Impact of internal curvature gradient on the power and accommodation of the crystalline lens

Abstract

Human crystalline lens has a layered, shell-like structure with the refractive index increasing from cortex to nucleus (gradient index or GRIN structure). Moreover, every iso-indicial layer has a certain curvature which also varies from cortex to nucleus, with a gradient of curvature (G). In the present manuscript, the role of G on the lens power is investigated along with its implications regarding the lens paradox (change of lens power with age) and intra-capsular accommodation mechanism (larger than expected changes of lens power during accommodation compared to a homogenous lens). To this end, a simplified formulation of paraxial lens power based on thin lens approximation is developed and applied to the anterior and posterior parts of the lens. The main theoretical result is that the power of both anterior and posterior lens is given by the sum of the power of a lens with a homogeneous refractive index equal to that of the nucleus and power associated with the contribution of the internal GRIN structure, which depends on G. This general result suggests that the sign of G is fundamental in increasing or decreasing the lens power. We found that the curvature gradient has a strong impact on lens power, helping to explain both the lens paradox and intra-capsular accommodation mechanism.