Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions

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Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions Pablo Peña-García a,n, Cristina Peris-Martínez b,c, Alessandro Abbouda d, José M. Ruiz-Moreno a a

Department of Ophthalmology, Castilla La Mancha University, Albacete, Spain Fisabio Oftalmologia Médica (FOM), Cornea and Anterior Segment Diseases Unit, Valencia, Spain c Eye Clinic Aviñó-Peris, Valencia, Spain d Department of Ophthalmology, University of Rome, Sapienza, Italy b

ar t ic l e i nf o

a b s t r a c t

Article history: Accepted 21 December 2015

The purpose of the present study was to develop a discriminant function departing from the biomechanical parameters provided by a non-contact tonometer (Corvis-ST, Oculus Optikgeräte, Wetzlar, Germany) to distinguish subclinical keratoconus from normal eyes. 212 eyes (120 patients) were divided in two groups: 184 healthy eyes of 92 patients aged 32.9977.85 (21–73 years) and 28 eyes of 28 patients aged 37.79714.21 (17– 75 years) with subclinical keratoconus. The main outcome measures were age, sex, intraocular pressure (IOP), corneal central thickness (CCT) and other specific biomechanical parameters provided by the tonometer. Correlations between all biomechanical parameters and the rest of variables were evaluated. The biomechanical measures were corrected in IOP and CCT (since these variable are not directly related with the corneal structure and biomechanical behavior) to warrant an accurate comparison between both types of eyes. Two discriminant functions were created from the set of corrected variables. The best discriminant function created depended on three parameters: maximum Deformation Amplitude (corrected in IOP and CCT), First Applanation time (corrected in CCT) and CCT. Statistically significant differences were found between groups for this function (p¼2  10  10; Mann–Withney test). The area under the Receiving Operating Characteristic was 0.89370.028 (95% confidence interval 0.838–0.949). Sensitivity and specificity were 85.7% and 82.07% respectively. These results show that the use of biomechanical parameters provided by noncontact tonometry, previous normalization, combined with the theory of discriminant functions is a useful tool for the detection of subclinical keratoconus. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Corneal biomechanics Tonometry Subclinical keratoconus Discriminant functions

1. Introduction Viscoelastic corneal properties depend on the internal structure and composition of the cornea. They vary among subjects according to many factors, such as gender (Sen et al., 2014), age (Kamiya et al., 2009), ethnicity, presence of certain hormones (Gatzioufas and Thanos, 2008; Scheler et al., 2012; Spoerl et al., 2007), and illnesses directly related, or not, to collagen synthesis (Spoerl et al., 2007; Kara et al., 2012). The human cornea is composed of six microscopic layers: the epithelium, Bowman's membrane, the stroma, Dua's layer (Dua et al., 2013), Descemet's membrane and the endothelium. The stroma, which mainly comprises extracellular matrix and collagen fibers, represents 90% of the corneal tissue. Collagen fibers in the stroma are arranged in parallel forming lamellae with different n

Correspondence to: C/ Abú Isaac no. 6, 18005, Granada, Spain. Tel.: þ34 658828742. E-mail address: [email protected] (P. Peña-García).

orientations, conferring stiffness (Pandolfi and Holzapfel, 2008). Therefore, from a biomechanical point of view, the stroma forms the corneal scaffold and determines the mechanical behavior of the cornea (Lago et al., 2015; Studer et al., 2010). Thus, a detailed mechanical description of the cornea should involve the analysis of microscopic parameters. However, this is not possible in the current clinical practice of ophthalmologists and the only alternative for clinicians is to evaluate the mechanical properties of the cornea through a macroscopic description. For this purpose, up to now, two devices based on non-contact tonometry have been developed (Vellara and Patel, 2015; Piñero and Alcón, 2015): the Ocular Response Analyzer (ORA) (Reichert Technologies, New York, USA) and the Corvis-ST (Oculus Optikgeräte, Wetzlar, Germany). Essentially, both systems work in a similar way: first they produce a mechanical stimulus (an air pulse projected perpendicularly to the cornea), then they determine different parameters related to the deformation of the cornea, and finally, a set of different variables (depending on the device) is shown to the user in order to provide a mechanical characterization of the cornea. The main limitation of

http://dx.doi.org/10.1016/j.jbiomech.2015.12.031 0021-9290/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

