Cardinal points and image-object magnification with an accommodative lens implant (1 CU)

Prediction of ocular magnification and aniseikonia after cataract surgery

BACKGROUND

Ocular magnification and aniseikonia after cataract surgery has been widely ignored in modern cataract surgery. The purpose of this study was to analyse ocular magnification and inter-individual differences in a normal cataract population with a focus on monovision.

METHODS

From a large dataset containing biometric measurements (IOLMaster 700) of both eyes of 9734 patients prior to cataract surgery, eyes were indexed randomly as primary (P) and secondary (S). Intraocular lens power (IOLP) was derived for the HofferQ, Haigis and Castrop formulae for emmetropia for P and emmetropia or myopia (-0.5 to -2 dpt) for S to simulate monovision. Based on the pseudophakic eye model in addition to these formulae, ocular magnification was extracted using matrix algebra (refraction and translation matrices and a system matrix describing the optical property of the entire spectacle corrected or uncorrected eye).

RESULTS

With emmetropia for P and S the IOLP differences (S-P) showed a standard deviation of 0.162/0.156/0.157 dpt and ocular magnification differences yielded a standard deviation of 0.0414/0.0405/0.0408 mm/mrad for the HofferQ/Haigis/Castrop setting. Simulating monovision, the myopic eye (S) showed a systematically smaller mean absolute spectacle corrected ocular magnification than the emmetropic eye (-0.0351/-0.0340/-0.0336, respectively, relative magnification around 2%). If myopia in the S eye remains uncorrected, the reduction of ocular magnification is much smaller (around 0.2-0.3%).

CONCLUSION

Vergence formulae for IOLP calculation sometimes implicitly define a pseudophakic eye model which can be directly used to predict ocular magnification after cataract surgery. Despite a strong similarity of both eyes, ocular magnification does not fully match between eyes and the prediction of ocular magnification and aniseikonia might be relevant to avoid eikonic problems in the pseudophakic eye.

Pascal's ring, cardinal points, and refractive compensation

Pascal's ring is a hexagon each of whose corners represents one of the six cardinal points of an optical system and whose sides represent relationships of relative axial position of the cardinal points. Changes to the ring represent the axial displacements of the cardinal points of the visual optical system of an eye that are caused when a spectacle lens compensates for the ametropia. Pascal's schema was described some 70 years ago with little theoretical justification. The purpose of this paper is to derive expressions for the axial locations of the cardinal points of a compound system consisting of an optical instrument and a visual optical system and for the shift caused by the instrument, and to provide theoretical justification for Pascal's schema. The cardinal points are treated not as separate entities but in a unified manner as special cases of an infinite class of special points. Expressions are derived using Gaussian optics. The results are specialized for the case of the eye's ametropia compensated by optical instruments in general and by spectacle lenses in particular. Pascal's schema is shown to be broadly correct although some modification is necessary for the effects on the incident cardinal points especially for the myopic eye.

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.

Calculations of Corneal Power After Corneo-Refractive Surgery from Keratometry and Change of Spectacle Refraction: Some Considerations on the “Clinical History Method”

PURPOSE

To derive corneal power after kerato-refractive laser surgery (KRS) to be used for a subsequent intraocular lens (IOL) power calculation.

MODEL

Based on the proportion of curvatures of the corneal front and back surface, the central thickness, and the ablation characteristics, we demonstrate a vergence-based formalism to derive the equivalent and back vertex corneal power before and after KRS from the preoperative measured keratometry. As a second option, we demonstrate in the paper how to derive the respective values from the postoperative (instead of the preoperative) measured keratometry.

EXAMPLE

Initial refraction before/after KRS, -12.0/-2.0 D; corneal thickness, 550/440 microm; front/back surface power 48.20-5.81 D, measured Zeiss keratometry before KRS, 42.5 D. After KRS, we calculate a corneal front surface power of 39.82 D and an equivalent/back vertex power and keratometry of 34.08/34.48/35.11 D (result of the "Clinical History Method" at spectacle/corneal plane 32.50/33.96 D). Calculated corneal power values are around 2-3 D lower than measured Zeiss keratometry (37.0 D), which will lead to an IOL power overestimation of about 3-4 D and subsequent hyperopia.

