# Assessment of Pattern and Shape Symmetry of Bilateral Normal Corneas by Scheimpflug Technology

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## Abstract

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_{0}and Y

_{0}(p < 0.001) for the anterior corneal surface, and the rotation angle gamma (p < 0.001) for the posterior surface. Similarly, no statistically significant differences were identified for direct symmetry (p ≥ 0.20) and enantiomorphism (p ≥ 0.75), except for some elevation data in the posterior surface (p < 0.01). Conclusions: The level of symmetry of both corneas of a healthy individual is high, with only some level of disparity between fellow corneas in rotation and translation references. Abnormalities in this pattern of interocular asymmetry may be useful as a diagnostic tool.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Participants and Examination Protocol

#### 2.2. Data Acquisition

#### 2.3. Methods

#### 2.3.1. Morphogeometric Symmetry

#### 2.3.2. Axial Symmetry at the Corneal Vertex

_{0}) at the vertex reference point (V

_{0}) from corneal shape parameters (Table 2). The procedure takes place as follows:

- Adjust the point cloud to a general quadric model (ellipsoid) and subsequently transform into a perfect ellipsoid. With the help of some algorithms programmed in Matlab software that use the equations defined in Navarro’s model [34], we adjust the finite and discrete set of spatial data representative of the spatial surfaces (raw data) to an ellipsoid. Then, we perform the algebraic transformation with the matrix equations of the obtained ellipsoid into a perfect ellipsoid at the vertex reference point (V
_{0}), whose main axes are the 3 main position and orientation orthogonal axes in 3D space (Figure 2).

#### 2.3.3. Angular-Spatial Symmetry

_{i}) on the corneal surface area by its elevation Cartesian coordinate (Z

_{i}) and angular position (α

_{i}) on each ring. These singular points are those with a higher elevation coordinate (Z

_{max}) with respect to the vertex of the Sirius reference system. In addition, in this work we also divide the spatial region into 8 octants to spatially identify each maximum and minimum per octant. This procedure is done as follows:

- Export the raw data CSV files from Sirius. This procedure is the same as in point 1 of Section 2.3.2.
- Identify the singular points for each ring by the elevation coordinate (Z
_{i}) and its angular position (α_{i}). The Cartesian coordinate matrix (raw data) size is 20 × 256, where the 20 rows correspond to the projection of the 20 Placido’s discs (radius: 0, 0.2, 0.4, 0.6, 1, … 4 mm) on the corneal surface area, so they cover the corneal region for those corneas with a radius equal to 4 mm. Each matrix point i has a Cartesian elevation coordinate (Z_{i}) and an angular position (α_{i}) in relation to the projection ring of the Placido’s disc (anticlockwise). By the algorithm programmed in Matlab, we obtained the uppermost (Z_{max}) points in relation to the corneal vertex, and their angular positions (α_{Zmax}) in relation to the projection ring. This algorithm also helped us to identify each singular point with respect to the 8 defined octants.

#### 2.3.4. Direct Symmetry (Equal Octants) and Enantiomorphism (Mirror Octants)

_{X′}–Z

_{X″}) are studied in this pattern (equal octants/mirror octants). The procedure for both symmetries is summarized as follows:

- Export the raw data CSV files from Sirius. This procedure is the same as in point 1 of Section 2.3.3. Identify the intersection points (Z
_{X′}–OD/Z_{X″}–OD) between the octant axes and the Placido’s discs. For the Cartesian coordinate matrix described in the previous patterns, the points placed on all 8 axes that divide the corneal region are identified. Using another algorithm programmed in Matlab, we identify the 8 points for each Placido’s disc by their angular position, which must coincide with the angles of the octant axes, and obtain the Cartesian elevation coordinates for the right eye (Z_{A′}… Z_{H′}) and the left eye (Z_{A″}… Z_{H″}) (Figure 4). Our study considered only the intersection points between the octant axes and the Placido’s discs for radius r = 1, 2, 3, and 4 mm. - Apply enantiomorph (mirror octants). In this pattern, the octants of the right eye do not coincide with the octants of the left eye. Instead, each right eye (OD) octant has a corresponding octant in the left eye (OS) via its specular image; that is, by its specular image, octant I-OD corresponds to octant IV-OS (Figure 5). As in the previous point, by means of another algorithm programmed in Matlab, the differences between the elevation coordinates for each pair of points are calculated (Table 3).

#### 2.4. Statistical Analysis

## 3. Results

#### 3.1. Analysis of Morphogeometric Corneal Symmetry

_{ant}, with a trend toward higher values in left eyes (p = 0.055). No significant differences between right and left eyes were found for the rest of the morphogeometric parameters evaluated (p ≥ 0.488).

#### 3.2. Analysis of Axial Symmetry at the Corneal Vertex

_{0}, and Y

_{0}(p < 0.001) (Table 6).

_{0}, Y

_{0}, Z

_{0}(Figure 6). The vertex mean value (V) of both right and left eyes with normal corneas are located on the nasal and inferior-nasal sides of the vertex (V

_{0}) in anterior and posterior surface corneas (Cornea

_{0}, ellipsoid), respectively (Figure 6). These results provide further evidence of mirror symmetry relative to the median vertical plane YZ.

_{0}) (Figure 7). Angles α and β had similar distributions in bilateral corneas with the same angle signs in fellow corneas (Figure 7), indicating a high degree of direct symmetry (both rotated toward the nasal side) relative to the median vertical plane XY. Similar results were obtained for angle γ, although in this case the values for right and left corneas had opposite signs, indicating a high degree of mirror symmetry relative to the median vertical plane YZ.

#### 3.3. Analysis of Angular-Spatial Symmetry

_{max}calculated for four circular areas with a radius of 1, 2, 3, and 4 mm (p ≥ 0.171). Likewise, Z

_{max}in most cases was located in the same octants in the right and left eyes, as displayed in Figure 8.

