25 mm. 
Figure 7
 
Fit of the mean anterior corneal surface height change profile to an eighth-order symmetric polynomial.
Figure 7
 
Fit of the mean anterior corneal surface height change profile to an eighth-order symmetric polynomial.
Figure 8
 
Correlation of the mean change in epithelial thickness with the mean curvature of the anterior corneal surface height change. The smoothing constants from the model of Huang et al.12 were calculated from the linear slopes indicated.
Figure 8
 
Correlation of the mean change in epithelial thickness with the mean curvature of the anterior corneal surface height change. The smoothing constants from the model of Huang et al.12 were calculated from the linear slopes indicated.
Anterior Stroma Profile Remodeling
Using Equation 1 and the profiles in Figures 3 and 5, mean change in Bowman's layer shape (ΔBowShape) was calculated and is shown in Figure 9 (thick solid line). The change to the shape of Bowman's layer reflects the biomechanical alteration of the stroma anterior to the inlay. Figure 9 compares ΔBowShape profile to the nominal inlay's designed thickness profile (dashed line). The inlay's volume was calculated by integrating the circularly symmetric radial inlay thickness profile and is 0.073 mm3. To estimate the volume under the ΔBowShape from the mean cross-sectional profile in Figure 9, a single radial profile was derived by averaging the right and left segments of the profile around r = 0, the center of the inlay. Assuming again circular symmetry, integrating this single profile within the 1.25 mm radius where the mean ΔBowShape profile is nonzero, an estimate of the volume under the change in Bowman's layer is 0.076 ± 0.038 mm3. This is equal to the inlay's designed volume to within the measurement accuracy. Centrally, the anterior stromal rose 28.2 ± 8.3 μm, slightly less than the inlay's 33-μm central thickness. The inlay volume lost within the anterior stroma immediately above the inlay diameter (2 mm) was recovered just outside the inlay diameter (Fig. 9). 
Figure 9
 
The mean change of the Bowman's layer profile (thick solid line), calculated from the anterior surface and epithelial change profiles (thin solid lines). Error bars denote 1 SD. The nominal inlay profile (dashed line).
Figure 9
 
The mean change of the Bowman's layer profile (thick solid line), calculated from the anterior surface and epithelial change profiles (thin solid lines). Error bars denote 1 SD. The nominal inlay profile (dashed line).
Figure 10 correlates the central (±0.4 mm from inlay center) rise in Bowman's layer with the operative flap thickness and the ratio of flap to total corneal thickness. There is only a suggestion of greater penetration of the inlay (a larger change in Bowman's elevation) with shallower operative flaps, which is not statistically significant. Note also that the change in central Bowman's height exceeded the nominal inlay thickness (33 μm centrally averaged) with a few patients. The difference for most of these points was equivalent to two pixels or less, highlighting the limitations inherent in these OCT measurements. Also, the central rise in Bowman's layer was not correlated with either preoperative age (R2 < 0.01) or preoperative corneal power (R2 < 0.01). 
Figure 10
 
Correlation of the rise in the central Bowman's layer thickness at the 6-month visit with the operative flap thickness and relative flap thickness.
Figure 10
 
