FormalPara Key Summary Points

Why carry out this study?

Patients with keratoconus consider cross-linking to halt disease progression and reduce their dependence upon spectacles and/or contact lenses. A major hurdle is advising the individual patient on the visual acuity they are likely to achieve after cross-linking.

What did the study ask? What was the study’s hypothesis?

Could objective measurements of the cornea estimate corrected distance visual acuity after cross-linking? Corrected distance visual acuity, corneal optical density, thickness, and surface shapes were monitored over 1 year after routine uncomplicated cross-linking and tested to formulate models for estimating the corrected distance visual acuity.

What was learned from the study?

Cross-linking changes corneal optical density, thickness, and surface shapes. Preoperative values of these factors correlated with the corrected distance visual acuity 6 and 12 months after cross-linking.

Automated objective measurements of the cornea estimate the corrected distance of visual acuity after corneal cross-linking when the preoperative assessment of acuity is unreliable.

Introduction

Corneal cross-linking (CXL) is an established treatment for decelerating, if not arresting, the progression of keratoconus and improving corrected distance visual acuity (CDVA) by remodeling the cornea [1,2,3,4]. Several attempts have been made to predict the CDVA following CXL. Better outcomes are expected when the preop CDVA is ≥ 20/40, corneal thickness is < 450μm, surface power is > 45D, and the keratoconic apex is centrally located [5,6,7]. Corneal thickness tends to reduce [6,7,8] whereas the turbidity, or optical density, within the treated region increases after CXL [6, 8,9,10,11,12,13,14,15,16]. The objective estimations of corneal optical density (COD) correlate with the biomicroscopic grading of corneal haze, predominantly located in the anterior aspects of the CXL-treated cornea [17]. Other reports also confirm that COD changes occur mainly in the cornea’s anterior central and paracentral regions after CXL [12, 13, 18, 19]. Corneal transparency has long been linked to visual acuity [20]. The reduced CDVA often observed in Fuch’s dystrophy [21] or after photorefractive keratectomy (PRK) [22, 23] is associated with increasing corneal turbidity. The increase in COD after CXL could counterbalance, if not exceed, the potential gain in CDVA resulting from the remodeling of the corneal surface in some instances. An increase in corneal turbidity tends to affect the CDVA after treatment of keratoconus with CXL [16] or CXL combined with PRK [24]. In contrast to these findings, a few reports claim there are poor correlations between the increase in COD, as measured by Pentacam™, and CDVA after CXL [6, 10, 11, 25]. COD increases tend to plateau by 3 months and gradually decrease toward the end of the first year following CXL [6]. At the same time, corneal thickness follows an inverse trajectory by reducing up to the third month then gradually increasing toward the end of the first year after CXL [26].

Pentacam uses a Scheimpflug imaging process to create a three-dimensional (3D) model of the diameter, curvatures, front and back surface elevations, topographic thickness, and with additional software, the optical density variations over the cornea [27]. The model displays COD on a 0–100 scale in grayscale units (GSU). A relatively high GSU score indicates a region where the cornea is hazy, and a relatively low GSU score for a region where the cornea is more transparent.

Anecdotal (unpublished) evidence based on 20 randomly selected cases implied that Pentacam-derived measures of preoperative COD and thinnest corneal thickness (TCT) may be associated with the CDVA after CXL. The preop CDVA and ratio (ARC/PRC) between the averaged anterior (ARC) and posterior (PRC) corneal radii of curvature, over a 3-mm-diameter region covering the thinnest region of the cornea, values are highly correlated with the CDVA after CXL [28]. So, if the COD and TCT values are significantly associated with CDVA after CXL, then models could be constructed to estimate CDVA on the basis of objective and subjective factors or just objective factors evaluated at the preoperative stage. Measurements of subjective visual acuity can be unreliable or suspicious, if not impossible in some cases. A model derived from purely objective measurements sourced preoperatively might be useful for predicting the likely CDVA that could be achieved after CXL in such cases.

This study aimed to monitor changes in CDVA, COD, TCT, ARC, and PRC over 12 months after routine uncomplicated CXL for keratoconus and determine whether there were any associations between these characteristics. Should significant associations be uncovered, the study would be extended to determine whether models could be developed that may be useful to estimate the CDVA after CXL on the basis of subjective and/or objective data acquired before CXL.