#### 3.4. Analysis of Direct Symmetry (Equal Octants) and Enantiomorphism (Mirror Octants)

## 4. Discussion

_{0}(different sign) confirming the presence of mirror symmetry relative to the median vertical plane YZ, a significant difference was also found in Y

_{0}, with mean values of opposite sign for the right and left eyes. This also confirms the presence of mirror symmetry relative to the median horizontal plane XZ. This last type of mirror symmetry was not found by Bao et al. [8], especially in the posterior corneal surface. One factor that potentially accounts for this is the difference between the devices used in their study and in the current study to characterize the posterior corneal surface [43]. This difference between devices may also explain the different trend reported by Bao et al. [8] in terms of rotational displacement angles. In our sample, significant differences between fellow eyes were found in beta angle for the anterior corneal surface and in gamma angle for the posterior corneal surface, with more negative values for the left eye.

_{max}and its position (defined by octants) between right and left eyes for the anterior corneal surface. For the posterior corneal surface, differences in octant position of Z

_{max}were found between eyes, suggesting lower levels of symmetry. This was confirmed with the analysis of direct and mirror symmetry, obtaining significant differences between eyes in terms of corneal elevation in equal and mirror octants for different areas of analysis. However, differences in anterior corneal elevation between fellow eyes in equal and mirror octants were not statistically significant for different diameters, suggesting that both types of symmetry coexist in the anterior corneal surface. Although there was mirror symmetry in terms of apex position in anterior corneal surface, the geometric distribution is quite regular, leading to no significant differences in elevation between equal and mirror octants along the central and mid-peripheral corneal areas. This regularity of anterior corneal surface in contrast to the higher level of irregularity in the posterior corneal surface may be due to, among other factors, the potential effect of regularization of the eyelid during blinking [44]. In the posterior corneal surface, differences in the effect of intraocular pressure over the corneal structure may explain this lower level of symmetry by octants. Indeed, alterations in posterior corneal surface elevation and curvature have been proposed as efficient ways to detect incipient stages of corneal ectatic disorders, as the intraocular pressure may begin the deformation of the corneal geometry when the structure becomes weakened [45].