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these devices is that the variables they provide depend on factors like intraocular pressure (IOP) and central corneal thickness (CCT), among others, not directly related to corneal stiffness. This results in limited diagnostic capability regarding, for example, ecstatic corneal disorders like keratoconus. Keratoconus is a corneal alteration related to a progressive thinning and protrusion of this tissue that results in irregular astigmatism, large values of the high order optical aberrations, and decrease in vision (Peña-García et al., 2014). Nowadays, keratoconus represents one of the main causes of corneal transplantation and the detection of its subclinical form is still a challenge in ophthalmology (Vellara and Patel, 2015; Piñero and Alcon, 2015; Schweitzer et al., 2010; Lanza et al., 2014; Tian et al., 2014; Arbelaez et al., 2012; Ruiseñor Vázquez et al., 2013; Smadja et al., 2013). An accurate diagnosis of this disorder would allow a better selection of candidates for refractive surgery and would avoid the generation of iatrogenic ectasia (Bühren et al., 2013). The main purpose of the present study is to identify the most useful parameters provided by non-contact tonometry for the biomechanical characterization of the cornea and to determine from them an optimized function based on corrected variables in IOP and CCT to discriminate between healthy eyes and eyes with subclinical keratoconus. 2. Methods In this retrospective, consecutive, non-randomized study 212 eyes of 120 patients (32 men and 88 women) were analyzed with the Corvis-ST tonometer. The eyes were divided into two groups: (a) healthy eyes (184 eyes of 92 patients) and (b) eyes with subclinical keratoconus (28 eyes from 28 patients). See Table 1. The eyes with subclinical keratoconus fulfilled the most accepted definition in the literature for this condition (Smadja et al., 2013; Klyce., 2009; Li et al., 2004). These eyes had no clinical signs of keratoconus (Vogt's striae, Fleischer rings, or corneal scarring), their topography was normal with no asymmetric bowtie and no focal or inferior steepening pattern; however, they were contralateral eyes of clinically evident keratoconus in the fellow eye. See Fig. 1. Keratoconus diagnosis was based on a complete ophthalmologic examination, including corneal topography and tomography data using a Scheimpflug-based topographic system (Pentacam, Oculus Optikgeräte GmbH), slit lamp examination and visual acuity with and without optical compensation. Age, gender, and clinical history were also recorded. Inclusion criteria in the group of healthy patients were as follows: patients with no presence of any kind of corneal ectasia, no previous ocular surgery, and no presence of any active corneal or systemic disease. Three consecutive measures in each eye, at the same visit, were taken with the Corvis-ST in both groups of patients. This device is a non-contact tonometer that uses an ultrahigh-speed Scheimpflug camera that captures 4330 images per second and covers 8.0 mm of the cornea. The light source is a LED light of 455 nm in wavelength. This tonometer produces an air pulse with a maximum pressure of 25 kPa perpendicularly projected onto the cornea. During the first phase of measuring, the cornea is pushed back until it reaches the first applanation state. After this, the cornea goes through a phase of indentation followed by a short period of oscillations. When the pressure decreases, the cornea reaches the second applanation state and finally it goes back to its natural state of rest. The main phases of this process are shown in Fig. 2. The main mechanical parameters measured were (Fig. 2): IOP, CCT, maximum Deformation Amplitude (DA) (maximum length of deformation at the highest concavity state), A1time (time from starting until first applanation), A1length (horizontal length of the portion of flattened cornea at the first applanation), A1velocity (speed of corneal apex at first applanation). A2time, A2length and A2velocity were measured analogously for the second applanation state. Other parameters measured were: HCtime (time form starting until Highest Concavity state is reached), Peak distance (distance between the two peaks at HC state) and Radius (radius of the central cornea at HC state) All measures were taken at the Fisabio Oftalmología Médica clinic by the same experienced observer. The study adhered to the tenets of the Declaration of Helsinki and it was approved by the Ethics Committee. All patients signed a consent form to allow the use of their clinical data for scientific purposes.

3. Statistical analysis The statistical program used was SPSS 22.0 for Windows (SPSS, Chicago, IL, USA). All values for each parameter came from the mean of

Table 1 Description of the samples analyzed.