Methods

Pilot Study

A preliminary study was undertaken to determine the minimum sample size that should be considered before embarking on the main study. The preoperative COD, TCT, and CDVA values at 1 year postoperatively were sourced from 20 randomly selected records of patients who had undergone unremarkable CXL for keratoconus. The correlations between CDVA at 1 year and preoperative anterior COD and TCT were –0.485 (p = 0.03) and 0.862 (p < 0.01), respectively. Hence, a more substantial investigation should include no fewer than 20 cases.

Main Study

A prospective, partially masked, interventional clinical trial was undertaken between April 2018 and July 2023 in the refractive surgery department of the Sistina Ophthalmology Hospital in Skopje. The criteria for selecting cases for cross-linking were set by the overseeing Ethics Committees at Sistina Oftalmologija in Skopje and Svjetlost in Zagreb. The authors complied with the ethics committee. The study was conducted in accordance with the Helsinki Declaration of 1964 and its later amendments. All patients were fully informed about the procedures, risks, and benefits and provided signed informed consent. All patients and subjects were examined, operated where appropriate, and followed up by the same clinical team. The study was registered with Clinical Trials Protocol Registration and Results System (ref: NCT06522789).

Preliminary Assessment and Indications for Cross-Linking

A complete ophthalmological examination was performed at the first and all follow-up visits. The examination included assessment of CDVA (Aitomu LCD Digital Vision Eye Chart, Shanghai, China), refraction, tonometry, corneal characteristics using Pentacam HR (Oculus, Optikgeräte GmbH, Wetzlar, Germany), biomicroscopy, and dilated fundus examination. Corneal topography, thickness distribution, and COD profiles were captured for later analysis. The COD profile describes the turbidity of the cornea in the central apical region and three concentric annular zones (central 0–2 mm, paracentral 2–6 mm and 6–10 mm, peripheral 10–12 mm) within three separate layers along the depth of the cornea (anterior 120 µm, posterior 60 µm, and central bed between the anterior and posterior layers). The Pentacam software computes a figure, ranging from 0 (totally clear) to 100 (totally opaque), along a greyscale describing the optical density in each of the 12 regions. A high figure signifies increased turbidity and reduced transparency, and a low figure signifies the opposite. The software also averages the total optical density in the apex, each concentric zone, each layer, and the cornea. A total of 20 COD values are generated for a single cornea. COD values for the central 0–2 mm region covering the anterior (0–2 ant) and central layers (0–2 cent), paracentral 2–6 mm annulus covering the anterior (2–6 ant) and central layers (2–6 cent), total anterior region layer (tot ant), total central layer (tot cent), and whole cornea (tot) were recorded. Separate COD values for the peripheral (6–10 mm and 10–12 mm annuli) and posterior (60 µm) regions of the cornea were excluded as these regions are least likely to be affected by CXL [11, 13]. On all occasions, three consecutive Pentacam scans were taken in a dark room, and the best-quality scan was selected for recording and analysis. For each case, the COD (in greyscale units), thinnest corneal thickness (TCT, µm), and anterior (ARC) and posterior (PRC) corneal radii of curvature (mm) values measured over a 3-mm-diameter zone covering the cone of the cornea were obtained from the best scan.

Keratoconus subjects were classed as those scheduled for CXL (group 1) and those who would remain untreated (group 2). Group 1 consisted of cases where the astigmatism had increased by 1D or more, according to subjective refraction and/or corneal surface topography over the previous year. The majority of group 2 subjects consisted of confirmed keratoconus without signs of progression who opted to continue with their prescription glasses and tear-enhancing drops where necessary. A small number of cases who declined CXL treatment, content with their prescription glasses, were also included in this group. A control group, of age- and gender-matched individuals without signs of keratoconus was also included (group 3). All cases had clear corneas free of scarring on slit-lamp examination. The clinical team members who performed refraction duties always harvested data from the Pentacam but remained unaware of each subject’s group allocation.