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Hickox, L.J.; Ashby, B.M.; Alderink, G.J. Exploration of the validity of the two-dimensional sagittal plane assumption in modeling the standing long jump. J. Biomech.
**2016**, 49, 1085–1093. [Google Scholar] [CrossRef] [PubMed] - Jayasuriya, S.A.; Liew, A.W.C.; Law, N.F. Symmetry plane detection in brain image analysis: A survey. Curr. Med. Imaging Rev.
**2013**, 9, 230–247. [Google Scholar] [CrossRef] - Alterson, R.; Plewes, D.B. Bilateral symmetry analysis of breast mri. Phys. Med. Biol.
**2003**, 48, 3431–3443. [Google Scholar] [CrossRef] [PubMed] - Chan, S.; Chen, J.H.; Li, S.; Chang, R.; Yeh, D.C.; Chang, R.F.; Yeh, L.R.; Kwong, J.; Su, M.Y. Evaluation of the association between quantitative mammographic density and breast cancer occurred in different quadrants. BMC Cancer
**2017**, 17, 274. [Google Scholar] [CrossRef] [PubMed] - Navalho, M.; Resende, C.; Rodrigues, A.M.; Ramos, F.; Gaspar, A.; Pereira Da Silva, J.A.; Fonseca, J.E.; Campos, J.; Canhão, H. Bilateral mr imaging of the hand and wrist in early and very early inflammatory arthritis: Tenosynovitis is associated with progression to rheumatoid arthritis. Radiology
**2012**, 264, 823–833. [Google Scholar] [CrossRef] [PubMed] - Volkau, I.; Prakash, B.; Ananthasubramaniam, A.; Gupta, V.; Aziz, A.; Nowinski, W.L. Quantitative analysis of brain asymmetry by using the divergence measure: Normal-pathological brain discrimination. Acad. Radiol.
**2006**, 13, 752–758. [Google Scholar] [CrossRef] [PubMed] - Arba Mosquera, S.; Verma, S. Bilateral symmetry in vision and influence of ocular surgical procedures on binocular vision: A topical review. J. Optom.
**2016**, 9, 219–230. [Google Scholar] [CrossRef] [PubMed] - Bao, F.; Chen, H.; Yu, Y.; Yu, J.; Zhou, S.; Wang, J.; Wang, Q.; Elsheikh, A. Evaluation of the shape symmetry of bilateral normal corneas in a Chinese population. PLoS ONE
**2013**, 8, e73412. [Google Scholar] [CrossRef] [PubMed] - Li, Y.; Bao, F.J. Interocular symmetry analysis of bilateral eyes. J. Med. Eng. Technol.
**2014**, 38, 179–187. [Google Scholar] [CrossRef] [PubMed] - Galletti, J.D.; Vázquez, P.R.R.; Minguez, N.; Delrivo, M.; Bonthoux, F.F.; Pförtner, T.; Galletti, J.G. Corneal asymmetry analysis by pentacam scheimpflug tomography for keratoconus diagnosis. J. Refract. Surg.
**2015**, 31, 116–123. [Google Scholar] [CrossRef] [PubMed] - Guggenheim, J.A.; Zayats, T.; Prashar, A.; To, C.H. Axes of astigmatism in fellow eyes show mirror rather than direct symmetry. Ophthalmic Physiol. Opt.
**2008**, 28, 327–333. [Google Scholar] [CrossRef] [PubMed] - Myrowitz, E.H.; Kouzis, A.C.; O’Brien, T.P. High interocular corneal symmetry in average simulated keratometry, central corneal thickness, and posterior elevation. Optom. Vis. Sci.
**2005**, 82, 428–431. [Google Scholar] [CrossRef] [PubMed] - Prakash, G.; Ashok Kumar, D.; Agarwal, A.; Sarvanan, Y.; Jacob, S.; Agarwal, A. Evaluation of bilateral minimum thickness of normal corneas based on fourier-domain optical coherence tomography. J. Cataract Refract. Surg.
**2010**, 36, 1365–1372. [Google Scholar] [CrossRef] [PubMed] - Wang, L.; Dai, E.; Koch, D.D.; Nathoo, A. Optical aberrations of the human anterior cornea. J. Cataract Refract. Surg.
**2003**, 29, 1514–1521. [Google Scholar] [CrossRef] - Zha, Y.; Feng, W.; Han, X.; Cai, J. Evaluation of myopic corneal diameter with the orbscan ii topography system. Graef. Arch. Clin. Exp. Ophthalmol.
**2013**, 251, 537–541. [Google Scholar] [CrossRef] [PubMed] - Piñero, D.P. Technologies for anatomical and geometric characterization of the corneal structure and anterior segment: A review. Semin. Ophthalmol.
**2015**, 30, 161–170. [Google Scholar] [CrossRef] [PubMed] - Wang, Q.; Savini, G.; Hoffer, K.J.; Xu, Z.; Feng, Y.; Wen, D.; Hua, Y.; Yang, F.; Pan, C.; Huang, J. A comprehensive assessment of the precision and agreement of anterior corneal power measurements obtained using 8 different devices. PLoS ONE
**2012**, 7, e45607. [Google Scholar] [CrossRef] [PubMed] - Ferreira, T.B.; Ribeiro, F.J. Comparability and repeatability of different methods of corneal astigmatism assessment. Clin. Ophthalmol.
**2018**, 12, 29–34. [Google Scholar] [CrossRef] [PubMed] - Camps, V.J.; Miret, J.J.; García, C.; Tolosa, A.; Piñero, D.P. Simulation of the effect of different presbyopia-correcting intraocular lenses with eyes with previous laser refractive surgery. J. Refract. Surg.
**2018**, 34, 222–227. [Google Scholar] [CrossRef] [PubMed] - Simonini, I.; Angelillo, M.; Pandolfi, A. Theoretical and numerical analysis of the corneal air puff test. J. Mech. Phys. Solids
**2016**, 93, 118–134. [Google Scholar] [CrossRef] - Ramos-López, D.; Martínez-Finkelshtein, A.; Castro-Luna, G.M.; Piñero, D.; Alió, J.L. Placido-based indices of corneal irregularity. Optom. Vis. Sci.
**2011**, 88, 1220–1231. [Google Scholar] [CrossRef] [PubMed] - Asher, R.; Gefen, A.; Moisseiev, E.; Varssano, D. An analytical approach to corneal mechanics for determining practical, clinically-meaningful patient-specific tissue mechanical properties in the rehabilitation of vision. Ann. Biomed. Eng.
**2015**, 43, 274–286. [Google Scholar] [CrossRef] [PubMed] - Lanchares, E.; Buey, M.A.D.; Cristóbal, J.A.; Calvo, B.; Ascaso, F.J.; Malvè, M. Computational simulation of scleral buckling surgery for rhegmatogenous retinal detachment: On the effect of the band size on the myopization. J. Ophthalmol.
**2016**, 2016. [Google Scholar] [CrossRef] [PubMed] - Simonini, I.; Pandolfi, A. Customized finite element modelling of the human cornea. PLoS ONE
**2015**, 10, e0130426. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ariza-Gracia, M.Á.; Zurita, J.; Piñero, D.P.; Calvo, B.; Rodríguez-Matas, J.F. Automatized patient-specific methodology for numerical determination of biomechanical corneal response. Ann. Biomed. Eng.
**2016**, 44, 1753–1772. [Google Scholar] [CrossRef] [PubMed] - Seven, I.; Vahdati, A.; De Stefano, V.S.; Krueger, R.R.; Dupps, W.J. Comparison of patient-specific computational modeling predictions and clinical outcomes of lasik for myopia. Invest. Ophthalmol. Visual Sci.
**2016**, 57, 6287–6297. [Google Scholar] [CrossRef] [PubMed] - Bataille, L.; Cavas-Martínez, F.; Fernández-Pacheco, D.G.; Cañavate, F.J.F.; Alio, J.L. A study for parametric morphogeometric operators to assist the detection of keratoconus. Symmetry
**2017**, 9, 302. [Google Scholar] [CrossRef] - Cavas-Martínez, F.; Bataille, L.; Fernández-Pacheco, D.G.; Cañavate, F.J.F.; Alio, J.L. Keratoconus detection based on a new corneal volumetric analysis. Sci. Rep.
**2017**, 7, 15837. [Google Scholar] [CrossRef] [PubMed] - Cavas-Martínez, F.; Bataille, L.; Fernández-Pacheco, D.G.; Cañavate, F.J.F.; Alió, J.L. A new approach to keratoconus detection based on corneal morphogeometric analysis. PLoS ONE
**2017**, 12, e0184569. [Google Scholar] [CrossRef] [PubMed] - Zheng, X.; Yang, W.; Huang, L.; Wang, J.; Cao, S.; Geraghty, B.; Zhao, Y.; Wang, Q.; Bao, F.; Elsheikh, A. Evaluating the repeatability of corneal elevation through calculating the misalignment between successive topography measurements during the follow up of lasik. Sci. Rep.
**2017**, 7, 3122. [Google Scholar] [CrossRef] [PubMed] - Zheng, Y.; Huang, L.; Zhao, Y.; Wang, J.; Zheng, X.; Huang, W.; Geraghty, B.; Wang, Q.; Chen, S.; Bao, F.; et al. Repeatability of corneal elevation maps in keratoconus patients using the tomography matching method. Sci. Rep.
**2017**, 7. [Google Scholar] [CrossRef] [PubMed] - McKendrick, A.M.; Brennan, N.A. The axis of astigmatism in right and left eye pairs. Optom. Vis. Sci.
**1997**, 74, 668–675. [Google Scholar] [CrossRef] [PubMed] - Lohfeld, S.; Barron, V.; McHugh, P.E. Biomodels of bone: A review. Ann. Biomed. Eng.
**2005**, 33, 1295–1311. [Google Scholar] [CrossRef] [PubMed] - Navarro, R.; González, L.; Hernández, J.L. Optics of the average normal cornea from general and canonical representations of its surface topography. J. Opt. Soc. Am. A
**2006**, 23, 219–232. [Google Scholar] [CrossRef] - Bookstein, F.L. Landmark methods for forms without landmarks: Morphometrics of group differences in outline shape. Med. Image Anal.
**1997**, 1, 225–243. [Google Scholar] [CrossRef] - Asharlous, A.; Khabazkhoob, M.; Yekta, A.; Hashemi, H. Comprehensive profile of bilateral astigmatism: Rule similarity and symmetry patterns of the axes in the fellow eyes. Ophthal. Physiol. Opt.
**2017**, 37, 33–41. [Google Scholar] [CrossRef] [PubMed] - Bao, F.J.; Yu, A.Y.; Kassem, W.; Wang, Q.M.; Elsheikh, A. Biometry of the cornea in myopic chinese patients. J. Refract. Surg.
**2011**, 27, 345–355. [Google Scholar] [CrossRef] [PubMed] - Durr, G.M.; Auvinet, E.; Ong, J.; Meunier, J.; Brunette, I. Corneal shape, volume, and interocular symmetry: Parameters to optimize the design of biosynthetic corneal substitutes. Investig. Ophthalmol. Visual Sci.
**2015**, 56, 4275–4282. [Google Scholar] [CrossRef] [PubMed] - Hashemi, H.; Asharlous, A.; Yekta, A.; Ostadimoghaddam, H.; Mohebi, M.; Aghamirsalim, M.; Khabazkhoob, M. Enantiomorphism and rule similarity in the astigmatism axes of fellow eyes: A population-based study. J. Optom.
**2018**, 18. [Google Scholar] [CrossRef] [PubMed] - Zheng, X.; Bao, F.; Geraghty, B.; Huang, J.; Yu, A.; Wang, Q. High intercorneal symmetry in corneal biomechanical metrics. Eye Vis.
**2016**, 3, 7. [Google Scholar] [CrossRef] [PubMed] - Montalban, R.; Pinero, D.P.; Javaloy, J.; Alio, J.L. Intrasubject repeatability of corneal morphology measurements obtained with a new scheimpflug photography-based system. J. Cataract. Refract. Surg.
**2012**, 38, 971–977. [Google Scholar] [CrossRef] [PubMed] - Saenz-Frances, F.; Bermudez-Vallecilla, M.C.; Borrego-Sanz, L.; Janez, L.; Martinez-de-la-Casa, J.M.; Morales-Fernandez, L.; Santos-Bueso, E.; Garcia-Sanchez, J.; Garcia-Feijoo, J. Anatomical characterization of central, apical and minimal corneal thickness. Int. J. Ophthalmol.
**2014**, 7, 668–672. [Google Scholar] [PubMed] - Hernandez-Camarena, J.C.; Chirinos-Saldana, P.; Navas, A.; Ramirez-Miranda, A.; de la Mota, A.; Jimenez-Corona, A.; Graue-Hernindez, E.O. Repeatability, reproducibility, and agreement between three different scheimpflug systems in measuring corneal and anterior segment biometry. J. Refract. Surg.
**2014**, 30, 616–621. [Google Scholar] [CrossRef] [PubMed] - Savino, G.; Battendieri, R.; Riso, M.; Traina, S.; Poscia, A.; D’Amico, G.; Caporossi, A. Corneal topographic changes after eyelid ptosis surgery. Cornea
**2016**, 35, 501–505. [Google Scholar] [CrossRef] [PubMed] - Martinez-Abad, A.; Pinero, D.P. New perspectives on the detection and progression of keratoconus. J. Cataract. Refract. Surg.
**2017**, 43, 1213–1227. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Morphogeometric variables defined for fellow corneas. OD: right eye (orange); OS: left eye (green).

