Modeling the aging crystalline lens: a quantitative explanation of the lens paradox

The lens paradox refers to the phenomenon where the human lens loses refractive power, despite the increase in external curvature and thickness associated with aging. In this study, we develop an age-dependent GRINCU (gradient index and gradient curvature of the iso-indicial surfaces) lens model and propose a quantitative explanation for the lens paradox. Drawing on various sources in the literature, we configured a lens with an age-dependent geometry and implemented this model for an age range of 23-73 years. By adjusting the internal curvature gradient for each age, we optimized the lens refractive power to match experimental measurements within this age range. To compare the results obtained by varying the curvature gradient of the iso-indicial surfaces (IISs), we also modeled a concentric configuration for each age. Among the two configurations, only the model with a variable curvature gradient successfully replicated the decline in refractive power associated with aging, whereas the concentric configuration showed an increasing trend in power with age. To accurately explain the lens paradox, it is crucial to consider not only the changes in refractive index with aging but also the changes in the internal curvature gradient of the lens.