Journal of Refractive Surgery

Original Article Supplemental Data

Epithelium Zernike Indices and Artificial Intelligence Can Differentiate Epithelial Remodeling Between Flap and Flapless Refractive Procedures

Pooja Khamar, MD, PhD; Rachana Chandapura, MTech; Rohit Shetty, MD, PhD, FRCS; Zelda Dadachanji, MD; Gairik Kundu, MD; Yash Patel, MTech; Rudy M.M.A. Nuijts, MD, PhD; Abhijit Sinha Roy, PhD

Abstract

PURPOSE:

To evaluate epithelial Zernike indices as a differentiator of epithelial remodeling after different refractive procedures.

METHODS:

Optical coherence tomography (OCT) images of 22 laser in situ keratomileusis, 22 small incision lenticule extraction, 15 photorefractive keratectomy (PRK), and 17 transepithelial PRK eyes were evaluated retrospectively before and after surgery. A custom algorithm was used to calculate the epithelial Zernike indices from the three-dimensional distribution of epithelial thickness distribution. The epithelial Zernike indices were also compared with the local measurements of epithelial thickness, used conventionally from the current clinical OCT. A decision tree classifier was built, one in which flap/cap and surface procedures were classified (2G) and another in which all surgical groups were classified separately (4G).

RESULTS:

Local measurements of thicknesses changed significantly after all surgeries (P < .05), but these changes were similar in magnitude between the surgical platforms (P > .05). The surgeries not only changed the epithelial Zernike indices (P < .05), but also resulted in differential changes in epithelial thickness distribution based on the type of surgery (P < .05). In the 2G analyses with local measurements of epithelial thickness, the area under the curve, sensitivity, and specificity were 0.57 ± 0.07, 42.11%, and 57.89%, respectively. Further, the accuracy was limited to less than 60%. In the 2G analyses with epithelial Zernike indices, the area under the curve, sensitivity, and specificity were 0.79 ± 0.05, 86.4%, and 71.9%, respectively. Here, the accuracy was limited between 70% and 80%. Similar trends were observed with 4G analyses.

CONCLUSIONS:

The epithelial Zernike indices were significantly better in identifying surgery-specific three-dimensional remodeling of the thickness compared to local measurements of epithelial thickness. Further, the changes in Zernike indices were independent of the magnitude of refractive error but not the type of surgery.

[J Refract Surg. 2020;36(2):97–103.]

Abstract

PURPOSE:

To evaluate epithelial Zernike indices as a differentiator of epithelial remodeling after different refractive procedures.

METHODS:

Optical coherence tomography (OCT) images of 22 laser in situ keratomileusis, 22 small incision lenticule extraction, 15 photorefractive keratectomy (PRK), and 17 transepithelial PRK eyes were evaluated retrospectively before and after surgery. A custom algorithm was used to calculate the epithelial Zernike indices from the three-dimensional distribution of epithelial thickness distribution. The epithelial Zernike indices were also compared with the local measurements of epithelial thickness, used conventionally from the current clinical OCT. A decision tree classifier was built, one in which flap/cap and surface procedures were classified (2G) and another in which all surgical groups were classified separately (4G).

RESULTS:

Local measurements of thicknesses changed significantly after all surgeries (P < .05), but these changes were similar in magnitude between the surgical platforms (P > .05). The surgeries not only changed the epithelial Zernike indices (P < .05), but also resulted in differential changes in epithelial thickness distribution based on the type of surgery (P < .05). In the 2G analyses with local measurements of epithelial thickness, the area under the curve, sensitivity, and specificity were 0.57 ± 0.07, 42.11%, and 57.89%, respectively. Further, the accuracy was limited to less than 60%. In the 2G analyses with epithelial Zernike indices, the area under the curve, sensitivity, and specificity were 0.79 ± 0.05, 86.4%, and 71.9%, respectively. Here, the accuracy was limited between 70% and 80%. Similar trends were observed with 4G analyses.

CONCLUSIONS:

The epithelial Zernike indices were significantly better in identifying surgery-specific three-dimensional remodeling of the thickness compared to local measurements of epithelial thickness. Further, the changes in Zernike indices were independent of the magnitude of refractive error but not the type of surgery.

[J Refract Surg. 2020;36(2):97–103.]

