# Studying the Radial and Tangential Velocity Components of the Epithelization Healing Post Photorefractive Keratectomy Surgery of the Human Eye

### Abstract

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Photorefractive keratectomy (PRK) is the refractive technique that began with a physical scraping of the epithelial layer of cornea subsequent by laser treatment. Post this procedure to about 48 hours the removed epithelial layer regenerated to protect the eye again. The regeneration process (called re-epithelization) started from the limbus of the cornea toward the central part of it. The re-epithelization mechanism consists of a change in cell density (mitosis) and cell concentration (migration) with a velocity in two directions: radial and tangential. In the present study, an estimation for both radial (responsible for the overlapped layers toward the outward direction of the cornea) and tangential components (contour shape wave from limbus to the center) has been done for the first time, not like the previous studies that always estimate the velocity values of the re-epithelization only. Results showed that the trend shape of both components agrees with the kinematic behaviour of the mitosis and migration, where the maximum cell density fluctuated toward the central part in exponential decay shape. For a healing diameter of 2mm, the maximum redial velocity was 16.85 µm/h, while the maximum tangential velocity was 55.48 µm/h. These two components give a speed of re-epithelization of 58 µm/h which agrees with the biological and practical healing speed measured of 60 µm/h. Estimating these two components will open the way to understand the relationship between the total epithelial layer required and the total healing time to control the medication period for the patient post-surgery.

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### References

J.L. Alio, F.A. Soria, A. Abbouda and P. Peña-García, "Fifteen years' follow-up of PRK up to 10 D of myopia: outcomes and analysis of the refractive regression," British J. Ophth. Vol. 100, iss. 5, pp. 626-32, 2016.

J.A. Sherratt and J.D. Murray, "Models of Epidermal Wound Healing," Proceedings of the Royal Society of London B: Biological Sciences, pp. 29-36, 1990.

J.A Sherratt and J.D. Murray, "Mathematical analysis of a basic model for epidermal wound healing," J. of Mathematical Biology, Vol. 29 iss. 5, pp. 389–404, 1991.

C.H. Karabatsas, "Studying corneal epithelium in vivo: A new tool in clinical practice," Advances in Ophth. & visual system, vol. 4, iss. 2, pp 3–5, 2016.

P.D. Dale, P.K. Maini and J.A. Sherratt, "Mathematical modeling of corneal epithelial wound healing," Mathematical Biosciences, Vol. 124, iss. 2, pp. 127–147, 1994.

P.D. Dale, J.A. Sherratt and P.K. Maini, "The Speed of Corneal Epithelial Wound Healing," Applied Mathematical Letters, Vol. 7, iss. 2, pp. 11–14, 1994.

P.D. Dale, J.A. Sherratt and P.K. Maini, "Corneal Epithelial Wound Healing," J. of Biological Systems, Vol. 3, iss. 4, pp. 957–965, 1995.

S.W. Chang, F.R. Hu and P.K. Hou, "Corneal epithelial recovery following photorefractive keratectomy," The British J. of Ophth., Vol. 80, iss 7, pp. 663–668, 1996.

H. Sheardown and Y. Cheng, "Mechanisms of Corneal Epithelial Wound Healing," Chemical Engineering Science, Vol. 51, iss.19, pp. 4517–4529, 1996.

E.A. Gaffney, P.K. Maini, J.A. Sherratt, P.D. Dale, "Wound Healing in the Corneal Epithelial: Biologic Mechanisms and Mathematical Models," J. of Theor. Medicine, Vol. 1, iss. 1, pp. 13–23, 1996.

V.V. Kourenkov, O.N. Mytiagina and A.G. Pavluk, "Stimulating Re-epithelialization after Photorefractive Keratectomy," J. of Refr. Surg., Vol. iss. 15, pp. 234–237, 1999.

E.A. Gaffney, P.K. Maini, J.A. Sherratt and S. Tufu, The Mathematical Modelling of Cell Kinetics in Corneal Epithelial Wound Healing," J. of Theoretical Biology, Vol. 197, iss. 1, pp. 15–40, 1999.

R.H. Silverman, F.L. Lizzi, B.G. Ursea, L. Cozzarelli, J.A. Ketterling, C.X. Deng and J. Coleman, "Safety Levels for Exposure of Cornea and Lens to Very High-Frequency Ultrasound," J. Ultrasound Med, Vol. 20, pp. 979–986, 2001.

S. Serrao and M. Lombardo, "Corneal epithelial healing after photorefractive keratectomy: Analytical study," J. of Cataract and Refractive Surgery, Vol. 31, iss. 5, pp. 930–937, 2005.

