Journal of Refractive Surgery

Translational Science Supplemental Data

Analysis of the Optical Quality of Spherical and Aspheric Intraocular Lenses in Simulated Nanophthalmic Eyes

Bruno Lovaglio Cançado Trindade, MD; Felipe Tayer Amaral, PhD; Davies William de Lima Monteiro, PhD

Abstract

PURPOSE:

To analyze the optical performance of different implant strategies in simulated nanophthalmic eyes.

METHODS:

An optical design software was used. Analysis included eye models that required 30.00, 45.00, and 60.00 diopters (D) intraocular lenses (IOLs) to achieve emmetropia. Spherical and aspheric IOLs were designed. They were tested either with a single implant setting S or by splitting the power into two lenses. Setting P1 had an even split of the power between the lenses and setting P2 had an uneven power split with one-third of the power in the anterior lens and two-thirds in the posterior IOL. The area under the modulation transfer function (MTF) curve was calculated and spherical aberration was recorded in each setting.

RESULTS:

Setting S had the worst optical performance in the spherical group and the best performance in the aspheric group. A statistically significant difference was found between setting S and the piggyback options (settings P1 and P2) in all analyzed variables for the spherical and aspheric groups for the 45.00 and 60.00 D IOL requirement. No statistically significant difference was found between the piggyback settings.

CONCLUSIONS:

Single aspheric IOLs had better optical performance than piggybacking lower-power aspheric IOLs. In the spherical lenses group, the results were the opposite, with the piggyback options having higher optical quality than the single IOL. MTF shows that single aspheric lenses provide the highest contrast sensitivity among all of the analyzed settings.

[J Refract Surg. 2016;32(3):193–200.]

Abstract

PURPOSE:

To analyze the optical performance of different implant strategies in simulated nanophthalmic eyes.

METHODS:

An optical design software was used. Analysis included eye models that required 30.00, 45.00, and 60.00 diopters (D) intraocular lenses (IOLs) to achieve emmetropia. Spherical and aspheric IOLs were designed. They were tested either with a single implant setting S or by splitting the power into two lenses. Setting P1 had an even split of the power between the lenses and setting P2 had an uneven power split with one-third of the power in the anterior lens and two-thirds in the posterior IOL. The area under the modulation transfer function (MTF) curve was calculated and spherical aberration was recorded in each setting.

RESULTS:

Setting S had the worst optical performance in the spherical group and the best performance in the aspheric group. A statistically significant difference was found between setting S and the piggyback options (settings P1 and P2) in all analyzed variables for the spherical and aspheric groups for the 45.00 and 60.00 D IOL requirement. No statistically significant difference was found between the piggyback settings.

CONCLUSIONS:

Single aspheric IOLs had better optical performance than piggybacking lower-power aspheric IOLs. In the spherical lenses group, the results were the opposite, with the piggyback options having higher optical quality than the single IOL. MTF shows that single aspheric lenses provide the highest contrast sensitivity among all of the analyzed settings.

[J Refract Surg. 2016;32(3):193–200.]

Intraocular lenses (IOLs) are commercially available in a limited range of dioptric powers, which usually covers the convergence needs of most eyes undergoing cataract surgery. Some IOL models have an extended power availability, but they are often limited to +40.00 diopters (D). The calculated IOL power can exceed the available range of commercial models. This occurs when high levels of hyperopic refraction are present,1 and especially in nanophthalmic eyes.

The definition of nanophthalmia is somewhat confusing and does not always reflect clinical differences. Classic concept defines nanophthalmia as eyes having axial lengths lower than two standard deviations of a normal population.2–4 Parrish et al. differentiated between three separate groups of short eyes.5 The first group has normal anterior chamber depth (ACD) but short axial length and is named axial high hyperopia. The second group has short ACD but normal axial length, and is named relative anterior microphthalmos. The third group has short ACD and axial length and is named nanophthalmos or colobomatous or complex microphthalmos depending on associated congenital malformations. Although the first group behaves as a normal eye with only a refractive error issue, the latter two have a tendency toward angle-closure glaucoma and are more prone to surgical and postoperative complications.6–8

