Finite element analysis of the lens profile during accommodation

Abstract

The magnitude of zonular forces required to change the shape of the human lens while focusing at near; i.e., accommodating, is still under investigation. During accommodation, ciliary muscle contraction induces a large increase in lens central optical power (COP). Here we used finite element (FE) analysis to evaluate the correlation between zonular forces and lens surface curvatures, central thickness, COP, overall lens shape and longitudinal spherical aberration (LSA). Fresh isolated lenses from donors aged 20, 24, 26, and 30 years were the basis for the analyses. Lens nucleus elastic moduli were specified as equal to, 2, 3, 10, 20 and 30 times greater than its cortex. When equatorial zonular (Ez) force was increased in 3.125 x 10 ^-6 N steps while the anterior zonular (Az) and posterior zonular (Pz) forces were decreased in 3.125 x 10 ^-6 N steps, COP was evaluated. Independent of the increase in lens nuclear modulus, less than 0.02 N of Ez force was required to increase COP 10 diopters while Az and Pz forces were decreased. The lens peripheral surfaces flattened, central surfaces steepened, central lens thickness increased, COP increased and LSA shifted in the negative direction consistent with published in vivo accommodation studies. The minimal Ez force required to obtain 10 diopters of COP increase supports that increasing Ez force with decreasing Az and Pz force is the basis for the change in lens shape during accommodation. Since the COP increase was independent of increasing elastic modulus of the nucleus, stiffening of the lens nucleus is not the etiology of the universal age-related decline in accommodative amplitude that results in presbyopia in the fifth decade of life. Increased Ez zonular tension during accommodation has implications for the development and potential treatments of myopia, glaucoma, presbyopia, cortical cataracts and accommodative intraocular lens design.