Correlation of the rise in the central Bowman's layer thickness at the 6-month visit with the operative flap thickness and relative flap thickness.
Discussion
When the Raindrop Near Vision Inlay is placed under a flap inside the cornea, the inlay raises the stroma anterior to the inlay, which is reflected in a change to the shape of Bowman's layer (Fig. 9). To within measurement accuracy, the volume under the change in Bowman's layer shape is equal to the inlay's designed volume. However, the central (±0.4 mm from inlay center) increase in stromal thickness above the inlay (28 μm) is on average 85% of the inlay's designed central thickness (33 μm). The stromal volume lost directly above the inlay diameter is recovered just outside the inlay diameter (Fig. 9). Thus, there is a small amount of stromal redistribution, but the actual mechanism is not revealed in these measurements. 
The rise in stroma anterior to the inlay, reflected in the change to Bowman's layer shape, initially lifts the overlying epithelium. After remodeling, the central epithelial thickness thins by approximately 18 μm, accounting for 64% of the anterior stromal thickness increase (28 μm). Peripheral to the inlay diameter (2 mm), the epithelial thinning reduces quickly (Fig. 9), and there is a hint of a peripheral thickening. The latter is also seen in OCT images (Fig. 1). However, the thickening is less than 2 μm, which is less than the resolution of the OCT measurement technique. The remaining 10 μm of anterior stromal rise (28 − 18 μm) is reflected in the final elevation of the anterior corneal surface (Fig. 9). Because of the redistribution of the epithelium, the inlay effect extends to approximately twice the inlay diameter (Fig. 9). 
Various mechanisms underlying epithelial remodeling in myopic LASIK, hyperopic LASIK, and keratoconus have been proposed. Foremost is the concept that regions of the anterior corneal surface with the greatest change in curvature are likely to experience the greatest redistribution of epithelial cells, in response to exterior forces such as the eye lids and/or interepithelial cell tension.1316 This is at least partially confirmed by a mathematical model of epithelial remodeling, based on flow in response to tan anterior corneal surface gradient,12 which predicts the general epithelial changes with myopic and hyperopic LASIK. The model of Huang et al.12 predicts a linear relationship between the curvature of the alteration to the anterior corneal surface and the change in epithelial thickness. This was tested in Figure 8, making use of two independent measurements: the wavefront technique for the anterior surface change and OCT analysis for the change in epithelial thickness. The linear relationship is confirmed in Figure 8, but, interestingly, two linear regions are found. 
The driver for initiation of the epithelial remodeling in the Huang formalism is the rise in the stroma, anterior to the inlay, induced by the inlay's volume and reflected in the change to Bowman's layer shape (Fig. 9). The epithelium responds by thinning, altering the anterior corneal surface shape (Ref. 12, Equation 12). The magnitude of the epithelial thinning is proportional to the local curvature of the anterior corneal surface height change (Ref. 12, Equation 13), which initially must be very strong. In time, this curvature must decrease as the anterior corneal surface height spreads more peripherally, reducing the central anterior corneal surface height and flow to the periphery. However, the underlying (static) anterior stromal profile remains. The differential or step-by-step change to the anterior corneal surface is quantified by Equation 14 in Huang et al.,12 accounting for the influence of the static anterior stromal shape and the local diffusion induced by the anterior corneal surface height change. Eventually, an equilibrium is achieved with the epithelium thinning over the center of the inlay, a possible slight epithelial thickening midperiphery, and a return to the unaltered epithelial thickness in the far periphery (Fig. 9). 
In equilibrium, over the inlay where both the epithelial thinning is greatest (17–19 μm) and the slope of the underlying anterior stromal change is flattest (within ±0.6 mm from inlay center; Fig. 9), a linear region exists in Figure 8 with a Huang smoothing value of 0.48. The curvature of the anterior corneal surface is negative, maintaining a tendency to reduce in the local epithelial thickness (Equation 3). The smoothing constant is within the range of values found for hyperopic and myopic LASIK, discussed in Huang et al.,12 and likely reflective of the gradual ablation profiles found with moderate hyperopic and myopic LASIK. A second linear region exists in Figure 8, equivalent to the radial region beyond 0.7 mm from the inlay center, where the epithelial thinning decreases and the slope of the underlying anterior stromal change (Fig. 9) is stronger. The Huang smoothing constant is 1.25, and the curvature of the anterior corneal height change (Fig. 8) is positive. This maintains a tendency for epithelial thickening (Equation 3), suggested in Figure 9 but limited by the accuracy of the measurements. The existence of a second linear region, with a different smoothing constant, hints that the process of epithelial “flow” is more complex, as anticipated by Huang et al.12 Nevertheless, the thesis that epithelial remodeling is driven by the local curvature of the underlying stromal change is supported by the two linear regions in Figure 8, corresponding to the two significantly different regions of underlying anterior stromal change shapes in both slope and curvature. 
However, what stops the remodeling, leading to the equilibrium state (e.g., the central thickening in myopic LASIK17 and the central thinning in hyperopic LASIK18 or over the keratoconic cone)?19 One proposal is that the local slope drops below some threshold, resulting in a diminished response to the force moving epithelial cells.13,14 Another proposal is that the connections between adjacent epithelial cells eventually overcome the response due to the epithelial gradient.16 In the case of this inlay, the equilibrium state maintains a large epithelial thinning gradient (16 μm over 0.5 mm) with a Huang smoothing constant nearly twice that of LASIK. 
We propose another concept based on the epithelial cell anatomy, which can include the above two mechanisms. This new concept was initially prompted by observation that the epithelial thinning was not clearly correlated with other parameters (Fig. 6) and the observation in Figure 11, which plots the central postoperative epithelial thickness against the preoperative epithelial thickness. The range (14 μm) and SD (4.4 μm) of postoperative epithelial thicknesses are smaller than the range (20 μm) and SD (5.9 μm) of preoperative thicknesses. Combined, this suggests that some physical element of the epithelium may limit the epithelial thinning. Figure 12 diagrams one ideal representation of the preoperative epithelial thickness anatomy, consistent with the mean preoperative epithelial thickness of the 30 patients (52 ± 5.9 μm). The representation was motivated by the discussion of epithelial anatomy found in chapter 1 in Cornea.20 Remembering that OCT measurements include the tear film, in this representation, the true epithelium is composed here of three layers of superficial cells, two layers of wing cells, and a single layer of basal cells. The cells morph from vertically columnar basal cell to much thinner horizontally extended outer superficial cells. Because of this geometry, the superficial cells are more likely to be “fluid” in response to external forces. In response to the stromal lift from the inlay's volume, we propose that the superficial cells in the regions of greatest epithelial thickness curvature “flow” more peripherally until the resistance of the lower wing cells stops the flow. We propose that the shape of the more columnar cells is an additional factor in the resistance, in addition to intercellular connections. The mean postoperative epithelial thickness (34 ± 4.4 μm) can be accounted for by removal of the three superficial cell layers and modification of the lower wing cells into something in shape and size between wing and superficial cell geometry (see the postoperative diagram in Fig. 12). This concept is very difficult to study in vivo with commercial diagnostics. However, histology with animal studies or very careful confocal scans in a research environment might be able to differentiate components of the various proposals. 
Figure 11
 