Faucher et al. reported a medium-sized series of nanophthalmic eyes with axial lengths ranging from 15.67 to 17.61 mm (average: 16.52 mm) and mean keratometry value of 48.95 D with a maximum value of 50.0 D.9 In their series of nanophthalmic eyes, Singh et al. found an average refractive error of +13.60 D (range: +7.25 to +20.00 D).10 Mean posterior chamber IOL power in another small adult eyes series was found to be +36.00 D (range: 35.00 to 49.00 D).11

Cataract surgery on these eyes presents several difficulties8,10 because they exhibit not only a short axial length but also thickened sclera, shallow anterior chamber, iris convexity, and high lens-to-eye ratio.8,10,12 Weakened zonules and a crowded anterior segment are also a surgical challenge13; nevertheless, in cases where a high-power IOL is needed, primary piggyback implantation of two or more lenses has been proposed by various authors.1,12,14,15 They advocate that a high-power IOL would introduce high amounts of optical aberration and produce image blur.12,14,16,17

In comparison to lower-powered lenses, high power spherical IOLs present higher spherical aberration that degrades the image quality.15,16 That limits the availability of higher-powered lenses due to the difficulty on passing modulation transfer function (MTF) standards with an IOL power of greater than +34.00 D. To minimize that, aspheric surfaces can be manufactured with computerized numerical control turning technologies, yielding better optical resolution.

To the authors' knowledge, there is no published study to date that analyzes the optical quality of the different options of implants for nanophthalmic eyes, comparing spherical and aspheric single high-power and piggyback IOLs. This study analyzes the optical quality of different types of implant options. Both spherical and aspheric IOLs were assessed. The aspheric design tested induced zero IOL spherical aberration, thus leaving the eyes with some positive residual spherical aberration. This way it is possible to draw conclusions based on the newest available profiles.

Materials and Methods

An optical design software (version 13.0; Radiant Zemax, LLC, Redmond, WA) was used to design and test the optical performance of different types of IOLs.

Based on the literature on nanophthalmia, we tested the implants on three different sets of eyes. First, a set of short eyes with axial lengths varying from 22.07 to 20.10 mm that needed a 30.00 D lens to achieve emmetropia (30.00 D set). Second, a set of shorter eyes (19.34 to 17.94 mm) that needed a 45.00 D lens to achieve emmetropia (45.00 D set). Third, a set of even shorter eyes (17.46 to 16.39 mm) that needed a 60.00 D lens to achieve emmetropia (60.00 D set). Because we tested different axial lengths, corneal keratometric power (K) was varied to maintain the IOL power to achieve emmetropia constant and equal to 30.00, 45.00, and 60.00 D, respectively, in each set.

For all sets of eyes, the required IOL power was tested under three different conditions: a single lens with the full required power (setting S) and two different piggyback options. The first had an even split of the power between two separate lenses (setting P1) and the second had an uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens (setting P2).

Lens Design

The IOLs were designed in two separate groups: spherical and aspheric. Each group had eight different dioptric power IOLs (10.00, 15.00, 20.00, 22.50, 30.00, 40.00, 45.00, and 60.00 D). The lenses were designed as follows.

First, a set of anterior and posterior curvatures were chosen to guarantee the desired dioptric power using the equation shown:

ΦIOL=(nIOL−naq)Rant+(nvit−nIOL)Rpos−[(nIOL−naq)Rant⋅(naq−nIOL)Rpos⋅tIOLnIOL]
where ϕIOL is the IOL dioptric power in diopters; nIOL, naq, and nvit are the IOL, aqueous humor, and vitreous refractive index, respectively; Rant and Rpos are the IOL anterior and posterior radii of curvature given in meters, respectively; and tIOL is the IOL center thickness given in meters.

Anterior (aqueous) and posterior (vitreous) refractive index were 1.336 and the IOL refractive index chosen was 1.50. The edge thickness was maintained constant and equal to 0.4 mm.

