title: Mathematical analysis of corneal remodelling after intracorneal ring surgery in keratoconus.
abstract: OBJECTIVE
  To represent mathematically the intersection between the ectatic corneal geometry and the plane of intracorneal ring implants (ICRS) in order to determine the corneal response to ICRS surgery in keratoconus (KC). Thereafter, to present the concept and early results of a newly derived topography-guided nomogram for ICRS surgery for the treatment of keratectasia.
  
  
  METHODS
  The corneal rings plane intersection was modelled to a conic section. Ring effect was the result of: the ring size, position (steepvsflat), location (distance from the geometric centre of the cornea), and the discrepancy between the ring's curvature and the tunnel's curvature. Femtosecond laser was used to create the tunnels and the incision sites were chosen according to the nomogram in order to place the thickest ring in the steepest portion of the cornea regardless of the astigmatism axis of refraction.
  
  
  RESULTS
  The conic section had a more prolate shape in the steep area of the cornea than in the flat area, depending on the corneal sagittal curvature. Equal ring size had more flattening effect in the steep area than in the flat area. Thick segment should be implanted under the steep portion of the cornea regardless of the cylinder axis of refraction. Single segment in the steep area was sufficient in early and moderate cases of KC. The new nomogram provided more topographic regularity with significant reduction of astigmatism and better improvement in uncorrected visual acuity (UCVA) and best-corrected visual acuity (BCVA) than the conventional nomogram.
  
  
  CONCLUSIONS
  The newly derived nomogram can produce better results than the conventional nomogram. Moreover, based on this concept, a new nomogram can be integrated into the femtosecond laser software to create topography-guided, customized, elliptical tunnels with modified focal asphericity that allows for customized focal flattening of the irregularly steepened ectatic cornea.
authors.affiliation: Beirut Eye Specialist Hospital, Beirut P.O box 116-5311, Lebanon; Mediclinic, Dubai Mall, Dubai P.O box 282890, United Arab Emirates.
authors.forename: Elias F
authors.initials: EF
authors.lastname: Jarade
authors.affiliation: Beirut Eye Specialist Hospital, Beirut P.O box 116-5311, Lebanon; Saint-Joseph University, Faculty of Medicine, Beirut P.O Box 11-5076, Lebanon.
authors.forename: Elise
authors.initials: E
authors.lastname: Slim
authors.affiliation: Beirut Eye Specialist Hospital, Beirut P.O box 116-5311, Lebanon.
authors.forename: Carole
authors.initials: C
authors.lastname: Cherfan
authors.affiliation: Saint-Joseph University, Faculty of Medicine, Beirut P.O Box 11-5076, Lebanon.
authors.forename: Hala
authors.initials: H
authors.lastname: El Rami
authors.affiliation: Saint-Joseph University, Faculty of Medicine, Beirut P.O Box 11-5076, Lebanon.
authors.forename: Toufic
authors.initials: T
authors.lastname: Hassan
authors.affiliation: Saint-Joseph University, Faculty of Medicine, Beirut P.O Box 11-5076, Lebanon.
authors.forename: Elias
authors.initials: E
authors.lastname: Chelala
keywords: cornea; intracorneal ring; keratoconus; mathematical model; nomogram; topography guided