Sex (males and females) Age (years) Mean 7 sd Median IQR Range Corneal Thickness (microns) Mean 7 sd Median IQR Range Intraocular Pressure (mm Hg) Mean 7 sd Median IQR Range Mean keratometry (Diopters) Mean 7 sd Median IQR Range

Group A (Healthy eyes N ¼184)

Group B (Subclinical keratoconus eyes N¼ 28)

p Value (Mann–Whitney test)

(56/128)

(11/17)

p ¼ 0.007*

33 7 8 33 8 21–73

38 714 36 23 17–75

p ¼ 0.054

542.23 7 30.43 542 46 480–650

512.127 31.32 513.50 38.75 485–575

p o 0.001

12.23 7 2.93 12.50 3.50 5.00–27.50

11.707 2.57 12.25 4.13 6.00–17.70

p ¼ 0.338

43.43 7 1.66 43.30 1.90 39.85–47.01

46.277 1.32 46.01 1.75 44.99–47.61

p o 0.001

IQR (Interquartile range). *

Chi-Square test.

the three measures taken in each eye. The repeatability of the measures was evaluated with the intra-class correlation coefficient (ICC). The Kolmogorov–Smirnov test was applied for all data samples in order to check normality. The Mann–Whitney test was used to compare parameters between groups. Bivariate correlations were evaluated using Pearson's or Spearman's correlation coefficients, depending on the normality of the samples. The level of significance used was p o0.05. The significantly correlated variables with a predicted variable were introduced into a multiple linear regression and the “stepwise” method was selected for the development of the linear regression models. Once all variables were corrected in IOP, CCT, or both, they were tested for the development of linear discriminant functions. Only the variables that showed statistically significant differences between groups were considered. The discriminant functions can distinguish between observations belonging to different classes. These functions are formed by a linear combination of variables and can be written thus F¼a1X1 þ a2X2 þa3X3 þ…þ anXn þb. Where a1 to an, and b, are constant, and X1 to Xn are linearly independent variables. The selection of the variables that formed the discriminant function was made by the software according to a “stepwise” algorithm based on the Wilks’s lambda value and the correlation between the variables selected. Finally, Receiver Operating Characteristic (ROC) curves were plotted for the discriminant functions and the area below the curve was calculated.

4. Results The most repeatable mechanical variables provided by the tonometer were CCT (ICC ¼0.958) and IOP (ICC ¼0.852). See ICC for the rest of parameters in Table 2. The comparison between the biomechanical variables showed statistically significant differences between the group of healthy eyes and the group of eyes with subclinical keratoconus (Table 2).

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

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Fig. 1. Topographic maps of the cornea in a patient with manifest keratoconus in the right eye (A) and subclinical keratoconus in the left eye (B). Each figure includes an elevation map of the anterior and posterior cornea (in microns), sagital curvature map of the anterior cornea (in diopters) and corneal thickness map (in microns). The ectatic zone (corresponding to the hottest colors) can be clearly appreciated in the posterior elevation map and in the sagital curvature map in the lower part of the cornea in figure A. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2. Screenshot with the biomechanical parameters provided by the Corvis-ST and pictures sequence of a healthy cornea during the deformation process due to the air pulse.

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

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However, these differences could be due to factors like IOP, CCT, gender, or age, among others. The following step in the present investigation was to check the significant correlations between the biomechanical variables and the external factors mentioned in order to obtain corrected variables. These correlations were checked in the group of healthy eyes to obtain the most accurate results.

a) Corrected variables in which significant differences between groups were found: DAc, A1timec, A1lengthc, A2timec, A2velocityc, and Radiusc b) Variables that showed statistically significant differences between groups and did not need correction for IOP or CCT: HCtime, A2length, and CCT. The discriminant functions obtained were the following:

4.1. Correlation analysis and determination of the corrected biomechanical variables There was a statistically significant difference between the percentage of men and women forming both groups (Table 1), however, no significant correlations were found between biomechanical parameters and gender. Correlation coefficients for the dependence between gender and the biomechanical variables were between 0.021 and 0.145 (absolute value) with p values between 0.791 and 0.062, respectively (p 40.05 in all cases). Regarding age, correlation coefficients were between 0.008 and 0.140 (absolute value) with p values between 0.911 and 0.065. Therefore, we found no statistically significant correlations between parameters determined by the device under study and age. IOP and CCT were the most influential factors on corneal parameters determined by the tonometer, especially the former. The correlation of each biomechanical variable with IOP and CCT is shown in Table 3. In addition, a correction in these external factors (not directly related to the corneal structure and resistance) was performed for each biomechanical parameter. The most significant correlations found for each mechanical variable with IOP and CCT are shown in Figs. 3–5. In general, in non-contact tonometry, IOP is determined from first applanation time (Fig. 4A), and this is true for the device used in this study. This fact was also checked considering the correlation between IOP and A1time for the eyes with subclinical keratoconus: the correlation and coefficients of the linear regression were exactly the same. Since the correction of A1time in IOP would not be correct we did not transform this variable. 4.2. Comparisons between healthy eyes and subclinical keratoconus eyes using corrected biomechanical variables Table 2 shows the values of the corrected variables in IOP and CCT and the differences between the groups under study. Some of the p values changed significantly when comparing the noncorrected and corrected variables. For example, in the case of the maximum deformation amplitude the difference between groups achieved a p value of p ¼2.75  10  6 for the non-corrected variable and p¼ 7.36  10  9 for the corrected variable, which is a 373 times lower p value. The ratio between standard deviation and mean was lower for some of the corrected variables. For example, in the case of the pre-corrected maximum deformation amplitude the mean was 1.02 70.26 (in the group of healthy eyes), while the mean of the corrected maximum deformation amplitude for the same group was 1.36 70.06. This means that the great variability observed in some of the biomechanical variables vanishes when these are corrected in IOP and CCT. 4.3. Determination of the discriminant biomechanical functions Two discriminant functions were obtained. The variables tested for their construction were the following:

1. F1 ¼13.676*DAc  1.187*A1timec  0.013*CCT  5.775 2. F2 ¼1.105*A1timec 2.287*A2timec þ 10.842*A2velocityc þ0.010*CCT þ44.846 Table 4 gives a description of the functions that were tested. Fig. 6 shows the ROC curves for the discriminant functions. Both discriminant functions showed differences between groups with p values several thousands of times lower than the lowest p value obtained for the most discriminant parameters directly provided by the tonometer (maximum deformation amplitude and first applanation time). Fig. 6C and D shows the ROC curves for the most discriminant parameters provided by the tonometer without correction in IOP or CCT (the deformation amplitude and the first applanation time). The specificity and sensitivity values obtained for the noncorrected variables provided by the tonometer are significantly lower when compared with those obtained using the discriminant functions (Table 4). Moreover, the use of corrected parameters has the advantage of applying more than one parameter at the same time to produce an optimized discriminant function. This is not possible in the case of the non-corrected parameters directly provided by the device since most of them are linearly dependent (through their dependence with IOP or CCT).

5. Discussion A great number of clinical studies have been developed on the biomechanical characterization of the human cornea, however, their results vary greatly (Vellara and Patel, 2015; Piñero and Alcón, 2015). Most of them did not take into account the effect of IOP and CCT to make comparisons. Only a few studies divided the sample they analyzed into groups according to differences in IOP and CCT, but none of them defined a set of variables that was independent of these factors. Different authors have reported the influence of IOP and CCT on corneal deformation parameters measured with the Corvis-ST (Chen et al., 2014; Ali et al., 2014; Huseynova et al., 2014; Lanza et al., 2014; Salvetat et al., 2014; Tian et al., 2014) and IOP was identified as the most dominant factor while the influence of CCT varied depending on the study. A recent study (Valbon et al., 2014) evaluated 90 healthy eyes and found that CCT was an influential factor in eight out of ten corneal deformation parameters determined by the Corvis-ST, although this influence was low. Other authors (Chen et al. 2014; Huseynova et al., 2014; Hon and Lam, 2013) also found low or relatively low influence (although significant) of CCT in the mechanical parameters. We confirmed the influence of IOP on DA, A1time, A2time, A2velocity, HCtime, and Radius (  0.849 rr r0.988) especially in the first three variables. We also found a significant, but weak, correlation of CCT with DA, A1length, A2time, A2velocity, and Radius ( 0.386 rr r0.414) Another issue dealt with in the present study was the possible influence of gender and age in the biomechanics of the cornea. Other authors (Ali et al., 2014; Nemeth et al., 2013) analyzed these factors in previous studies but did not find statistically significant correlations between age, gender, or ethnicity and the

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Table 2 Biomechanical variables measured with the Corvis-ST in both groups of patients before and after correction in intraocular pressure (IOP) and central corneal thickness (CCT). ICC value 95% CI interval

Maximum deformation amplitude (mm) Mean 0.745 95% CI [0.595, 0.865] Median IQR Range

A1time (ms) Mean 95% CI

0.787 [0.658, 0.899]