**Figure 2.**Algebraic transformation protocol (translation + rotation) implemented in axial symmetry of the corneal vertex pattern.

**Figure 3.**Direct symmetry (equal octants) and enantiomorphism (mirror octants) between right eye (OD) and left eye (OS).

**Figure 6.**Values of X

_{0}, Y

_{0}, and Z

_{0}translation displacements (mm) estimated for the vertex (V) of a normal cornea (Cornea) toward the vertex (V

_{0}) of a perfect cornea (Cornea

_{0}).

**Figure 7.**Values of α, β, γ rotation angles (degrees) estimated for the vertex (V) of a normal cornea (Cornea) toward the vertex (V

_{0}) of a perfect cornea (Cornea

_{0}).

**Figure 8.**Values of uppermost (Z

_{max}) points (mm) in relation to the corneal vertex and its angular positions (α

_{Zmax}) (degrees) in relation to its projection ring (anticlockwise).

Morphogeometric Variable | Acronym | Description |
---|---|---|

Corneal volume (mm^{3}) | CV | Volume defined by the solid model generated |

Anterior/posterior corneal surface area (mm^{2}) | A_{ant}/A_{post} | Area of the exterior/interior surface |

Corneal surface area (mm^{2}) | A_{tot} | Area defined by the solid model generated |

Anterior/posterior apex deviation (mm) | D_{apexant}/D_{apexpost} | Distance from the optical axis to the apex of the anterior/posterior corneal surfaces |

Anterior/posterior minimum thickness point deviation (mm) | D_{mctant}/D_{mctpost} | Distance in the XY plane from the optical axis to the minimum thickness points of the anterior/posterior corneal surfaces |

Shape Parameters | Acronym | Description |
---|---|---|

Horizontal/vertical apical radius (mm) | R_{X}/R_{Y} | Radius of curvature at apex with respect to x and y axes |

Horizontal/vertical asphericity | Q_{X}/Q_{Y} | Average variation of instantaneous curvature at each point P along corneal meridian with respect to x and y axes |

Angular coordinates of rotational displacement (°) | α/β/γ | Rotation in angular coordinates (α, β, γ) of x, y, and z axes with respect to the vertex (V) of a normal cornea (projection in XOY plane of a normal ellipsoid) toward the vertex (V_{0}) of a perfect cornea (projection in XOY plane of a perfect ellipsoid) |

Cartesian coordinates of translational displacement (mm) | X_{0}/Y_{0}/Z_{0} | Distance in Cartesian coordinates (x, y, z) of the vertex (V) of a normal cornea (projection in XOY plane of a normal ellipsoid) toward the vertex (V_{0}) of a perfect cornea (projection in XOY plane of a perfect ellipsoid) |

Parameters of the ellipsoid (mm) | a/b/c | Main parameters of the canonical representation of ellipsoid of major adjustment |

**Table 3.**Protocol of differences in the Cartesian elevation coordinates between pairs of points in direct symmetry and enantiomorphism.