The lenses were then optimized using a 6-mm pupil diameter to achieve the smallest root mean square wavefront error. Optimization variables were the anterior and posterior radii of curvature in the spherical group and anterior and posterior radii of curvature and conic constants for both surfaces in the aspheric group. Hence, the resulting aspheric IOLs had null spherical aberration.

This process was repeated for each chosen dioptric power.

Table A (available in the online version of this article) shows the induced spherical aberration for each IOL power in the spherical and aspheric groups.

Spherical Aberration Induced by Each IOL Power (µm)

Table A:

Spherical Aberration Induced by Each IOL Power (µm)

Nanophthalmic Eye Models

A modified pseudophakic Liou and Brennan eye model was used to test the implant options. This model was chosen because its surfaces correctly represent the anatomical structures of the eye. This way, it is easier to transform it into pseudophakic and to modify it to better simulate a nanophthalmic eye. Pupil decentration and globe rotation were not considered because our main interest was to compare the relative optical performance of different implant strategies in an already highly aberrated eye. Taking these deviations into account would add a considerable amount of aberrations that would sacrifice precision.

A Matlab (MathWorks, Natick, MA) code was written to create the 30.00, 45.00, and 60.00 D set of eye models. First, a modified Liou and Brennan eye model was loaded in the Zemax program (Table B, available in the online version of this article) and one of the aspheric lenses (either 300, 45.00, or 60.00 D) previously designed was inserted into the eye model. The ACD (central corneal epithelium to anterior lens surface) was set to 3.95 mm because this was the average value found by Chang et al.18 Then, K was varied between 40.00 and 47.00 D in 0.25-D steps, keeping the anterior to posterior curvature ratio constant using a refractive index of 1.376 and a central corneal thickness of 0.500 mm. For each refractive value, autofocus was applied to create different axial lengths while maintaining the implant in a constant position. Pupil diameter size was set to 1-mm to limit the autofocus to paraxial rays only. After focusing, pupil diameter was restored to 3 mm. This way, we ended up with three different sets of eye models (30.00, 45.00, and 60.00), each containing 29 eyes that shared the same dioptric power requirement to achieve emmetropia.

Modified Liou and Brennan Eye Model Characteristics With 60.00 D Aspheric IOL and a 5-mm Pupil

Table B:

Modified Liou and Brennan Eye Model Characteristics With 60.00 D Aspheric IOL and a 5-mm Pupil

Implant Tests

The implants were tested in three different settings. Settings S, P1, and P2 were evaluated with either only spherical or only aspheric lenses. At first, the difference between the settings was tested and, if a statistical significant difference was found, each setting was compared individually with the other two.

A Matlab code was written to test the lens options. For each set of eyes (30.00, 45.00, and 60.00 D), a combination of a K power and a calculated axial length was loaded. Then, the spherical single high-power lens was inserted into the eye model and the anterior chamber value was set to variable. Optimization was performed to achieve the smallest wavefront error. This way, the IOL was positioned at the best possible place to yield its maximum optical performance. Although ACD was varied, the axial length was kept constant. This process was repeated for the piggyback settings. After the lens loading and optimization, pupil diameter was set to 3 and 5 mm and the MTF chart was plotted for each scenario. The area under the MTF and the diffraction limit curves were calculated and the former was divided by the latter. The closer their ratio is to the unit, the better the lens contrast sensitivity. Spherical aberration was also calculated using the Zernike standard coefficients at the retinal plane for each pupil diameter. This entire process was repeated for each of the 29 eye models.

After all of the spherical lenses had been tested, aspheric lenses were also evaluated following the exact same strategy.

According to the International Organization for Standardization 11979-2 standard for IOL optical properties and test methods, evaluation of the IOL performances was under a 550-nm monochromatic wavelength.19

Measured Variables

The MTF at the retina was recorded for each setting. MTF was used to assess image quality of the implant options in the model eye because it gives the contrast response across a range of different spatial frequencies. The higher the area under the curve, the higher the contrast provided. The diffraction limit is the maximum MTF possible for an aberration-free optical system. The area under the MTF curve was calculated and divided by that of the diffraction limit. This division shows the ratio of the maximum possible performance achieved for that particular optical system.

