title: Mathematical analysis of specific anatomic foveal configurations predisposing to the formation of macular holes.
abstract: OBJECTIVE
  To mathematically analyze and to clinically describe specific anatomic foveal configurations predisposing to the formation of macular holes in comparison with normal foveal anatomy.
  
  
  METHODS
  In a retrospective observational case-control series, a total of 3882 optical coherence tomography (OCT) foveal thickness maps were analyzed; 96 foveal maps were identified before the formation of macular holes. Maps were analyzed using several anatomic measurements including: retinal thickness, foveal slope, and length of foveal depression. The mathematical analog of the foveal configuration was analyzed using automated symbolic regression software and the equation to describe the mathematical relationship in a 0.083 fit was derived for premacular hole foveas compared with normal age-matched foveas.
  
  
  RESULTS
  Premacular hole anatomic configuration was found to be significantly different from normal foveal anatomy for maximal slope (P < 0.05) and for central length of foveal depression (P < 0.05). The mathematical regression function followed a first-order cosine curve of level 12 complexity for normal fovea compared with a complex sine curve of level 30 complexity function for premacular hole fovea. Normal foveas had higher symmetry (0.86 ± 0.1, P = 0.03) along the midline, whereas premacular hole foveas had steeper maximal slopes (40 ± 18°, P = 0.01); 75% of these patients had similar foveal configuration in the fellow eye and 50% developed bilateral macular holes.
  
  
  CONCLUSIONS
  Premacular hole foveal configurations are significantly different from normal foveal configurations. Suspicious macular configurations are easy to recognize on OCT scans and may allow early diagnosis, follow-up, and better management of macular hole-prone patients.
authors.affiliation: Department of Ophthalmology and Visual Sciences, University of Louisville, Kentucky, USA.
authors.forename: Yoreh
authors.initials: Y
authors.lastname: Barak
authors.forename: Mark P
authors.initials: MP
authors.lastname: Sherman
authors.forename: Shlomit
authors.initials: S
authors.lastname: Schaal
mesh_terms: D000368:Aged; D016022:Case-Control Studies; D042241:Early Diagnosis; D005500:Follow-Up Studies; D005584:Fovea Centralis / Q000033:anatomy & histology* / Q000473:pathology*; D006801:Humans; D008875:Middle Aged; D008954:Models, Biological; D015203:Reproducibility of Results; D012167:Retinal Perforations / Q000473:pathology*; D012189:Retrospective Studies; D012984:Software; D041623:Tomography, Optical Coherence / Q000379:methods* / Q000592:standards