Mathematical function describing visual gain curves following vitrectomy for different macular diseases.

Purpose: To determine whether the time course of average visual recovery (visual gain curve) after vitrectomy for different macular diseases can be described by a mathematical function.

Methods: The medical records of 1951 eyes that underwent vitrectomy for different macular diseases such as macular hole, epiretinal membrane, and macular edema were reviewed. All surgeries were performed by one surgeon (NO), and simultaneous phacoemulsification with intraocular lens implantation was performed on all phakic patients who were >40 years of age. All patients were followed at least 30 months postoperatively. The best-corrected visual acuity (BCVA) in decimal units was converted to the logarithm of the minimum angle of resolution (logMAR) for the analyses. The visual gain (G) was defined as the preoperative BCVA minus postoperative BCVA in logMAR units. The average visual gain was plotted as a function of the postoperative time, T, in months. T(m) was defined as the postoperative time required to reach one-half the maximum visual gain (G(max)). We examined whether the visual gain curve for different macular diseases could be fit by a hyperbolic function, G = G(max) × T/(T(m) + T).

Results: The visual gain curve for an idiopathic macular hole (n = 485) can be fit by the hyperbolic function G = 0.63T/(0.86 + T) with r(2) = 0.98. In the other macular diseases, significant correlations were also obtained (0.88 ≤ r(2) ≤ 0.99).

Conclusions: Although the mechanism was not determined, the visual gain curve after vitrectomy for different macular diseases can be well fit by a hyperbolic function.