Median IQR Range

A1length (mm) Mean 95% CI Median IQR Range

A1velocity(m/s) Mean 95% CI

Group B

p Value

(Healthy eyes, N ¼ 184) Value before correction in IOP and CCT

(subclinical keratoconus eyes, N ¼ 28) Value before correction in IOP and CCT

(Mann–Whitney test) Value before correction in IOP and CCT

(Healty eyes, N ¼184) Value after correction in IOP and CCT

(subclinical keratoconus eyes, N¼ 28) Value after correction in IOP and CCT

(Mann–Whitney test) Value after correction in IOP and CCT

1.02 70.26

1.13 7 0.08

p o 0.001

1.36 7 0.06

1.45 7 0.01

p o 0.001

[1.00, 1.03] 1.01

[1.10, 1.17] 1.10

[1.35, 1.37] 1.41

[1.43, 1.48] 1.50

0.13 0.72–1.35

0.14 0.99–1.29

0.09 1.20–1.55

0.06 1.32–1.59

7.447 0.30 [7.40, 7.49]

7.22 70.26 [7.11, 7.32]

5.78 70.28 [5.75, 5.83 ]

5.65 7 0.21 [5.56, 5.73 ]

7.46 0.36 6.74–9.00

7.18 0.36 6.78–7.78

5.78 0.36 5.18–7.14

5.62 0.36 5.28–6.01

p o 0.001

p o 0.001

1.39 7 0.08 [1.38, 1.40] 1.41 0.05 1.03–1.53

2.84 7 0.07 [2.81, 2.84] 1.37 0.10 2.52–2.89

p o 0.001

0.167 0.03 [0.15, 0.16] 0.16

0.167 0.03 [0.15, 0.18] 0.15

p ¼ 0.246

–

–

–

0.03 0.08–0.21

0.04 0.11–0.22

21.63 70.44 [21.57, 21.70]

21.977 0.49 [21.76, 22.17]

p ¼ 0.002

23.3570.24 [23.32, 23.39]

23.56 7 0.04 [23.40, 23.73]

p ¼ 0.014

21.58 0.60 20.44–22.91

21.92 0.80 20.97–23.04

21.93 0.30 22.82–24.29

22.12 0.60 22.97–24.44

1.777 0.29 [1.71, 1.79] 1.88

1.577 0.39 [1.42, 1.74] 1.60

p ¼ 0.034

–

–

–

0.27 0.31–2.03

0.67 0.95–2.37

 0.34 7 0.08 [  0.35,  0.32]  0.33

 0.42 7 0.08 [  0.46,  0.39]  0.40

p o 0.001

 0.34 7 0.07 [  0.35,  0.33]  0.65

 0.43 7 0.07 [  0.46,  0.40]  0.71

p o 0.001

0.09  0.70 to  0.10

0.11  0.67 to  0.31

0.07  0.54 to  0.21

0.11  0.62 to  0.31

16.46 7 0.45 [16.39, 16.52]

16.79 7 0.44 [16.61, 16.97]

–

–

0.381 [0.240, 0.504]

0.749 [0.611, 0.860

0.262 [0.104, 0.395]

0.535 [0.325, 0.659]

Median IQR Range

HCtime (ms) Mean 95% CI

Group A

p ¼ 0.001

Median IQR Range

A2velocity (m/s) Mean 95% CI

p Value

1.717 0.11 [1.67, 1.75] 1.73 0.10 1.46–1.85

Median IQR Range

A2length (mm) Mean 95% CI

Group B

1.777 0.09 0.08 [1.75, 1.78] [0.06, 0.182] 1.79 0.05 1.36–1.88

Median IQR Range

A2time (ms) Mean 95% CI

Group A

0.289 [0.125, 0.415]

p ¼ 0.001

–

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Table 2 (continued ) ICC value 95% CI interval

Median IQR Range

Peak distance (mm) Mean 95% CI

0.208 [0.067, 0.343]

Median IQR Range

Radius (mm) Mean 95% CI Median IQR Range

0.564 [0.332, 0.759]

Group A

Group B

p Value

Group A

Group B

p Value

(Healthy eyes, N ¼ 184) Value before correction in IOP and CCT

(subclinical keratoconus eyes, N ¼ 28) Value before correction in IOP and CCT

(Mann–Whitney test) Value before correction in IOP and CCT

(Healty eyes, N¼ 184) Value after correction in IOP and CCT

(subclinical keratoconus eyes, N ¼ 28) Value after correction in IOP and CCT

(Mann–Whitney test) Value after correction in IOP and CCT

16.63 0.46 15.02 to 17.56

16.71 0.43 15.94 to 17.79 –

–

–

4.50 7 1.00 [4.33, 4.62]

