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Astigmatism induced by intraocular lens tilt evaluated via ray tracing
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LABORATORY SCIENCE
Astigmatism induced by intraocular lens tilt evaluated via ray tracing Mitchell P. Weikert, MD, Abhinav Golla, MS, MPH, Li Wang, MD, PhD
Purpose: To evaluate astigmatism induced by aspheric and toric intraocular lens (IOL) tilt using a ray-tracing model.
Setting: Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA. Design: Experimental study.
ATR astigmatism. For 5 degrees of tilt, induced astigmatism was 0.08 D, 0.11 D, and 0.14 D for 16.0 D, 22.0 D, and 28.0 D aspheric IOLs, respectively. Ten degrees of IOL tilt produced 0.33 D, 0.44 D, and 0.56 D of induced astigmatism for 16.0 D, 22.0 D, and 28.0 D aspheric IOLs, respectively. Tilting toric IOLs aligned at 90 degrees around a vertical meridian increased the magnitude of induced ATR astigmatism. Tilting toric IOLs aligned at 180 degrees decreased the magnitude of induced WTR astigmatism.
Methods: Ray-tracing eye models with aspheric IOLs (16.0 diopters [D], 22.0 D, and 28.0 D) and toric IOLs (16.0 D, 22.0 D, and 28.0 D each with toricities of 1.50 D, 3.75 D, and 6.00 D) were used. The IOLs were tilted from 1 to 10 degrees horizontally around a 90-degree vertical meridian. Toric IOLs were aligned at 90 degrees and 180 degrees to correct with-the-rule (WTR) and against-the-rule (ATR) corneal astigmatism, respectively. Astigmatism at the corneal plane induced by IOL tilt was calculated.
Conclusions: Tilting aspheric IOLs horizontally around a vertical meridian induced ATR astigmatism. Tilting toric IOLs aligned at 90 degrees increased ATR astigmatism, resulting in overcorrection. Tilting toric IOLs aligned at 180 degrees decreased WTR astigmatism, producing undercorrection.
Results: Induced astigmatism increased with increasing IOL tilt and power. Horizontal tilt around a vertical meridian induced
J Cataract Refract Surg 2018; -:-–- Q 2018 ASCRS and ESCRS
I
ntraocular lens (IOL) tilt has the potential to induce astigmatism. Until now, IOL tilt could not be measured routinely in the clinical setting because a separate device, such as the ultrasound biomicroscope, Purkinje reflection device, Scheimpflug camera system, or anterior segment optical coherence tomography (OCT), was needed.1–4 Recently, swept-source OCT (SS-OCT) biometers were introduced; these include the IOLMaster 700 (Carl Zeiss Meditec AG), Argos (Movu, Inc.), and OA-2000 (Tomey Corp.). Recent studies using the IOLMaster 700 SS-OCTA,5 reported that this device can measure crystalline lens tilt, and preoperative phakic lens tilt can be used to predict postoperative IOL tilt. This makes it possible to obtain crystalline lens or IOL tilt information during optical biometry and perhaps factor its effect into the selection of IOL toricity. The impact of tilted or decentered IOLs on retinal image quality has been investigated using an optical bench, adaptive optics, and in clinical patients.6–8 However, data on the
effect of IOL tilt on induced astigmatism are scarce. The purpose of this study was to evaluate the astigmatism induced by aspheric and toric IOL tilt in a theoretical model constructed using optical design software. MATERIALS AND METHODS Eye Model Opticstudio (Zemax, LLC) generates ray tracing models of optical systems from user-designed specifications. With this software, theoretical eye models were constructed using the parameters outlined below. Corneal Data The cornea was modeled as 2 aspheric surfaces with a central thickness of 0.550 mm. Detailed parameters are listed in Table 1 and are the same as those used in the study by Holladay and Simpson.9 Pupil Plane The pupillary aperture was set at 6.00 mm and was placed 4.05 mm behind the anterior corneal surface. Intraocular Lens Data The anterior IOL surface was placed 0.50 mm behind the pupil plane or 4.55 mm posterior to the
Submitted: February 7, 2018 | Final revision submitted: March 22, 2018 | Accepted: April 1, 2018 From Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine, Houston, Texas, USA. Supported in part by an unrestricted grant from Research to Prevent Blindness, New York, New York, USA. Corresponding author: Mitchell P. Weikert, MD, Cullen Eye Institute, Baylor College of Medicine, 6565 Fannin, NC 205, Houston, Texas 77030, USA. Email: mweikert@ bcm.edu. Q 2018 ASCRS and ESCRS Published by Elsevier Inc.
