The Lentis Mplus LS-312MF IOL (Oculentis GmbH, Berlin, Germany) has a particular rotationally asymmetrical multifocal design based on a bifocal lens created by the presence of an addition, similar to a bifocal spectacle lens, mainly generating primary coma aberration1–9 and thus extending the depth of field.10,11 Several studies have shown that this type of IOL could provide good near and distance visual outcomes, good contrast sensitivity, and a positive impact on patient quality of life.1–9
Because the IOL is placed close to the eye stop and moves with the eye, the image quality should, in principle, be independent of the angular orientation of the addition, except that a larger decrease in visual performance is to be expected in a particular sector of the cornea. However, there is no scientific literature exploring the optical quality of this type of IOL under different intraocular orientations. When an IOL is implanted into an eye it becomes part of a more complex optical system. Because the cornea has its own aberrations, including asymmetrical ones,12 it seems logical to consider that the optical quality of the eye’s asymmetric IOL system will differ depending on the intraoperative orientation of the IOL.
The purpose of this study was to ascertain with objective methods whether implantation of this rotationally asymmetric IOL with a particular orientation can significantly influence final visual quality in patients.
Patients and Methods
The Lentis Mplus LS-312MF (Figure A, available in the online version of this article) is a biconvex single-piece multifocal acrylic IOL with an aspheric posterior surface design. The IOL has an overall length of 11.0 mm and an optic of 6.0 mm. The plate haptics design was used in the current study. The IOL is a nonrotational symmetric multifocal IOL with a refractive design, combining an aspheric asymmetric distance vision zone along with a sector-shaped near vision zone with a +1.50 diopters (D) or +3.00 D addition. In the current study, the +3.00 D addition model was used.
The Lentis Mplus LS-312MF intraocular lens (Oculentis GmbH, Berlin, Germany). The red line marks the point that was used in the current study as a reference point for intraocular orientation of the intraocular lens.
Corneal Aberration Measurements
Twenty eyes of 20 healthy patients without previous surgeries or diseases (10 women and 10 men) from 45 to 71 years old (mean: 58 ± 7 years) were included in the study. The spherical equivalent ranged between −4.00 and +3.00 D (mean: −0.425 ± 1.84 D) with corneal astigmatism below 0.50 D in all of the cases. A Scheimpflug-based imaging system (Pentacam; Oculus Optikgeräte GmbH, Wetzlar, Germany) was used to obtain the corneal aberrations of each eye, taking into account the first and second corneal surfaces. Zernike coefficients related to primary corneal astigmatism were removed from the calculations. An average of corneal aberration values of the 20 eyes was used as eye 21 (the “averaged eye”).
Optical Quality of the IOL
The irx3 Hartmann-Shack wavefront aberrometer (Imagine Eyes, Orsay, France) and a purpose-designed wet cell were used to obtain the in vitro optical quality of the IOL (IOL + wet cell). The Hartmann-Shack wavefront sensor has a square array of 1,024 lenslets and operates at 780 nm. The aberrations of the wet cell alone were measured and subtracted from the overall aberrations values following a previously described methodology.1–3 Repeatability and reproducibility of the system in measuring the modulation transfer function (MTF) of an IOL were within ±2% of the mean value obtained, in agreement with the expected values from the International Organization for Standardization 11979-2.13 The average of 10 measures with three different IOLs of +22.00 D (same type and IOL power, but different batches) was taken as a reference measure. This was to ensure that the results were not related to the manufacturing process of an individual IOL.
Simulations of Implantation and Measurement of Visual Quality on Patients
Wavefront simulations of implanting the IOL in each possible meridian, from 0° to 360° in steps of 1°, were calculated using a purpose-designed Matlab-based application (MathWorks, Inc., Natick, MA). The propagation of the wavefront from the cornea to the iris was disregarded in the simulations. In this manner, Zernike coefficients used for simulations were those obtained from the cornea in each case plus those obtained in vitro from the IOL for the same pupil diameter. The point of the IOL considered as a reference for orientation was the top of the IOL when placed to coincide with the line that separates the distance vision zone from the addition zone at 180° (horizontal direction), with the distance vision area situated in the upper side (Figure A). Given that the design of this particular IOL was of the distance-dominant type, distance focus was simulated for each orientation by finding the defocus term that maximizes the image quality using a visual contrast metric computed from wavefront error called visually modulated transfer function (VSMTF) metric and defined as the visual Strehl ratio computed in a frequency domain weighted by the neural contrast sensitivity function.14,15 This image quality metric is known from previous experiments to account well for changes in retinal image quality.14,15 It uses retinal image quality for grating objects, weighting the MTF by the neural contrast sensitivity function and is mathematically defined by16:
with the mean one-dimensional MTF being calculated as the average of all orientations of the two-dimensional MTF (radial profile).
Intermediate vision (66 cm) and near vision (33 cm) were also simulated for each orientation by performing a through-focus analysis for those two distances.
