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

Abstract

Background A nonlinear isotropic finite element (FE) model of a 29 year old human crystalline lens was constructed to study the effects of various geometrical parameters on lens accommodation. Methods The model simulates dis-accommodation by stretching of the lens and predicts the change in the lens capsule, cortex and nucleus surface profiles at select states of stretching/accommodation. Multiple regression analysis (MRA) is used to develop a stretch-dependent mathematical model relating the lens sagittal height to the radial position of the lens surface as a function of dis-accommodative stretch. A load analysis is performed to compare the FE results to empirical results from lens stretcher studies. Using the predicted geometrical changes, the optical response of the whole eye during accommodation was analysed by ray-tracing. Results Aspects of lens shape change relative to stretch were evaluated including change in diameter (d), central thickness (T) and accommodation (A). Maximum accommodation achieved was 10.29 D. From the MRA, the stretch-dependent mathematical model of the lens shape related lens curvatures as a function of lens ciliary stretch well (maximum mean-square residual error 2.5×10−3 µm, p<0.001). The results are compared with those from in vitro studies. Conclusions The FE and ray-tracing predictions are consistent with EVAS studies in terms of load and power change versus change in thickness. The mathematical stretch-dependent model of accommodation presented may have utility in investigating lens behaviour at states other than the relaxed or fully-accommodated states.

Contributions of shape and stiffness to accommodative loss in the ageing human lens: a finite element model assessment

“…Contrary to the results reported by Fisher [7], Wilde et al [10] showed that the lens nucleus becomes stiffer than the lens cortex around the fourth to fifth decade of life. The present study adopts a similar modelling concept as in several previous studies [36][37][38][39] by constructing axisymmetric lens models, each with three different sections of zonular fibres. Each developed model was constructed in accordance with geometries of an intact lens rather than an assemblage of parameters from various sources [36,38,39].…”

“…The present study adopts a similar modelling concept as in several previous studies [36][37][38][39] by constructing axisymmetric lens models, each with three different sections of zonular fibres. Each developed model was constructed in accordance with geometries of an intact lens rather than an assemblage of parameters from various sources [36,38,39]. In addition, a nodal coupling mechanism was introduced to anchorage points of zonular fibres on the lens capsule, to maintain smooth curvatures at the lens periphery during simulation.…”

“…In addition, a nodal coupling mechanism was introduced to anchorage points of zonular fibres on the lens capsule, to maintain smooth curvatures at the lens periphery during simulation. Instead of attaching the three zonular fibres to a single stretching point [36][37][38][39], the three different zonular fibres were provided with the capacity to move in three independent directions. A range of displacement combinations, of 0.5mm and 0.6mm, to three different sections of the zonule were simulated for the 16-year-old lens model.…”

A Modeling Approach for Investigating Opto-Mechanical Relationships in the Human Eye Lens

“…The anterior, equatorial and posterior sections of the zonule originate from different locations on the ciliary body [4]. Yet a number of modelling approaches simplify these forces as emanating from a single point [5], [6], [7], [8], [9]. Recently it was shown that separating directions of zonular force across the three sections makes a substantial difference to the shape change and renders the modelled simulation closer to the changes in shape seen in the biological lens [10].…”

“…Almost all previous modelling studies assumed uniform distributions of material properties in the lens nucleus and cortex, and used lens models based on limited ages [5], [6], [7], [8], [9]. This study describes advanced models that correlate distributions of material properties derived from in vitro optical measurements of refractive index [23] with in vivo mechanical analyses [22].…”