In irregular corneas, the epithelium masks the true undulations of the stromal surface.1 In refractive surgery, the compensatory remodeling of the epithelium in the ablation and non-ablation zones of the cornea is also well known.2–7 The epithelial thickness increased in the central cornea and decreased in the paracentral cornea after myopic refractive surgery.3,6 The postoperative refractive changes correlated with the changes in both the corneal and stromal thicknesses but not with the epithelial thickness changes over a 3-year follow-up.6 Since the introduction of corneal tomography, several indices to describe the spatial variation of corneal thickness have been defined.8–10 However, indices to assess the spatial variation of epithelial thickness are still lacking.11,12 An earlier study introduced a novel application of Zernike polynomials to assess the corneal thickness distribution of normal and keratoconic eyes.13 The study described the three-dimensional variation in corneal thickness with the well-known Zernike coefficients (eg, coma and trefoil).13 The Zernike analyses was also a significant differentiator between normal and keratoconic eyes.13

In the current study, the Zernike polynomials were applied to the three-dimensional epithelial thickness distribution of patient corneas. The Zernike calculations were then used to assess differences in the thickness remodeling of the epithelium between four different platforms of refractive surgeries: laser in situ keratomileusis (LASIK), small incision lenticule extraction (SMILE), photorefractive keratectomy (PRK), and transepithelial PRK (TransPRK).

Patients and Methods

This was a retrospective and observational study of medical records. The study was approved by the ethics committee of Narayana Nethralaya Eye Hospital, Bangalore, India. This research followed the tenets of the Declaration of Helsinki. The clinical records of patients who had undergone LASIK, SMILE, PRK, and TransPRK in the past 1 year were evaluated.

The LASIK ablation was performed with the Wave-Light EX500 excimer laser (Alcon Laboratories, Inc., Fort Worth, TX). The SMILE ablation was performed with the VisuMax femtosecond laser (Carl Zeiss Meditec, Jena, Germany). The PRK and TransPRK ablations were performed with the Amaris 1,050-Hz excimer laser (SCHWIND eye-tech-solutions, Kleinostheim, Germany). In PRK, the epithelium was manually removed from the central 8-mm zone. In TransPRK, the same was performed with the laser. In all procedures, the diameter of the optical zone was 6 mm. In TransPRK, the epithelium was removed specific to the area of stromal ablation zone only, which in turn depended on the planned refractive error. In both LASIK and SMILE, the location of the hinge and incision was superior to the corneal center.

All surgeries were performed successfully without any intraoperative or postoperative complications. All eyes had an uncorrected and corrected distance visual acuity of 6/6 or better postoperatively. Only patients with preoperative and postoperative optical coherence tomography (OCT) measurement in the database of the OCT scanner were selected for the study. The OCT imaging was performed with the RTVue device (Optovue Inc., Fremont, CA).

The OCT acquired eight radial frames of 6-mm span (16 semi-meridians) for each cornea. From each frame, the anterior edge (the air–epithelium interface) and the interface between the epithelium and Bowman's layer were segmented.14,15 From a given point on the air–epithelium interface, the point of intersection of the local normal with the epithelium–Bowman's layer edge was computed using the Newton–Raphson method. The linear distance between the point of intersection and the local point on the air–epithelium interface was the epithelial thickness at that location. In the central 5-mm map of epithelial thickness, the following were quantified: minimum and maximum thickness and mean thicknesses in the superior and inferior sectors. The mean central epithelial thickness was calculated by taking the average of all thicknesses measured in the central 2-mm zone. The OCT measurement report also derived the mean epithelial thickness in the same manner.

Further, the epithelial thicknesses were sampled with Zernike polynomials up to the 6th order and as a function of normalized radius and meridian. The Zernike polynomials are mapping functions that interpolate a two-dimensional (eg, function of x and y) distribution of a variable, which can be either aberrations or thickness.13 Thus, the polynomials could interpolate the two-dimensional data as a function of coordinates: x and y or radius and meridian. If used for interpolating thickness, the Zernike coefficients provided an efficient metric to describe the asymmetric distribution of epithelium and corneal thickness.13 For example, the coma term would imply a thickness distribution similar to the pictorial description of coma. Intuitively, the Zernike coefficients of 2nd order and above would be zero in magnitude for an inclined layer of uniform thickness. The Zernike coefficients describing the epithelial thickness distribution were calculated by the following equation:16

E(ρ,θ)=∑i=−mmbmiZmi

In the equation stated above, E = the epithelial thickness profile, θ = meridian in radians, ρ = normalized radius (0 ≤ ρ ≤ 1), m = order of Zernike fit, b = the Zernike polynomials, and Z = the Zernike coefficients. The equation was converted to a quadratic form to calculate the magnitudes of the Zernike coefficients, b.13 The notation, i, varied from −m to +m in steps of 2. The root mean square error (RMSE) of the Zernike fit was calculated as:

