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Dayyani R, Jafarzadehpur E, Salouti R, Mirzajani A. Estimation of Final Cylindrical Spectacle Correction by Pentacam. Func Disabil J 2020; 3 (1) :61-68
URL: http://fdj.iums.ac.ir/article-1-128-en.html
1- Department of Optometry, School of Rehabilitation Sciences, Iran University of Medical Sciences, Tehran, Iran.
2- Department of Optometry, Iran University of Medical Sciences, Tehran, Iran , jafarzadehpour.e@iums.ac.ir
3- Department of Ophthalmology, Poostchi Ophthalmology Research Center, Shiraz University of Medical Sciences, Shiraz, Iran.
4- Department of Optometry, Iran University of Medical Sciences, Tehran, Iran
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1. Introduction 
Keratoconus (KCN) is a non-inflammatory asymmetric corneal degenerative disease [1, 2] that is characterized by steepening and distortion of the cornea [3, 4]. KCN usually appears in the second or third decade of the life [5, 6]. The ocular symptoms and signs of KCN vary depending on disease severity [5]. Besides, one of the first indications of the disease is that the patients routinely complain about their spectacle correction [3].
Spectacle prescription is one of the most challenging issues in the optical correction of KCN. Although contact lenses provide better visual acuity, they are expensive, sophisticated to use, and need an adaptation period [4, 7, 8]. Also, the surgery approaches are complicated and unaffordable for many patients [9, 10, 11]. Therefore, spectacle correction should be considered as a first [7] and most favorable optical correction for KCN patient. In the early stages of KCN, the patient's vision can be fully correctable with spectacle [4, 7]. The patient’s best corrective visual acuity decreases as the disease progresses, thus, the optimal visual acuity does not always mean a complete visual acuity. Also, some patients may tend to wear spectacles because of their occupational conditions and visual needs. Moreover, some patients tend to use contact lenses when they need higher visual acuity and spectacles when they do not need full visual acuity. Therefore, spectacle correction can be considered as the most favorable optical correction for KCN patients, considering the disadvantages of the other methods of the management of KCN. However, spectacle correction is a great challenge for practitioner. The irregular cornea makes the objective data unreliable, besides, the subjective approaches need proper visual acuity and the excellent cooperation of patient. Practically, spectacle correction is not always achievable. Usually, the unsatisfying and unbearable spectacles of the KCN patients [7] may persuade them to use either contact lens or surgery. However, for many reasons, the contact lenses and surgery do not gratify KCN patients, and some of them prefer to use spectacles again. 
The objective refractive errors can be determined with several methods. Autorefractometry is an automated, fast, and reliable method of objective refraction [12]. However, autorefractometer readings are unobtainable in corneal irregularity, because most autorefractometer samples are located in the selected areas of the pupil, while the full pupil is used for vision. Also, the influences of the different areas of the pupil for vision differ from those used by the autorefractometer in the assessment of the refractive error. Therefore, if the cornea is irregular in the pupillary area, the effects of this irregularity are often revealed differently by the subjective results [3]. Retinoscopy is another objective method for the measurement of the refractive state. An inhomogeneous light-shadow movement is seen in retinoscopy. At the corneal center, the refraction may be slightly myopic, in comparison with the periphery. The scissors light movement is very common in KCN patients. Indeed, besides the highly-developed devices, classic retinoscopy can successfully classify KCN [6]. However, the retinoscopy endpoint is difficult to define accurately in KCN patients, because of distorted images [12]. In KCN patients, the data of subjective refraction significantly differ from those of the aberrometry-derived spherical equivalent refraction. Also, the subjective refraction data give significantly better logMAR acuity than the aberrometer’s auto-refraction data. Finally, further investigation into deriving objective refraction data from aberrometry measurements is warranted in KCN [13]. The logMAR visual acuity achieved using the subjective and aberrometry auto-refraction data were measured in the six keratoconic subjects. Results: The subjective and aberrometry-derived spherical equivalent refraction data were significantly different in the keratoconus group (p0.015).
It is very difficult and sometimes impossible to achieve the desired objective refraction with common methods in KCN patients. Thus, many examiners have to solely rely on subjective refraction, which is mostly performed by trial and error method in KCN patients [12]. Although the conventional subjective refraction is the standard method of refraction, it is a psychophysical examination (like the measurement of visual acuity) that can vary owing to several factors. The ability of persons to discern dioptric differences varies from 0.12 D to 1.0 D [14].
As the cornea is the main determinant factor of the ocular refractive status, the evaluation of the cornea may help to determine ocular astigmatism. The Pentacam is a reliable elevation-based corneal imaging system. The Pentacam findings show the power distribution of cornea in the anterior and posterior surfaces. These findings can be used to determine ocular astigmatism.

