**Purpose.**:
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.

^{ 1 }The development of the fovea has been described from midgestation (approximately fetal weeks 20–22), when outward migration of the inner retinal layers begins to form the foveal depression, to approximately 13 years, when final cone density is reached.

^{ 2 }The anatomy of this specialized area of retina has long been under investigation.

^{ 2,3 }With the introduction of optical coherence tomography (OCT), high-resolution cross-sectional images of the fovea were made possible, enabling in vivo study of foveal structure. Subsequently, the prevalence of OCT use in the management of various retinal disorders has increased significantly over the past decade.

^{ 4–7 }There is an increasing reliance on OCT to determine treatment plans for patients. As a result, it is imperative to differentiate normal aging process from abnormal pathological conditions.

^{ 8–10 }as well as the use of mathematical models to describe foveal morphology.

^{ 11,12 }This is the first study to mathematically analyze the anatomical changes in the healthy fovea that occur with normal aging from years 10 to 100.

*n*= 390) were subsequently divided into nine age groups representing each decade of life (10–19, 20–29, 30–39, 40–49, 50–59, 60–69, 70–79, 80–89, and 90–99 years).

^{ 13 }Using symbolic regression, Eureqa can create incredibly accurate equations. Eureqa allows the user to choose the level of accuracy in which the function fits the gathered data. The fit for the current study was chosen to be 0.085, which provided a close fit of the curve to the data in each group. A unique mathematical equation representing the mathematical analog of the foveal anatomy was derived for every decade of life, between 10 and 100 years. The behavior of each curve was subsequently studied and analyzed.

*P*< 0.05.

*R*

^{2}goodness of fit value. The level of complexity of the curve, referring to the complexity of the mathematical equation describing the curve analog of the foveal anatomic configuration, was used to characterize the behavior of the regression function graphically. For the second and third decade of life, the mathematical regression equation followed first-order sine curve of complexity levels 10 and 8, respectively. For the fourth and fifth decades of life, the mathematical regression equation also followed a sine curve but have additional terms present with slightly increased complexity levels of 14 and 11, respectively. Beginning in the sixth decade of life, the mathematical analog deviated from a trigonometric pattern and adopted curves of increasing complexity. For example, in the sixth decade of life, the curve illustrates the behavior of a polynomial function of level 25 complexity. The regression functions of highest complexity occur in the seventh and ninth decades of life with exponential functions of level 43 complexity (Fig. 2). The foveal complexity increased in a sigmoidal manner according to the decade of life and the formula:

**Figure 1**

**Figure 1**

**Figure 2**

**Figure 2**

*P*< 0.01) along the midline and significantly steeper maximal slopes (29 ± 32°,

*P*< 0.01). Foveal symmetry decreased quadratically with age according to the formula (Fig. 2):

**Table.**

**Table.**

Age Groups | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 | P Values |

Mean age, y | 17.16 ± 2.53 | 24.39 ± 2.95 | 33.03 ± 3.62 | 44.79 ± 2.73 | 54.98 ± 3.12 | 65.33 ± 2.77 | 74.37 ± 2.97 | 84.03 ± 2.97 | 91.44 ± 2.24 | 0.32 |

Volume, mm^{3} | 4.64 ± 1.37 | 4.55 ± 1.00 | 4.53 ± 1.72 | 4.39 ± 1.11 | 4.39 ± 1.00 | 3.87 ± 1.10 | 4.00 ± 1.33 | 3.70 ± 1.24 | 3.19 ± 0.89 | 0.21 |

Maximum slopes | 21 ± 12° | 23 ± 12° | 25 ± 13° | 26 ± 15° | 28 ± 17° | 29 ± 19° | 32 ± 22° | 28 ± 23° | 29 ± 32° | <0.01* |

Midline foveal symmetry | 0.92 ± 0.10 | 0.90 ± 0.12 | 0.89 ± 0.13 | 0.87 ± 0.15 | 0.83 ± 0.23 | 0.83 ± 0.24 | 0.79 ± 0.24 | 0.78 ± 0.25 | 0.76 ± 0.27 | <0.01* |

Regression function complexity | 10.00 | 8.00 | 14.00 | 11.00 | 25.00 | 43.00 | 16.00 | 43.00 | 21.00 | <0.01* |

