title: Three-axis ellipsoidal fitting of videokeratoscopic height data after penetrating keratoplasty.
abstract: OBJECTIVE
  After penetrating keratoplasty corneal topography tends to be irregular and the fitting of spectacle glasses or contact lenses may be difficult. The purpose of this study was to demonstrate a mathematical method for approximation of discrete corneal topography height data with an ellipsoid for better appreciation of the clinical outcome after PK.
  
  
  METHODS
  In 50 eyes (30 keratoconus, 20 Fuchs' dystrophy) penetrating keratoplasty was performed using nonmechanical trephination with the excimer laser 193 nm. Main outcome measures were objective corneal astigmatism (regular keratometry, corneal topography (TMS-1)), subjective refraction and best-corrected visual acuity (VA) in a fixed postoperative gate 3 and 12 month postoperatively and after suture removal. An approximation algorithm was applied for fitting a general ellipsoidal surface (not rotationally symmetric) to raw corneal topography height data. A set of parameters (meridional power, axis and asphericity) were calculated. The root mean square error (RMS) was determined between raw topography power data and the ellipsoidal model surface within an apical distance of 3 mm. The cylinder of subjective refraction was correlated with the keratometric readings, the Simulated Keratometry (SimK) of the topography system and the respective parameters of the model surface.
  
  
  RESULTS
  The amount of the SimK cylinder yielded higher values than keratometry and the ellipsoidal fit; subjective refraction yielded the lowest value at each follow-up interval. The ellipsoidal fit showed the best correlation to the refractive cylinder at all follow-up stages (p = 0.04 at 3, p = 0.01 at 12 months and p = 0.002 after suture removal). The axis of the best ellipsoidal fit showed a significant correlation with the axis of the refractive cylinder at all follow-up intervals (p = 0.02 at 3 months, p = 0.01 before suture removal and p = 0.002 after suture removal). The axis of the keratometric cylinder showed a mild correlation at all follow-up examinations (p = 0.05 at 3 months, p = 0.02 before suture removal and p = 0.04 after suture). The cylinder of the topographic modeling system, however, showed a significant correlation with the refractive cylinder axis only after suture removal (p = 0.04). The paracentral corneal power of SimK (45.9D at 3 months, 44.4D at 12 months and 43.0D after suture removal) exceeded the respective values of conventional keratometry (43.1D at 3 months, 42.9D at 12 months and 41.7D after suture removal) and the ellipsoidal fit (43.3D at 3 months, 43.0D at 12 months and 41.8D after suture removal). The corneal asphericity from the ellipsoidal fit reached an approximately spherical shape in radial direction (A = 1.0) in the initial time period after penetrating keratoplasty, remained stable before suture removal and decreased significantly (p = 0.02) to a final value of A = 0.86 indicating a (normal) prolate shape of the cornea. The approximation error between the raw corneal topography height data and the best ellipsoidal fit model surface was nearly unchanged before suture removal (1.8 +/- 0.7 microm at 3 months and 1.9 +/- 1.1 microm at 12 months, p = 0.30) and decreased significantly to the examination after suture removal (0.9 +/- 0.5 microm, p = 0.01).
  
  
  CONCLUSIONS
  The approximation of corneal topography height data with an ellipsoidal model surface renders reconstruction of clinically relevant corneal topography parameters including corneal asphericity. Even in markedly irregular corneal surfaces, such as after PK, the correlation of amount/axis of refractive cylinder with the model surface parameters is more accurate than with respective SimK values of corneal topography analysis.
authors.affiliation: Department of Ophthalmology, University of Erlangen-Nürnberg, Germany. achim.langenbucher@augen.imed.uni-erlangen.de
authors.forename: Achim
authors.initials: A
authors.lastname: Langenbucher
authors.forename: Berthold
authors.initials: B
authors.lastname: Seitz
authors.forename: Gottfried O H
authors.initials: GO
authors.lastname: Naumann
mesh_terms: D000328:Adult; D019781:Corneal Topography; D005260:Female; D005642:Fuchs' Endothelial Dystrophy / Q000473:pathology* / Q000601:surgery*; D006801:Humans; D007640:Keratoconus / Q000473:pathology* / Q000601:surgery*; D015948:Keratoplasty, Penetrating; D008297:Male; D008875:Middle Aged; D011184:Postoperative Period; D012189:Retrospective Studies