2. Materials and Methods
This study was conducted in the Salouti eye clinic, Shiraz, Iran. The patients who could collaborate on the experiments were included in the study. A total of 317 keratoconic patients took part in this study; they had no history of eye surgery or other eye diseases. Also, the patients were between 15 and 45 years old. 
Initially, if possible, we obtained approximate objective refraction from patients, using the autorefractometer or retinoscope. Then, we measured the uncorrected visual acuity using the logarithmic charts. Next, we started the subjective refraction. First, we put the amount of cylinder in front of the trial frame and rotated the frame’s screw, so that, the patient could report the resolution. Then, to correct the axis obtained, we changed it by 5 or 10 degrees and asked the patient about the resolution changing. We continued this process to obtain the best visual acuity. Then, the power of the cylinder was adjusted by increasing or decreasing it. Also, we refined the axis with each change in the power of the cylinder. Then, the amount of the sphere was modified. Again, the axis and the power of the cylinder were refined with each change in the amount of the sphere. We continued this process to obtain the best visual acuity. 
The patient’s cornea was imaged with the Pentacam system, after determining the best subjective refraction with the best visual acuity.
After determining the best subjective refraction with the best visual acuity, the patient's cornea was imaged using the Pentacam system. Then, 4-map refractive displays were extracted and the amount of corneal front surface astigmatism, corneal back surface astigmatism, and their axes were obtained with vector analysis [15-17]. Next, we used the following formulas to estimate the objective refraction.
1. Axis of corrective cylinder = flat corneal front surface axis.
2. Power of corrective cylinder = − corneal front surface astigmatism + (corneal back Surface astigmatism × cos2θ).
θ = |corneal front surface axis − corneal back surface axis|.
We then compared the calculated values separately with the cylindrical subjective refraction, using SPSS. Also, linear regression was used to determine the correction coefficients of these formulas.

3. Results
This study examined 317 eyes from KCN patients within the age range of 15 to 45 years. Tables 1 and 2 report the information about the age and amount of astigmatism, respectively.

We performed a regression analysis to find the relationship between the subjective and calculated cylindrical refractions, using the formulas mentioned before. Table 3 presents the obtained results.

According to Table 3, the P-value for the power and axis of the cylinder is lower than 0.001. The calculated cylindrical refraction is significantly related to the subjective cylindrical refraction, therefore, using the calculated formula, it is possible to predict the power and axis of the cylinder of subjective refraction, with a probability of 99.9%. In this regard, Figures 1 and 2 show that calculated cylindrical refraction has a normal distribution, and linear regression can express its changes.