CONCLUSIONS

This formalism may help to prevent hyperopia after cataract surgery subsequent to refractive surgery for myopia.

Restoration of accommodation: surgical options for correction of presbyopia

Accommodation is a dioptric change in the power of the eye to see clearly at near. Ciliary muscle contraction causes a release in zonular tension at the lens equator, which permits the elastic capsule to mould the young lens into an accommodated form. Presbyopia, the gradual age-related loss of accommodation, occurs primarily through a gradual age-related stiffening of the lens. While there are many possible options for relieving the symptoms of presbyopia, only relatively recently has consideration been given to surgical restoration of accommodation to the presbyopic eye. To understand how this might be achieved, it is necessary to understand the accommodative anatomy, the mechanism of accommodation and the causes of presbyopia. A variety of different kinds of surgical procedures has been considered for restoring accommodation to the presbyopic eye, including surgical expansion of the sclera, using femtosecond lasers to treat the lens or with so-called accommodative intraocular lenses (IOLs). Evidence suggests that scleral expansion cannot and does not restore accommodation. Laser treatments of the lens are in their early infancy. Development and testing of accommodative IOLs are proliferating. They are designed to produce a myopic refractive change in the eye in response to ciliary muscle contraction either through a movement of an optic or through a change in surface curvature. Three general design principles are being considered. These are single optic IOLs that rely on a forward shift of the optic, dual optic IOLs that rely on an increased separation between the two optics, or IOLs that permit a change in surface curvature to produce an increase in optical power in response to ciliary muscle contraction. Several of these different IOLs are available and being used clinically, while many are still in research and development.

Modeling of lateral magnification changes due to changes in corneal shape or refraction

BACKGROUND AND PURPOSE

Especially after corneal surgery the lateral magnification of the eye providing the retinal image size of an object is a crucial factor influencing visual acuity and binocularity. The purpose of this study is to describe a paraxial computing scheme calculating lateral magnification changes (ratio of the image sizes before and after surgery) due to variation in corneal shape and spectacle refraction.

CALCULATION STRATEGY

From the 4 x 4 refraction and translation matrices the system matrix representing the entire 'optical system eye' and the pupil matrix describing the sub-system from the spectacle correction to the aperture stop were defined for the state before and after surgery. As the chief ray is assumed to pass through the centre of the aperture stop, the 2 x 2 matrix of the lateral magnification ratio from preoperative to postoperative is described by the 2 x 2 sub-matrices of the respective pupil matrices. The cardinal meridians can be extracted by calculating the eigenvalues and eigenvectors.

WORKING EXAMPLE

Vertex distance 14 mm, measured distance between corneal apex and aperture stop 3.6mm, keratometry 39 D+6D/0 degrees to 47D+3D/30 degrees and refraction 3.5D-5-5D/5 degrees to -4.0 D-3.5D/25 degrees preoperatively to postoperatively. The matrix of magnification ratio from preop to postop yields (0.8960 -0.0085;0.0074 0.9371) and the eigenvalues decomposition provided a 10.7% minified image at 170.1 degrees and a minified image of 6.1% at 78.7 degrees , which both are clinically relevant.

CONCLUSION

We presented a straight-forward computer-based strategy for calculation of retinal image size changes using 4 x 4 matrix notation. With this model the meridional changes in lateral magnification from the preoperative to the postoperative stage or between follow-up stages can be estimated from keratometry, refraction, vertex distance and anterior chamber depth, which might be important for binocularity and vision tests in corneal surgery.

Magnification and accommodation with phakic intraocular lenses

BACKGROUND AND PURPOSE

The calculation of phakic lenses (PL) was described by van der Heijde et al. [Klin. Monatsbl. Augenheilkd (1988) Vol. 193, pp. 99-102], but a formalism for estimating relative magnification compared with spectacle correction and accommodation effects are not yet published. The purpose of this study was to describe a mathematical strategy for calculating PL and relative magnification as a function of object vergence (phakic accommodation).