Standard Dresden Protocol Corneal Cross-Linking Procedure

The CXL procedure adhered to the standard Dresden protocol. All patients received topical anesthetic (tetracaine 0.5%, Alcon Forth Worth, Texas) and miotic (Isopto Carpine 2%, Alcon, Fort Worth, Texas) drops 30 min before the procedure. The periocular region and conjunctival sac were washed with 10% povidone-iodine (Betadine 10%, Alcaloid, Skopje). Manual epithelial scraping with a crescent knife followed. Pachymetry was kept over 400 μm during the procedure and measured with an ultrasound hand pachymeter (Pocket II, Quantel Medical, Cournon d'Auvergne, France). Riboflavin (Peschke D, Peschke Trade, Huenenberg, Switzerland) was applied every 3 min for 30 min. We performed corneal UV-A radiation with a wavelength of 370 nm and energy of 3 mW using a UVA CXL lamp (VEGA CBM-X-Linker, Carleton Optical, Chesham, UK) for 30 min (six cycles of 5 min each). Device testing was performed before every procedure, and irradiance density measured between 2.7 and 3.3 mW/cm2 was tolerated. At the end of the corneal CXL procedure, topical atropine 1% (Atropine Sulphate, Cooper, Athens, Greece) and antibiotic (Tobrex, Alcon, Fort Worth, Texas) drops were instilled and a bandage soft contact lens (Air Optix Night & Day Aqua, Alcon, Texas) was placed over the cornea. Peschke® D riboflavin used in the study group was a standard riboflavin solution consisting of 0.1% riboflavin diluted into 20% dextran 500. The solution was recommended initially for the Dresden protocol; the soaking time was 20–30 min or until riboflavin particles were visible in the anterior chamber by microscopy. Tobradex (Alcon, Fort Worth, Texas) eyedrops, a suspension of 0.3% tobramycin and 0.05% dexamethasone, were prescribed for application after CXL. The dosage was four times per day for the first 2 weeks, then tapered twice daily for the next 2 weeks, and then to one drop per day for the last 2 weeks. All patients received topical steroids for a total of 6 weeks.

Postoperative Management

Postoperative treatment included a combination of antibiotic/corticosteroid drops (Tobradex, Alcon, Fort Worth, Texas) instilled four times daily for the next 2 weeks, after which the drops were tapered off gradually over 6 weeks. Postoperative examinations were scheduled for 1 day, 4 days, and 1 week until epithelization and bandage lens removal, then 1, 3, and 6 months and 1 year postoperatively. After that, the patients were advised to complete an ophthalmological examination at least annually.

Data Collection and Analysis

Data from the treated eye, or just the right eye in bilateral cases, were analyzed. Details of CDVA, COD, TCT, ARC, and PRC values were stored in Excel (Microsoft, Redmond, WA) and analyzed to determine the significance of any differences between groups (Mann–Whitney U test or unpaired t-test) and changes occurring within each group (Friedman test or one-way ANOVA for repeat measures, Wilcoxon signed rank, or paired t-test). If significant changes were found, the analysis was extended to determine the significance of any association between the change (i.e., preop value − postop value) in the parameter and the value at the start of the study (Spearman’s rho or Pearson correlation). Depending on the outcome of this analysis, the data were further scrutinized to determine whether a feasible model could be constructed (linear and multiple regression analysis) to predict the likely CDVA after CXL or after 1 year in untreated cases. Nonparametric tests were applied when data were not normally distributed (Kolmogorov–Smirnov test of normality). Changes and differences were considered statistically significant when p < 0.05.

Results

The total number of patients who underwent CXL was 77; 23 were females, and 54 were male, with a mean (± SD, range) age of 24.2 (± 7.0, 11–44) years (group 1). Twenty-three patients, including 6 females and 17 males with mean age of 27.3 (± 7.0, 17–44) years, were untreated (group 2). None of the patients were lost to follow-up. Twenty-four subjects, including 9 females and 15 males with mean age of 24.7 (± 7.6, 17–45) years, were recruited as controls (group 3). These subjects were examined at the start of the study and 12 months later. Significant intergroup differences existed in CDVA, COD, TCT, ARC, and PRC throughout the study. These are presented in Tables 1, 2, 3, 4, 5, and 6, with changes in CDVA, COD, TCT, ARC, and PRC in each group. The key findings were as follows.