A. Pajoohesh-Ganji and M.A. Stepp, "In search of markers for the stem cells of the corneal epithelium," Biology of the Cell / under the Auspices of the European Cell Biology Organization, Vol. 97, iss. 4, pp. 265–76, 2005.

T. Callaghan, E. Khain, L.M. Sander and R.M. Ziff, "A stochastic model for wound healing," J. of Statistical Physics, Vol. 122, iss. 5, pp. 909–924, 2006.

D.Z. Reinstein, T.J. Archer, M. Gobbe, R.H. Silverman and D.J. Coleman, "Epithelial thickness in the normal cornea: three-dimensional display with very high frequency ultrasound," J. of Refractive Surgery, Vol. 24, iss. 6, pp. 571–581, 2008.

D.Z. Reinstein, S. Srivannaboon, M. Gobbe, T.J. Archer, R.H. Silverman, H. Sutton and D.J. Coleman, "Epithelial thickness profile changes induced by myopic LASIK as measured by Artemis very high-frequency digital ultrasound," J. of Refractive Surgery, Vol. 25, iss. 5, pp. 444–450, 2009.

A. Ivarsen, W. Fledelius, and J.O. Hjortdal, "Three-year changes in epithelial and stromal thickness after PRK or LASIK for high myopia," Investigative Ophth. and Visual Science, Vol. 50, iss. 5, pp. 2061–2066, 2009.

F. Posta and T. Chou, "A mathematical model of intercellular signaling during epithelial wound healing," J. of Theoretical Biology, Vol. 266, iss. 1, pp. 70–78, 2010.

D.Z. Reinstein, M. Gobbe, T.J. Archer, R. H. Silverman and J. Coleman, "Epithelial, Stromal, and Total Corneal Thickness in Keratoconus: Three-dimensional Display with Artemis Very-high Frequency Digital Ultrasound, "J. of Refr. Surgery, Vol. 26, iss. 4, pp. 259–271, 2010.

Y. Li, O. Tan, R. Brass, J.L. Weiss, D. Huang, "Corneal Epithelial Thickness Mapping by Fourier Domain Optical Coherence Tomography in Normal and KCN Eyes," Ophth., Vol. 119, iss. 12, pp. 2425–2433, 2012.

A.J. Kanellopoulos, I.M. Aslanides and G. Asimellis, "Correlation between epithelial thickness in normal corneas, untreated ectatic corneas, and ectatic corneas previously treated with CXL; is overall epithelial thickness a very early ectasia prognostic factor?" Clinical Ophth., Vol. 6, iss. 1, pp. 789–800, 2012.

C. Du, J. Wang, L. Cui, S.A. Meixiao and Y. Yuan, "Vertical and horizontal corneal epithelial thickness profiles determined by ultra-high resolution OCT," Cornea, Vol. 1, iss. 9, pp. 1036–1043, 2012.

B.R. Fonslow, B.D. Stein, K.J. Webb, T. Xu, J. Choi, S. Kyu and J.R, Iii, "Wound Healing After Keratorefractive Surgery: Review of Biological and Optical Considerations," Cornea, Vol. 31, iss. 1, pp. 9–19, 2012.

A.J. Kanellopoulos and G. Asimellis, "Anterior segment OCT: Assisted topographic corneal epithelial thickness distribution imaging of a keratoconus patient," Case Reports in Ophth., Vol. 18, iss. 1, pp. 74-78, 2013.

A. Tao, Y. Shao, H. Jiang, Y. Ye, F. Lu, M. Shen and J. Wang, "Entire thickness profiles of the epithelium and contact lens in vivo imaged with high speed and high resolution OCT," Eye Contact Lens, Vol. 39, iss. 5, pp. 1–14, 2013.

A.J. Kanellopoulos, G. Asimellis, "In vivo 3D corneal epithelial thickness mapping as an indicator of dry eye: Preliminary clinical assessment," American J. of Ophth., Vol. 157 iss. 5, pp. 1116–1117, 2013.

X.J. Ma, L. Wang and D.D Koch, "Repeatability of corneal epithelial thickness measurements using Fourier-Domain OCT in normal and Post-LASIK eyes," Cornea, Vol. 32, iss. 12, pp. 1544–1548, 2013.

K.M. Rocha, C.P. Straziota, D. Stulting, B. Randleman, "Spectral-Domain OCT Analysis of Regional Epithelial Thickness Profiles in Keratoconus, Postoperative Corneal Ectasia, and Normal Eyes," J. of Refractive Surgery, Vol. 29, iss. 3, pp. 173–179, 2013.

X. Cui, J. Hong, F. Wang, S.X. Deng, Y. Yang, X. Zhu and J. Xu, "Assessment of Corneal Epithelial Thickness in Dry Eye Patients," Optom. Vis. Sci., Vol. 91, iss.12, pp. 1446–1454, 2014.