Equal Octants | Mirror Octants |
---|---|

Z_{A′}–Z_{A″} | Z_{A′}–Z_{E″} |

Z_{B′}–Z_{B″} | Z_{B′}–Z_{D″} |

Z_{C′}–Z_{C″} | Z_{C′}–Z_{C″} |

Z_{D′}–Z_{D″} | Z_{D′}–Z_{B″} |

Z_{E′}–Z_{E″} | Z_{E′}–Z_{A″} |

Z_{F′}–Z_{F″} | Z_{F′}–Z_{H″} |

Z_{G′}–Z _{G″} | Z_{G′}–Z _{G″} |

Z_{H′}–Z_{H″} | Z_{H′}–Z_{F″} |

**Table 4.**Summary of visual, refractive, and corneal topographic data in the right and left eyes of the sample evaluated. SD, standard deviation; SE, spherical equivalent; CDVA, corrected distance visual acuity; HOA, high-order aberration; RMS, root mean square; SA, spherical aberration; MCT, minimal corneal thickness; CCT, central corneal thickness.

Measurement | Right Eye (OD) | Left Eye (OS) | p-Value |
---|---|---|---|

Mean (SD) Median (Range) | Mean (SD) Median (Range) | ||

Sphere (D) | −0.03 (3.52) 0.25 (−10.00 to 8.50) | −0.20 (3.78) 0.00 (−12.00 to 8.00) | 0.159 |

Cylinder (D) | −0.60 (0.54) −0.50 (−2.00 to 0.00) | −0.76 (1.07) −0.50 (−5.75 to 0.00) | 0.316 |

SE (D) | −0.33 (3.46) 0.00 (−10.00 to 8.12) | −0.58 (3.72) 0.00 (−12.00 to 7.75) | 0.126 |

Decimal CDVA | 1.00 (0.09) 1.00 (0.60 to 1.20) | 1.00 (0.10) 1.00 (0.60 to 1.20) | 0.892 |

Q_{4.5} | −0.11 (0.26) −0.07 (−0.65 to 0.31) | −0.16 (0.24) −0.18 (−0.65 to 0.19) | 0.169 |

Q_{8} | −0.27 (0.21) −0.29 (−0.78 to 0.10) | −0.27 (0.18) −0.26 (−0.65 to 0.05) | 0.990 |

HOA RMS (μm) 6 mm pupil | 0.43 (0.12) 0.42 (0.25 to 0.76) | 0.41 (0.11) 0.39 (0.4 to 0.70) | 0.182 |

Coma RMS (μm) 6 mm pupil | 0.29 (0.11) 0.30 (0.08 to 0.49) | 0.27 (0.11) 0.27 (0.02 to 0.54) | 0.102 |

SA (μm) 6 mm pupil | 0.22 (0.05) 0.22 (0.13 to 0.35) | 0.22 (0.06) 0.23 (0.08 to 0.32) | 0.737 |

MCT (μm) | 539.2 (31.5) 541.9 (479.6 to 610.9) | 540.3 (29.0) 540.5 (485.4 to 609.0) | 0.448 |

CCT (μm) | 542.8 (31.8) 544.0 (482.0 to 615.0) | 543.9 (29.4) 546.0 (489.0 to 614.0) | 0.458 |

CV (mm^{3}) | 25.8 (1.6) 26.2 (23.2 to 29.1) | 25.9 (1.5) 26.1 (23.3 to 28.9) | 0.565 |

Measurement | Right Eye (OD) | Left Eye (OS) | p-Value |
---|---|---|---|

Mean (SD) Median (Range) | Mean (SD) Median (Range) | ||

A_{ant} (mm^{2}) | 43.09 (0.12) 43.08 (42.84 to 43.34) | 43.10 (0.12) 43.13 (42.83 to 43.32) | 0.055 |

A_{post} (mm^{2}) | 44.27 (0.26) 44.29 (43.53 to 44.72) | 44.28 (0.27) 44.28 (43.52 to 44.75) | 0.572 |

A_{tot} (mm^{2}) | 104.04 (1.24) 104.07 (100.72 to 106.15) | 104.08 (1.23) 104.14 (100.80 to 106.09) | 0.580 |

D_{apexant} (mm) | 0.00 (0.00) 0.00 (0.00 to 0.00 | 0.00 (0.00) 0.00 (0.00 to 0.00 | 0.999 |

D_{apexpost} (mm) | 0.07 (0.02) 0.08 (0.03 to 0.13) | 0.07 (0.02 to 0.65) 0.87 (0.22) | 0.488 |

D_{mctant} (mm) | 0.89 (0.27) 0.89 (0.45 to 1.66) | 0.87 (0.22) 0.88 (0.48 to 1.31) | 0.659 |

D_{mctpost} (mm) | 0.81 (0.23) 0.84 (0.40 to 1.53) | 0.79 (0.22) 0.77 (0.40 to 1.24) | 0.606 |

**Table 6.**Summary of axial symmetry data at the vertex of the anterior corneal surface in the right and left eyes of the sample evaluated.

Measurement | Right Eye (OD) | Left Eye (OS) | p-Value |
---|---|---|---|

Mean (SD) Median (Range) | Mean (SD) Median (Range) | ||

R_{x} (mm) | 7.62 (0.21) 7.58 (7.28 to 8.09) | 7.61 (0.23) 7.55 (7.10 to 8.07) | 0.549 |

R_{y} (mm) | 7.79 (0.19) 7.79 (7.52 to 8.24) | 7.79 (0.19) 7.76 (7.49 to 8.19) | 0.851 |

Q_{x} | −0.27 (0.11) −0.27 (−0.51 to −0.05) | −0.27 (0.12) −0.24 (−0.56 to −0.02) | 0.981 |

Q_{y} | −0.25 (0.11) −0.26 (−0.51 to −0.02) | −0.25 (0.12) −0.23 (−0.49 to 0.00) | 0.999 |

Alpha (°) | −4.17 (28.62) 1.24 (−161.10 to 13.31) | −3.87 (25.53) −0.39 (−143.08 to 13.49) | 0.814 |

Beta (°) | −0.05 (11.16) 1.10 (−52.67 to 27.55) | −2.05 (9.59) −1.70 (−49.32 to 18.71) | 0.012 |