Table 1 Comparison of median and mode of logMAR corrected distance visual acuity values between groups 1 and 2, and in group 3 between the start and 12 months (interquartile ranges in parenthesis)
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Table 2 Mean [± SD, 95% CI limits] corneal optical density (COD) values for the anterior (0–2 ant) and central layers (0–2 cent) within the corneal apex, paracentral 2–6 mm annulus covering the anterior (2–6 ant) and central layers (2–6 cent), total anterior layer (tot ant), total central layer (tot cent), and whole cornea (tot)
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Table 3 Comparison of mean thinnest corneal thickness (µm) values (± SD, 95% CI limits) between groups 1 and 2, and in group 3 between the start and 12 months
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Table 4 Comparison of mean anterior corneal radius (mm) values (± SD, 95% CI limits) between groups 1 and 2, and in group 3 between the start and 12 months
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Table 5 Comparison of mean posterior corneal radius (mm) values (± SD, 95% CI limits) between groups 1 and 2, and in group 3 between the start and 12 months
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Table 6 Correlations (r2) between corneal optical density values for the anterior apical (0–2 ant) layer, thinnest corneal thickness (TCT), anterior (ARC) and posterior (PRC) corneal radii of curvature, ARC/PRC ratio, logMAR corrected distance visual acuity (CDVA) values at the start of the study and CDVA at 1, 3, 6, and 12 months
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Corrected Distance Visual Acuity (CDVA)

In group 1 at 6 months, the CDVA had improved in 76 eyes and reduced in 1, and by 12 months the CDVA had improved in all 77 cases.

Table 1 shows that, compared with group 2, that CDVA was lower in group 1 at preop, 1 and 3 months postop, but not at 6 and 12 months postop. Compared with group 3, CDVA was lower in group 1 at pre- and 12 months postop. Over the year, CDVA significantly improved in group 1 (Friedman test, X2r = 200.4, n = 77, p < 0.01), but not in groups 2 (p = 0.60) and 3 (Wilcoxon signed-rank test p = 1.00).

Corneal Optical Density (COD)

In Table 2, the differences between groups 1 and 2 were significant at 1, 3, 6, and 12 months for all descriptors of COD (unpaired t-test, p < 0.01) but not at the start of the study. Similarly, differences between groups 1 and 3 were significant at 12 months (p < 0.01) but not at the start of the study except for the “0-2ant” descriptor of COD, which was higher in group 1. Apparent differences between groups 2 and 3 at the start and 12 months were not significant (p > 0.05).

In group 1, changes in all COD descriptors were significant over the entire period and after excluding the pre-CXL values (one-way ANOVA for repeat measures, p < 0.01). The post hoc Tukey test revealed that the difference in the results obtained at preop and 12 months after CXL were significant for all descriptors of COD (p < 0.05). In group 2, the COD descriptors “0–2 ant,” “0–2 cent,” “2–6 ant,” “2–6 cent,” and “tot ant” significantly reduced (one-way ANOVA for repeat measures, p < 0.01) over 12 months. In group 3, mean COD reduced (paired t-test, p < 0.05) except for “tot cent” (p > 0.05) and “tot” (p > 0.05).

At 12-months postop, the change in “2–6 cent” (r2 = 0.131), “tot ant” (r2 = 0.122), “tot cent” (r2 = 0.133), and “tot” (r2 = 0.129) descriptors in group 1 were significantly linked to the corresponding preop values. In group 2, the change in the “tot ant” (r2 = 0.261) descriptor, and in group 3 the change in the “0–2 ant” (r2 = 0.271) and “2–6 ant” (r2 = 0.246) descriptors, were significantly linked to the corresponding values at the start of the study.

Thinnest Corneal Thickness (TCT)

Table 3 shows that the intergroup differences in the mean TCT values were always significant. In group 1, the decrease in mean TCT after CXL was significant (one-way ANOVA for repeat measures, F = 45.47, p < 0.01). The post hoc Tukey test revealed that the apparent differences in mean TCT between 1, 3, 6, and 12 months postop pairings were not significant (p > 0.05). In groups 2 and 3, apparent changes in mean TCT were not significant (p > 0.05). In each of the three groups, there was no significant correlation between the change in the TCT and the TCT value at the start of the study (p > 0.05).

Anterior Corneal Radius (ARC)

Table 4 shows that the intergroup differences in the mean ARC values were always significant except between groups 1 and 2 at 12 months. In group 1, the initial decrease then gradual increase in mean ARC after CXL was significant (one-way ANOVA for repeat measures, F = 28.1, p < 0.01). The post hoc Tukey test revealed the apparent differences in mean ARC between 1, 3, 6, and 12 months postop pairings were not significant (p > 0.05). In groups 2 and 3, apparent changes in mean ARC values were not significant (p > 0.05). In each of the three groups, there was no significant correlation between the change in the ARC and the ARC value at the start of the study (p > 0.05).