Forty-five Zernike terms were used for the wavefront reconstruction at the retinal plane using Zernike standard coefficients and the spherical aberration was recorded for each setting.

Statistical Analysis

Statistical analysis was performed using SPSS for Windows software (version 19.0.0; SPSS, Inc., Chicago, IL). Normality was tested and rejected by the Shapiro– Wilk test. Kruskal–Wallis one-way analysis of variance test was used to compare the difference between spherical and aspheric settings and Mann–Whitney U test was used to compare each setting individually. A cut-off value of statistical significance was a P value of less than .05. To maintain a global level of significance of P value less than .05 for multiple tests, Bonferroni adjustment was applied.

Results

Spherical Lenses

Table C (available in the online version of this article) shows the median of the area under the MTF curve normalized by the diffraction limit and the 97.5% confidence interval limits for the spherical settings using the 3- and 5-mm pupil diameter for all sets of eyes.

Spherical Lenses: Area Under MTF Curve (Ratio of Diffraction Limit)

Table C:

Spherical Lenses: Area Under MTF Curve (Ratio of Diffraction Limit)

In all of the analyzed dioptric power required (30.00, 45.00, and 60,00 D) sets of eyes, the single lens (setting S) had the lowest optical performance (lowest MTF) in both pupil sizes when compared to the polypseudophakia models. Because spherical aberration increases with the lens dioptric power, the best performance was obtained splitting the total power within two lenses. Their relatively low spherical aberration was the reason settings P1 and P2 had the better performance as shown in Table D (available in the online version of this article) and these results are in agreement with the previous published studies.12,15–17

Spherical Lenses: Spherical Aberration (µm)

Table D:

Spherical Lenses: Spherical Aberration (µm)

The difference observed between the single IOL and the piggyback models was statistically significant in all analyzed variables (MTF and spherical aberration: 3- and 5-mm pupil diameter) as seen in Table 1. However, no statistically significant difference was found comparing the polypseudophakic models to each other.

Spherical Lenses: Area Under MTF Curve and Spherical Aberrationa

Table 1:

Spherical Lenses: Area Under MTF Curve and Spherical Aberration

Aspheric Lenses

Table E (available in the online version of this article) shows the median of the area under the curve normalized by the diffraction limit and the 97.5% confidence interval limits for the aspheric settings using the 3- and 5-mm pupil diameter for all sets of eyes.

Aspheric Lenses: Area Under MTF Curve (Ratio of Diffraction Limit)

Table E:

Aspheric Lenses: Area Under MTF Curve (Ratio of Diffraction Limit)

Here, the single lens had the highest optical performance when compared to the piggyback options. Note that all aspheric settings had a much higher MTF than their spherical counterparts (shown in Table C).

Table F (available in the online version of this article) shows the spherical aberration for the aspheric implant options using the 3- and 5-mm pupil sizes. The relative lower spherical aberration causes the optical performance of the aspheric lenses to be better than the spherical models and the single aspheric IOL setting to have the highest performance.

Aspheric Lenses: Spherical Aberration (µm)

Table F:

Aspheric Lenses: Spherical Aberration (µm)

Table 2 shows that the higher the IOL power requirement is, the more significant is the difference between the single lens and the polypseudophakic models. Different piggyback settings were statistically similar in all analyzed variables. Although setting S had a higher performance (higher MTF and lower spherical aberration) than settings P1 and P2, in all analyzed scenarios, this difference was statistically significant only in eyes for which high-powered IOLs are required. Because the analysis of variance test did not show any statistical difference between the settings in the 30.00 D eye set, no further testing was done.

Aspheric Lenses: Area Under MTF Curve and Spherical Aberrationa

Table 2:

Aspheric Lenses: Area Under MTF Curve and Spherical Aberration

Figures 14 show the comparison between spherical and aspheric lenses for all of the analyzed variables in all sets of eyes. It is important to note that all of the aspheric lenses have a better optical performance (higher MTF and lower spherical aberration) than the spherical IOLs.