4.217 1.27 [3.67, 4.71]

4.80 0.50 1.82–5.70

4.75 2.74 2.26–5.49

8.047 1.12 [7.85, 8.18]

6.90 7 0.86 [6.58, 7.28]

1.177 0.90 [1.03, 1.30]

0.48 70.62 [0.23, 0.74]

p o 0.001

8.05 1.45 5.39–10.88

6.79 1.19 5.75–8.97

1.87 1.14  4.22 to 3.28

1.01 0.50  0.98 to 1.99

p ¼ 0.697

p o 0.001

ICC (intraclass correlation coefficient). IQR (Interquartile rage).

biomechanical parameters; however Kamiya et al. (2009) evaluated 204 healthy eyes with the ORA and found statistically significant correlations of age with Corneal Hysteresis (CH) and Corneal Resistance Factor (CRF) although the influence was very low (r ¼  0.17, and r ¼ 0.18 p r0.02, respectively). We did not find significant correlation between age or gender and the corneal deformation parameters provided by the Corvis-ST, although the number of eyes was large and the age range was wide (17–75). In any case, the influence of these factors is negligible when compared with other factors like IOP and CCT since, even assuming a significant dependence similar to that found by Kamiya et al. for age, the influence in the regression models would be minimal (r2 r0.1822 ¼ 0.032). In our opinion, age is an influential factor in the mechanical response of the cornea since the elastic properties of the collagen fibers vary with age (Elsheikh et al., 2007, Curr Eye Res); however, the accuracy of non-contact tonometry could be insufficient to detect this effect, which is minimal compared with the effect of IOP or CCT. Possibly, new techniques for the biomechanical characterization of the cornea could provide a more powerful approach to identify differences due to age (Scarcelli and Yun, 2012). Some effects, such as dehydration and the influence of the sclera and ocular muscles on mechanical measures of the cornea have been addressed by other authors who tested in vitro conditions (Kling and Marcos, 2013). However, an accurate evaluation of these parameters in vivo is not possible at clinical level and therefore they were not considered in our study since the main application of the model developed is at the clinical diagnosis level. Other studies evaluated the capability of the Corvis-ST device for differentiating between normal and keratoconic eyes. One of these studies (Tian et al., 2014) compared a sample of 60 eyes with manifest keratoconus with 60 healthy eyes. The authors found significant differences in most of the biomechanical variables analyzed and DA showed the best combination of sensitivity and specificity (81.7% and 83.3%, respectively) for a DA cut-off value of 1.18 mm.

The significant correlation of DA with IOP and the importance of DA to characterize the corneal biomechanics have been confirmed also by other authors (Sinha Roy et al., 2015; Simonini and Pandolfi, 2015a, 2015b). Moreover, we found that the sensitivity and specificity of this parameter is highly improved if it is corrected in IOP and CCT. Another study (Ali et al., 2014) evaluated 45 keratoconic eyes (98% with moderate or severe keratoconus) and 103 healthy eyes. They found the most significant differences between groups for DA (po 0.001). Moreover they compared two subgroups of eyes comparable in IOP and CCT and again obtained statistically significant differences (p ¼0.006). They values of sensitivity and specificity they found were 61.1% and 80%, respectively, for a DA cut-off value of 1.215. We confirmed that DA is the best isolated discriminant variable with an area under the ROC curve of 0.775 (Fig. 6C). The best combination of sensitivity and specificity for this function was 53.6% and 79.3%, respectively for a cut-off value of 1.085. However, there were two major differences between these studies and our study: they compared manifest keratoconus (severe in many cases) with healthy eyes, and they did not use combinations of variables corrected by IOP and CCT. Previous studies (Schweitzer et al., 2010; Ruiseñor Vázquez et al., 2013) investigated the capability of the ORA to differentiate between subclinical keratoconus and healthy eyes although none of these studies found high combined values of sensitivity and specificity. In view of the results, we think the most suitable discriminant function for clinical use is F1 due to its easy interpretation. For a given value of IOP and corneal thickness, the higher DA and the lower A1time, the higher the value of F1, and therefore, the higher the probability of corneal damage, i.e. for a given value of IOP and CCT a keratoconic cornea deforms more and in less time than a normal cornea. Regarding the applicability of our technique to other devices like the ORA, we think an analysis of the response curves that can be obtained from this device (Lam et al., 2010) together with the