Posterior Corneal Radius (PRC)

Table 5 shows that the intergroup differences in the mean PRC values were always significant. In group 1, the initial increase and gradual decrease in mean PRC after CXL was significant (one-way ANOVA for repeat measures, F = 5.28, p < 0.01). The post hoc Tukey test revealed that the apparent differences in mean PRC between 1, 3, 6, and 12 months postop pairings were not significant (p > 0.05). In groups 2 and 3, apparent changes in mean PRC were not significant (p > 0.05). In each of the three groups, there was no significant correlation between the change in the PRC and the PRC value at the start of the study (p > 0.05).

Associations between COD, TCT, ARC, PRC, ARC/PRC Ratio, and CDVA Values at the Start of the Study and CDVA at Postop

Linear regression revealed some significant associations (p < 0.01) in groups 1 and 2, which are listed in Table 6. Furthermore, in group 2, the CDVA at all sessions correlated with the ARC, PRC, and ARC/PRC ratio at the start of the study. The r2 values at the start and 1, 3, 6, and 12 months were 0.285, 0.515, 0.436, 0.537, and 0.444 for ARC, 0.323, 0.533, 0.482, 0.531, and 0.411 for PRC, and 0.336, 0.397, 0.281, 0.372, and 0.221 for the ARC/PRC ratio. Table 6 shows that, in group 1, the correlations with CDVA were consistently higher with ARC and PRC in comparison with the ARC/PRC ratio. Thus, ARC and PRC could be considered as separate factors in subsequent analysis.

Multiple linear regression analysis revealed significant associations (p < 0.01) between postop CDVA (y) preop values and the covariates in Table 6. The key results of this analysis are listed in Table 7. The variance inflation factors (VIFs) for ARC and PRC were consistently above 15, indicating there may be a multicollinearity problem when ARC and PRC are considered as independent variables. The VIF for x1, x2, and x5 were less than 1.2, and the VIF for x6 was below 2.1. The likelihood of a multicollinearity problem affecting the estimation of postop CDVA is reduced by limiting the inclusion to just x1, x2, x5, and x6 in any predictive model.

Table 7 Least-squares expressions between logMAR corrected distance visual acuity (y), preop corneal optical density values for the anterior apical layer (x1), thinnest corneal thickness (x2), anterior (x3) and posterior (x4) corneal radii of curvature, x3/x4 ratio (x5), and preop logMAR corrected distance visual acuity (x6) at 6 and 12 months (m) postop
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Associations between Predicted and Actual CDVA following CXL

Table 7 presents the predicted mean (± SD, 95% CI limits) CDVA values and the limits of agreement (± 1.96 SD) between the predicted and actual CDVA at 6 and 12 months postop. The actual mean CDVA values were 0.17 (± 0.18, 0.13–0.21) and 0.14 (± 0.17, 0.10–0.18). The differences in the mean predicted values were not significant at 6 months (one-way ANOVA, p > 0.05), but were significant at 12 months (p = 4.765, p = 0.003). The limits of agreement (LoA) were narrower when preop CDVA values were included in the predictions. Figures 1 and 2 compare the predicted values, according to Eqs. 2 and 4, with the difference between the predicted and actual CDVA values. The respective mean (± SD, 95% CI limits) differences between the predicted and actual CDVA values were −0.03 (± 0.19, –0.08 to 0.12) and 0.00 (± 0.10, –0.02 to 0.03).

Fig. 1
figure 1

Differences between predicted and actual logMAR corrected distance visual acuity (CDVA) values at 12 months postop. The predicted values were computed by inputting objective measurements from the corneas at preop into Eq. 2. The solid black lines are the corresponding limits of agreement between the predicted and actual values

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Fig. 2
figure 2

Differences between predicted and actual logMAR corrected distance visual acuity (CDVA) values at 12 months postop. The predicted values were computed by inputting objective measurements from the cornea and CDVA at preop into Eq. 4. The solid black lines are the corresponding limits of agreement between the predicted and actual values