Comparison of MTF normalized between spherical and aspheric lenses for 3-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Figure 1.

Comparison of MTF normalized between spherical and aspheric lenses for 3-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Comparison of MTF normalized between spherical and aspheric lenses for 5-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Figure 2.

Comparison of MTF normalized between spherical and aspheric lenses for 5-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Comparison of spherical aberration between spherical and aspheric lenses for 3-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Figure 3.

Comparison of spherical aberration between spherical and aspheric lenses for 3-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Comparison of spherical aberration between spherical and aspheric lenses for 5-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Figure 4.

Comparison of spherical aberration between spherical and aspheric lenses for 5-mm pupil diameter. D = diopters; IOL = intraocular lens; MTF = modulation transfer function; P1 = even split of the power between two separate lenses; P2 = uneven split of the power with two-thirds of the required power in the posterior lens and one-third in the anterior lens; S = single lens with full required power

Discussion

Cataract surgery in high hyperopic and nanophthalmic eyes presents difficulties in the preoperative, intraoperative, and postoperative courses. IOL power calculation is challenged by the disproportionately small anterior segment when compared to the axial length.15,20 In most cases, the predicted dioptric power exceeds those commercially available. For that reason, many surgeons opt to use two standard lower-power IOLs to reach the predicted dioptric power. This was proposed by Gayton and Sanders in 199321 after they used two polymethylmethacrylate lenses to achieve +46.00 D when +35.00 D was the highest IOL power available. Cases have been published where three or even four IOLs were used to achieve the desired power.1,15

As described a few years later, piggyback implantation can cause late-onset complications such as interlenticular opacification, pigment dispersion, and glaucoma.22,23 Moreover, nanophthalmic eyes usually have a crowded anterior segment, causing implantation of two IOLs to be technically challenging.

Because the center thickness of a single lens is thinner than two piggybacked implants with equivalent power, implanting one lens leaves the eye with a deeper anterior chamber and a wider angle. It is known that cataract surgery can cause a reduction in intraocular pressure and this is proportional to the increase in the anterior chamber angle, especially in narrow-angle eyes.24 Using a single IOL is also technically easier and eliminates the risks of the complications mentioned above.

Several authors have shown that using a single IOL with high dioptric power causes image degradation, mainly because of high spherical aberration, and splitting up the power into two lenses lowers the total spherical aberration and produces a sharper image.12,14–17 This is true when considering only spherical IOL surfaces. IOL design has evolved in the past two decades and it is now possible to manufacture IOLs with aspheric surfaces, which greatly reduces spherical aberration. To date, there are two groups of aspheric IOLs: those that reduce the total spherical aberration of the eye (aberration correcting) and those that do not add any spherical aberration to the eye (aberration free). The latter type was used in the current study.

With the possibility of manufacturing high-power aspheric IOLs, the better performance of polypseudophakic eyes shown by the aforementioned studies may no longer be true.

We used a ray tracing optical design software that allows one to design, customize, and analyze the performance of different types of lenses with highly accurate models. This software has been validated and is widely used for medical, scientific, and engineering analysis of optical components and systems in both the industrial and academic domains.25

The Liou and Brennan eye model was chosen because it accurately represents corneal aspherical anterior and posterior surfaces and produces an average amount of spherical aberration, thus rendering a more realistic simulation. This eye model has an anterior cornea asphericity of −0.18 and a posterior corneal surface asphericity of −0.6.26 The total cornea spherical aberration produced by this model in a 6-mm pupil aperture is 0.295 μm, which is consistent with the population average.27

We modified the Liou and Brennan model to simulate a nanophthalmic eye with reduced ACD and axial length. In fact, 65 different eyes requiring a 60.00 D lens to correct aphakia were created by varying corneal curvature and adjusting the axial length, keeping the effective lens position constant.

Although there are numerous piggyback combination possibilities, we chose two types of power split combination based on clinical use and relevance. Our main goal was to provide data on what is optically better, the use of a single high-power IOL or piggybacking lower powered lenses.

