Predicting the performance of accommodating intraocular lenses using ray tracing

Clinical application of accommodating intraocular lens

The present review describes recent advances in application of accommodating intraocular lenses (AIOLs). Standard monofocal intraocular lenses (MIOLs) only correct distance vision, while AIOLs are designed to allow both good distance vision and near vision, which is achieved through the contraction and relaxation of ciliary muscles by providing transformation of the axial movement or curvature of the lens. Thus, AIOLs may be a better choice for those patients who demand a higher level of visual performance. Since techniques to analyze the performance of AIOLs have not been standardized, and there is a variety of both subjective and objective methods, it is hard to measure the performance of these intraocular lenses. By evaluating advantages and disadvantages of various AIOLs, and introducing techniques for measurement the performance postoperative, this paper can provide some relative information on choosing the type of AIOLs in the clinic.

Human eye ocular component analysis for refractive state and refractive surgery

AIM

To analyze the clinical factors influencing the human vision corrections via the changing of ocular components of human eye in various applications; and to analyze refractive state via a new effective axial length.

METHODS

An effective eye model was introduced by the ocular components of human eye including refractive indexes, surface radius (r1, r2, R1, R2) and thickness (t, T) of the cornea and lens, the anterior chamber depth (S1) and the vitreous length (S2). Gaussian optics was used to calculate the change rate of refractive error per unit amount of ocular components of a human eye (the rate function M). A new criterion of myopia was presented via an effective axial length.

RESULTS

For typical corneal and lens power of 42 and 21.9 diopters, the rate function Mj (j=1 to 6) were calculated for a 1% change of r1, r2, R1, R2, t, T (in diopters) M1=+0.485, M2=-0.063, M3=+0.053, M4=+0.091, M5=+0.012, and M6=-0.021 diopters. For 1.0 mm increase of S1 and S2, the rate functions were M7=+1.35, and M8=-2.67 diopter/mm, respectively. These rate functions were used to analyze the clinical outcomes in various applications including laser in situ keratomileusis surgery, corneal cross linking procedure, femtosecond laser surgery and scleral ablation for accommodation.

CONCLUSION

Using Gaussian optics, analytic formulas are presented for the change of refractive power due to various ocular parameter changes. These formulas provide useful clinical guidance in refractive surgery and other related procedures.

Axial movement of the dual-optic accommodating intraocular lens for the correction of the presbyopia: optical performance and clinical outcomes

Presbyopia occurs in the aging eye due to changes in the ciliary muscle, zonular fibers, crystalline lens, and an increased lens sclerosis. As a consequence, the capacity of accommodation decreases, which hampers to focus near objects. With the aim of restoring near vision, different devices that produce multiple focuses have been developed and introduced. However, these devices are still unable to restore accommodation. In order to achieve that goal, dual-optic accommodating Intraocular Lenses have been designed, whose anterior optic displaces axially to increase ocular power, and focus near objects. Although dual-optic accommodating IOLs are relatively new, their outcomes are promising, as they provide large amplitudes of accommodation and a greater IOL displacement than single-optic accommodating IOLs. The outcomes show comfortable near vision, higher patients' satisfaction rates, and minimal postoperative complications like Posterior Capsular Opacification and Anterior Capsular Opacification, due to their design and material.

Aberrometry in patients implanted with accommodative intraocular lenses

PURPOSE

To evaluate the objective accommodative response, change of aberrations, and depth of focus in eyes implanted with the Crystalens accommodative intraocular lens (IOL) at different accommodative demands.

DESIGN

Prospective, observational study.

METHODS

Eleven cataract patients (22 eyes) who underwent implantation of a Crystalens accommodative IOL, and control groups of 9 normal subjects (17 eyes) and 17 pseudophakic patients (17 eyes) implanted with monofocal IOLs were evaluated. A custom-developed laser ray tracing aberrometer was used to measure the optical aberrations. The monochromatic wave aberrations were described using a sixth-order Zernike polynomial expansion. Measurements were obtained under dilated and natural viewing conditions (for accommodative efforts ranging from 0 to 2.5 diopters [D]). The accommodative response was obtained by analyzing changes in paraxial defocus (associated to changes in defocus) and by evaluating the differences in the effective defocus (associated with defocus, spherical aberrations, and pupil diameter) with the accommodative demand. Depth of focus was estimated from through-focus objective optical quality.

