title: A mathematical approach to human pterygium shape.
abstract: OBJECTIVE
  Pterygium is a common lesion affecting the population in countries with high levels of ultraviolet exposure. The final shape of a pterygium is the result of a growth pattern, which remains poorly understood. This manuscript provides a mathematical analysis as a tool to determine the shape of human pterygia.
  
  
  METHODS
  Eighteen patients, all affected by nasal unilateral pterygia, were randomly selected from our patient database independently of sex, origin, or race. We included all primary or recurrent pterygia with signs of proliferation, dry eye, and induction of astigmatism. Pseudopterygia were excluded from this study. Pterygia were outlined and analyzed mathematically using a Cartesian coordinate system with two axes (X, Y) and five accurate landmarks of the pterygium.
  
  
  RESULTS
  In 13 patients (72%), the shape of the pterygia was hyperbolic and in five patients (28%), the shape was rather elliptical.
  
  
  CONCLUSIONS
  This analysis gives a highly accurate mathematical description of the shape of human pterygia. This might help to better assess the clinical results and outcome of the great variety of therapeutic approaches concerning these lesions.
authors.affiliation: Eye Clinic ORASIS, Swiss Eye Research Foundation, Reinach AG, Switzerland; Department of Physics, Faculty of Sciences, University of Novi Sad, Novi Sad; Faculty of Medicine of the Military Medical Academy, University of Defence, Belgrade, Serbia; Division of Ophthalmology, Department of Clinical Neurosciences, Geneva University Hospitals, Geneva, Switzerland.
authors.forename: Bojan
authors.initials: B
authors.lastname: Pajic
authors.affiliation: Eye Clinic ORASIS, Swiss Eye Research Foundation, Reinach AG, Switzerland.
authors.forename: Iraklis
authors.initials: I
authors.lastname: Vastardis
authors.affiliation: Department of Mathematics, Faculty of Mechanical Engineering, University of Niš, Niš, Serbia.
authors.forename: Predrag
authors.initials: P
authors.lastname: Rajkovic
authors.affiliation: Eye Clinic ORASIS, Swiss Eye Research Foundation, Reinach AG, Switzerland.
authors.forename: Brigitte
authors.initials: B
authors.lastname: Pajic-Eggspuehler
authors.affiliation: Department of Radiation Oncology, Inselspital, Bern University Hospital, Bern, Switzerland.
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Aebersold
authors.affiliation: Department of Physics, Faculty of Sciences, University of Novi Sad, Novi Sad.
authors.forename: Zeljka
authors.initials: Z
authors.lastname: Cvejic
keywords: etiology; limbal stem cells; mathematical shape analysis; pterygium; stem cells dysfunction