Our results show that when comparing a single high-power spherical IOL to piggybacking lower-powered spherical lenses, MTF is higher in the latter option. The magnitude of spherical aberration increases with the dioptric power of the IOL. Therefore, the high-power single spherical IOL induces more spherical aberration than the piggyback options, thus compromising the MTF. The relative lower spherical aberration induced by splitting the IOL power into two lenses makes the optical performance of the piggyback options more favorable. However, if the same test is done using aspheric IOLs, the results are the opposite and favor the use of a single high-power lens. The convergence produced by the first IOL in the piggyback models causes the second lens to behave differently from how it was initially designed. This way, these lenses, even though aspheric, induce a small amount of spherical aberration. The piggyback combinations tested showed no statistically significant difference between them in either the spherical or the aspheric groups. Moreover, implanting a single IOL is technically easier, especially in short eyes with a crowded anterior segment, and safer because these eyes usually have weak zonules.

It is important to point out that retinal and cortical processing and neuroadaptation can lead to better image perception despite a poor image formation on the retina, and none of these effects were taken into account in the current study.

Industry is able to manufacture high-power aspheric IOLs with the current available technology and these should not be kept away from production and commercialization because they could provide technical safety for the surgeon and greater visual quality for the patient.

Conclusion

The simulations showed that a single high-power aspheric IOL had a better optical performance than piggybacking lower-power aspheric lenses. MTF analysis revealed that a single high-power aspheric lens provides higher contrast when compared to the piggyback options. Spherical aberration was lower in the single IOL group when the tested lenses were aspheric. Spherical lenses showed contrast sensitivity degradation, especially due to high spherical aberration, and their implantation should be avoided in nanophthalmic eyes.

This study did not consider differences in incision sizes or in the final position of the lenses and, therefore, further investigation is needed to assess the clinical impact of these factors.

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Spherical Lenses: Area Under MTF Curve and Spherical Aberrationa

Set of Eyes Implant Setting Area Under MTF Curve Spherical Aberration


3-mm Pupil 5-mm Pupil 3-mm Pupil 5-mm Pupil
30.00 D S vs P1 0.48032 vs 0.53811 (< .001) 0.17906 vs 0.20007 (< .001) 0.04974 vs 0.04100 (< .001) 0.38982 vs 0.31729 (< .001)
S vs P2 0.48032 vs 0.53652 (< .001) 0.17906 vs 0.19953 (< .001) 0.04974 vs 0.04114 (< .001) 0.38982 vs 0.31883 (< .001)
P1 vs P2 0.53811 vs 0.53652 (1.000) 0.20007 vs 0.19953 (1.000) 0.04100 vs 0.04114 (1.000) 0.31729 vs 0.31883 (1.000)
45.00 D S vs P1 0.40550 vs 0.48714 (< .001) 0.14441 vs 0.18230 (< .001) 0.08383 vs 0.05471 (< .001) 0.67985 vs 0.42462 (< .001)
S vs P2 0.40550 vs 0.48107 (< .001) 0.14441 vs 0.17943 (< .001) 0.08383 vs 0.05611 (< .001) 0.67985 vs 0.43781 (< .001)
P1 vs P2 0.48714 vs 0.48107 (1.000) 0.18230 vs 0.17943 (1.000) 0.05471 vs 0.05611 (1.000) 0.42462 vs 0.43781 (1.000)
60.00 D S vs P1 0.32511 vs 0.44707 (< .001) 0.12513 vs 0.16163 (< .001) 0.14429 vs 0.07497 (< .001) 1.25233 vs 0.58722 (< .001)
S vs P2 0.32511 vs 0.43885 (< .001) 0.12513 vs 0.15790 (< .001) 0.14429 vs 0.07844 (< .001) 1.25233 vs 0.62223 (< .001)
P1 vs P2 0.44707 vs 0.43885 (.305) 0.16163 vs 0.15790 (.305) 0.07497 vs 0.07844 (.535) 0.58722 vs 0.62223 (.267)