To find an average value of the improvement of the methodology proposed, we computed the mean value of the corneal wavefront of all patients and simulated the effect of the IOL in a hypothetical eye with such a cornea. This “averaged eye” corresponds to eye 21 in the current study. Point spread function (PSF) and its convolution with a test whose font size is equivalent to 20/20 Snellen visual acuity was performed for distance vision in the averaged eye.
All of the simulations were performed using a 5.0-mm pupil. The choice of pupil diameter was based on a study by Winn et al.,17 who found that the mean pupil diameter under mesopic conditions was approximately 5.0 mm in patients older than 60 years.
The addition sector of this IOL is correlated with large values of coma (Figure 1).4 Results of simulated IOL implantation oriented toward the supplementary angle of the comatic axis, obtained from horizontal coma and vertical coma components of Zernike polynomials Z31 and Z3−1, were reported because it could be the intuitive optimal orientation for this particular IOL. Thus, the corneal coma could be partially compensated by the coma component of the IOL.
In vitro wavefront aberration map (µm) for the Lentis Mplus LS-312MF intraocular lens (Oculentis GmbH, Berlin, Germany) for a 5.0-mm pupil. The defocus term was subtracted from the measurement.
Differences in VSMTF values between orientations were compared using one-way analysis of variance. For statistically significant outcomes, two-by-two group differences were evaluated using a suitable post-hoc test; Tukey test was chosen for the case of unequal variance within the groups. Homogeneity of variance within groups was preliminarily tested by Levene statistics. A P value less than .05, corresponding to a significance level greater than 95%, was considered significant. All of the statistical analyses were performed using SPSS software (version 13.0; SPSS, Inc., Chicago, IL).
Figure 1 shows the wavefront aberration map for an intermediate plane between distance and near vision produced by the IOL for a 5.0-mm pupil. The image clearly shows a high vertical coma (in the y-axis) as a result of the addition, which causes the z-value of the wavefront map to have a positive and a negative value in the lower and upper part of the lens, respectively.
The VSMTF values of each eye with the IOL placed with the orientation that yielded the highest value of VSMTF (best orientation), placed with the orientation providing the lowest value of VSMTF (worst orientation) and with the IOL oriented toward the supplementary angle of the comatic axis for distance, intermediate, and near vision, are shown in Figure 2. Similarly, Table 1 shows the mean values of VSMTF at different distances for the orientations that provided the best and worst results for distance vision and for the supplementary angle of comatic axis orientation. One-way analysis of variance showed no statistically significant differences between the mean values of the three orientations for intermediate vision (P = .15) and near vision (P = .4). Significant differences between the mean values of the three orientations were found for distance vision (P < .001). Post-hoc analysis (Tukey test) showed that the mean value of VSMTF for the worst orientation was significantly lower than that for the best orientation (P < .001) and the supplementary angle of comatic axis orientation (P < .001) for distance vision. Moreover, the mean value of VSMTF for the best orientation was better than that for the supplementary angle of comatic axis orientation for distance vision (P = .008).
Image quality visually modulated transfer function (VSMTF) metric values for the best and wost possible orientation of the intraocular lens (IOL) and for the IOL oriented toward the supplementary angle of the comatic axis (5.0-mm pupil) for (A) distance, (B) intermediate, and (C) near vision.
Mean VSMTF of the Image Quality Metric for Distance, Intermediate, and Near Vision
Analyzing VSMTF values as percentages for distance vision, there was a mean difference of 58% ± 19% (range: 20% to 121%) between the best and the worst orientations, 22% ± 16% (range: 4% to 67%) between the best and the supplementary angle of comatic axis orientations, and 30% ± 17% (range: 4% to 70%) between the supplementary angle of the comatic axis and the worst orientations.
Figure 3 shows where the best, worst, and supplementary angle of comatic axis orientations were found in each eye for distance vision.
Positions where the best (green circles), worst (red crosses), and supplementary angle of comatic axis (blue triangles) orientations of each intraocular lens in 21 eyes studied were found at distance vision.
The normalized radial profiles of the MTF of the averaged eye with the IOL at the best, worst, and supplementary angle of comatic axis orientations for distance vision are shown in Figure 4. Retinal contrast threshold curve at a retinal illuminance of 500 Troland was included. The cut-off frequency for the eye with the IOL was calculated as the intersection between the MTF of the eye and the neural curve. When the IOL was placed with the worst orientation, the cut-off frequency was approximately 34 cycles per degree. The best and the supplementary angle of comatic axis orientations provided a cut-off frequency of approximately 39 cycles per degree.
Radial projection averaged over all orientations of the two-dimensional modulation transfer function (MTF) (780 nm of wavelength and 5.0 mm of pupil) for the averaged eye with the intaocular lens in the best and worst possible orientations for distance vision and oriented toward the supplementary angle of the comatic axis. In addition, the retinal contrast threshold curve for a retinal illuminance of 500 Troland was included. Error bars have been omitted for clarity. The deviation of the modulation transfer for every spatial frequency was typically around 10% of the mean value.
The PSFs and their convolution for the IOL at the best, worst, and supplementary angle of comatic axis orientations for distance vision in the averaged eye are shown in Figure B (available in the online version of this article).