0886-3350/$ - see frontmatter https://doi.org/10.1016/j.jcrs.2018.04.035
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
anterior corneal surface. Aspheric IOLs and toric IOLs were included in the eye models. For aspheric IOLs, the specific optical parameters for the Acrysof IQ monofocal IOL (SN60WF) were provided by the manufacturer, Alcon Laboratories, Inc. The parameters included the anterior and posterior curvatures, asphericity, and thickness. Eye models with powers of 16.0 diopters (D), 22.0 D, and 28.0 D were constructed. For toric IOLs, specific optical parameters were not available for the Acrysof IQ. Thus, general optical parameters for the SN60WF, including the lens asphericity conic constant and lens thickness, were used for toric IOL construction. To create a toric IOL with a specific lens power, the anterior radius of curvature of a SN60WF IOL with the same refractive power was used. The radii of curvature for the steep and flat meridians of the posterior surface were then determined using OpticStudio optical design software to produce the desired overall IOL power. For example, to create a 22.0 D lens with a cylinder power of 6.0 D, the radius of curvature on the anterior surface was the same as the radius of curvature on the anterior surface for a 22.0 D aspheric IOL and radii of curvature to produce equivalent power of 19.0 D and 25.0 D were determined and used for the flat meridian and steep meridian on the back surface. Eye models were constructed using 16.0 D, 22.0 D, and 28.0 D toric IOLs with cylinder powers of 1.50 D (SN6AT3), 3.75 D (SN6AT6), and 6.00 D (SN6AT9). Intraocular Lens Tilt Previous studiesA,4 have reported that IOLs were tilted greatest in a nasal direction. In the model used, aspheric IOLs and toric IOLs were tilted horizontally around a vertical meridian with the nasal border tilted anteriorly and the temporal border tilted posteriorly in 1-degree steps up to 10 degrees. For the toric IOLs, horizontal lens tilt was performed with the IOLs aligned at 90 degrees (as if correcting with-the-rule [WTR] corneal astigmatism) and at 180 degrees (as if correcting against-the-rule [ATR] corneal astigmatism). Data Analysis For each eye model and IOL power, the ray-tracing software was used to optimize the vitreous cavity length before the IOL was titled. Wavefront aberrations at the corneal plane up to the 7th order were calculated for a 6.0 mm pupil and IOL tilt from 0 to 10 degrees. Second-order astigmatism data without and with IOL tilt were evaluated. Because the IOL was tilted horizontally, only the astigmatism term Z(2,2) was relevant in this study. For easy comprehension, Zernike coefficient values of the 2nd-order astigmatism Z(2,2) ðC22 Þ in micrometers were converted to diopters (D) using the following equation: pffiffiffi C Z 4 6 C22 R2
where C is the dioptric power of the cylinder and R is the radius of the pupil in mm. This equation pffiffiffiis a modification of the original conversion equation CZ 4 6 C22 =R2 described by Applegate et al.10 In this study, the equivalent dioptric power of C22 in micrometers, not the traditional cylinder correction format, was calculated. The 2nd-order astigmatism induced by IOL tilt at corneal plane was calculated.
RESULTS Aspheric Intraocular Lens Tilt
Figure 1 shows the aspheric IOL tilt-induced ATR astigmatism. Table 2 shows the induced 2nd-order astigmatism by degree of tilt. The astigmatism induced by IOL tilt increased as both IOL tilt and power were increased. Toric Intraocular Lens Tilt
Toric IOL tilt induced astigmatism that was dependent on IOL alignment and power (Figure 2 and Table 2). When the toric IOLs were aligned at 90 degrees, IOL tilt increased the ATR astigmatic effect at the corneal plane. The induced ATR astigmatism also increased as tilt increased. When the toric IOLs were aligned at 180 degrees, IOL tilt decreased the WTR astigmatic effect at the corneal plane. The deduction in WTR astigmatism increased as tilt increased and decreased as toricity increased. DISCUSSION In a previous study using the IOLMaster 700 SS-OCT biometer to examine postoperative IOL position, Hirnschall et al.5 found IOL tilt was greatest in a horizontal direction (around a vertical meridian) with the nasal border displaced anteriorly and the temporal border displaced posteriorly at an average magnitude of 6.2 degrees. Tilt direction and magnitude were similar in right eyes and left eyes. In a comparable study at our institution,A we found similar tilt directions and magnitudes, with a mean IOL tilt of 4.9 degrees (range 2 to 10 degrees). In this study, which used OpticStudio ray-tracing software, we evaluated the astigmatism induced by aspheric and toric IOL tilts ranging from 0 to 10 degrees. We also investigated the effect of IOL power, IOL toricity, and toric
Table 1. Nominal values used in the eye model. Parameter Corneal anterior surface radius (mm) Corneal anterior surface Q value Corneal index of refraction @555 nm Corneal thickness (mm) Corneal posterior surface radius (mm) Corneal posterior surface Q value Pupil plane behind anterior corneal surface (mm) IOL anterior surface plane behind anterior corneal surface (mm) IOL Z intraocular lens; Q value Z asphericity
Volume - Issue - - 2018
Value 7.76 0.26 1.376 0.55 6.36 0.24 4.05 4.55
Figure 1. Tilt-induced ATR astigmatism (D) in eyes with aspheric IOLs (ATR Z against-the-rule; IOL Z intraocular lens).