Correlation of the central postoperative (at 6 months) and preoperative epithelial thicknesses, with the range and SD of each shown.
Figure 11
 
Correlation of the central postoperative (at 6 months) and preoperative epithelial thicknesses, with the range and SD of each shown.
Figure 12
 
A theoretical representation of the preoperative and postoperative epithelial cellular structure, showing the superficial, wing, and basal layers, consistent with the mean epithelial changes observed. The structural differences illustrate the suggestion that during epithelial remodeling, superficial layers are removed, wing cell layers reshape to more superficial shapes, and the basal layer is unaltered.
Figure 12
 
A theoretical representation of the preoperative and postoperative epithelial cellular structure, showing the superficial, wing, and basal layers, consistent with the mean epithelial changes observed. The structural differences illustrate the suggestion that during epithelial remodeling, superficial layers are removed, wing cell layers reshape to more superficial shapes, and the basal layer is unaltered.
Thinning of the epithelium occurs with other ophthalmic refractive procedures or corneal pathologies. In hyperopic LASIK, the untreated central zone thins by approximately 8 μm in response to the peripheral ablation and midperipheral thickening.18 Comparing the mean of keratoconic (KC) subjects to normals, the epithelium above the cone thins on the order of 9 μm, in response to the stromal thinning and anterior buldging.19 Keratoconic thinning is a function of the KC grade, thinning between approximately 14 and 19 μm at the highest level.21 Our review of the hyperopic LASIK literature and that for mildly keratoconic subjects revealed no discussion of a conclusive secondary adverse corneal condition associated with the epithelial thinning. This is consistent with the longer-term outcomes (1 year) of these 30 Raindrop Near Vision Inlay patients.10 
Overall, the stromal and epithelial remodeling induced by the corneal shape changing Raindrop Near Vision Inlay provides significant improvement in near and intermediate visual acuity, with no loss of binocular distance acuity. By combining independent wavefront and OCT measurements, we confirm that regions of higher local curvature experience more epithelial thickness changes in equilibrium. The underlying driver of the remodeling, the stromal shape change, gives rise to multiple linear regions characterized by different Huang12 smoothing scales. We propose that geometry of the superficial, wing, and basal cells, in addition to intercellular connections, may play a role in the cessation of epithelial remodeling (flow), especially with a strong epithelial thickness gradient in equilibrium. 
Acknowledgments
The authors wish to acknowledge the reviewers whose particularly detailed and thoughtful review, with an important request for additional analysis, significantly improved this manuscript. 
Disclosure: A.J. Lang, (E), P; K. Holliday, (E), P; A. Chayet, (C); E. Barragán-Garza, (C); N. Kathuria, (E) 
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Figure 1
 