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

Mechanical Variable

Correlation between the mechanical variable and external variables

Linear regression model obtained

Equation for the corrected variable

Correlation of the corrected variable with IOP and Pachymetry (CCT)

DA

DA-IOP (r¼  0.810, p o 0.001)

DA ¼ 1.415  0.028*IOP  0.0001*CCT r2 ¼0.66, po 0.001

DAc ¼DA þ 0.028*IOP þ0.0001*CCT

DAc-IOP (r ¼  0.106, p ¼ 0.156)

A1time ¼5.789 þ0.0031*CCT r2 ¼0.15, po 0.001 A1length ¼ 1.399 þ 0.0007*Pachymetry r2 ¼0.11, p o 0.001

A1timec ¼ A1time  0.0031*CCT

DAc-CCT (r ¼  0.105, p¼ 0.158) A1timec-CCT (r ¼0.001, p¼ 0.994)

–

–

A1time A1length A1velocity A2time A2length A2velocity

HCtime Peak distance Radius

DA-CCT (r ¼  0.386, p o 0.001) A1time-IOP (r¼ 0.988, p o0.001) A1time-CCT (r ¼0.387, p o 0.001) A1length-IOP (r ¼0.143, p ¼ 0.052) A1length-CCT (r¼ 0.397, p o 0.001) A1velocity-IOP (r¼ -0.133, p¼ 0.075) A1velocity-CCT (r ¼ 0.162, p¼ 0.054) A2time-IOP (r¼  0.849, p o0.001) A2time-CCT (r ¼  0.174, p o 0.041) A2length-IOP (r ¼0.042, p ¼ 0.575) A2length-CCT (r¼ 0.142, p ¼0.056) A2velocity-IOP (r ¼0.556, p o 0.001) A2velocity-CCT (r¼ 0.259, p o 0.001) HCtime-IOP (r¼ 0.175, p ¼ 0.019) HCtime-CCT (r ¼0.096, p ¼ 0.199) PD-IOP (r¼ 0.310, p¼ 0.098) PD-CCT (r ¼0.291, p ¼0.115) Radius-IOP (r¼ 0.467, p o0.001) Radius-CCT (r¼ 0.414, p o 0.001)

A1lengthc ¼A1length  0.0007*Pachymetry

A2time ¼21.936  0.137*IOP þ0.0025*CCT r2 ¼ 0.74, p o 0.001 A2timec ¼ A2time þ0.137*IOP  0.0025*CCT

A1lengthc-IOP (r ¼0.035, p ¼ 0.643) A1lengthc-CCT (r¼  0.124, p ¼0.097) – A2timec-IOP (r¼  0.112, p ¼0.137) A2timec-CCT (r o0.001, p ¼1.000) –

–

–

A2velocity ¼  0.655 þ 0.013*IOP þ0.0003*CCT R2 ¼0.369, p o 0.001

A2velocityc ¼ A2velocity  0.013*IOP  0.0003*CCT A2velocityc-IOP (r¼ 0.019, p ¼0.784)

r2 ¼0.031 (neglectable)

–

A2velocityc-CCT (r ¼0.071, p ¼0.310) –

–

–

–

Radius ¼ 1.658 þ 0.149*IOP þ0.008*CCT R2 ¼0.35, p o 0.001

Radiusc ¼ Radius  0.149*IOP  0.008*CCT

Radiusc-IOP (r¼ 0.075, p ¼0.317) Radiusc-CCT (r ¼0.275, p ¼0.085)

P. Peña-García et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

Table 3 Summary of the correlations among the biomechanical variables with IOP and pachymetry (Corneal Central Thickness, CCT) and equations for the corrected variables.

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Fig. 3. (A) Correlation between the maximum deformation amplitude (DA, in mm) and intraocular pressure (IOP, in mm Hg). (B) Correlation between the maximum deformation amplitude (DA, in mm) and central corneal thickness (CCT, in microns).

