Aspects of eye accommodation evaluated by finite elements

Abstract

Axisymmetric nonlinear finite models of accommodation incorporating the posteriorly sloped force and vitreous effects have been studied by means of their effectiveness in mechanical and optical performances. All materials were assumed to be linearly elastic, vitreous and lens matrices were incompressible. The present model is subjected to certain indicated shortcomings, however, the behavior of the model is predictable, reasonable and favourably consistent with different published data, supporting the Helmholtz theory of accommodation.

Stretch‐dependent changes in surface profiles of the human crystalline lens during accommodation: A finite element study

“…Results suggest that even with an idealised, purely horizontal ciliary stretch, a small posterior shift occurs during dis‐accommodation. This can be seen in the slight posterior shift in the equatorial plane of the lens in Figure and suggests that, in the converse direction, a concomitant anterior shift occurs during accommodation, although the vertical component of this shift in the finite element prediction is small, at around 80 μm, while in the correct direction, the predicted shift is small compared to values in the literature . It is worth emphasising that the antero‐posterior movement of the model on stretching is in ‘free space’, constrained only by the anchoring point of the zonules at the ciliary body.…”

“…The Burd Model is well established and much cited, providing predictions for 11, 29 and 45 years of age and is reasonably straightforward to implement. This model can portray most of the lens behaviours during accommodation and has been widely used to investigate aspects of accommodation and presbyopia.…”

“…Finite element (FE) models have been constructed and used to investigate lens behaviour during accommodation. Some have been used to evaluate certain theories of accommodation: to estimate the required dis‐accommodative force exerted by the ciliary muscle to study the age‐dependence of the zonular forces as a proposed cause for presbyopia to verify the effectiveness of proposed treatments for presbyopia to investigate the effects of changing the lens material properties to examine the importance of including the influence of the vitreous in accommodation and to perform sensitivity analyses on the crystalline lens and accommodation …”

Corneal biomechanics: a review

“…Ljubimova, Eriksson and Bauer and Burd, Judge and Cross adopted a static non‐linear axisymmetric analysis, assuming that the eye is a body of revolution, discarding gravity and applying an axisymmetry perpendicular to the optical axis. Their studies were focused on understanding the accommodative process . Other studies have considered a thin‐shell linearly elastic spherical model for corneal analysis, assuming that the shell is symmetrical about a central axis and that the modulus of elasticity is the same in all directions…”

Models of shells and plates in the problems of ophthalmology

“…Volkov [17], today, studying the accommodation, it is important to take into account the facts obtained in clinical practice during the last 20-30 years: "It became clear that the role of the structures tangential to the crystalline lens (sclera, vitreous body, external eye muscles) could not be ruled out." A number of studies simulating the accommodation process by the finite element method using an ABAQUS package taking new data into account have been conducted together with mechanics from the Royal Institute of Technology in Stockholm [45,46]. The studies performed that proved the main conclu sions of the Helmholtz theory and disproved Schahar's and Fukasaku's accommodation theories appeared in the end of the 20th century [29].…”