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Yoreh Barak, Mark P. Sherman, Shlomit Schaal; Mathematical Analysis of Specific Anatomic Foveal Configurations Predisposing to the Development of Macular Holes. Invest. Ophthalmol. Vis. Sci. 2011;52(14):1038.
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To mathematically analyze specific anatomic foveal configurations predisposing to the formation of macular holes in comparison to normal foveal anatomy.
3882 optical coherence tomography (Stratus OCT 3000, Zeiss) foveal thickness maps were analyzed. 96 foveal maps were identified prior to the formation of macular holes. Maps were analyzed using several measurements: (1) Retinal thickness around the fovea at 50 micron consecutive intervals, (2) Parafoveal maximum retinal thickness at two points lateral to the central foveal depression, (3) The distance between two points of maximum retinal thickness, (4) Maximal foveal slope at two intervals lateral to the central foveal depression, and (5) Central length of foveal depression. The mathematical analog of the foveal configuration was analyzed using the automated symbolic regression software Eureqa (version 0.82 beta) and the equation to describe the mathematical relationship in a 0.083 fit was derived for pre-macular-hole foveas in comparison to normal foveas.
Pre-macular hole anatomical 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 for normal fovea followed a first order cosine curve of level 11 complexity. The mathematical regression function for pre-macular-hole fovea followed a complex sine curve of level 30 complexity. Normal foveas had higher symmetry (0.84±0.11) along the midline whereas pre-macular hole foveas had steeper maximal slopes (1.23±0.6). 75% of pre-macular hole patients had similar foveal configuration in the fellow eye, 50% of these indeed consequently developed bi-lateral macular holes.
Pre-macular hole foveal anatomical configuration was found to be significantly different from normal foveal configuration. The ability to identify a suspicious macular configuration on OCT scans may allow early diagnosis, follow up and better management of macular-hole-prone patients.
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