METHODS

Parameters used for the calculations are the spectacle refraction before and after (target refraction) surgery, the vertex distance, corneal refraction, and the predicted position of the phakic intraocular lens. The lens power is determined as the difference in vergences between the spectacle-corrected eye and the uncorrected eye at the reference plane of the predicted lens position. If we simplify the crystalline lens to a single refracting surface located at the principal plane of the crystalline lens, the vergence of the eye with spectacle correction and with PL is determined as a function of object distance [object vergence 0 D (infinity) to 10 D (object at a distance of 10 cm)] to evaluate accommodation effects of the crystalline lens.

RESULTS

The method was applied to two clinical examples. In example 1 we calculated the power of a PL for correction of a 10-D myopia and determined the relative magnification and the vergence at the principal plane of the crystalline lens as a function of object vergence. Magnification gain increases with objects at near from 17% to 26%, whereas the vergence at the principal plane of the crystalline lens changes by 3.04 D less than in the spectacle-corrected eye. In example 2, a 20-D myopia was corrected with a PL. The gain in magnification changed from 33% to 58% with nearer objects. The change in vergence at the principal plane of the crystalline lens with objects at near was much higher with the PL compared with the spectacle correction, which implies that the refractive change necessary for focusing objects at near distance is much higher in the PL correction.

CONCLUSIONS

Even if the predictability of postoperative refraction with PL is comparable or better than in other methods of correcting high or excessive ametropia, the effects of lateral magnification change and accommodation have to be considered to avoid image-size disparities (aniseikonia) and to maintain binocular vision, especially with monocular PL implantation and anisometropia.

Ray tracing through a schematic eye containing second-order (quadric) surfaces using 4 x 4 matrix notation

Ray tracing is used in ophthalmology for evaluation of the optical properties of the eye. We demonstrate an algebraic method for tracing a bundle of rays through the optical system of an eye containing aspheric surfaces. Restricting to second-order surfaces (quadric surfaces) such as ellipsoids, paraboloids or hyperboloids, a surface is described by a 4 x 4 matrix. In this case, the normal vector can be derived analytically and the ray-surface intersection is calculated by solving a quadratic equation. We applied this straightforward matrix-based strategy to the spherical 4-surface Le Grand schematic eye, and the Le Grand eye modified by Kooijman containing four aspheric surfaces. We calculated the spot diagram for the focal plane as well as a pre- and post-focal plane for both model eyes, and found that the optical quality of the aspheric model characterized by the ray scatter in the spot diagram at the focal plane is much better than that of the spherical model. This calculation strategy may be helpful for evaluating the image distortion of decentred or tilted spherical or aspheric artificial intra-ocular lenses.

Predicting the performance of accommodating intraocular lenses using ray tracing

PURPOSE

To predict and compare the amount of accommodation achievable by pseudophakic accommodating intraocular lenses (IOLs) using optical ray-tracing analysis.

SETTING

Computational laboratory.

METHODS

Two-element IOLs (2E-IOL, with mobile front or back optical elements) were compared with single-element IOLs (1E-IOL). Modeling using computer-assisted ray tracing of both IOL types assumed lens elements were equiconvex/equiconcave. The 4 possible combinations of configurations representing a wide range of varying positive and negative power (up to +40 diopters [D]) of front and back optical elements were evaluated.

RESULTS

The 1E-IOLs offered limited amplitude of accommodation with axial shift (approximately 1.2 D/mm). For 2E-IOLs, configurations with high positive-power front elements returned the best amplitude of accommodation (up to approximately 3.0 D/mm when the front element power was +40 D).

CONCLUSIONS

Considering the maximum potential amounts of axial shifts available, 1E-IOLs were predicted to provide 1.0 D of accommodation or less and 2E-IOLs were predicted to provide up to 3.0 D to 4.0 D depending on design configuration and amount of axial shift achievable. Potential issues relating to accommodative aniseikonia and spherical aberration have been identified.