Fig. 4. (A) Correlation between the first applanation time (A1time, in ms) and intraocular pressure (IOP, in mm Hg). (B) Correlation between the first applanation time (A1time, in ms) and central corneal thickness (CCT, in microns).

use of the discriminant functions theory could probably provide similar results to those obtained in the present study. The main finding of the present study is that the diagnosis of subclinical keratoconus forms, which is of crucial importance to avoid post-surgical ectasia, can be improved. However, the use of the discriminant functions, capable of differentiating between

different biomechanical states, poses other potential applications. Some of these are the following: differentiation between different grades of keratoconus, evaluation of ectatic progression, testing of the efficacy of treatments for the reinforcement of the corneal collagen, such as crosslinking (Hatami-Marbini and Rahimi, 2015), and evaluation of the biomechanical effect of other types of

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

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Fig. 5. (A) Correlation between the second applanation time (A2time, in mm) and intraocular pressure (IOP, in mm Hg). (B) Correlation between the second applanation time (A2time, in mm) and central corneal thickness (CCT, in microns). (C) Correlation between the velocity of the corneal apex when returning to its original position (A2velocity, in m/s) and intraocular pressure (IOP, in mm Hg). (D) Correlation between the velocity of the corneal apex when returning to its original position (A2velocity, in m/s) and central corneal thickness (CCT, in microns).

corneal surgical procedures. Finally, another application of our model could be, through its combined use with computational models, (Pinsky et al, 2005; Pandolfi and Manganiello, 2006; Studer et al., 2013; Simonini and Pandolfi, 2015a, 2015b) the prediction of mechanical changes due to refractive surgery (Pepose et al., 2007; Chen et al., 2014; Pedersen et al., 2014; Peña-Garcia et al., 2014; Peris-Martínez et al., 2012; Bühren et al., 2013). As a limitation of the present study, it must be mentioned that more eyes with subclinical keratoconus should be used in order to define a third group of eyes as a validation set to check sensitivity and specificity values more precisely. However, it is difficult to detect cases of subclinical keratoconus and generating a validation set with a considerable number of eyes could take a very long time. Moreover, the results achieved are logical and the levels of significance are very low. In addition, we provide the exact algorithm to construct the discriminant functions so that another researcher can verify or refine the coefficients of the functions as much as possible to increase their diagnostic capability. It must be noted that the repeatability of some variables provided by the tonometer analyzed is not high and, therefore, it is advisable to take several measures. In this regard, it must be mentioned that the models use the variables with the best repeatability (ICC between 0.745 and 0.958)

Table 4 Results produced by the most discriminant functions found. Discriminant function

Statistical difference between groups (p value)n

Area under the curve mean7 sd 95% CI

Sensitivity/ specificity (%)

F1

2.0  10  10

85.7/82.07

F2

2.5  10  10

0.893 70.028 [0.838, 0.949] 0.892 70.032 [0.829, 0.953] 0.7757 0.044 [0.689, 0.861] 0.7367 0.055 [0.628, 0.843]

Deformation 2.8  10  6 Amplitude (DA) First Applanation 5.4  10  4 time (A1time) n

Cut-off value

0.01

78.6/79.9

 0.48

53.6/79.3

1.09

50/79.9

7.46

(Mann–Whitney test). 95% CI (95% confidence interval).

Although the combination of corneal topography and tomography is nowadays the gold standard for identifying subclinical keratoconus (Arbelaez et al., 2012; Smadja et al., 2013) we believe that the biomechanical approach can complement the accuracy of the diagnosis in a very efficient manner.

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

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Fig. 6. (A) Receiver Operating Characteristic for F1. (B) Receiver Operating Characteristic for F2. (C) Receiver Operating Characteristic for maximum Deformation Amplitude (DA). (D) Receiver Operating Characteristic for first applanation time (A1time). The area under the ROC curve in the case of F1 and F2 is significantly larger compared to the area under the ROC curve in the case of DA and A1time (the most discriminant parameters provided by the tonometer). Sensitivity and specificity are also highly increased using F1 or F2.

6. Conclusions

References

To the best of our knowledge, this is the first study in which parameters provided by non-contact tonometry are corrected by IOP and CCT and combined using the theory of discriminant functions to optimize the capability of this kind of devices to detect subclinical keratoconus. The methodology described is general and could be extended to other tonometers as well as to investigating other issues related to corneal biomechanics. Although more research and larger samples are needed, we believe the present study will help clinicians detect subclinical keratoconus.

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Conflict of interest statement The authors have no proprietary or commercial interest in the medical devices involved in this manuscript and they have no other potential conflict of interest to disclose.

Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i

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Please cite this article as: Peña-García, P., et al., Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2015.12.031i