RESULTS

Wave aberration measurements were highly reproducible. Vertical trefoil (Z3(-3)) was the predominant higher-order aberration in the Crystalens group and significantly higher (P < .0001) than in the young group, but similar to the monofocal IOL group. The coma root mean square also was higher (P < .005) in the Crystalens group than in the young group. On average, the defocus term (Z2(0)), astigmatism, or higher-order aberrations did not change systematically with accommodative demand in Crystalens eyes. As found for paraxial defocus, the effective defocus in Crystalens eyes did not show significant differences between conditions: 0.34 ± 0.48 D (far), 0.32 ± 0.50 D (intermediate), and 0.34 ± 0.44 D (near). Depth of focus was statistically significantly higher in the Crystalens eyes than in the control groups.

CONCLUSIONS

The accommodative response of eyes implanted with the Crystalens accommodative IOLs, measured objectively using laser ray tracing aberrometry, was lower than 0.4 D in all eyes. Several subjects showed changes in astigmatism, spherical aberration, trefoil, and coma with accommodation, which must arise from geometrical and alignment changes in the lens with accommodative demand. Pseudoaccommodation from increased depth of focus may contribute to near vision functionality in Crystalens-implanted patients.

Advances in lens implant technology

Cataract surgery is one of the oldest and the most frequent outpatient clinic operations in medicine performed worldwide. The clouded human crystalline lens is replaced by an artificial intraocular lens implanted into the capsular bag. During the last six decades, cataract surgery has undergone rapid development from a traumatic, manual surgical procedure with implantation of a simple lens to a minimally invasive intervention increasingly assisted by high technology and a broad variety of implants customized for each patient’s individual requirements. This review discusses the major advances in this field and focuses on the main challenge remaining – the treatment of presbyopia. The demand for correction of presbyopia is increasing, reflecting the global growth of the ageing population. Pearls and pitfalls of currently applied methods to correct presbyopia and different approaches under investigation, both in lens implant technology and in surgical technology, are discussed.

Comparison of retinal image quality with spherical and customized aspheric intraocular lenses

We hypothesize that an intraocular lens (IOL) with higher-order aspheric surfaces customized for an individual eye provides improved retinal image quality, despite the misalignments that accompany cataract surgery. To test this hypothesis, ray-tracing eye models were used to investigate 10 designs of mono-focal single lens IOLs with rotationally symmetric spherical, aspheric, and customized surfaces. Retinal image quality of pseudo-phakic eyes using these IOLs together with individual variations in ocular and IOL parameters, are evaluated using a Monte Carlo analysis. We conclude that customized lenses should give improved retinal image quality despite the random errors resulting from IOL insertion.

Paraxial analysis of the depth of field of a pseudophakic eye with accommodating intraocular lens

PURPOSE

To investigate the depth of field of pseudophakic eye implanted with translating optics accommodating intraocular lenses (AIOLs).

METHODS

Theoretical analyses using paraxial optics equations were used. The crystalline lens in the Navarro eye model was replaced with an AIOL modeled as a thin-lens system with either a single lens element (1E-AIOL) or two element (2E-AIOL). To quantify the depth of field, a reference limit for retinal blur circle diameter was adopted from typical values of depth of field of the normal eye. Effect of various factors including AIOL type, lens element power, implant position, and pseudophakic accommodation on depth of field were analyzed.

RESULTS

Depth of field increased with more posterior positioning of the AIOL and decreased with pseudophakic accommodation by translation of optics. However, the changes did not exceed 0.02 D over the range of factors tested. Effective depth of field, defined as the magnification adjusted depth of field, is relatively independent of the implant position and power combination of AIOL. Effects of varying design factors on the depth of field of AIOL are too small to be clinically observable.

CONCLUSIONS

Although depth of field extends the range of near vision with AIOL, varying design and surgical factors such as depth of implantation and optical power of lens element(s) within clinically practical limits modifies depth of field by an insignificant amount. In the practical sense, attempting to enhance the depth of field of AIOL by varying design factors such as the position of implantation would be unrewarding.

