Mechanism of human accommodation as analyzed by nonlinear finite element analysis

Simultaneous Measurement of Objective and Subjective Accommodation in Response to Step Stimulation

Purpose

This study aimed to evaluate differences in objective and subjective accommodation dynamically and simultaneously.

Methods

Thirty-four pre-presbyopic healthy volunteers (mean age ± SD, 41.0 ± 3.2 years) participated in this study. Initially, the reaction time for detecting a change in the target was measured at near. Dynamic accommodation was then monocularly recorded using an open-view Shack-Hartmann aberrometer and compared with the amplitude and velocity of subjective accommodation.

Results

The objective amplitude of accommodation (0.97 ± 0.32 diopter [D]) was significantly greater than the subjective amplitude of accommodation (0.62 ± 0.43 D; P < 0.001). The accommodative velocity was significantly faster for the "before the accommodation" response time (0.47 ± 0.38 D/s) than the "after the accommodation" response time (0.21 ± 0.22 D/s; P = 0.007).

Conclusions

The human eye under the monocular condition quickly adjusts to the focal plane to clearly archive the nearby object, and the focal plane thereafter is slowly and accurately adjusted to the visual target after visual recognition.

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

OBJECTIVE

The human visual system alters its focus by a shape change of the eye lens. The extent to which the lens can adjust ocular refractive power is dependent to a significant extent on its material properties. Yet, this fundamental link between the optics and mechanics of the lens has been relatively under-investigated. This study aims to investigate this opto-mechanical link within the eye lens to gain insight into the processes of shape alteration and their respective decline with age.

METHODS

Finite Element models based on biological lenses were developed for five ages: 16, 35, 40, 57, and 62 years by correlating in vivo measurements of the longitudinal modulus using Brillouin scattering with in vitro X-ray interferometric measurements of refractive index and taking into account various directions of zonular force.

RESULTS

A model with radial cortical Young's moduli provides the same amount of refractive power with less change in thickness than a model with uniform cortical Young's modulus with a uniform stress distribution and no discontinuities along the cortico-nuclear boundary. The direction of zonular angles can significantly influence curvature change regardless of the modulus distribution.

CONCLUSIONS

The present paper proposes a modelling approach for the human lens, coupling optical and mechanical properties, which shows the effect of parameter choice on model response.

SIGNIFICANCE

This advanced modelling approach, considering the important interplay between optical and mechanical properties, has potential for use in design of accommodating implant lenses and for investigating non-biological causes of pathological processes in the lens (e.g., cataract).

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

Ageing changes to the various components of the accommodative system of the eye lens contribute to the loss of focusing power. The relative contributions of each ageing component, however, are not well defined. This study investigates the contribution of geometric parameters and material properties on accommodation, simulated using models based on human lenses aged 16, 35, and 48 years. Each model was tested using two different sets of material properties and a range of zonular fiber angles and was compared to results from in vivo measurements. The geometries and material parameters of older and younger lens models were interchanged to investigate the role of shape and material on accommodative capacity. Results indicate that geometry has the greater role in accommodation.

Advances and challenges of intraocular lens design [Invited]

Phacoemulsification technique with intraocular lens implantation has been a common treatment for cataract patients. With rising demand among the public, new technologies for lens design have emerged to minimize intraocular aberrations, improving visual quality to the largest extent. This paper systematically reviews the development of materials applied in lens manufacturing, the different categories of intraocular lenses, and respective design principles. The advantages and potential drawbacks of intraocular lenses are illustrated in the paper, and prospective research to improve the design are presented in the end.

The importance of parameter choice in modelling dynamics of the eye lens

The lens provides refractive power to the eye and is capable of altering ocular focus in response to visual demand. This capacity diminishes with age. Current biomedical technologies, which seek to design an implant lens capable of replicating the function of the biological lens, are unable as yet to provide such an implant with the requisite optical quality or ability to change the focussing power of the eye. This is because the mechanism of altering focus, termed accommodation, is not fully understood and seemingly conflicting theories require experimental support which is difficult to obtain from the living eye. This investigation presents finite element models of the eye lens based on data from human lenses aged 16 and 35 years that consider the influence of various modelling parameters, including material properties, a wide range of angles of force application and capsular thickness. Results from axisymmetric models show that the anterior and posterior zonules may have a greater impact on shape change than the equatorial zonule and that choice of capsular thickness values can influence the results from modelled simulations.

Gradient moduli lens models: how material properties and application of forces can affect deformation and distributions of stress

The human lens provides one-third of the ocular focussing power and is responsible for altering focus over a range of distances. This ability, termed accommodation, defines the process by which the lens alters shape to increase or decrease ocular refractive power; this is mediated by the ciliary muscle through the zonule. This ability decreases with age such that around the sixth decade of life it is lost rendering the eye unable to focus on near objects. There are two opponent theories that provide an explanation for the mechanism of accommodation; definitive support for either of these requires investigation. This work aims to elucidate how material properties can affect accommodation using Finite Element models based on interferometric measurements of refractive index. Gradients of moduli are created in three models from representative lenses, aged 16, 35 and 48 years. Different forms of zonular attachments are studied to determine which may most closely mimic the physiological form by comparing stress and displacement fields with simulated shape changes to accommodation in living lenses. The results indicate that for models to mimic accommodation in living eyes, the anterior and posterior parts of the zonule need independent force directions. Choice of material properties affects which theory of accommodation is supported.