Gamma (°) | −43.08 (91.21) −80.75 (−151.45 to 152.23) | −29.53 (10.50) −80.55 (−176.10 to 173.43) | 0.596 |

X_{0} (mm) | 0.20 (0.19) 0.14 (−0.13 to 0.88) | −0.18 (0.26) −0.15 (−1.37 to 0.08) | <0.001 |

Y_{0} (mm) | −0.003 (0.219) −0.016 (−0.630 to 0.560) | 0.036 (0.204) −0.001 (−0.470 to 0.690) | <0.001 |

Z_{0} (mm) | 10.61 (1.70) 10.43 (8.12 to 15.25) | 10.65 (1.86) 10.00 (8.19 to 15.99) | 0.325 |

a (mm) | 8.98 (0.68) 9.00 (8.00 to 10.64) | 8.98 (0.72) 8.80 (8.16 to 10.69) | 0.994 |

b (mm) | 9.07 (0.68) 9.08 (8.17 to 10.84) | 9.08 (0.77) 8.86 (8.22 to 11.46) | 0.345 |

c (mm) | 10.63 (1.69) 10.43 (8.27 to 15.26) | 10.67 (1.87) 10.01 (8.25 to 16.11) | 0.845 |

**Table 7.**Summary of axial symmetry data at the vertex of the posterior corneal surface in the right and left eyes of the sample evaluated.

Measurement | Right Eye (OD) | Left Eye (OS) | p-Value |
---|---|---|---|

Mean (SD) Median (Range) | Mean (SD) Median (Range) | ||

R_{x} (mm) | 6.21 (0.29) 6.25 (5.74 to 6.90) | 6.22 (0.30) 6.27 (5.75 to 6.94) | 0.466 |

R_{y} (mm) | 6.49 (0.29) 6.49 (6.00 to 7.06) | 6.50 (0.27) 6.48 (6.00 to 7.13) | 0.535 |

Q_{x} | −0.35 (0.21) −0.33 (−0.99 to −0.08) | −0.34 (0.19) −0.30 (−0.79 to−0.07) | 0.606 |

Q_{y} | −0.32 (0.22) −0.30 (−0.98 to −0.05) | −0.31 (0.19) −0.28 (−0.75 to −0.04) | 0.685 |

Alpha (°) | 6.15 (30.07) −1.59 (−14.15 to 132.15) | 4.70 (23.66) −3.46 (−9.19 to 86.79) | 0.562 |

Beta (°) | −8.80 (19.68) −3.87 (−73.89 to 7.58) | −6.30 (15.42) −5.24 (−59.11 to 40.24) | 0.506 |

Gamma (°) | −22.62 (87.81) −75.31 (−98.32 to 120.09) | −78.51 (45.54) −90.51 (−108.98 to 86.76) | 0.004 |

X_{0} (mm) | 1.49 (7.81) 0.06 (−0.62 to 44.91) | −0.23 (0.54) −0.09 (−2.37 to 0.26) | 0.229 |

Y_{0} (mm) | 1.09 (4.64) 0.17 (−0.10 to 26.81) | 0.31 (0.42) 0.19 (−0.16 to 2.14) | 0.335 |

Z_{0} (mm) | 22.39 (67.41) 9.97 (6.59 to 397.35) | 10.99 (4.28) 9.34 (6.63 to 26.71) | 0.331 |

a (mm) | 9.08 (7.14) 7.63 (6.04 to 48.19) | 7.95 (1.42) 7.57 (6.10 to 12.24) | 0.342 |

b (mm) | 9.28 (7.35) 7.73 (6.16 to 49.58) | 8.13 (1.52) 7.71 (6.21 to 13.32) | 0.345 |

c (mm) | 22.00 (67.99) 9.48 (6.32 to 400.21) | 10.51 (4.29) 8.83 (6.34 to 26.39) | 0.330 |

**Table 8.**Summary of angular-spatial symmetry elevation data of anterior and posterior corneal surfaces in the right and left eyes of the sample evaluated for a radius of 1, 2, 3, and 4 mm.

Right Eye (OD) | Left Eye (OS) | p-Value | |
---|---|---|---|

Measurement | Mean (SD) Median (Range) Most Common Position | Mean (SD) Median (Range) Most Common Position | |

Radius 1 mmAnterior Z_{max} (mm) | 0.07 (0.02) 0.07 (0.06 to 0.13) Octants 7 (27.3%) and 3 (18.2%) | 0.07 (0.01) 0.07 (0.06 to 0.13) Octants 7 (33.3%) and 6 (18.2%) | 0.984 |

Posterior Z_{max} (mm) | 0.63 (0.03) 0.64 (0.57 to 0.71) Octants 2 (60.6%) and 1 (27.3%) | 0.63 (0.03) 0.64 (0.58 to 0.70) Octants 3 (69.7%) and 4 (21.2%) | 0.247 |

Radius 2 mmAnterior Z_{max} (mm) | 0.27 (0.03) 0.27 (0.25 to 0.39) Octants 3 (24.2%) and 7 (21.2%) | 0.27 (0.03) 0.27 (0.25 to 0.38) Octants 7 (30.3%) and 3 (15.2%) | 0.950 |

Posterior Z_{max} (mm) | 0.88 (0.04) 0.89 (0.81 to 0.97) Octants 2 (72.7%) and 3 (24.2%) | 0.89 (0.04) 0.90 (0.81 to 0.97) Octants 3 (84.8%) and 2 (9.1%) | 0.171 |

Radius 3 mmAnterior Z_{max} (mm) | 0.62 (0.05) 0.61 (0.57 to 0.79) Octants 3 (36.4%) and 7 (18.2%) | 0.62 (0.04) 0.62 (0.57 to 0.78) Octants 2 (24.2%) and 7 (18.2%) | 0.900 |

Posterior Z_{max} (mm) | 1.31 (0.05) 1.32 (1.18 to 1.42) Octants 2 (57.6%) and 3 (27.3%) | 1.32 (0.05) 1.33 (1.18 to 1.40) Octants 3 (72.7%) and 2 (15.2%) | 0.560 |

Radius 4 mmAnterior Z_{max} (mm) | 1.05 (0.27) 1.12 (0.00 to 1.18) Octants 3 (27.3%) and 2 (21.2%) | 1.05 (0.27) 1.12 (0.00 to 1.18) Octants 2 (24.2%) and 8 (24.2%) | 0.936 |

Posterior Z_{max} (mm) | 1.93 (0.07) 1.94 (1.71 to 2.05) Octants 7 (30.3%) and 3 (24.2%) | 1.93 (0.07) 1.94 (1.73 to 2.05) Octants 3 (36.4%) and 6 (27.3%) | 0.745 |

**Table 9.**Summary of direct symmetry (equal octant) elevation data of anterior and posterior corneal surfaces between right (OD) and left (OS) eyes of the sample evaluated for a radius of 1, 2, 3, and 4 mm.