RMSE=∑k=1p(Ek−E¯K)2p

In the RMSE equation, E was the measured epithelial thickness measured and Ē was the estimated thickness from Zernike coefficients at the same coordinate (ρ,θ). The variable k represented each coordinate location. The mean RMSE was 0.745 ± 0.363 µm for Zernike order up to 6. This error was less than 1 µm or 1.5% (assuming a 50-µm uniform preoperative epithelial thickness). The increase in the order of Zernike polynomials beyond 6 did not result in any further reduction of RMSE. Henceforth, the Zernike coefficients (Z) calculated from the epithelial thickness distribution (E) will be referred to as the epithelial Zernike indices. The double indexed notation of Zernike coefficients was also used to represent the epithelial Zernike indices. The following epithelial Zernike indices (µm) were analyzed before and after surgery:

  • Z20,
  • RMS of Z2−2 and Z2+2,
  • RMS of lower order coefficients (LOC) Z2−2, Z20, and Z2+2,
  • RMS of Z40 and Z60,
  • RMS of Z3−1 and Z3+1,
  • RMS of 3rd order Z3−3, Z3−1, Z3+1, Z3+3,
  • RMS of 4th order Z4−4, Z4−2, Z40, Z4+2, Z4+4,
  • RMS of higher order coefficients (HOC) from order 3 to 6

These indices were generated for all eyes that underwent LASIK, SMILE, PRK, and TransPRK. The epithelial Zernike indices were used to build a decision tree classifier (random forest). Two classifiers were built. In the first classifier, flap/cap and surface (PRK/TransPRK) procedure eyes were kept in two separate groups (2G). In the second classifier, all procedures were kept in their respective four groups (4G). The aim of building the classifier was to evaluate whether the thickness parameters and epithelial Zernike indices were able to describe surgery-specific features of epithelium remodeling at follow-up. Only the preoperative minus postoperative epithelial Zernike indices were used as input data to the classifier.

Statistical Analyses

All variables were reported as mean ± standard deviation (SD) after confirming normality of distribution. The paired t test was used to analyze the changes from preoperative to postoperative. The one-way analysis of variance (ANOVA) with Bonferroni correction was used to compare the change in the indices between the four groups of eyes. A P value less than .05 was considered statistically significant. MedCalc v18.9.1 software (MedCalc, Inc., Ostend, Belgium) was used to perform the analyses. The decision tree classifiers were built using the Orange data mining toolbox.16 The decision tree classifiers were trained and cross-validated using the “leave-one-out” method. In this method, all eyes except for one were used to train the classifier and the one eye was used to validate the accuracy. Multiple classifiers were automatically built with one eye left out each time from the total group of eyes and the average of the metrics of all classifiers (taken together) were evaluated. The results of the classifier were assessed using the metrics: area under the curve (AUC) ± standard error, sensitivity, specificity (DeLong method in MedCalc), and accuracy. The classification scores generated by the classifier were used to calculate sensitivity, specificity, and accuracy.

Results

The study included 22 SMILE, 22 LASIK, 15 PRK, and 17 TransPRK eyes of 62 patients. The postoperative follow-up time point varied from 3 to 4 months. Table 1 summarizes the demographics of the groups. Age and axis of refraction were similar between the groups (P > .05). However, refractive error of the PRK eyes was significantly lower than the other groups (P < .05). Table 2 lists the change in mean, minimum, maximum, superior, and inferior epithelial thicknesses. The preoperative magnitudes of all indices were statistically similar between the LASIK, SMILE, PRK, and TransPRK groups (P > .05). The change in all thicknesses was statistically significant (P < .05) from preoperative to postoperative state irrespective of the type of refractive surgery. A decision tree classifier based on these parameters yielded interesting results. In the 2G analyses, the AUC, sensitivity, and specificity were 0.57 ± 0.07, 42.11%, and 57.89%, respectively. Overall, 59.10% (26 of 44) and 53.13% (17 of 32) of the eyes were accurately classified by the decision tree in flap/cap and surface procedure groups, respectively. In the 4G analyses, the AUC, sensitivity, specificity, and accuracy were as follows: SMILE: 0.52 ± 0.07, 28.95%, 71.05%, 36.36%; LASIK: 0.69 ± 0.07, 28.95%, 71.05%, 36.36%; PRK: 0.55 ± 0.08, 19.74%, 80.26%, 26.67%; and TransPRK: 0.57 ± 0.08, 22.37%, 77.63%, 5.88%.