Hyperelastic modelling of the crystalline lens: Accommodation and presbyopia

Purpose

The modification of the mechanical properties of the human crystalline lens with age can be a major cause of presbyopia. Since these properties cannot be measured in vivo, numerical simulation can be used to estimate them. We propose an inverse method to determine age-dependent change in the material properties of the tissues composing the human crystalline lens.

Methods

A finite element model of a 30-year-old lens in the accommodated state was developed. The force necessary to achieve full accommodation in a 30-year-old lens of known external geometry was computed using this model. Two additional numerical models of the lens corresponding to the ages of 40 and 50 years were then built. Assuming that the accommodative force applied to the lens remains constant with age, the material properties of nucleus and cortex were estimated by inverse analysis.

Results

The zonular force necessary to reshape the model of a 30-year-old lens from the accommodated to the unaccommodated geometry was 0.078 newton (N). Both nucleus and cortex became stiffer with age. The stiffness of the nucleus increased with age at a higher rate than the cortex.

Conclusions

In agreement with the classical theory of Helmholtz, on which we based our model, our results indicate that a major cause of presbyopia is that both nucleus and cortex become stiffer with age; therefore, a constant value of the zonular forces with aging does not achieve full accommodation, that is, the accommodation capability decreases.

Aspects of eye accommodation evaluated by finite elements

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.

Three-dimensional ultrasound biomicroscopy, environmental and conventional scanning electron microscopy investigations of the human zonula ciliaris for numerical modelling of accommodation

PURPOSE

Biomechanical modelling of the accommodation process is a useful tool for studying the mechanism of accommodation and presbyopia and can aid in the development of accommodative lens-replacing materials. Existing biomechanical models, however, use a very simplified zonula structure. The aim of this study was to use three-dimensional ultrasonic imaging and scanning electron microscopy to provide a more detailed, three-dimensional description of the structure of the human zonula to improve the modelling of accommodation.

METHODS

Five human eyes were examined without invasive manipulation using a custom-made three-dimensional ultrasonic imaging technique that allows scanning of features with a spatial resolution of 30 microm. Environmental and conventional scanning electron microscopy (SEM) provided information to complement the ultrasonic images for use in development of a more anatomically correct finite-element model of the zonula structures. These data along with the material properties of the ocular tissue structures were used to construct an advanced geometric model for finite-element simulation of the accommodation process.

RESULTS

Images were obtained through three-dimensional ultrabiomicroscopy (3D-UBM) of anatomical features heretofore not directly imagable in their native state. Ciliary processes and zonula structures were clearly separated by both the 3D-UBM and the SEM methods. It was found that fibres inserting on the anterior and posterior lens capsule emerge anteriorly at the ciliary body. Fibres emerging near the pars plana insert on the lens and the ciliary body. No X-shaped crossing fibres were found. Modelling of the accommodation process with both the simple and the more complex geometric models produced refractive power changes comparable with in vivo findings.

CONCLUSIONS

The 3D-UBM allowed examination of zonula structures in their native state with minimized preparation artefacts. While these data were incorporated into a complex and more anatomically correct finite-element simulation of intraocular features including lens, zonular system and ciliary body it was found that a simplified zonular model is sufficient for the numerical simulation of the accommodation process.

Modelling the mechanics of accommodation and presbyopia

Finite element methods have been used to compute the expected relationship between changes in ciliary body diameter and the change in refractive power implied by the change in geometry of the human ocular lens, using values for the material properties and initial geometry taken from the literature (notably the slit lamp photography of Brown (1973) and the studies by Fisher (1969) of the lens material properties). The results show that if the non-linearity associated with the changing geometry is taken into account the lens does not respond to ciliary body stretch by an increase in power [as recently claimed by Schachar et al. (1993), but in the conventional way with a decrease in power. The models show a decrease in the amplitude of accommodation between the age of 29 and 45 years (using Brown's data, 1973), but using Brown's data for the 11-year-old eye leads to the paradoxical conclusion that accommodation amplitude in this eye would have been small. In the process of carrying out the modelling, we have examined the consistency of the published measurements and also the validity of the mathematical methods used in interpreting them, and this analysis suggests that further work is needed before one can be confident that the assumptions about geometry and material properties on which the modelling is based are sound.

Numerical modelling of the accommodating lens

Data on geometric and material properties of the human lens derived from various published sources are used to construct axisymmetric, large displacement, finite element models of the accommodating lens of subjects aged 11, 29 and 45 years. The nucleus, cortex, capsule and zonule are modelled as linearly elastic materials. The numerical model of the 45-year lens is found to be significantly less effective in accommodating than the 29-year lens, suggesting that the modelling procedure is capable of capturing at least some of the features of presbyopia. The model of the 11-year lens shows some anomalous behaviour, and reasons for this are explored.