title: Mathematical analysis of the normal anatomy of the aging fovea.
abstract: OBJECTIVE
  To mathematically analyze anatomical changes that occur in the normal fovea during aging.
  
  
  METHODS
  A total of 2912 spectral-domain optical coherence tomography (SD-OCT) normal foveal scans were analyzed. Subjects were healthy individuals, aged 13 to 97 years, with visual acuity ≥20/40 and without evidence of foveal pathology. Using automated symbolic regression software Eureqa (version 0.98), foveal thickness maps of 390 eyes were analyzed using several measurements: parafoveal retinal thickness at 50 μm consecutive intervals, parafoveal maximum retinal thickness at two points lateral to central foveal depression, distance between two points of maximum retinal thickness, maximal foveal slope at two intervals lateral to central foveal depression, and central length of foveal depression. A unique mathematical equation representing the mathematical analog of foveal anatomy was derived for every decade, between 10 and 100 years.
  
  
  RESULTS
  The mathematical regression function for normal fovea followed first order sine curve of level 10 complexity for the second decade of life. The mathematical regression function became more complex with normal aging, up to level 43 complexity (0.085 fit; P < 0.05). Young foveas had higher symmetry (0.92 ± 0.10) along midline, whereas aged foveas had significantly less symmetry (0.76 ± 0.27, P < 0.01) along midline and steeper maximal slopes (29 ± 32°, P < 0.01).
  
  
  CONCLUSIONS
  Normal foveal anatomical configuration changes with age. Normal aged foveas are less symmetric along midline with steeper slopes. Differentiating between normal aging and pathologic changes using SD-OCT scans may allow early diagnosis, follow-up, and better management of the aging population.
authors.affiliation: Department of Ophthalmology and Visual Sciences University of Louisville, Louisville, Kentucky, United States.
authors.forename: Brooke
authors.initials: B
authors.lastname: Nesmith
authors.affiliation: University of Louisville School of Medicine, Louisville, Kentucky, United States.
authors.forename: Akash
authors.initials: A
authors.lastname: Gupta
authors.affiliation: Department of Ophthalmology and Visual Sciences University of Louisville, Louisville, Kentucky, United States.
authors.forename: Taylor
authors.initials: T
authors.lastname: Strange
authors.affiliation: Speed School of Engineering, Department of Computer Science and Computer Engineering, University of Louisville School of Medicine, Louisville, Kentucky, United States.
authors.forename: Yuval
authors.initials: Y
authors.lastname: Schaal
authors.affiliation: Department of Ophthalmology and Visual Sciences University of Louisville, Louisville, Kentucky, United States.
authors.forename: Shlomit
authors.initials: S
authors.lastname: Schaal
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000375:Aging; D002648:Child; D005260:Female; D005584:Fovea Centralis / Q000033:anatomy & histology*; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D012016:Reference Values; D041623:Tomography, Optical Coherence / Q000379:methods / Q000592:standards*; D055815:Young Adult
keywords: aging fovea; mathematical analysis; normal anatomy; spectral-domain optical coherence tomography