title: Mathematical model of corneal surface smoothing after laser refractive surgery.
abstract: OBJECTIVE
  To construct a quantitative model of corneal surface smoothing after laser ablation for refractive correction.
  
  
  METHODS
  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.
authors.affiliation: Cole Eye Institute, The Cleveland Clinic, Cleveland, Ohio 44195, USA. huangd@ccf.org
authors.forename: David
authors.initials: D
authors.lastname: Huang
authors.forename: Maolong
authors.initials: M
authors.lastname: Tang
authors.forename: Raj
authors.initials: R
authors.lastname: Shekhar
mesh_terms: D001251:Astigmatism / Q000601:surgery; D002455:Cell Division; D002465:Cell Movement; D003198:Computer Simulation; D003315:Cornea / Q000166:cytology* / Q000502:physiology* / Q000601:surgery; D004847:Epithelial Cells / Q000502:physiology; D006801:Humans; D006956:Hyperopia / Q000503:physiopathology / Q000601:surgery; D020731:Keratomileusis, Laser In Situ; D008954:Models, Biological; D008962:Models, Theoretical; D009216:Myopia / Q000503:physiopathology / Q000601:surgery; D012189:Retrospective Studies