Demographics of the Eyes

Table 1:

Demographics of the Eyes

Epithelial Thickness Parameters Before and After SMILE, LASIK, PRK, and TransPRK

Table 2:

Epithelial Thickness Parameters Before and After SMILE, LASIK, PRK, and TransPRK

Using the variables in Table 2, none of the AUCs were significantly different (P > .05) either between the 2G and 4G groups or among the 4G groups. Thus, the change in the epithelial thicknesses (Table 2), when evaluated in specific regions, did not yield any significant differences in epithelium remodeling between the surgical platforms.

Table A (available in the online version of this article) lists the change in the epithelial Zernike indices in all eyes. In the SMILE eyes, Z2+2, RMS of Z2−2 and Z2+2, RMS of LOC, RMS of Z3−1 and Z3+1, RMS of 3rd order Z3−3, Z3−1, Z3+1, Z3+3, RMS of 4th order Z4−4, Z4−2, Z40, Z4+2, Z4+4, and RMS of HOC were significantly altered (P < .05). In the LASIK eyes, Z3+1, Z3−1, and RMS of Z40 and Z60 were significantly altered by surgery (P < .05) in addition to the indices altered in SMILE surgery. Thus, a differential epithelial remodeling pattern was evident between the SMILE and LASIK eyes. In the PRK eyes, only Z3+1, Z40, and RMS of LOC were significantly altered by surgery (P < .05). In the TransPRK eyes, Z2+2, Z2−2, Z3+1, Z40, RMS of Z2−2 and Z2+2, and RMS of HOC were significantly altered (P < .05). Thus, there were clear differences between the PRK and TransPRK eyes. Further, statistically significant epithelial Zernike indices for PRK and TransPRK eyes were not the same as the SMILE and LASIK eyes. Applying ANOVA to the epithelial Zernike indices, the following significant differences (P < .05) were observed between the surgical groups (in pairs):

  • Z3+1: SMILE versus TransPRK, LASIK versus TransPRK,
  • RMS of Z2−2 and Z2+2: SMILE versus LASIK, SMILE versus PRK,
  • RMS of Z3−1 and Z3+1: SMILE versus PRK, LASIK versus PRK,
  • RMS of 3rd order Z3−3, Z3−1, Z3+1), Z3+3): LASIK versus PRK, LASIK versus TransPRK,
  • RMS of 4th order (Z4−4, Z4−2, Z40, Z4+2, Z4+4): LASIK versus PRK,
  • RMS of Z40 and Z60: LASIK versus PRK,
  • RMS of HOC from order 3 to 6: SMILE versus PRK, LASIK versus PRK
Mean ± Standard Deviation of Epithelial Zernike Indices of Eyes

Table A:

Mean ± Standard Deviation of Epithelial Zernike Indices of Eyes

Thus, there were clear differences between the surgical groups in terms of epithelial remodeling (using epithelial Zernike indices) after surgery.

The decision tree classifier for 2G and 4G analyses were also generated using the epithelial Zernike indices. In the 2G analyses, the AUC, sensitivity, and specificity were 0.79 ± 0.05, 86.4%, and 71.9%, respectively. Overall, 75.0% (33 of 44) and 71.88% (23 of 32) of the eyes were accurately classified by the decision tree in the flap/cap and surface procedure groups, respectively. Compared to the 2G analyses with only thickness variables (Table 2), the 2G epithelial Zernike indices classifier was significantly better (P < .01). In the 4G analyses, the AUC, sensitivity, specificity and accuracy were as follows: SMILE: 0.67 ± 0.07, 59.9%, 83.3%, 59.1%; LASIK: 0.71 ± 0.07, 68.2%, 74.1%, 50.0%; PRK: 0.76 ± 0.09, 66.7%, 96.7%, 66.67%; and TransPRK: 0.71 ± 0.08, 58.8%, 91.5%, 58.82%.

Compared to the 4G classifier with only thickness variables (Table 2), the 4G epithelial Zernike indices classifier was significantly better for the SMILE, PRK, and TransPRK groups (P < .05). Using the epithelial Zernike indices, none of the AUCs were significantly different (P > .05) either between the 2G and 4G groups or among the 4G groups.