The upper part shows point spread function (PSF), for a 5.0-mm pupil, of the intraocular lens placed with the best orientation (left), the worst orientation (middle), and toward the supplementary angle of the comatic axis (right). The lower part shows PSF convolution with different letters corresponding to a visual acuity of 20/20.
The aim of the current study was to evaluate the optical behavior of the Lentis Mplus LS-312MF nonrotational symmetric 3.00 D aspheric IOL under different intraocular orientations using a computerized model eye that enables quantification of changes in MTF values. The analysis of MTFs provided information that correlated with the visual performance of eyes with different intraocular orientations of the IOL, resulting in a more complete evaluation of optical performance than visual acuity. It provides information on the loss of contrast at different spatial frequencies, including aberrations and light scatter effects. In particular, image contrast degradation with different IOL orientations was assessed through analysis of the VSMTF image quality metric that uses retinal image quality for grating objects, weighting the MTF by the neural contrast sensitivity function.
Statistical analysis showed significant differences in mean VSMTF values between orientations for distance vision. An optimal orientation of the IOL showed a mean improvement of 58% in VSMTF values with respect to the worst possible orientation. When the IOL was oriented toward the supplementary angle of comatic axis, only a moderate mean improvement of 30% in VSMTF was obtained with respect to the worst orientation (Figure 2). For the different orientations, intermediate and near vision VSMTF values were statistically indistinguishable.
An additional MTF analysis was performed for distance vision in the averaged eye, providing data closely related to vision quality (ie, contrast sensitivity). Optimal orientation of the IOL resulted in improved MTF values at all of the spatial frequencies compared with the worst orientation (Figure 4), particularly at high spatial frequencies, closely approximating the diffraction-limited curve, therefore providing higher optical quality. These MTF outcomes were reflected in the PSF images (Figure B). Note that the maximum transferred spatial frequency was reduced from approximately 39 cycles per degree for the best orientation to approximately 34 cycles per degree for the worst orientation. Orientation toward the supplementary angle of the comatic axis showed intermediate results, but they were closer to those obtained with the best orientation.
The PSF of the IOL oriented toward the supplementary angle of the comatic axis was slightly degraded when compared with the PSF of the best orientation (Figure B). The worst orientation showed a significantly degraded PSF, which is related to the poorer MTF values (Figure 4).
Figure 2 shows higher values of image quality metrics for distance vision than intermediate vision, which in turn were higher than the values calculated for near vision. This may be because the simulations were performed assuming that the equivalent sphere of the eye bearing the IOL was 0 for distance vision. Using a different IOL power should improve the image quality of intermediate or near vision with respect to distance vision. However, because the effect of coma is to deteriorate high spatial frequencies, we assumed that it was preferable to optimize distance vision, which usually presents a larger content of high spatial frequencies. Under these circumstances, a strong dependence of visual quality on IOL orientation can be expected for distance vision (Figure 2). This suggests that customized intraoperative orientation of this IOL could improve visual outcomes without degrading intermediate or near vision.
The axis that provides the best visual quality varied between eyes due to different wavefront profiles between corneas (Figure 3), so the optimal orientation should be calculated for each surgery. If the surgeon does not have the software necessary to perform the proper analysis to calculate the optimal orientation for each patient, as a simple rule of thumb, the supplementary angle of the comatic axis of corneal topography was found to be a reasonable approximation, although not totally optimal. This is due to the fact that large coma values in this IOL were partially compensated by the coma values in the eye.
It is important to note that this particular IOL is actually implanted at 90° as recommended by the manufacturer. Figure 3 shows that 25% of the worst orientations in the 21 eyes were found near 90° (range: 45° to 135°). These results suggest that when the supplementary angle of the comatic axis is chosen as the implant axis in normal eyes, the results should be better than those obtained in the case of systematic orientation at 90°. A topographer that shows Zernike values or software that calculates them from a topography file can be used to determine the supplementary angle of comatic axis orientation. It can be easily calculated from the two third-order Zernike coma values, C33and C3−3, as:
This angle is measured from the horizontal right position of the eye and has positive values in the anti-clockwise direction.18 So the IOL to be inserted should have its addition pointing to that comatic angle (or the distance vision area pointing to the comatic angle +180° [supplementary angle of comatic axis orientation]).
Our analysis suggests that this IOL produces better optical quality if it is implanted on a customized axis. Clinical studies are required to analyze the real visual benefits for patients with optimally oriented IOLs in comparison with any other orientation.
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Mean VSMTF of the Image Quality Metric for Distance, Intermediate, and Near Visiona
|Parameter||Mean VSMTF (Range)|
|Best||0.24 ± 0.04 (0.16 to 0.31)b||0.12 ± 0.01 (0.1 to 0.16)||0.08 ± 0.02 (0.04 to 0.12)|
|Worst||0.15 ± 0.02 (0.11 to 0.19)b||0.11 ± 0.01 (0.09 to 0.14)||0.08 ± 0.02 (0.06 to 0.12)|
|Comatic||0.2 ± 0.04 (0.15 to 0.29)b||0.12 ± 0.02 (0.1 to 0.18)||0.08 ± 0.01 (0.06 to 0.12)|