Mathematical model of corneal surface smoothing after laser refractive surgery

Research output: Contribution to journalArticle

90 Citations (Scopus)

Abstract

PURPOSE: To construct a quantitative model of corneal surface smoothing after laser ablation for refractive correction. DESIGN: Experimental study, interventional case series, and meta-analysis of literature. METHODS: A theory of epithelial smoothing in response to corneal contour change is derived from differential equations that describe epithelial migration, growth, and loss. Computer simulations calculate the effects on postoperative epithelial thickness, topography, refraction, and spherical aberration. Model parameter is matched with laser in situ keratomileusis (LASIK) outcome in literature and in a retrospective study of primary spherical myopic (77 eyes) and hyperopic (19 eyes) corrections. Surgically induced refractive change was the main outcome measure. RESULTS: Simulated epithelial remodeling after myopic ablation produces central epithelial thickening, reduction in achieved correction, and induction of oblate spherical aberration. Simulation of hyperopic ablation shows peripheral epithelial thickening, a larger reduction in correction, and induction of prolate spherical aberration. Simulation using a minus cylinder laser ablation pattern shows decreased astigmatism correction and increased hyperopic shift. In the LASIK series, linear regression of achieved correction vs ablation setting in hyperopic and minus cylinder corrections shows slopes of 0.97, 0.71, and 0.74, respectively. These clinical results match model predictions when the smoothing constant is set at 0.32, 0.63, and 0.55 mm, respectively. CONCLUSIONS: Epithelial thickness modulations after ablation can be modeled mathematically to explain clinically observed regression and induction of aberration. The cornea appears to smooth over ablated features smaller than approximately 0.5 mm. The model provides an approach for designing ablation patterns that precompensate for the smoothing to improve final outcome.

Original languageEnglish (US)
Pages (from-to)267-278
Number of pages12
JournalAmerican Journal of Ophthalmology
Volume135
Issue number3
DOIs
StatePublished - Mar 1 2003
Externally publishedYes

Fingerprint

Refractive Surgical Procedures
Laser In Situ Keratomileusis
Laser Therapy
Theoretical Models
Phosmet
Astigmatism
Computer Simulation
Cornea
Meta-Analysis
Linear Models
Retrospective Studies
Outcome Assessment (Health Care)
Growth

ASJC Scopus subject areas

  • Ophthalmology

Cite this

Mathematical model of corneal surface smoothing after laser refractive surgery. / Huang, David; Tang, Maolong; Shekhar, Raj.

In: American Journal of Ophthalmology, Vol. 135, No. 3, 01.03.2003, p. 267-278.

Research output: Contribution to journalArticle

@article{4a937218f0d94ff08b0e22861c622863,
title = "Mathematical model of corneal surface smoothing after laser refractive surgery",
abstract = "PURPOSE: To construct a quantitative model of corneal surface smoothing after laser ablation for refractive correction. DESIGN: Experimental study, interventional case series, and meta-analysis of literature. METHODS: A theory of epithelial smoothing in response to corneal contour change is derived from differential equations that describe epithelial migration, growth, and loss. Computer simulations calculate the effects on postoperative epithelial thickness, topography, refraction, and spherical aberration. Model parameter is matched with laser in situ keratomileusis (LASIK) outcome in literature and in a retrospective study of primary spherical myopic (77 eyes) and hyperopic (19 eyes) corrections. Surgically induced refractive change was the main outcome measure. RESULTS: Simulated epithelial remodeling after myopic ablation produces central epithelial thickening, reduction in achieved correction, and induction of oblate spherical aberration. Simulation of hyperopic ablation shows peripheral epithelial thickening, a larger reduction in correction, and induction of prolate spherical aberration. Simulation using a minus cylinder laser ablation pattern shows decreased astigmatism correction and increased hyperopic shift. In the LASIK series, linear regression of achieved correction vs ablation setting in hyperopic and minus cylinder corrections shows slopes of 0.97, 0.71, and 0.74, respectively. These clinical results match model predictions when the smoothing constant is set at 0.32, 0.63, and 0.55 mm, respectively. CONCLUSIONS: Epithelial thickness modulations after ablation can be modeled mathematically to explain clinically observed regression and induction of aberration. The cornea appears to smooth over ablated features smaller than approximately 0.5 mm. The model provides an approach for designing ablation patterns that precompensate for the smoothing to improve final outcome.",
author = "David Huang and Maolong Tang and Raj Shekhar",
year = "2003",
month = "3",
day = "1",
doi = "10.1016/S0002-9394(02)01942-6",
language = "English (US)",
volume = "135",
pages = "267--278",
journal = "American Journal of Ophthalmology",
issn = "0002-9394",
publisher = "Elsevier USA",
number = "3",