4. Discussion 
Achieving cylindrical spectacle power can be very difficult and time-consuming in keratoconic patients, because of the irregular shape of the cornea. Therefore, other surgical and non-surgical methods have been developed, each of which has its disadvantages and cannot be done for all patients [18, 19, 20, 21]. Also, the patients with KCN constitute an important group because of the high prevalence, younger age of onset, active lifestyle, and higher visual requirements [19]. As mentioned before, the patients’ vision can be fully corrected with spectacle, in the early stages of KCN. But in the later stages of the disorder, it is up to the patient to choose between more comfort and optical correction or better vision and the disadvantages of the other methods. Thus, the spectacle is of priority in
KCN patients, because the use of glasses is easier, safer, and cheaper. Therefore, if the patient can get a good vision with spectacles, has a history of using glasses, and is more comfortable with them, it is important to consider the prescription of glasses.
The study samples were in the different stages of KCN (Table 1). Therefore, the present results can be extended to the different stages of the disorder. The present study has preference over other similar studies, regarding the sample size and the extent of astigmatis [22, 23]. Also, using corneal astigmatism, most of the studies have determined refractive astigmatism related to regular astigmatism [24, 25]. Moreover, the study participants were in the peak age range of the incidence and prevalence of KCN (Table 1). Research has considered the age range corresponding to the present study as the main age range for the appearance of symptoms and problems of KCN [26, 27, 28].
Table 2 shows the role of anterior and posterior corneal surface astigmatism in refractive astigmatism. Atsuo Tomidokoro et al. conducted a study titled Changes in Anterior and Posterior Corneal Curvatures in Keratoconus and concluded that both anterior and posterior corneal curvatures were affected in KCN; these changes were observed in the early stage of the disorder [29].  Also, David P. Pinero et al. revealed a strong correlation between the anterior and posterior surface astigmatism in KCN groups. Besides, the eyes with clinical or subclinical KCN had the higher levels of the manifest, anterior, and posterior corneal astigmatism [30]. In eyes with KCN, the magnitudes of anterior and posterior corneal astigmatism are significantly correlated with each other, also, the presence of posterior corneal astigmatism is not negligible for the accurate astigmatic correction [31]. Hence, we used both anterior and posterior corneal astigmatism to achieve refractive astigmatism. Consistent with our findings, Feizi et al. achieved the mean magnitude of 1.0 D for posterior astigmatism (range, 0.0-2.90 D) [32] Based on all these studies, we used both anterior and posterior corneal surface astigmatism to determine refractive astigmatism. 
It is widely accepted that there is a statistical linear relationship between the corneal and refractive astigmatism [24]. This relationship was first postulated by Javal in 1890, in an early attempt to use the keratometer as an aid in objective refraction. More than 30 years later, Grosvenor et al. refined and simplified the Javal rule, based on more rigorous analyses. The results were confirmed by other authors. However, both the conventional and simplified Javal rules only considered WTR (with the rule) and ATR (against the rule) astigmatism [25]. Using power vectors, Laura Remon examined the relationship between corneal and refractive astigmatism in adults. The power vectors can predict WTR, ATR, and also oblique astigmatism [25].
Using Pentacam, we determined the power and axis of the anterior and posterior surface astigmatism of the cornea. Also, refractive astigmatism was determined with subjective refraction in the present study. Then, linear regression analysis was used to determine the relationship between corneal astigmatism and refractive astigmatism, which included both axis and power. According to Table 3, these regression formulas can accurately predict (with a probability of 99%) refractive astigmatism, using corneal astigmatism (P<0.001). Other studies have established linear relationships between corneal astigmatism and refractive astigmatism in regular corneas [24, 25], while the present regression formulas can be used in irregular corneas. In patients with KCN, subjective refraction is determined based on trial and error. On the contrary, these regression formulas predict cylindrical refraction and present it as objective cylindrical refraction.
Many sources present the mathematical models of the power and axial changes of regular cylinders. These changes are sinusoidal in regular astigmatism [33, 34]. Also, some studies have used the Fourier series harmonic analysis to extract the irregular components of astigmatism and convert them into regular components; thus, these studies have proposed various models to quantify irregular astigmatism [33, 34, 35, 36] regular astigmatic (2′ harmonic).
The graphs obtained in this study (Figures 1 and 2) clearly show the sinusoidal nature of the axis and power of the astigmatism changes.

Therefore, both the numerical indices and the graphs of the proposed model indicate the synchronicity of the model with the real changes in the axis and power of astigmatism. This study provides a suitable and practical model not only for determining subjective astigmatism but also for describing irregular astigmatism. Although other studies suggest the decomposition of irregular astigmatism components into regular components [33, 34, 35, 36] regular astigmatic (2′ harmonic, the present model is clinically applicable and can be easily extracted and used.

5. Conclusion 
The present study provides a suitable model for estimating corrective astigmatism of glasses, based on Pentacam findings. According to the proposed model, it can be understood from the methods of determining the decomposed astigmatism harmonics to similar models to determine corrective astigmatism. Also, the proposed model may be used to achieve appropriate results, using other similar corneal imaging devices. The final formulas of regression analysis of the model are as follows:
1. For calculating the axis of the cylinder of refraction, we can use the following formula:
axis of cylinder = 24 + 0.73 × (flat corneal front surface axis).
2. For calculating the power of the cylinder of refraction, we can use the following formula:
power of cylinder = −0.8 + 0.5 × (−corneal front surface astigmatism + (corneal back surface astigmatism × cos2θ)).
θ = |corneal front surface axis − corneal back surface axis|.

Ethical Considerations
Compliance with ethical guidelines

This study was approved by the Ethics Committee of Iran University of Medical Sciences. (Code: IR.IUMS.REC.1398.236 ).

The paper was extracted from the MSc. thesis of first author, Department of Optometry, School of Rehabilitation Sciences, Iran University of Medical Sciences, Tehran.

Authors' contributions
General design, data collection, analysis and discussion: Raziye Dayyani; Data analysis: Ebrahim Jafarzadehpur; General design and data presentation:Ramin Salouti; Discussion: Ali Mirzajani.

Conflict of interest
The authors declared no conflict of interest.

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Type of Study: Research | Subject: Optometry
Received: 2020/08/2 | Accepted: 2020/10/15 | Published: 2020/12/30

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