A mathematical model of factors that influence the performance of accommodative intraocular lenses

In this work a mathematical model of capsule movement during pseudophakic accommodation is described to allow identification and evaluation of factors that may explain the variation in effect of accommodative intraocular lenses (IOLs) between patients. The model assumes that increasing vitreous pressure pushes the lens capsule forward as a circular diaphragm and that this movement is from a fixed fulcrum. With an IOL in situ, the capsule is taken to have a non-uniform thickness due to the presence of the anterior capsulorhexis. The model assumes a uniform capsular elasticity and ignores contributions from cellular elements such as posterior capsule opacification. Using our model and a regression formula to calculate capsular bag size, taking into account axial length and keratometry values, we are able to predict accommodative effect in individual patients. By simple geometry we have developed a mathematical model to identify variables that are important in pseudophakic accommodation. It provides the basis for the development of a more complex model that would address the movement of a lens taking into account the influence of the zonular system during accommodation.