Discussion

There are diverse studies analyzing the outcomes of refractive surgeries.5–7,14,17–19 The changes in the thickness of the cornea and epithelium were correlated to refractive regression in PRK and LASIK eyes.3,6 However, postoperative refractive changes did not correlate with the changes in epithelial thickness.6 The change in epithelial thickness differed between the central and peripheral sectors of the epithelial thickness map (RTVue) and SMILE eyes tended to stabilize earlier.7 Further, the change in central epithelial thickness was positively correlated with the amount of myopia.7 In this study, we assessed the spatial distribution of epithelial thickness with Zernike polynomials and not just the magnitude of central epithelial thickness. Thus, regional differences in epithelial thickness patterns were identified, which surprisingly were independent of treated refractive error but were mostly specific to the type of surgery (random forest). This was interesting because other metrics of refractive outcomes can show differences between types of refractive surgery. The epithelial healing time, safety, and efficacy were superior in TransPRK compared to conventional PRK.20 On the other hand, similar outcomes between the two were observed at 3 months postoperatively in another study.18 A study on LASIK eyes demonstrated a positive linear relationship between RMS of higher order aberrations and preoperative level of myopia.17,21 In addition, the knowledge of the epithelial thickness distribution may be essential before surgery because it affected the final refraction.22 This demonstrates the relevance of our study.

Although TransPRK had longer recovery time than LASIK, comparable outcomes were reported between the two (1-year follow-up).23 A significant central thickening of epithelium was observed 1 month after LASIK (59.9 ± 5.9 to 64.6 ± 6.1 µm, P = .008).24 In the current study, mean epithelial thickness increased (P < .0001) by 5.2 ± 3.26, 3.86 ± 2.28, 5.63 ± 3.17, and 4.47 ± 3.61 µm in SMILE, LASIK, PRK, and TransPRK, respectively. Significant changes were also observed in the superior and inferior hemispheres (Table 1). However, the increases in mean epithelial and other thickness were similar between the surgery groups. Thus, changes in regional values of epithelial thickness instead of evaluation of the entire three-dimensional structure cannot be a surgery-specific marker of epithelial remodeling. Further study with longer follow-up and epithelial Zernike indices could help us understand temporal changes in epithelial thickness distribution much better.

A previous study had derived indices using pachymetry Zernike analyses.13 The increase in the magnitude of pachymetry Zernike analyses indices was directly related to severity of the disease.13 In the current study, the increase in the magnitude of epithelial Zernike indices indicated differential postoperative remodeling between LASIK, SMILE, PRK, and TransPRK. In concept, an increase in magnitude of LOC indicated a global change in epithelial thickness. For example, a near uniform change in thickness from 50 to 60 µm will be described primarily by a change in LOC. However, a localized change in epithelial thickness will be better represented by change in HOC (eg, keratoconic eyes). Further, preoperative RMS of LOC and HOC (Table A) demonstrated that the assumption of a uniform preoperative epithelial thickness was inaccurate for most eyes. This could have implications for the TransPRK procedure, which assumed a uniform preoperative epithelial thickness. The results from the tables clearly indicated a dissimilar epithelial remodeling between the refractive surgeries because no groups of epithelial Zernike indices were common between them.

An interesting observation was made with respect to change in the 3rd order epithelial Zernike indices (the Zernike coma). In this case, both LASIK and SMILE differed from PRK and TransPRK (Table A), with LASIK eyes undergoing more remodeling than SMILE eyes (Table A). This could be due to the presence of a hinge/incision in LASIK/SMILE and absence of the same in PRK/TransPRK. Further, the presence of a near 360° flap in LASIK could also account for the differences in the 3rd order epithelial Zernike indices. However, this effect was not captured by the local thickness magnitudes (Table 2). Based on the RMS of LOC, LASIK caused the least change (Table A) and SMILE (Table A) (similar to PRK) caused the greatest change in epithelial thickness distribution. Based on the RMS of HOC, PRK caused the least change in epithelial thickness distribution (Table A), whereas both LASIK and SMILE (Table A) caused much greater changes. Another interesting result was the difference between the PRK and TransPRK eyes (Table A). The PRK eyes had a manual scraping of epithelium in the central 8-mm zone before stromal ablation. The TransPRK eyes had their epithelium removed by the laser specific to the area of the stromal ablation zone only. This zone was smaller in area than a circular central 8-mm diameter zone. Although the two groups had similar changes in local epithelial thickness (Table 2), the epithelial Zernike indices clearly showed a difference between PRK and TransPRK eyes because the region to be repopulated with epithelial cells (migrating from the limbal area) was larger in the PRK eyes than TransPRK eyes.