Aspheric Lenses: Area Under MTF Curve and Spherical Aberrationa

Set of Eyes Implant Setting Area Under MTF Curve Spherical Aberration


3-mm Pupil 5-mm Pupil 3-mm Pupil 5-mm Pupil
30.00 Db S vs P1 0.59600 vs 0.57142 (.247) 0.21873 vs 0.21043 (.209) 0.03581 vs 0.03764 (.471) 0.27989 vs 0.29131 (.607)
S vs P2 0.59600 vs 0.58004 (.247) 0.21873 vs 0.21319 (.209) 0.03581 vs 0.03682 (.471) 0.27989 vs 0.28536 (.607)
P1 vs P2 0.57142 vs 0.58004 (.247) 0.21043 vs 0.21319 (.209) 0.03764 vs 0.03682 (.471) 0.29131 vs 0.28536 (.607)
45.00 D S vs P1 0.62369 vs 0.55542 (< .001) 0.23196 vs 0.20855 (< .001) 0.03752 vs 0.04391 (.001) 0.29961 vs 0.34053 (.010)
S vs P2 0.62369 vs 0.56906 (.003) 0.21196 vs 0.21302 (.002) 0.03752 vs 0.04234 (.031) 0.29961 vs 0.32982 (.088)
P1 vs P2 0.55542 vs 0.56906 (1.000) 0.20855 vs 0.21302 (1.000) 0.04391 vs 0.04234 (1.000) 0.34053 vs 0.32982 (1.000)
60.00 D S vs P1 0.66714 vs 0.54290 (< .001) 0.24951 vs 0.20557 (< .001) 0.033745 vs 0.05047 (< .001) 0.31304 vs 0.39423 (< .001)
S vs P2 0.66714 vs 0.56471 (< .001) 0.24951 vs 0.21332 (< .001) 0.03745 vs 0.04748 (< .001) 0.31304 vs 0.37501 (.001)
P1 vs P2 0.54290 vs 0.56471 (.372) 0.20557 vs 0.21332 (.383) 0.05047 vs 0.04748 (.491) 0.39423 vs 0.37501 (.636)

Spherical Aberration Induced by Each IOL Power (µm)

IOL Power (D) Spherical Aspheric
10 0.001614 −0.000000
15 0.005506 0.000000
20 0.132668 −0.000000
22.5 0.190862 −0.000000
30 0.471263 −0.000001
40 1.212005 −0.000003
45 1.823502 −0.000005
60 5.515092 −0.000009

Modified Liou and Brennan Eye Model Characteristics With 60.00 D Aspheric IOL and a 5-mm Pupil

Surface Name Radius (mm) Thickness (mm) n Diameter (mm) Conic
1 Object Infinity Infinity 0.000 0.000 0.000
2 Front cornea 7.770 0.500 1.376 10.000 −0.180
3 Back cornea 6.400 3.370 1.336 10.000 −0.600
4 Pupil Infinity 0.000 1.336 5.000 0.000
5 IOL anterior 6.453 1.739 1.550 6.000 −0.629
6 IOL posterior −6.257 10.687 1.336 6.000 −3.911
7 Retina −12.000 23.960 0.000

Spherical Lenses: Area Under MTF Curve (Ratio of Diffraction Limit)

Set of Eyes Implant Setting 3-mm Pupil 5-mm Pupil


Median 97.5% CI Median 97.5% CI


Lower Upper Lower Upper
30.00 D S 0.48032 0.46544 0.49800 0.17906 0.17224 0.18567
P1 0.53811 0.51046 0.56992 0.20007 0.19086 0.20933
P2 0.53652 0.50961 0.56740 0.19953 0.19050 0.20848
45.00 D S 0.40550 0.39764 0.41249 0.14441 0.14321 0.14622
P1 0.48714 0.47299 0.50355 0.18230 0.17545 0.18910
P2 0.48107 0.46845 0.49547 0.17943 0.17315 0.18579
60.00 D S 0.32511 0.32307 0.32675 0.12513 0.12491 0.12548
P1 0.44707 0.43828 0.45534 0.16163 0.15772 0.16576
P2 0.43885 0.43063 0.44632 0.15790 0.15472 0.16129