Vergence analysis reveals the influence of axial distances on accommodation with age and axial ametropia

Despite numerous investigations, the aetiology and mechanism of accommodation and presbyopia remains equivocal. Using Gaussian first-order ray tracing calculations, we examine the contribution that ocular axial distances make to the accommodation response. Further, the influence of age and ametropia are also considered. The data show that all changes in axial distances during accommodation reduce the accommodation response, with the reduction in anterior chamber depth contributing most to this overall attenuation. Although the total power loss due to the changes in axial distances remained constant with increasing age, hyperopes exhibited less accommodation than myopes. The study, therefore, enhances our understanding of biometric accommodative changes and demonstrates the utility of vergence analysis in the assessment of accommodation.

Analysis and applications of accommodative lenses for vision corrections

Analysis and applications of vision correction via accommodating intraocular lens (AIOL) are presented. By Gaussian optics, analytic formulas for the accommodation rate function (M) for two-optics and three-optics systems are derived and compared with the exact numerical results. In a single-optics AIOL, typical value of M is (0.5-1.5) D∕mm, for an IOL power of (10-20) diopter. For a given IOL power, higher M is achieved in positive-IOL than negative-IOL. In the dual-optics AIOL, maximum accommodation is predicted when the front positive-optics moves toward the corneal plan and the back negative-optics moves backward. Our analytic formulas predict that greater accommodative rate may be achieved by using a positive-powered front optics, a general feature when either front or back optics is mobile. The M function is used to find the piggy-back IOL power for customized design based on the individual ocular parameters. Many of the new features demonstrated in this study can be easily realized by our analytic formulas, but not by raytracing method.

Magnifications of single and dual element accommodative intraocular lenses: paraxial optics analysis

PURPOSE

Using an analytical approach of paraxial optics, we evaluated the magnification of a model eye implanted with single-element (1E) and dual-element (2E) translating-optics accommodative intraocular lenses (AIOL) with an objective of understanding key control parameters relevant to their design. Potential clinical implications of the results arising from pseudophakic accommodation were also considered.

METHODS

Lateral and angular magnifications in a pseudophakic model eye were analyzed using the matrix method of paraxial optics. The effects of key control parameters such as direction (forward or backward) and distance (0 to 2 mm) of translation, power combinations of the 2E-AIOL elements (front element power range +20.0 D to +40.0 D), and amplitudes of accommodation (0 to 4 D) were tested. Relative magnification, defined as the ratio of the retinal image size of the accommodated eye to that of unaccommodated phakic (rLM(1)) or pseudophakic (rLM(2)) model eyes, was computed to determine how retinal image size changes with pseudophakic accommodation.

RESULTS

Both lateral and angular magnifications increased with increased power of the front element in 2E-AIOL and amplitude of accommodation. For a 2E-AIOL with front element power of +35 D, rLM(1) and rLM(2) increased by 17.0% and 16.3%, respectively, per millimetre of forward translation of the element, compared to the magnification at distance focus (unaccommodated). These changes correspond to a change of 9.4% and 6.5% per dioptre of accommodation, respectively. Angular magnification also increased with pseudophakic accommodation. 1E-AIOLs produced consistently less magnification than 2E-AIOLs. Relative retinal image size decreased at a rate of 0.25% with each dioptre of accommodation in the phakic model eye. The position of the image space nodal point shifted away from the retina (towards the cornea) with both phakic and pseudophakic accommodation.

CONCLUSION

Power of the mobile element, and amount and direction of the translation (or the achieved accommodative amplitude) are important parameters in determining the magnifications of the AIOLs. The results highlight the need for caution in the prescribing of AIOL. Aniso-accommodation or inter-ocular differences in AIOL designs (or relative to the natural lens of the contralateral eye) may introduce dynamic aniseikonia and consequent impaired binocular vision. Nevertheless, some designs, offering greater increases in magnification on accommodation, may provide enhanced near vision depending on patient needs.