Only the mapping of the spatial distribution of epithelial thickness was successful in capturing the effect of flap and cap on postoperative remodeling. The decision tree classifiers clearly showed that there were differences in the nature of epithelial remodeling between LASIK/SMILE and PRK/TransPRK with the epithelial Zernike indices. In other words, intrastromal procedures such as SMILE and LASIK had a different quantitative healing pattern based on epithelial Zernike indices than PRK and TransPRK. Further, the classifiers based on epithelial Zernike indices significantly outperformed the local thickness measurements (Table 2) in both 2G and 4G analyses (P < .05). The greatest number of eyes were accurately classified by the epithelial Zernike indices 4G classifier and indicated unique remodeling based on epithelial Zernike indices specific to a given refractive surgery. Interestingly, none of the changes in the epithelial Zernike indices were correlated with the preoperative refractive error. In a contralateral eye study of LASIK versus SMILE with OCT, the difference between the maximum and minimum epithelial thickness changed over a 2-year follow-up despite similar central epithelial thickness between the eyes, and the LASIK eyes always had a greater difference.24 In both studies, the SMILE eyes stabilized earlier than the LASIK eyes.7,24 Another study on SMILE eyes with OCT also detected differential and sectoral increases in epithelial thicknesses with time, which was modeled with an exponential function.25 Using OCT, the paracentral epithelial thickness differed significantly from the central epithelial thickness and thickness in the mid-corneal regions of eyes after SMILE.26 Thus, the epithelial Zernike indices may serve as a universal and simpler alternative to study these changes.

A limitation of the current study was that the analyses were limited only to the 6-mm central zone. Newer devices can map the epithelial thickness in excess of 6 mm, and this may help delineate the effects of optical and transition zone on epithelial remodeling.27

The epithelial Zernike indices may be useful in assessment of corneas and their outcomes under confounding scenarios (eg, two corneas may have the same central epithelial thickness but different epithelial Zernike indices or vice versa). A combination of epithelial Zernike indices and pachymetry Zernike analyses13 together may be a better differentiator of corneal tomographic remodeling than either one of them alone in a classifier. This study established epithelial Zernike indices as a new metric in clinical evaluation of corneas with OCT. In future work, the curvature and aberrations from the air–epithelium interface, epithelium–Bowman's layer interface and posterior corneal surface along with the epithelial Zernike indices and pachymetry Zernike analyses derived from OCT thickness maps could be combined to provide the next-generation of corneal tomography diagnostics.

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Demographics of the Eyes

CharacteristicSMILE (n = 22)LASIK (n = 22)PRK (n = 15)TransPRK (n = 17)
Age (y)24.3 ± 3.427.6 ± 3.823.8 ± 2.524.8 ± 2.2
Sphere (D)−4.28 ± 1.58−4.45 ± 1.43−2.07 ± 1.19−3.93 ± 2.11
Cylinder (D)−0.77 ± 0.49−0.80 ± 0.63−0.99 ± 0.85−0.81 ± 0.45
Axis107.67 ± 69.30124.38 ± 66.23140.18 ± 52.32124.23 ± 73.17
MRSE (D)−4.62 ± 1.72−4.84 ± 1.57−2.43 ± 1.07−4.28 ± 2.27

Epithelial Thickness Parameters Before and After SMILE, LASIK, PRK, and TransPRK

ParameterPreoperativePostoperativeChangeP
SMILE
  Meana54.08 ± 4.6359.28 ± 5.19−5.20 ± 3.26< .0001
  Minimumb49.28 ± 4.9051.24 ± 4.75−1.95 ± 3.31.01
  Maximumb57.08 ± 4.2864.52 ± 5.99−7.44 ± 4.48< .0001
  Superiorb53.65 ± 4.6058.76 ± 5.21−5.11 ± 3.29< .0001
  Inferiorb54.64 ± 4.7059.97 ± 5.21−5.32 ± 3.37< .0001
LASIK
  Meana51.29 ± 3.0555.15 ± 3.43−3.86 ± 2.28< .0001
  Minimumb45.06 ± 4.2846.92 ± 3.68−1.85 ± 4.97.01
  Maximumb53.80 ± 3.5459.53 ± 3.85−5.73 ± 3.58< .0001
  Superiorb51.25 ± 3.0355.11 ± 3.59−3.86 ± 2.31< .0001
  Inferiorb51.34 ± 3.0755.20 ± 3.29−3.87 ± 2.37< .0001
PRK
  Meana54.31 ± 2.5259.94 ± 2.98−5.63 ± 3.17< .0001
  Minimumb50.28 ± 2.7352.35 ± 3.50−2.07 ± 3.46.01
  Maximumb57.69 ± 2.0563.34 ± 2.72−5.65 ± 2.81< .0001
  Superiorb54.29 ± 2.6959.95 ± 2.94−5.65 ± 3.33< .0001
  Inferiorb54.32 ± 2.3559.92 ± 3.07−5.60 ± 3.01< .0001
Trans-PRK
  Meana54.26 ± 4.0458.73 ± 2.93−4.47 ± 3.61< .0001
  Minimumb49.72 ± 3.0851.72 ± 4.41−2.00 ± 4.68.01
  Maximumb57.21 ± 4.8962.36 ± 3.05−5.15 ± 4.54< .0001
  Superiorb54.11 ± 3.9158.39 ± 3.28−4.28 ± 3.75< .0001
  Inferiorb54.46 ± 4.2759.17 ± 2.64−4.71 ± 3.72< .0001