Radius 1 mm | Radius 2 mm | Radius 3 mm | Radius 4 mm | ||
---|---|---|---|---|---|

Z_{X′} (OD) –Z _{X″} (OS)(Equal Octants) | Mean (SD) Median (Range) | Mean (SD) Median (Range) | Mean (SD) Median (Range) | Mean (SD) Median (Range) | p-Value (1 mm vs. 4 mm) |

Anterior Corneal Surface | |||||

A′–A″ (µm) | −0.09 (10.56) −0.25 (−29.70 to 30.83) | −1.16 (21.56) −1.39 (−63.46 to 63.42) | −5.48 (35.12) -4.39 (-111.02 to 99.96) | −16.90 (384.25) −10.15 (−1128.54 to 1061.36) | 0.80 |

B′–B″ (µm) | −0.07 (10.29) −0.05 (−30.10 to 29.59) | −0.33 (20.53) −0.02 (−63.00 to 58.30) | −0.58 (31.59) 0.33 (−95.62 to 91.05) | −2.92 (386.91) 2.90 (−1110.24 to 1088.41) | 0.97 |

C′–C″ (µm) | 0.09 (9.76) 0.17 (−28.74 to 28.38) | 0.98 (18.94) 1.34 (−54.76 to 55.54) | 4.75 (28.78) 4.73 (−75.78 to 86.28) | 11.19 (387.67) 6.41 (−1109.13 to 1098.68) | 0.87 |

D′–D″ (µm) | 0.17 (10.06) 0.07 (−27.72 to 30.11) | 0.79 (20.04) 0.30 (−54.64 to 60.80) | 3.83 (31.91) 3.25 (−83.97 to 97.74) | 12.57 (384.88) 15.39 (−1108.79 to 1085.62) | 0.86 |

E′–E″ (µm) | −0.01 (10.53) −0.01 (−29.09 to 30.68) | −0.27 (21.47) −0.09 −58.18 to 62.89) | 0.25 (34.58) 1.54 (−92.19 to 100.23) | 1.41 (387.93) 5.13 (−1128.11 to 1092.12) | 0.98 |

F′–F″(µm) | −0.22 (10.34) −0.22 (−29.25 to 29.88) | −1.14 (20.42) −1.22 (−58.06 to 57.71) | −3.08 (31.37) −2.92 (−89.28 to 85.70) | −10.02 (394.50) −4.20 (−1164.97 to 1094.93) | 0.89 |

G′–G″ (µm) | −0.01 (10.02) −0.16 (−28.37 to 28.96) | −0.75 (19.56) −0.93 (−57.28 to 56.69) | −3.68 (30.24) −2.25 (−91.96 to 85.11) | −15.21 (388.90) −14.95 (−1147.93 to 1072.35) | 0.83 |

H′–H″ (µm) | 0.13 (22.37) −0.13 (−62.49 to 65.21) | −0.58 (42.56) −1.48 (−119.22 to 126.11) | −4.16 (65.42) −5.10 (−189.76 to 193.95) | −20.20 (381.52) −19.01 (−1128.63 to 1048.49) | 0.77 |

Posterior Corneal Surface | |||||

A′–A″(µm) | 6.47 (14.79) 7.17 (−34.30 to 34.07) | 16.40 (21.20) 17.39 (−37.99 to 54.74) | 24.59 (28.43) 27.42 (−46.15 to 79.81) | −0.80 (50.65) 2.81 (−153.69 to 97.13) | 0.43 |

B′–B″(µm) | −1.96 (11.86) −3.13 (−36.25 to 18.43) | −1.81 (13.51) −2.61 (−37.95 to 26.85) | −0.78 (16.93) −0.79 (−46.78 to 35.16) | −5.75 (35.00) −3.18 (−97.58 to 94.60) | 0.54 |

C′–C″(µm) | −9.43 (13.38) −8.70 (−48.50 to 12.81) | −16.81 (20.07) −17.29 (−68.24 to 30.00) | −21.44 (30.21) −27.50 (−86.19 to 40.59) | 0.40 (46.52) −2.52 (−90.91 to 103.92) | 0.22 |

D′–D″(µm) | −16.97 (16.73) −18.04 (−60.09 to 18.51) | −30.09 (27.06) −33.49 (−92.33 to 41.95) | −43.19 (39.46) −49.00 (−130.73 to 62.94) | −45.62 (58.76) −54.94 (−185.60 to 81.02) | <0.01 |

E′–E″ (µm) | −12.02 (14.19) −11.53 (−53.86 to 16.79) | −23.78 (21.59) −27.86 (−79.60 to 30.69) | −37.76 (31.63) −44.22 (−113.25 to 43.88) | −47.13 (46.55) −52.98 (−148.28 to 74.72) | <0.01 |

F′–F″ (µm) | −4.03 (12.16) −3.13 (−39.68 to 12.03) | −5.85 (13.13) −4.84 (−49.54 to 12.84) | −7.74 (16.81) −4.66 (−68.22 to 16.58) | −9.24 (24.93) −3.74 (−88.05 to 33.27) | 0.20 |

G′–G″(µm) | 5.45 (14.90) 5.75 (−32.47 to 30.66) | 14.99 (21.18) 15.17 (−33.76 to 49.16) | 26.09 (31.88) 26.32 (−35.20 to 91.49) | 34.39 (44.94) 36.42 (−58.31 to 135.05) | <0.01 |

H′–H″ (µm) | 11.15 (17.61) 10.94 (−29.37 to 43.27) | 24.40 (27.58) 23.86 (−50.35 to 73.36) | 39.14 (40.38) 41.86 (−63.25 to 115.43) | 44.10 (56.82) 53.20 (−84.18 to 136.37) | <0.01 |

**Table 10.**Summary of enantiomorphism (mirror octants) elevation data of anterior and posterior corneal surfaces between right (OD) and left (OS) eyes of the sample evaluated for a radius of 1, 2, 3, and 4 mm.

