Purchase this article with an account.
M.J. Trager, R.M. Vagefi, S.D. McLeod; A Mathematical Model for Estimating Degree of Accommodation by Defocus Curves . Invest. Ophthalmol. Vis. Sci. 2005;46(13):717.
Download citation file:
© ARVO (1962-2015); The Authors (2016-present)
Purpose: With the development of new accommodative intraocular lenses, quantitative methods of estimating accommodation are necessary. Defocus curves have been used to estimate accommodative range, but incorporate both depth of focus as well as true accommodation. The purpose of this study is to propose a novel mathematical model for estimating accommodation using defocus curves of phakic and pseudophakic individuals. Methods: Twenty–four patients, including 8 pseudophakics and 16 phakics of various ages, were refracted to best corrected visual acuity. Minus power lenses were then added in 0.5 diopter intervals until visual acuity was reduced by more than three lines. Returning to the original refraction, plus power lenses were added in a similar fashion. Resulting defocus curves were plotted as logMAR against diopters of lenses added. A second degree best–fit curve was produced for minus and plus power lenses, respectively. The integral, or area under the curve, was calculated for each curve at 1.5 diopters of defocus. Assuming that true accommodation is limited to the minus curve, and that depth of focus is symmetrically distributed over both plus and minus curves, accommodation (Ac) was estimated by determining the difference between the integrals of the plus and minus curves for each patient, where higher Ac values are expected to correlate with greater degree of accommodation. Means and ranges of Ac were compared among age groups, phakic, and pseudophakic patients, to demonstrate consistency within each group and appropriate variability between groups for this model. Results: Eight pseudophakics, with a mean age of 76, had a mean Ac of 1.044 with a range of –.466 to 2.495. Sixteen phakics, with a mean age of 47, had a mean Ac of 1.623 with a range of –.466 to 4.94. Phakic patients in their 20th, 30 th, 40 th, 50 th, 60 th, and 70 th decade of life had mean Ac’s of 2.506, 2.0517, 2.616, 1.3572, 0.092, and 1.75, respectively. As expected, patients in their forties had the widest range of Ac values, from –.1002 to 5.1993. Among patients in their seventies, the mean Ac was calculated as 1.74645 for two phakics and 0.0058525 for 3 pseudophakics. Conclusions: A new mathematical model of analyzing defocus curves to estimate degree of accommodation is proposed. By accounting for depth of focus and variation in the shape of defocus curves, this model may serve as a useful alternative to previous methods of defocus curve analysis.
This PDF is available to Subscribers Only