Functionalised polysiloxanes as injectable, in situ curable accommodating intraocular lenses

The aged eye's ability to change focus (accommodation) may be restored by replacing the hardened natural lens with a soft gel. Functionalised polysiloxane macromonomers, designed for application as an injectable, in situ curable accommodating intraocular lens (A-IOL), were prepared via a two-step synthesis. Prepolymers were synthesised via ring opening polymerisation (ROP) of octamethylcyclotetrasiloxane (D(4)) and 2,4,6,8-tetramethylcyclotetrasiloxane (D(4)(H)) in toluene using trifluoromethanesulfonic acid (TfOH) as catalyst. Hexaethyldisiloxane (HEDS) was used as the end group to control the molecular weight of the prepolymers, which were then converted to macromonomers by hydrosilylation of the SiH groups with allyl methacrylate (AM) to introduce polymerisable groups. The resulting macromonomers had an injectable consistency and thus, were able to be injected into and refill the empty lens capsular bag. The macromonomers also contained a low ratio of polymerisable groups so that they may be cured on demand, in situ, under irradiation of blue light, in the presence of a photo-initiator, to form a soft polysiloxane gel (an intraocular lens) in the eye. The pre-cure viscosity and post-cure modulus of the polysiloxanes, which are crucial factors for an injectable, in situ curable A-IOL application, were controlled by adjusting the end group and D(4)(H) concentrations, respectively, in the ROP. The macromonomers were fully cured within 5 min under light irradiation, as shown by the rapid change in modulus monitored by photo-rheology. Ex vivo primate lens stretching experiments on an Ex Vivo Accommodation Simulator (EVAS) showed that the polysiloxane gel refilled lenses achieved over 60% of the accommodation amplitude of the natural lens. An in vivo biocompatibility study in rabbits using the lens refilling (Phaco-Ersatz) procedure demonstrated that the soft gels had good biocompatibility with the ocular tissue. The polysiloxane macromonomers meet the targeted optical and mechanical properties of a young natural crystalline lens and show promise as candidate materials for use as injectable, in situ curable A-IOLs for lens refilling procedures.

Evaluation of the performance of accommodating IOLs using a paraxial optics analysis

PURPOSE

We employed an analytical approach to evaluate the key parameters for the potential design optimisation of accommodating intra-ocular lenses (AIOL) and to use these parameters to predict their accommodative performance.

METHODS

Paraxial thin-lens equations to predict the accommodative performances of single-element (1E) and two-element (2E) AIOLs were developed. 2E-AIOLs with either mobile front or back lens elements were analysed as well as 1E-AIOL for their accommodative performance. A paraxial model including key ocular components (corneal surfaces, pupil and retina) as well as AIOL was used to evaluate the key control parameters and optimal design configurations. A range of variants of the model, representing varying powers of front and back optical elements and with either front or back optical element mobile was tested.

RESULTS

Optimal accommodative performance of 2E-AIOL is governed by the power combinations of its optical elements; design variants with higher positive front element power produced greater accommodative efficacy, while mobility of the front element contributed more to the accommodative performance than the back element. The performance of 1E-AIOL is primarily governed by the power of the AIOL; the higher the AIOL power, the better the accommodative performance.

CONCLUSIONS

From an accommodative performance standpoint, the optimal design of 2E-AIOL should comprise a high plus power front element. Considering the maximum potential amounts of element translation available clinically, 2E-AIOLs are predicted to offer higher accommodative performance compared to 1E-AIOL.

Comparison of the behavior of natural and refilled porcine lenses in a robotic lens stretcher

The mechanism by which the eye dynamically changes focal distance (accommodation), and the mechanism by which this ability is lost with age (presbyopia), are still contested. Due to inherent confounding factors in vivo, in vitro measurements have been undertaken using a robotic lens stretcher to examine these mechanisms as well as the efficacy of lens refilling - a proposed treatment for presbyopia. Dynamic forces, anterior and posterior curvatures, and lens thickness are all correlated for young natural and refilled porcine lenses. Comparisons are made to lenses refilled with a homogeneous polymer system. The amplitude of accommodation of the young porcine lens is very small such that it may be a suitable model for presbyopia. The behavior of refilled lenses was highly dependent on the refill volume. The volume could be tuned to maximize accommodative amplitude in the refilled lens.