X. Cui, J. Hong, F. Wang, Y.J. Yang, "Assessment of corneal epithelial thickness in dry eye patients evaluated by Fourier-domain optical coherence tomography," ARVO 2014 Annual Meeting, pp. 1–2, 2014.

W. Zho and A. Stojanovic, "Comparison of Corneal Epithelial and Stromal Thickness Distributions between Eyes with Keratoconus and Healthy Eyes with Corneal Astigmatism ≤ 2.0 D," Plos One, Vol. 9, iss. 1, pp. 1–7, 2014.

R.H. Silverman, R. Urs, A. Roychoudhury, T.J. Archer, M. Gobbe, D.Z. Reinstein, "Epithelial Remodeling as Basis for Machine-Based Identification of Keratoconus" Cornea, Vol. 55, iss 3, pp. 1580–1587, 2014.

A.J. Kanellopoulos, G. Asimellis, "OCT corneal epithelial topographic asymmetry as a sensitive diagnostic tool for early and advancing keratoconus," Clin. Ophth., Vol. 4, iss. 8, pp. 2277–2287, 2014.

S. Wu, A. Tao, H. Jiang, Z. Xu, V. Perez and J. Wang, "Vertical and Horizontal Corneal Epithelial Thickness Profile Using Ultra-High Resolution and Long Scan Depth OCT," Plos One, Vol. 9, iss. 5, pp. 1–7, 2014.

D.Z. Reinstein, T.E. Yap, T.J. Archer, M. Gobbe, R.H. Silverman, "Comparison of Corneal Epithelial Thickness Measurement between Fourier-Domain OCT and Very High-Frequency Digital Ultrasound," J. of Refr. Surgery, Vol. 31, iss. 7, pp. 438–445, 2015.

M. Tang, Y. Li D. Huang, "Corneal Epithelial Remodeling after LASIK Measured by Fourier-Domain Optical Coherence Tomography," J. of Ophth, pp. 1–5, 2015.

C. Temstet, O. Sandali, N. Bouheraoua, T. Hamiche, A. Galan, M. El Sanharawi and V. Borderie, "Corneal epithelial thickness mapping using Fourier-domain optical coherence tomography for detection of form fruste keratoconus. J. of Cataract and Refr. Surgery, Vol. 41, iss.4, pp. 812–820, 2015.

J. Tomás, A.M. Larra and L. Hanneken, "Corneal Regeneration after Photorefractive Keratectomy: A Review," J. of Optometry, Vol. 8, pp. 149–169, 2015.

X. Wang, J. Dong, Q. Wu, "Corneal thickness, epithelial thickness and axial length differences in normal and high myopia", BMC Ophthal., Vol. 15, iss. 9, pp. 1–5, 2015.

D.R. Koehn, K.J. Meyer and M.G. Anderson, "Genetic Evidence for Differential Regulation of Corneal Epithelial and Stromal Thickness," Investigative Ophth. & Visual Science, Vol. 56, iss. 9, pp. 5599-5607, 2015.

Y. Ma, X. He, X. Zhu, L. Lu, J. Zhu H. Zou, "Corneal Epithelium Thickness Profile in 614 Normal Chinese Children age 7–15 Years Old," Sc. Reports, Vol. 6, iss.10, pp. 234-242, 2016.

Q. Liang, H. Liang, H. Liu, Z. Pan, C. Baudouin and A. Labbé, "Ocular Surface Epithelial Thickness Evaluation in Dry Eye Patients: Clinical Correlations," J. of Ophth., Vol. 12, iss. 3, pp. 15-21, 2016.

C.H. Karabatsas, "Studying corneal epithelium in vivo: A New Tool in Clinical Practice," Advances in Ophth. and Visual System, Vol. 4, iss. 2, pp. 3–5, 2016.

D.J. Tritton, "Physical Fluid Dynamics", 2nd ed. Oxford, UK. Oxford Univ. Press, pp519, 1988.

A.H.A. Al Timemy, K.A. Shetha and N. H. Ghaeb, "A Proposed Artificial Intelligence Algorithm for Assessing of Risk Priority for Medical Equipment in Iraqi Hospital," Al-Khwarizmi Eng. J., Vol. 5, No. 1, pp 71-82, 2009.

N.H. Gheab, S.N. Saleem, "Comparison Study of EMG Using Wavelet and Neural Network," Al-Khwarizmi Eng. J., Vol. 4, No. 3, pp 108-119, 2008.

*Al-Khwarizmi Engineering Journal*,

*16*(4), 27-40. https://doi.org/10.22153/kej.2020.09.003

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