Mean ± Standard Deviation of Epithelial Zernike Indices of Eyes

ParameteraPreoperativePostoperativeChangebP
SMILE
  Z20−0.92 ± 0.42−1.13 ± 1.040.21 ± 1.14.40
  Z2+2−0.19 ± 0.350.29 ± 0.70−0.49 ± 0.80.009c
  Z2−2−0.05 ± 0.170.13 ± 0.76−0.17 ± 0.71.27
  Z3+1−0.05 ± 0.150.11 ± 0.54−0.16 ± 0.56.19
  Z3−10.02 ± 0.170.02 ± 0.51−0.01 ± 0.54.94
  Z400.13 ± 0.18−0.10 ± 0.410.22 ± 0.42.02c
  RMS of Z2−2 and Z2+20.38 ± 0.220.92 ± 0.54−0.54 ± 0.53.0001c
  RMS of Z3−1 and Z3+10.21 ± 0.080.64 ± 0.37−0.43 ± 0.40.0001c
  RMS of 3rd order (Z3−3, Z3−1, Z3+1, Z3+3)0.29 ± 0.110.54 ± 0.38−0.25 ± 0.38.005c
  RMS of 4th order (Z4−4, Z4−2, Z40, Z4+2, Z4+4)0.31 ± 0.180.66 ± 0.42−0.35 ± 0.48.003c
  RMS of Z40 and Z600.16 ± 0.160.31 ± 0.30−0.15 ± 0.35.05
  RMS of LOCs (Z2−2, Z20, and Z2+2)1.05 ± 0.331.67 ± 0.84−0.62 ± 0.85.003c
  RMS of HOCs from 3rd to 6th order0.63 ± 0.231.40 ± 0.55−0.77 ± 0.61< .0001c
LASIK
  Z20−0.85 ± 0.57−0.73 ± 0.86−0.12 ± 1.16.65
  Z2+20.05 ± 0.290.07 ± 0.51−0.02 ± 0.61.91
  Z2−2−0.01 ± 0.28−0.03 ± 0.370.02 ± 0.36.77
  Z3+10.08 ± 0.110.31 ± 0.45−0.23 ± 0.44.02c
  Z3−1−0.01 ± 0.17−0.26 ± 0.420.25 ± 0.47.02c
  Z40−0.32 ± 0.18−0.73 ± 0.390.41 ± 0.46.0004c
  RMS of Z2−2 and Z2+20.36 ± 0.170.53 ± 0.33−0.17 ± 0.33.03c
  RMS of Z3−1 and Z3+10.20 ± 0.080.63 ± 0.37−0.43 ± 0.36< .0001c
  RMS of 3rd order (Z3−3, Z3−1, Z3+1, Z3+3)0.28 ± 0.180.81 ± 0.40−0.53 ± 0.43< .0001c
  RMS of 4th order (Z4−4, Z4−2, Z40, Z4+2, Z4+4)0.46 ± 0.150.86 ± 0.38−0.41 ± 0.37< .0001c
  RMS of Z40 and Z600.37 ± 0.180.73 ± 0.39−0.36 ± 0.37.0002c
  RMS of LOCs (Z2−2, Z20, and Z2+2)0.96 ± 0.521.07 ± 0.71−0.10 ± 1.02.64
  RMS of HOCs from 3rd to 6th order0.63 ± 0.221.31 ± 0.50−0.68 ± 0.55< .0001c
PRK
  Z20−0.95 ± 0.48−1.43 ± 0.730.48 ± 0.84.03c
  Z2+20.03 ± 0.270.23 ± 0.40−0.20 ± 0.42.06
  Z2−2−0.07 ± 0.170.02 ± 0.23−0.09 ± 0.27.16
  Z3+1−0.06 ± 0.15−0.22 ± 0.170.15 ± 0.20.006c
  Z3−10.13 ± 0.250.00 ± 0.310.14 ± 0.41.17
  Z400.24 ± 0.19−0.12 ± 0.390.36 ± 0.39.001c
  RMS of Z2−2 and Z2+20.47 ± 0.810.46 ± 0.260.01 ± 0.74.96
  RMS of Z3−1 and Z3+10.32 ± 0.220.29 ± 0.200.04 ± 0.29.60
  RMS of 3rd order (Z3−3, Z3−1, Z3+1, Z3+3)0.51 ± 0.540.48 ± 0.210.03 ± 0.61.83
  RMS of 4th order (Z4−4, Z4−2, Z40, Z4+2, Z4+4)0.57 ± 0.860.51 ± 0.290.07 ± 0.91.75
  RMS of Z40 and Z600.30 ± 0.270.33 ± 0.24−0.03 ± 0.40.76
  RMS of LOCs (Z2−2, Z20, and Z2+2)1.03 ± 0.421.60 ± 0.53−0.57 ± 0.73.004c
  RMS of HOCs from 3rd to 6th order0.67 ± 0.170.80 ± 0.20−0.13 ± 0.26.06
TransPRK
  Z20−0.90 ± 0.48−0.98 ± 0.770.08 ± 1.00.76
  Z2+2−0.09 ± 0.270.43 ± 0.42−0.53 ± 0.57.002c
  Z2−2−0.13 ± 0.150.07 ± 0.33−0.20 ± 0.37.04c
  Z3+10.04 ± 0.16−0.20 ± 0.290.24 ± 0.25.001c
  Z3−10.06 ± 0.25−0.09 ± 0.350.15 ± 0.44.17
  Z400.15 ± 0.27−0.25 ± 0.420.40 ± 0.37.0004c
  RMS of Z2−2 and Z2+20.31 ± 0.150.59 ± 0.36−0.28 ± 0.33.003c
  RMS of Z3−1 and Z3+10.27 ± 0.130.40 ± 0.29−0.14 ± 0.37.15
  RMS of 3rd order (Z3−3, Z3−1, Z3+1, Z3+3)0.32 ± 0.180.47 ± 0.33−0.15 ± 0.32.08
  RMS of 4th order (Z4−4, Z4−2, Z40, Z4+2, Z4+4)0.38 ± 0.170.54 ± 0.34−0.15 ± 0.31.07
  RMS of Z40 and Z600.25 ± 0.180.36 ± 0.32−0.12 ± 0.37.22
  RMS of LOCs (Z2−2, Z20, and Z2+2)0.98 ± 0.451.23 ± 0.69−0.26 ± 0.87.24
  RMS of HOCs from 3rd to 6th order0.68 ± 0.240.98 ± 0.43−0.30 ± 0.45.015c
Authors