Subjective and objective performance of the Lenstec KH-3500 "accommodative" intraocular lens

AIM

To determine whether eyes implanted with the Lenstec KH-3500 "accommodative" intraocular lenses (IOLs) have improved subjective and objective focusing performance compared to a standard monofocal IOLs.

METHODS

28 participants were implanted monocularly with a KH-3500 "accommodative" IOL and 20 controls with a Softec1 IOL. Outcome measures of refraction, visual acuity, subjective amplitude of accommodation, objective accommodative stimulus response curve, aberrometry, and Scheimpflug imaging were taken at approximately 3 weeks and repeated after 6 months.

RESULTS

Best corrected acuity with the KH-3500 was 0.06 (SD 0.13) logMAR at distance and 0.58 (0.20) logMAR at near. Accommodation was 0.39 (0.53) D measured objectively and 3.1 (1.6) D subjectively. Higher order aberrations were 0.87 (0.85) microm and lower order were 0.24 (0.39) microm. Posterior subcapsular light scatter was 0.95% (1.37%) greater than IOL clarity. In comparison, all control group measures were similar except objective (0.17 (0.13) D; p = 0.032) and subjective (2.0 (0.9) D; p = 0.009) amplitude of accommodation. Six months following surgery, posterior subcapsular scatter had increased (p<0.01) in the KH-3500 implanted subjects and near word acuity had decreased (p<0.05).

CONCLUSIONS

The objective accommodating effects of the KH-3500 IOL appear to be limited, although the subjective and objective accommodative range is significantly increased compared to control subjects implanted with conventional IOLs. However, this "accommodative" ability of the lens appears to have decreased by 6 months post-surgery.

Impact of decentration of astigmatic intra-ocular lenses on the residual refraction after cataract surgery*

PURPOSE

The purpose of this study is to assess the impact of decentration of astigmatic intra-ocular lenses on the residual refraction after cataract surgery, using a computing scheme with 5 x 5 system matrices.

METHODS

Based on the definition of an optical system in the paraxial Gaussian space containing astigmatic surfaces without restrictions to coaxiality, we derived a method (using 5 x 5 refraction and translation matrices) for calculating the residual refraction and the compensating prism in the spectacle plane after decentred implantation of thin and thick astigmatic intra-ocular lenses. The 'optical system eye' may contain astigmatic refractive surfaces with their axes at random.

RESULTS

The capabilities of this computing scheme are demonstrated with two examples. In example 1 we calculate the residual refraction of a decentred 'thin astigmatic lens' for compensation of corneal astigmatism to achieve a spherical target refraction. In example 2 we compute the residual refraction after implantation of a 'thick astigmatic lens', where the spherical and cylindrical power as well as the implantation axis of the lens do not fully match the pre-operative recommendations and the lens is decentred relative to the optical axis. For both examples, we derive the residual prismatic effect in the spectacle plane and the lateral displacement of a ray exiting the spectacle correction when starting coaxially at the retina.

CONCLUSIONS

We have presented an en bloc matrix-based strategy for the calculation of the residual spherocylindrical refraction at the spectacle plane after implantation of a decentred thin or thick astigmatic intra-ocular lens without restrictions to coaxiality. The resulting system matrix is written as a product of 5 x 5 refraction and translation matrices.

Comparisons between pharmacologically and Edinger-Westphal-stimulated accommodation in rhesus monkeys

PURPOSE

Accommodation results in increased lens thickness and lens surface curvatures. Previous studies suggest that lens biometric accommodative changes are different with pharmacological and voluntary accommodation. In this study, refractive and biometric changes during Edinger-Westphal (EW) and pharmacologically stimulated accommodation in rhesus monkeys were compared.

METHODS

Accommodation was stimulated by an indwelling permanent electrode in the EW nucleus of the midbrain in one eye each of four rhesus monkeys. Dynamic refractive changes were measured with infrared photorefraction, and lens biometric changes were measured with high-resolution, continuous A-scan ultrasonography for increasing stimulus current amplitudes, including supramaximal current amplitudes. Accommodation was then stimulated pharmacologically and biometry was measured continuously for 30 minutes.