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Discussion

It has been reported that 3% of eyes lose two or more lines of acuity by 12 months after CXL [28]. Just one eye in our cohort of 77 had reduced CDVA at 6 months, which was resolved by 12 months postop. In keeping with most studies, CDVA tended to improve after the first month following CXL [2,3,4, 9, 29]. However, there have been reports of CDVA reducing by 1 month [16] or remaining unchanged by 3 months after CXL [14]. Some have claimed that, the poorer the pre-CXL CDVA, the more significant the improvement in CDVA after CXL [5, 9]. The data shown in Fig. 3 support this assertion. However, there is a tendency for the improvement in CDVA to become less predictable when the pre-CXL CDVA is worse than 0.4. Subtle variations in treatment delivery and patient-specific factors cannot be ruled out as potential sources leading to differing outcomes and increased divergence when the pre-CXL CDVA is worse than 0.4.

Fig. 3
figure 3

LogMAR corrected distance visual acuity (CDVA) at pre- and 12 months postop. The least-squares line is described by y = 0.42x – 0.02 (r2 = 0.566, n = 77, p  < 0.01). The dotted lines represent the borders of 95% confidence limits

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In keeping with previous findings, all measured descriptors of COD increased after CXL [6, 9,10,11,12, 30,31,32]. There is some controversy regarding COD recovery after CXL. Reports claim that COD values return to baseline 12 months after CXL [13, 15, 31, 32], while others claim that COD remains above baseline at 12 months [12, 14]. Assessing COD in different zones of the cornea revealed that the effect of CXL was not uniform, and none of the COD indicators returned to baseline values by 12 months. Some COD indicators were reduced slightly in the untreated groups. Ideally, there should be no change in a control group, but Table 2 reveals that these reductions were small compared with the substantial increases recorded in the treated group.

Nemeth et al. proposed a method to ameliorate the Pentacam-generated COD values by quantifying COD in greyscale values/corneal volume units [19]. However, the subtlety of their correction is not expected to impact the overall outcomes of our study. Changes in four of the seven COD indicators correlated with the preoperative values, so the treatment associated with the preoperative status influences the postoperative COD. Increasing corneal turbidity is expected to impact on the image-forming properties of the eye and vision [23, 24]. Increasing COD should have a deleterious effect on vision, and the opposite should occur when COD is reduced. This theory is a reasonable explanation for the gradual improvement in CDVA when the COD values tended to fall between 1 and 12 months postop, along with other factors such as reorganization of corneal architecture and stiffness. However, this does not account for the improvement in CDVA with a simultaneous COD increase observed at 3 months. The COD estimated by Pentacam is based on the proportion of incident rays backscattered out of the eye. It is assumed that this backscatter is a marker of the forward scatter of rays traversing toward the retina, and the wavelengths of these rays represent those sensitive to the retinal receptors. Forward light scatter reduces contrast sensitivity and increases glare sensitivity, but not necessarily high contrast acuity [20, 33].

The increase in COD may affect visual performance, but any undesirable impact on CDVA appears to be mitigated by the concurrent effects of changes in TCT and corneal shape (ARC and PRC).

The mean TCT was reduced by 1 month, remained stable in the untreated control groups, and this fall in thickness supports previous findings [34, 35]. Mean TCT remained stable between 1 and 12 months postop, while COD continued to reduce and CDVA continued to improve. The cornea is still undergoing biophysical changes, but these are not affecting the lowest value of corneal thickness. The lack of any correlation between TCT before treatment and change in TCT following treatment shows that the change in TCT cannot be predicted on a case-by-case basis, even though mean TCT fell by an average of 30 µm.

Tables 4 and 5 show that ARC and PRC changed in the treated group, remaining stable in the control groups. The change in ARC was an initial reduction followed by a gradual increase, while the change in PRC was an initial increase followed by a reduction over the postop period. This gradual flattening of the cone after the first month is in keeping with previous reports [1, 36,37,38,39]. Our group had previously reported that the ARC/PRC ratio at preop was a convenient amalgamation associated with postop CDVA [28]. However, Table 6 shows that, in the current study, the individual preop ARC and PRC values have more powerful correlations with CDVA at postop compared with the preop ARC/PRC ratio. For the CDVA at 12 months postop, the respective r2 values were 0.505, 0.467, and 0.162, suggesting that each factor is likely to correctly estimate CDVA in 51%, 47%, and 16% of cases. Interestingly, in the untreated cases (group 2), the corresponding r2 values can also be used to correctly estimate CDVA at 1 year later in up to 44% of cases. Table 6 shows that the correlations (r2) between pre- and postop CDVA were 0.574 and 0.566 at 6 and 12 months postop. The r2 values of Eqs. 1 and 2 in Table 7 were 0.563 and 0.533 when the preop TCT and COD (0-2ant) values were included in the analysis with preop ARC and PRC values. This implies that using objective measurements taken from the preop cornea to predict CDVA does not provide an advantage above the prediction according to the preop CDVA. Nevertheless, Eqs. 1 and 2 provide an objective value, supplanting any guesswork when the preop CDVA is unreliable or cannot be measured.