Radius 1 mm | Radius 2 mm | Radius 3 mm | Radius 4 mm | ||
---|---|---|---|---|---|

Z_{X′} (OD)–Z _{X″} (OS)(Mirror Octants) | Mean (SD) Median (Range) | Mean (SD) Median (Range) | Mean (SD) Median (Range) | Mean (SD) Median (Range) | p-Value (1 mm vs 4 mm) |

Anterior Corneal Surface | |||||

A′–E″ (µm) | 0.58 (10.32) 0.40 (−27.33 to 30.89) | 1.77 (20.54) 0.74 (−53.01 to 62.89) | 3.14 (32.21) 0.87 (−84.19 to 99.34) | 5.72 (381.94) 8.53 (−1108.79 to 1061.36) | 0.94 |

B′–D″ (µm) | 0.50 (10.02) 0.27 (−28.03 to 29.46) | 2.58 (19.31) 2.03 (−52.23 to 58.00) | 7.84 (29.07) 8.44 (−73.10 to 91.29) | 13.75 (386.94) 15.69 (−1109.13 to 1088.41) | 0.84 |

D′–B″ (µm) | −0.33 (10.21) −0.29 (−30.15 to 30.03) | −2.42 (21.03) −2.21 (−65.08 to 61.32) | −5.73 (35.17) −5.30 (−110.80 to 98.36) | 10.23 (380.81) −8.30 (−1128.5 to 1085.6) | 0.88 |

E′–A″ (µm) | −1.62 (17.15) 0.12 (−62.01 to 31.01) | −2.29 (33.19) −0.04 (−116.23 to 64.37) | −2.45 (52.18) −0.19 (−180.32 to 105.19) | 2.16 (386.87) −0.66 (−1128.63 to 1092.12) | 0.96 |

F′–H″ (µm) | 0.30 (10.19) 0.14 (−27.81 to 30.23) | 0.48 (20.22) −0.39 (−54.80 to 59.90) | 0.02 (31.73) −2.51 (−83.85 to 94.17) | −5.74 (391.77) −6.42 (−1147.93 to 1094.93) | 0.93 |

H′–F″ (µm) | 1.74 (17.62) −0.26 (−29.22 to 65.39) | 1.44 (33.94) −2.50 (−61.17 to 124.64) | −1.46 (52.06) −5.17 (−101.63 to 188.99) | −20.95 (382.57) −17.90 (−1128.11 to 1048.49) | 0.75 |

Posterior Corneal Surface | |||||

A′–E″ (µm) | 1.30 (13.15) 3.53 (−35.48 to 30.05) | 9.27 (16.09) 10.75 (−39.66 to 47.90) | 19.23 (23.57) 21.42 (−60.39 to 61.40) | 3.03 (43.54) 1.46 (−122.71 to 88.32) | 0.80 |

B′–D″ (µm) | −2.07 (12.42) −0.41 (−39.52 to 19.39) | 2.50 (16.74) 2.37 (−46.78 to 40.59) | 11.73 (23.89) 8.10 (−54.86 to 61.41) | 19.70 (35.15) 23.77 (−83.97 to 75.25) | <0.01 |

D′–B″ (µm) | −1.18 (12.10) −9.28 (−47.86 to 9.28) | −2.29 (14.93) −19.59 (−59.99 to 2.77) | −3.78 (21.35) −38.66 (−85.13 to 3.66) | −4.94 (32.51) −51.41 (−134.6 to 35.74) | <0.01 |

E′–A″ (µm) | −3.15 (11.82) −1.86 (−38.47 to 16.47) | −2.04 (13.41) 1.18 (−36.67 to 21.08) | 1.98 (18.06) 4.25 (−47.29 to 45.80) | 11.07 (30.47) 11.78 (−69.37 to 95.99) | <0.01 |

F′–H″ (µm) | 1.44 (13.00) 1.84 (−35.00 to 18.67) | 10.58 (16.16) 8.61 (−25.13 to 45.23) | 22.22 (22.23) 22.50 (−29.92 to 77.71) | 29.84 (37.33) 34.44 (−56.98 to 115.93) | <0.01 |

H′–F″ (µm) | 2.29 (13.48) 2.30 (−35.86 to 24.85) | 2.67 (15.91) 2.29 (−44.93 to 36.23) | −0.60 (21.62) 1.71 (−69.32 to 44.15) | −14.09 (34.85) −7.11 (−126.26 to 43.76) | <0.01 |

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## Share and Cite

**MDPI and ACS Style**

Cavas-Martínez, F.; Piñero, D.P.; Fernández-Pacheco, D.G.; Mira, J.; Cañavate, F.J.F.; Alió, J.L.
Assessment of Pattern and Shape Symmetry of Bilateral Normal Corneas by Scheimpflug Technology. *Symmetry* **2018**, *10*, 453.
https://doi.org/10.3390/sym10100453

**AMA Style**

Cavas-Martínez F, Piñero DP, Fernández-Pacheco DG, Mira J, Cañavate FJF, Alió JL.
Assessment of Pattern and Shape Symmetry of Bilateral Normal Corneas by Scheimpflug Technology. *Symmetry*. 2018; 10(10):453.
https://doi.org/10.3390/sym10100453

**Chicago/Turabian Style**

Cavas-Martínez, Francisco, David P. Piñero, Daniel G. Fernández-Pacheco, Jorge Mira, Francisco J. F. Cañavate, and Jorge L. Alió.
2018. "Assessment of Pattern and Shape Symmetry of Bilateral Normal Corneas by Scheimpflug Technology" *Symmetry* 10, no. 10: 453.
https://doi.org/10.3390/sym10100453