RESULTS

During EW-stimulated accommodation, lens surfaces move linearly with refraction, with an increase in lens thickness of 0.06 mm/D, an anterior movement of the anterior lens surface of 0.04 mm/D, and a posterior movement of the posterior lens surface of 0.02 mm/D. Peak velocity of accommodation (diopters per second) and lens thickness (in millimeters per second) increased with supramaximal stimulus currents, but without further increase in amplitude or total lens thickness. After carbachol stimulation, there was initially an anterior movement of the anterior lens surface and a posterior movement of the posterior lens surface; but by 30 minutes, there was an overall anterior shift of the lens.

CONCLUSIONS

Ocular biometric changes differ with EW and pharmacological stimulation of accommodation. Pharmacological stimulation results in a greater increase in lens thickness, an overall forward movement of the lens and a greater change in dioptric power.

Determination of pseudophakic accommodation with translation lenses using Purkinje image analysis

PURPOSE

To determine pseudophakic accommodation of an accommodating posterior chamber intraocular lens (translation lens) using Purkinje image analysis and linear matrix methods in the paraxial space.

METHODS

A 2 x 2 system matrix was defined for each Purkinje image I to IV using refraction, translation and mirror matrices. Image size (m) and axial image position (z) was determined as an example for an off-axis object (a 0.2 m off-axis object located 0.5 m in front of the cornea.). First, our method was applied to the phakic relaxed (emmetropic) and accommodated (6.96 D) Le Grand eye. Secondly, for demonstration of the applicability of the calculation scheme to the pseudophakic eye, we provide a clinical example where we determine the accommodation amplitude of the translation lens (1 CU, HumanOptics, Erlangen, Germany) from photographed Purkinje images in the relaxed and accommodated state. From the biometric data: axial length 23.7 mm, corneal power 43.5, corneal thickness 550 microns, implanted intraocular lens (IOL) with a refractive power of 20.5 D (shape equi-biconvex, refractive index 1.46), and refractive indices of the cornea, aqueous and vitreous from the Le Grand model eye, we calculated the refractive state and the sizes of Purkinje images I and III initiated from two off-axis light sources.

RESULTS

For the Le Grand model eye, Purkinje image II (z/m = 3.5850 mm/0.0064) is slightly smaller than and directly in front of image I (z/m = 3.8698 mm/0.0077). Purkinje image III (z/m = 10.6097 mm/0.0151) is nearly double the size of image I and during accommodation it moves from the vitreous into the crystalline lens. Purkinje IV (z/m = 4.3244 mm/-0.0059) is inverted, three quarters the size of image I, lies in the crystalline lens and moves slightly towards the retina. For the pseudophakic eye, pseudophakic accommodation of 1.10 D was calculated from the proportion of distances between both Purkinje images I and III in the relaxed (3.04) and accommodated (2.75) state, which is in contrast to the total subjective accommodation of 2.875 D evaluated with an accommodometer.

CONCLUSIONS

We present a straightforward mathematical strategy for calculation of the Purkinje images I-IV. Results of our model calculation resemble the values provided by Le Grand. In addition, this approach yields a simple en bloc scheme for determination of pseudophakic accommodation in pseudophakic eyes with accommodative lenses (translation lenses) using Purkinje image photography.

Matrix-based calculation scheme for toric intraocular lenses

BACKGROUND AND PURPOSE

While a number of intraocular lens power prediction formulas are well established for determination of spherical lenses, no common strategy is published for the computation of toric intraocular lenses. The purpose of this study is to describe a paraxial computing scheme using 4 x 4 system matrices to describe the 'optical system eye' containing astigmatic refractive surfaces with their axes at random.

METHODS

Based on the definition of a centred optical system in the paraxial Gaussian space containing astigmatic surfaces using 4 x 4 refraction and translation matrices, we derived a methodology for calculating the refractive power of thin and thick toric intraocular lenses by solving a linear equation system. In a second step, we derived a methodology for prediction of the residual spectacle refraction after implantation of any toric lens implant with any orientation.

