title: Bivariate polar value analysis of surgically induced astigmatism.
abstract: OBJECTIVE
  To demonstrate the use of bivariate polar value analysis of surgically induced astigmatism following various cataract incisions.
  
  
  METHODS
  In a prospective study, we investigated surgically induced astigmatism following cataract surgery through 9.0-mm, 5.5-mm, and 4.0-mm superior corneal incisions. Autokeratometry was performed preoperatively and during the first year. All net astigmatisms were converted to polar values with reference to the 90 degrees meridian. Univariate and bivariate polar value analyses were performed.
  
  
  RESULTS
  After 1 year, univariate polar value analysis disclosed flattening averaging 1.02 D for 9.0-mm incisions, 0.71 D for 5.5-mm incisions, and 0.64 D for 4.0-mm incisions. The induced torque was 0.46 D counterclockwise for the 9-mm incision and close to zero for the 5.5 and 4-mm incisions. Bivariate polar value analysis disclosed a statistically significant (P < .05) difference in surgically induced astigmatism between the 9.0-mm incisions and the two smaller incisions at all follow-up points.
  
  
  CONCLUSIONS
  Univariate polar value analysis demonstrated the surgically induced steepening and torque. Bivariate analysis demonstrated the joint variation in these entities and therefore always yielded the correct result. Univariate and bivariate polar values may be used for analysis of surgically induced astigmatism following cataract surgery in any meridian.
authors.affiliation: Department of Ophthalmology, Alborg Sygehus Syd, Denmark. 173@RC.aaa.dk
authors.forename: Kristian
authors.initials: K
authors.lastname: Naeser
authors.forename: Ellen Birthe
authors.initials: EB
authors.lastname: Knudsen
authors.forename: Mette Kaas
authors.initials: MK
authors.lastname: Hansen
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D001251:Astigmatism / Q000175:diagnosis* / Q000209:etiology; D002387:Cataract Extraction / Q000009:adverse effects*; D019781:Corneal Topography; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D055095:Optics and Photonics; D011446:Prospective Studies