}

TY - JOUR

T1 - Mathematical model of corneal surface smoothing after laser refractive surgery

AU - Huang, David

AU - Tang, Maolong

AU - Shekhar, Raj

PY - 2003/3/1

Y1 - 2003/3/1

N2 - PURPOSE: To construct a quantitative model of corneal surface smoothing after laser ablation for refractive correction. DESIGN: Experimental study, interventional case series, and meta-analysis of literature. METHODS: A theory of epithelial smoothing in response to corneal contour change is derived from differential equations that describe epithelial migration, growth, and loss. Computer simulations calculate the effects on postoperative epithelial thickness, topography, refraction, and spherical aberration. Model parameter is matched with laser in situ keratomileusis (LASIK) outcome in literature and in a retrospective study of primary spherical myopic (77 eyes) and hyperopic (19 eyes) corrections. Surgically induced refractive change was the main outcome measure. RESULTS: Simulated epithelial remodeling after myopic ablation produces central epithelial thickening, reduction in achieved correction, and induction of oblate spherical aberration. Simulation of hyperopic ablation shows peripheral epithelial thickening, a larger reduction in correction, and induction of prolate spherical aberration. Simulation using a minus cylinder laser ablation pattern shows decreased astigmatism correction and increased hyperopic shift. In the LASIK series, linear regression of achieved correction vs ablation setting in hyperopic and minus cylinder corrections shows slopes of 0.97, 0.71, and 0.74, respectively. These clinical results match model predictions when the smoothing constant is set at 0.32, 0.63, and 0.55 mm, respectively. CONCLUSIONS: Epithelial thickness modulations after ablation can be modeled mathematically to explain clinically observed regression and induction of aberration. The cornea appears to smooth over ablated features smaller than approximately 0.5 mm. The model provides an approach for designing ablation patterns that precompensate for the smoothing to improve final outcome.

AB - PURPOSE: To construct a quantitative model of corneal surface smoothing after laser ablation for refractive correction. DESIGN: Experimental study, interventional case series, and meta-analysis of literature. METHODS: A theory of epithelial smoothing in response to corneal contour change is derived from differential equations that describe epithelial migration, growth, and loss. Computer simulations calculate the effects on postoperative epithelial thickness, topography, refraction, and spherical aberration. Model parameter is matched with laser in situ keratomileusis (LASIK) outcome in literature and in a retrospective study of primary spherical myopic (77 eyes) and hyperopic (19 eyes) corrections. Surgically induced refractive change was the main outcome measure. RESULTS: Simulated epithelial remodeling after myopic ablation produces central epithelial thickening, reduction in achieved correction, and induction of oblate spherical aberration. Simulation of hyperopic ablation shows peripheral epithelial thickening, a larger reduction in correction, and induction of prolate spherical aberration. Simulation using a minus cylinder laser ablation pattern shows decreased astigmatism correction and increased hyperopic shift. In the LASIK series, linear regression of achieved correction vs ablation setting in hyperopic and minus cylinder corrections shows slopes of 0.97, 0.71, and 0.74, respectively. These clinical results match model predictions when the smoothing constant is set at 0.32, 0.63, and 0.55 mm, respectively. CONCLUSIONS: Epithelial thickness modulations after ablation can be modeled mathematically to explain clinically observed regression and induction of aberration. The cornea appears to smooth over ablated features smaller than approximately 0.5 mm. The model provides an approach for designing ablation patterns that precompensate for the smoothing to improve final outcome.

UR - http://www.scopus.com/inward/record.url?scp=0037374609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037374609&partnerID=8YFLogxK

U2 - 10.1016/S0002-9394(02)01942-6

DO - 10.1016/S0002-9394(02)01942-6

M3 - Article

C2 - 12614741

AN - SCOPUS:0037374609

VL - 135

SP - 267

EP - 278

JO - American Journal of Ophthalmology

JF - American Journal of Ophthalmology

SN - 0002-9394

IS - 3

ER -