Table 7 shows that the r2 values increased after including preop COD (0-2ant), TCT, ARC and PRC values alongside the preop CDVA in the estimation of postop CDVA. The r2 values of Eqs. 4 and 8 indicate that CDVA can be correctly predicted in 64% and 61% of cases at 12 months postop. These figures must be viewed with caution as erroneous conclusions could occur if problems associated with multicollinearity are not considered. The variance inflation factors (VIFs) for ARC and PRC were greater than 15; such high values are generally interpreted as indicative of considerable multicollinearity and should not be considered as independent variables [40,41,42]. Furthermore, the differences in mean CDVA values estimated using Eqs. 2, 4, 6, and 8 were significant. The VIF values for COD (0-2ant), TCT, ARC/PRC ratio, and preop CDVA were all below 2.1. Such low values suggest that multicollinearity can be interpreted as not important when these factors are used to estimate CDVA.

Therefore, according to strict statistical practice, the predictions according to Eqs. 5 and 6 supersede those of Eqs. 1 and 2, and Eqs. 7 and 8 supersede Eqs. 3 and 4. However, there is little variation in the limits of agreement (LoA) values associated with Eqs. 1–8. Differences between the predictive models may be statistically significant, but the predictions resulting from these expressions are within clinically acceptable boundaries.

In many countries, the legal requirements for driving include a CDVA of no worse than 0.3 [43]. Turning to Figs. 1 and 2, the limits of agreement between the predicted and actual CDVA values are equivalent to ± 2 lines on an Early Treatment Diabetic Retinopathy Study (ETDRS) acuity chart. Therefore, the chances of achieving a CDVA of 0.30 or better by 12 months postop could be 95% when the predicted CDVA is 0.1 or better. How does this compare with an estimate based just on preop CDVA? Figure 3 compares the actual pre- and postop CDVA values at 12 months.

The CDVA improved to 0.30 or better when the preop CDVA was no worse than 0.40.

Figure 4 shows the limits of agreement between the actual postop CDVA values and the values predicted according to just the preop CDVA. The limits of agreement in Fig. 4 are indistinguishable compared with those shown in Fig. 1. The likely error in the estimation of CDVA at 1 year postop according to objective measurements of the preop cornea is on par with the error according to just preop subjective CDVA. Other models have been advanced for predicting postop CDVA based on preop CDVA, corneal curvature and COD values [44]. We have not found any other reports predicting postop CDVA based solely on objective measurements of preop COD (“0-2ant”), TCT, ARC, and PRC.

Fig. 4
figure 4

Differences between predicted and actual logMAR corrected distance visual acuity (CDVA) values at 12 months postop. The predicted values were computed using the equation describing the least-squares line in Fig. 3. The solid black lines are the corresponding limits of agreement between the predicted and actual values

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Limitations of the Study

The outcomes of this study are limited by the number of cases, the CXL protocol used, the follow-up period, and possibly genetic factors of the patients enrolled. Longer-term studies involving a broader spectrum of patients in different territories, treated with other CXL protocols, including other aspects of acuity should be conducted to determine the real value of the models uncovered in this study. Future studies may identify other key factors that should be considered for estimating CDVA after CXL.

Conclusions

CXL increases the turbidity, reduces the thickness, flattens the front, and steepens the back surface of the cornea. The preoperative values of these factors are correlated with the CDVA at 6 and 12 months postop. Analysis of data obtained from 77 cases shows that CXL improves CDVA to better than 0.20 in most cases and that there is a 95% chance the CDVA will be 0.30 or better when the preop CDVA is no worse than 0.40. Automated objective measurements of the cornea at the preoperative stage hold the potential to rapidly estimate the postop CDVA that could be achieved by CXL when the assessment of preop acuity is unreliable.