title: [Mathematical presentation of postoperative regular corneal astigmatism].
abstract: BACKGROUND
  There are several contradictory approaches to describe a change in corneal astigmatism induced by operations.
  
  
  METHODS
  Assuming a rotational ellipsoid for the outer surface of the cornea we derived formulas that represent the change in astigmatism. Also, the change of the corneal power in the axis of the intervention (e.g. operation) has been determined.
  
  
  RESULTS
  The exact derivation yield formulas for the absolute value of the astigmatism change identical to those of Naylor and Jaffe but includes, in addition, algorithms for "with-the-rule" and "against-the-rule" components. The spherical change of the cornea is also obtained. The models of Cravy and Naeser are mathematically inconsistent and should be avoided.
  
  
  CONCLUSIONS
  The presentation of the change in astigmatism should depend on the primary question. In many cases, the complicated non-linear vector calculation is not necessary since the actual changes in corneal shape may be demonstrated by simpler formulas. The results of these formulas are much easier to interpret.
authors.affiliation: Augenklinik im Universitätsklinikum Rudolf Virchow, Freie Universität Berlin.
authors.forename: T
authors.initials: T
authors.lastname: Seiler
authors.forename: J
authors.initials: J
authors.lastname: Wollensak
mesh_terms: D001251:Astigmatism / Q000503:physiopathology*; D002387:Cataract Extraction; D003315:Cornea / Q000503:physiopathology*; D006801:Humans; D007910:Lenses, Intraocular; D008962:Models, Theoretical; D055095:Optics and Photonics; D011183:Postoperative Complications / Q000503:physiopathology*; D012029:Refraction, Ocular