From Narayana Nethralaya Eye Hospital, Bangalore, India (PK, RS, ZD, GK); Imaging, Biomechanics and Mathematical Modeling Solutions Lab, Narayana Nethralaya Foundation, Bangalore, India (RC, YP, ASR); and the Department of Ophthalmology, Maastricht University Medical Center, Maastricht, The Netherlands (RMMAN).

Supported in part by the Indo-German Science and Technology Center, Gurugam, India.

Drs. Sinha Roy and Shetty have a pending patent application on the use of OCT for Bowman's layer imaging. Dr. Nuijts serves as a consultant for Alcon, Asico, Chiesi, and Theapharma, and a speaker for Abbott, Alcon, Bausch & Lomb, Carl Zeiss, Chiesi, HumanOptics, Ophtec, Oculentis, and Gebauer. The remaining authors have no financial or proprietary interest in the materials presented herein.

AUTHOR CONTRIBUTIONS

Study concept and design (RS, RMMAN, ASR); data collection (PK, RC, ZD, GK); analysis and interpretation of data (PK, RC, ZD, YP); writing the manuscript (PK, RC, ZD, GK, YP, ASR); critical revision of the manuscript (RS, RMMAN, ASR); statistical expertise (ASR); administrative, technical, or material support (PK, RC, ZD, GK, YP)

Correspondence: Abhijit Sinha Roy, PhD, Narayana Nethralaya Foundation, #258/A Hosur Road, Bommasandra, Bangalore 560099, India. E-mail: asroy27@yahoo.com

Received: April 18, 2019
Accepted: January 02, 2020

10.3928/1081597X-20200103-01

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