Wei Hau Lew¹, David Borja¹, Derek Nankivil¹; ¹Alcon Research, LLC

Binocular summation models traditionally predict cyclopean performance in contrast discrimination and detection based on monocular inputs. A key question is whether these models can extend to visual acuity (VA). Clinically, measurements of binocular VA curves across accommodative demand are used to evaluate presbyopic corrections (intraocular lenses, multifocal contacts). These curves reveal how binocular summation changes across vergence planes and the impact of interocular differences. We adapted two binocular summation models (Legge & Gu 1989—LG and Ding & Sperling 2006—DS) to predict binocular VA curves using retrospective data from seven published clinical studies (collectively, n = 320 subjects). The LG model employs quadratic summation of monocular contrast inputs, while the DS model incorporates weight for gain control between the two eyes’ contrast. To improve the LG model, a scaling factor and a cross-term were added to allow penalization for intraocular differences, thereby giving both models two degrees of freedom. Parameters were optimized under constraints to minimize the root mean square error (RMSE) of the pooled data. Leave-one-out cross-validation was performed to assess model generalizability. Mean RMSE for LG was 0.030 [range: 0.020-0.044] while DS model was 0.019 [range: 0.010-0.035] logMAR. All clinical data exhibited summation, and both models predicted summation consistently. Maximum absolute error was 0.083 logMAR for LG (< 0.05 in 51/56 predictions) and 0.065 for DS (<0.05 in 54/56 predictions). While both models typically achieved accuracy within half a line of VA, the DS model more closely matched clinical data and behaved more reasonably outside the observed data range. In summary, both models reliably predicted binocular VA curves meeting clinical standards for accuracy. DS model may serve as a useful tool in developing and evaluating presbyopic correction strategies. However, results are based on retrospective data; further validation and calibration across diverse populations are needed to confirm generalizability.