Spherical Lenses: Spherical Aberration (µm)

Set of Eyes Implant Setting 3-mm Pupil 5-mm Pupil


Median 97.5% CI Median 97.5% CI


Lower Upper Lower Upper
30.00 D S 0.04974 0.04584 0.05401 0.38982 0.35938 0.42317
P1 0.04100 0.03718 0.04516 0.31729 0.28763 0.34961
P2 0.04114 0.03738 0.04524 0.31883 0.28965 0.35064
45.00 D S 0.08383 0.07995 0.08808 0.67985 0.64958 0.71305
P1 0.05471 0.05063 0.05914 0.42462 0.39302 0.45892
P2 0.05611 0.05214 0.06043 0.43781 0.40701 0.47128
60.00 D S 0.14429 0.14091 0.14802 1.25233 1.22683 1.28072
P1 0.07497 0.07074 0.07955 0.58722 0.55452 0.62265
P2 0.07844 0.07441 0.08282 0.62223 0.59108 0.65607

Aspheric Lenses: Area Under MTF Curve (Ratio of Diffraction Limit)

Set of Eyes Implant Setting 3-mm Pupil 5-mm Pupil


Median 97.5% CI Median 97.5% CI


Lower Upper Lower Upper
30.00 D S 0.59600 0.55660 0.63907 0.21873 0.20654 0.23151
P1 0.57142 0.53707 0.60980 0.21043 0.20020 0.22224
P2 0.58004 0.54454 0.61930 0.21319 0.20252 0.22510
45.00 D S 0.62369 0.58409 0.66593 0.23196 0.21851 0.24552
P1 0.55542 0.52961 0.58794 0.20855 0.19866 0.21924
P2 0.56906 0.53838 0.60354 0.21302 0.20290 0.22456
60.00 D S 0.66714 0.62628 0.70907 0.24951 0.23509 0.26484
P1 0.54290 0.51911 0.57025 0.20557 0.19597 0.21519
P2 0.56471 0.53729 0.59563 0.21332 0.20328 0.22405

Aspheric Lenses: Spherical Aberration (µm)

Set of Eyes Implant Setting 3-mm Pupil 5-mm Pupil


Median 97.5% CI Median 97.5% CI


Lower Upper Lower Upper
30.00 D S 0.03581 0.03187 0.04013 0.27989 0.24902 0.31370
P1 0.03764 0.03381 0.04182 0.29131 0.26154 0.32375
P2 0.03682 0.03304 0.04094 0.28536 0.25598 0.31736
45.00 D S 0.03752 0.03342 0.04200 0.29961 0.26709 0.33513
P1 0.04391 0.03977 0.04840 0.34053 0.30845 0.37534
P2 0.04234 0.03827 0.04675 0.32982 0.29819 0.36414
60.00 D S 0.03745 0.03331 0.04197 0.31304 0.27931 0.34983
P1 0.05047 0.04608 0.05522 0.39423 0.36012 0.43110
P2 0.04748 0.04317 0.05213 0.37501 0.34142 0.41131
Authors

From the Department of Ophthalmology (BLCT), the Graduate Program in Electrical Engineering (FTA), and the Department of Electrical Engineering (DWLM), Federal University of Minas Gerais, Belo Horizonte, Brazil.

The authors have no financial or proprietary interest in the materials presented herein.

AUTHOR CONTRIBUTIONS

Study concept and design (BLCT, FTA, DWLM); data collection (BLCT, FTA); analysis and interpretation of data (BLCT, FTA, DWLM); writing the manuscript (BLCT); critical revision of the manuscript (BLCT, FTA, DWLM); supervision (DWLM)

Correspondence: Bruno Lovaglio Cançado Trindade, Rua Manaus, 595 – 30150-35 Belo Horizonte-MG, Brazil. E-mail: bruno@ioct.org

Received: March 19, 2015
Accepted: November 03, 2015

10.3928/1081597X-20160119-01

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