RESULTS

The capabilities of this computing scheme are demonstrated with three examples. In example 1 we calculate a 'thin toric lens' for compensation of a corneal astigmatism to achieve a spherical target refraction. In example 2 we compute a 'thick toric lens', which has to compensate for an oblique corneal astigmatism and rotate the spectacle cylinder to the 'against the rule' position to enhance near vision. In example 3 we predict the residual refraction at the corneal plane after implantation of a thick toric lens, when the cylinder of the lens implant is compensating the corneal cylinder in part and the axis of implantation is not fully aligned with the axis of the corneal astigmatism.

CONCLUSION

We present an en bloc matrix-based strategy for the calculation of thick or thin toric intraocular lenses, with the flexibility of crossing an unlimited number of cylinders with restrictions to paraxial optics. The resulting system matrix S is written as a product of 4 x 4 refraction and translation matrices. Residual refraction at the corneal (contact lens) or spectacle plane can be derived by inverting the order of matrices for calculation of the system matrix.

Compensation of aniseikonia with toric intraocular lenses and spherocylindrical spectacles

BACKGROUND AND PURPOSE

Magnification disparity between the two eyes (aniseikonia) is one of the major unresolved problems in modern cataract surgery, potentially degrading binocular visual function or causing diplopia. The purpose of this study is to describe a paraxial computing scheme using 4x4 system matrices to simulate a corrected pseudophakic 'optical system eye' with a meridional magnification that matches the magnification of a given contralateral eye.

METHODS

Based on the definition of a centred optical system in the paraxial Gaussian space containing astigmatic surfaces using 4x4 refraction and translation matrices, we derived a methodology for calculating the refractive power and axis of toric intraocular lenses and spherocylindrical spectacle corrections for (i) fully correcting the optical system eye and (ii) realizing an arbitrary meridional magnification by solving a linear equation system.

RESULTS

The capabilities of this computing scheme are demonstrated with two examples. In example 1 we calculate a toric lens and a spherocylindrical spectacle correction for compensation of a corneal astigmatism to realize a predefined iso-meridional magnification. In example 2 we first determine the meridional magnification of the contralateral eye, which has been treated with cataract surgery and toric lens implantation, and then we compute the appropriate combination of a fully correcting toric lens and spherocylindrical spectacle refraction, which exactly matches the meridional magnification of the contralateral eye.

CONCLUSION

We presented an en bloc matrix based strategy for the calculation of an optical system eye containing an astigmatic cornea, a toric lens implant and a spherocylindrical spectacle correction, where the toric lens and the spherocylindrical spectacle correction are determined to fully correct the system and to realize an arbitrary meridional magnification i.e. to eliminate aniseikonia.

Functional vision after cataract removal with multifocal and accommodating intraocular lens implantation

PURPOSE

To compare the efficacy (functional vision, spectacle dependence) of the Array multifocal intraocular lens (IOL) (Advanced Medical Optics) and the 1CU accommodating IOL (HumanOptics AG).

SETTING

Hartswood Hospital, Brentwood, United Kingdom.

METHODS

This prospective study comprised patients scheduled to have standard phacoemulsification surgery with IOL implantation. Patients expressing a preference for spectacle independence were allocated to the Array multifocal IOL group. Those expressing no preference received the 1CU accommodating IOL. Efficacy measures included distance and near uncorrected visual acuity (UCVA), dynamic retinoscopy, and patient-reported spectacle independence.

RESULTS

Seventeen patients (34 eyes) had bilateral implantation of the Array multifocal IOL, and 5 patients (9 eyes) had implantation of the 1CU accommodating IOL. Six to 18 months after surgery, 82.4% of eyes in the multifocal IOL group and 77.8% in the accommodating IOL group achieved a distance UCVA of 20/20 (Snellen) or better; the difference between groups was not significant. However, a significantly greater proportion in the multifocal IOL group than in the accommodating IOL group (76.5% versus 44.4%) achieved a near UCVA of N5 (Snellen 20/40) or better (P=.0068). Sixteen patients (94.1%) with Array IOLs and 2 patients (50.0%) with 1CU IOLs reported spectacle independence. Dynamic retinoscopy showed that the mean accommodative effect in the 1CU group was 0.44 diopter.