Eyes, n | 31 | 59 | 30 | 39 | 59 | 79 | 49 | 35 | 9 | 0.52 |

Males, % | 41.9 | 74.6 | 53.3 | 41.0 | 33.9 | 35.4 | 49.0 | 37.1 | 44.4 | 0.53 |

Females, % | 58.1 | 25.4 | 46.7 | 59.0 | 66.1 | 64.6 | 51.0 | 62.9 | 55.6 | 0.53 |

Caucasians, % | 74.2 | 69.5 | 80.0 | 82.1 | 84.7 | 83.5 | 89.8 | 91.4 | 88.9 | 0.33 |

Asian, % | 12.9 | 10.2 | 0.0 | 5.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | N/A† |

Middle Eastern, % | 12.9 | 6.8 | 6.7 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | N/A† |

African Americans, % | 0.0 | 6.8 | 6.7 | 12.8 | 15.3 | 16.5 | 10.2 | 8.6 | 11.1 | N/A† |

Hispanics, % | 0.0 | 6.8 | 6.7 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | N/A† |

*P*= 0.53). Subjects included those from different ethnic backgrounds; however, due to limited sample size for these populations, no conclusions could be made as to any possible difference in foveal parameters according to race. An attempt to compare between the two eyes of each individual failed because many of the subjects were seen for another condition in the fellow eye. There was no correlation between different visual acuities within each decade of life and the mathematical analog of the foveal anatomy.

^{ 14–16 }However, generalized macular thickness measurements across a broad population of patients are not sufficient. The effect of other parameters on macular thickness has been studied, including age, race, axial length, high myopia, and sex.

^{ 8–10,17–20 }Males and Caucasians have been shown to have greater macular thickness on OCT than females and African-Americans, respectively.

^{ 9,10,19,21 }Results have varied as to age, with some studies finding no change in macular thickness

^{ 9,16 }and others finding a decrease in macular thickness with age.

^{ 8,19 }

^{ 12 }used an automated algorithm to extract the slope, depth, and diameter of the foveal pit from OCT images of 65 patients, finding considerable variation in all parameters. Wagner-Schuman et al.

^{ 21 }also used an algorithm to assess foveal pit morphology in 90 patients. In that study, there was no difference between males and females in foveal pit morphology and African Americans had significantly deeper and broader foveal pits than Caucasian.

^{ 21 }In the current study, the focus was to investigate the change in normal foveal anatomical configuration with each decade of life.

^{ 22 }We described a significant difference between normal foveal configurations and premacular hole foveal configurations, which allowed earlier diagnosis and follow-up of patients prone to the development of macular holes.

^{ 22 }Mathematical modeling of the fovea is also being used in other diseases, such as Parkinson,

^{ 23 }in order to distinguish normal fovea from pathologic. With this increasing use of mathematical analysis of the fovea to distinguish normal from pathologic, the need for an understanding of normal foveal structure over the decades of life is of even more significance.

**B. Nesmith**, None;

**A. Gupta**, None;

**T. Strange**, None;

**Y. Schaal**, None;

**S. Schaal**, None

*Invest Ophthalmol Vis Sci*. 2011; 52: 5105–5110. [CrossRef] [PubMed]

*Am J Ophthalmol*. 2012; 154: 767–778. e762. [CrossRef] [PubMed]

*Ophthalmology*. 1984; 91: 603–612. [CrossRef] [PubMed]

*Am J Ophthalmol*. 2004; 138: 732–739. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2013; 54: 1080–1085. [CrossRef] [PubMed]

*Ophthalmology*. 2011; 118: 2434–2441. [CrossRef] [PubMed]

*Ophthalmology*. 2013; 120: 2611–2619. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Science*. 2013; 54: 7968–7976. [CrossRef]

*PloS One*. 2012; 7: e37638. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2008; 49: 2668–2672. [CrossRef] [PubMed]

*Exp Eye Res*. 2013; 119C: 19–26.

*British J Ophthalmol*. 2009; 93: 1223–1227. [CrossRef]

*Science*. 2009; 324: 81–85. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2009; 50: 3432–3437. [CrossRef] [PubMed]

*Ophthalmology*. 2010; 117: 1585–1594. [CrossRef] [PubMed]

*Am J Ophthalmol*. 2009; 148: 266–271. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2011; 52: 8769–8779. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2013; 54: 4934–4940. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2010; 51: 3913–3918. [CrossRef] [PubMed]

*Eye*. 2008; 22: 551–555. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2011; 52: 625–634. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2011; 52: 8266–8270. [CrossRef] [PubMed]

*J Neural Transm*. doi:10.1007/s00702-014-1214-2 .