An example of the preoperative and postoperative (6 month) OCT images for one patient implanted with the inlay, with an overlay of the images showing the digitized preoperative surfaces in red and the postoperative surfaces in blue.
Figure 1
 
An example of the preoperative and postoperative (6 month) OCT images for one patient implanted with the inlay, with an overlay of the images showing the digitized preoperative surfaces in red and the postoperative surfaces in blue.
Figure 2
 
A diagram showing the change in anterior corneal surface shape (ΔAntCornShape), the change in epithelial thickness (EpiThickpost − EpiThickpre), and the change in Bowman's layer shape (ΔBowShape), induced by the inlay.
Figure 2
 
A diagram showing the change in anterior corneal surface shape (ΔAntCornShape), the change in epithelial thickness (EpiThickpost − EpiThickpre), and the change in Bowman's layer shape (ΔBowShape), induced by the inlay.
Figure 3
 
The mean change (N = 30) of the anterior corneal surface height, derived from wavefront measurements (solid line). Error bars denote 1 SD. The axial power, induced by this anterior surface change (dashed line).
Figure 3
 
The mean change (N = 30) of the anterior corneal surface height, derived from wavefront measurements (solid line). Error bars denote 1 SD. The axial power, induced by this anterior surface change (dashed line).
Figure 4
 
Correlation of the change in central anterior corneal surface height at the 6-month visit with the preoperative corneal and preoperative epithelial thicknesses.
Figure 4
 
Correlation of the change in central anterior corneal surface height at the 6-month visit with the preoperative corneal and preoperative epithelial thicknesses.
Figure 5
 
The mean change in epithelial thickness derived from OCT measurements. Error bars denote 1 SD.
Figure 5
 
The mean change in epithelial thickness derived from OCT measurements. Error bars denote 1 SD.
Figure 6
 
Correlation of the central epithelial thinning at the 6-month visit with the preoperative corneal thickness and the postoperative central anterior corneal surface height change.
Figure 6
 
Correlation of the central epithelial thinning at the 6-month visit with the preoperative corneal thickness and the postoperative central anterior corneal surface height change.
Figure 7
 
Fit of the mean anterior corneal surface height change profile to an eighth-order symmetric polynomial.
Figure 7
 
Fit of the mean anterior corneal surface height change profile to an eighth-order symmetric polynomial.
Figure 8
 
Correlation of the mean change in epithelial thickness with the mean curvature of the anterior corneal surface height change. The smoothing constants from the model of Huang et al.12 were calculated from the linear slopes indicated.
Figure 8
 
Correlation of the mean change in epithelial thickness with the mean curvature of the anterior corneal surface height change. The smoothing constants from the model of Huang et al.12 were calculated from the linear slopes indicated.
Figure 9
 
The mean change of the Bowman's layer profile (thick solid line), calculated from the anterior surface and epithelial change profiles (thin solid lines). Error bars denote 1 SD. The nominal inlay profile (dashed line).
Figure 9
 
The mean change of the Bowman's layer profile (thick solid line), calculated from the anterior surface and epithelial change profiles (thin solid lines). Error bars denote 1 SD. The nominal inlay profile (dashed line).
Figure 10
 
Correlation of the rise in the central Bowman's layer thickness at the 6-month visit with the operative flap thickness and relative flap thickness.
Figure 10
 
Correlation of the rise in the central Bowman's layer thickness at the 6-month visit with the operative flap thickness and relative flap thickness.
Figure 11
 
Correlation of the central postoperative (at 6 months) and preoperative epithelial thicknesses, with the range and SD of each shown.
Figure 11
 
Correlation of the central postoperative (at 6 months) and preoperative epithelial thicknesses, with the range and SD of each shown.
Figure 12
 
A theoretical representation of the preoperative and postoperative epithelial cellular structure, showing the superficial, wing, and basal layers, consistent with the mean epithelial changes observed. The structural differences illustrate the suggestion that during epithelial remodeling, superficial layers are removed, wing cell layers reshape to more superficial shapes, and the basal layer is unaltered.
Figure 12
 
A theoretical representation of the preoperative and postoperative epithelial cellular structure, showing the superficial, wing, and basal layers, consistent with the mean epithelial changes observed. The structural differences illustrate the suggestion that during epithelial remodeling, superficial layers are removed, wing cell layers reshape to more superficial shapes, and the basal layer is unaltered.
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