CONCLUSIONS

In this single-surgeon single-site study, a greater proportion of Array multifocal IOL recipients than 1CU IOL recipients achieved functional near visual acuity. Only 1 patient with an Array IOL required corrective spectacles at the last visit.

Pseudophakic accommodation with translation lenses - dual optic vs mono optic

PURPOSE

To investigate the pseudophakic accommodation effect in dual and mono optic translation accommodative intraocular lenses (AIOL) using linear matrix methods in the paraxial space.

METHODS

Dual (anterior optic of power +32 D linked to a compensatory posterior optic of negative power) and mono lens power was determined in the non-accommodated state using linear geometric optics based on the Gullstrand model eye. The position of the AIOL was calculated from a regression formula. Pseudophakic accommodation was assessed with three systems: (1) forward shift of the mono optic lens, (2) anterior translation of the anterior optic in the dual optic lens system with an unchanged position of the posterior minus lens and (3) symmetrical anterior and posterior translation of the anterior and posterior lens. The Gullstrand model eye was modified by changing the axial length (and proportionally changing the phakic anterior chamber depth) to investigate the accommodative effect in myopic and hyperopic eyes.

RESULTS

The dual optic lens system (2) yields a nearly constant accommodation amplitude of 2.4-2.5 D mm(-1) movement over the total range of axial lengths. The mono optic lens (1) provides a higher accommodative effect only in extremely short eyes (high refractive power of the lens), whereas for normal eyes (1.4-1.5 D mm(-1) movement) and for long (myopic) eyes the accommodative effect is much less than the dual optic lens. The dual optic lens system under condition (3) yields less accommodation amplitude compared with the dual optic system under condition (2) over the total range of axial length but provides higher accommodation amplitude compared with the mono optic lens system (1) with axial lengths greater than 22.3 mm (lens power 25.5 D). In the accommodated state, with lens translation of 1 mm, the absolute value of the lateral magnification increases with the refractive power of the mono optic lens (1) and decreases in both dual optic lens systems (under conditions 2 and 3).

CONCLUSIONS

A mathematical strategy is presented for calculation of the accommodative effect of mono-optic and dual optic AIOL. The dual optic lens yielded a nearly constant accommodation amplitude of about 2.4-2.5 D mm(-1) translation, whereas the mono optic lens yielded an accommodative response of <2 D mm(-1) translation in long myopic or normal eyes. Only in extremely short eyes is the accommodative amplitude of the mono-optic lens higher than the dual optic lens.

Difficult lens power calculations

PURPOSE OF REVIEW

Although cataract extraction seems to be feasible without major technical obstacles, the surgical technique has changed completely, and patients are no longer satisfied with good spectacle-corrected vision but anticipate complete visual rehabilitation after cataract surgery, without correction. To fulfill this desire, toric or accommodative intraocular lenses are of increasing popularity, and the intraocular lens power calculation after keratorefractive surgery has been improved.

RECENT FINDINGS

In this review article, we provide an overview of different mathematical strategies of calculating the intraocular lens power with standard formulas and with new algorithms, such as paraxial or numeric ray-tracing. These enhanced techniques may improve the validity of lens power calculation due to reduction of the prediction error, especially in cases with high or excessive corneal astigmatism and after refractive laser surgery. Furthermore, a new calculation scheme for the determination of bitoric eikonic intraocular lenses allows a distortion-free imaging in astigmatic eyes. The biometric determinants for the different formulas and calculation schemes are discussed in detail.

SUMMARY

In difficult cases, standard calculation schemes are overemployed and new mathematical algorithms are necessary to adequately address these problems. Ray-tracing algorithms and other complex mathematical computation schemes are of increasing interest and will more and more replace conventional calculation formulas for determination of intraocular lens power.