title: The expression and comparison of healthy and ptotic upper eyelid contours using a polynomial mathematical function.
abstract: OBJECTIVE
  To derive a mathematical expression for the healthy upper eyelid (UE) contour and to use this expression to differentiate the normal UE curve from its abnormal configuration in the setting of blepharoptosis.
  
  
  METHODS
  The study was designed as a cross-sectional study. Fifty healthy subjects (26M/24F) and 50 patients with blepharoptosis (28M/22F) with a margin-reflex distance (MRD1) of ≤2.5 mm were recruited. A polynomial interpolation was used to approximate UE curve. The polynomial coefficients were calculated from digital eyelid images of all participants using a set of operator defined points along the UE curve. Coefficients up to the fourth-order polynomial, iris area covered by the UE, iris area covered by the lower eyelid and total iris area covered by both the upper and the lower eyelids were defined using the polynomial function and used in statistical comparisons. The t-test, Mann-Whitney U test and the Spearman's correlation test were used for statistical comparisons.
  
  
  RESULTS
  The mathematical expression derived from the data of 50 healthy subjects aged 24.1 ± 2.6 years was defined as y = 22.0915 + (-1.3213)x + 0.0318x(2 )+ (-0.0005x)(3). The fifth and the consecutive coefficients were <0.00001 in all cases and were not included in the polynomial function. None of the first fourth-order coefficients of the equation were found to be significantly different in male versus female subjects. In normal subjects, the percentage of the iris area covered by upper and lower lids was 6.46 ± 5.17% and 0.66% ± 1.62%, respectively. All coefficients and mean iris area covered by the UE were significantly different between healthy and ptotic eyelids.
  
  
  CONCLUSIONS
  The healthy and abnormal eyelid contour can be defined and differentiated using a polynomial mathematical function.
authors.affiliation: Department of Ophthalmology, School of Medicine, Hacettepe University , Ankara , Turkey .
authors.forename: Mehmet C
authors.initials: MC
authors.lastname: Mocan
authors.forename: Hacer
authors.initials: H
authors.lastname: Ilhan
authors.forename: Hasmet
authors.initials: H
authors.lastname: Gurcay
authors.forename: Ozlem
authors.initials: O
authors.lastname: Dikmetas
authors.forename: Erdem
authors.initials: E
authors.lastname: Karabulut
authors.forename: Ugur
authors.initials: U
authors.lastname: Erdener
authors.forename: Murat
authors.initials: M
authors.lastname: Irkec
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D001763:Blepharoptosis / Q000473:pathology*; D002648:Child; D002675:Child, Preschool; D003430:Cross-Sectional Studies; D005143:Eyelids / Q000033:anatomy & histology* / Q000473:pathology*; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D008875:Middle Aged; D015233:Models, Statistical; D055815:Young Adult