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
Table 2. Induced 2nd-order astigmatism Z(2,2) in dioptric power by tilt ( ). IOL Model and Power Aspheric IOL: increased ATR astigmatism 16.0 D 22.0 D 28.0 D 16.0 D toric IOL @90: increased ATR astigmatism SN6AT3 SN6AT6 SN6AT9 @180: decreased WTR astigmatism SN6AT3 SN6AT6 SN6AT9 22.0 D toric IOL @90: increased ATR astigmatism SN6AT3 SN6AT6 SN6AT9 @180: decreased WTR astigmatism SN6AT3 SN6AT6 SN6AT9 28.0 D toric IOL @90: increased ATR astigmatism SN6AT3 SN6AT6 SN6AT9 @180: decreased WTR astigmatism SN6AT3 SN6AT6 SN6AT9
1
2
3
4
5
6
7
8
9
10
0.00 0.00 0.01
0.01 0.02 0.02
0.03 0.04 0.05
0.05 0.07 0.09
0.08 0.11 0.14
0.11 0.16 0.20
0.16 0.21 0.27
0.21 0.28 0.35
0.26 0.36 0.45
0.33 0.44 0.56
0.00 0.00 0.00
0.01 0.02 0.02
0.03 0.04 0.04
0.06 0.06 0.07
0.09 0.10 0.11
0.13 0.14 0.16
0.17 0.20 0.22
0.23 0.26 0.29
0.29 0.33 0.36
0.36 0.41 0.45
0.00 0.00 0.00
0.01 0.01 0.01
0.03 0.02 0.02
0.05 0.04 0.03
0.07 0.06 0.05
0.10 0.09 0.07
0.14 0.12 0.10
0.19 0.16 0.13
0.24 0.20 0.16
0.30 0.25 0.20
0.00 0.01 0.01
0.02 0.02 0.02
0.04 0.05 0.05
0.07 0.08 0.09
0.12 0.13 0.14
0.17 0.18 0.20
0.23 0.25 0.27
0.30 0.33 0.36
0.38 0.42 0.46
0.47 0.52 0.57
0.00 0.00 0.00
0.02 0.01 0.01
0.04 0.03 0.03
0.06 0.06 0.05
0.10 0.09 0.08
0.15 0.13 0.11
0.20 0.18 0.16
0.26 0.23 0.20
0.33 0.30 0.26
0.41 0.37 0.32
0.01 0.01 0.01
0.02 0.02 0.03
0.05 0.05 0.06
0.09 0.10 0.10
0.14 0.15 0.16
0.21 0.22 0.24
0.28 0.30 0.32
0.37 0.40 0.42
0.47 0.50 0.54
0.58 0.63 0.67
0.01 0.00 0.00
0.02 0.02 0.02
0.05 0.04 0.04
0.08 0.07 0.07
0.13 0.12 0.11
0.18 0.17 0.15
0.25 0.23 0.21
0.33 0.30 0.27
0.42 0.39 0.35
0.52 0.48 0.43
ATR Z against-the-rule; IOL Z intraocular lens; WTR Z with-the-rule
IOL alignment at 90 degrees and at 180 degrees on the magnitude of tilt-induced astigmatism. Our results showed that IOL tilt induced astigmatism and the resultant astigmatism increased with increasing degree of tilt and IOL power. Horizontal aspheric IOL tilt around a vertical meridian (ie, tilt around 90 degrees meridian with the nasal border of the IOL displaced anteriorly and the temporal border displaced posteriorly) induced ATR astigmatism. Tilting a toric IOL that was aligned at 90 degrees (ie, greater IOL power along the horizontal meridian) in this manner increased the magnitude of the induced ATR astigmatism, resulting in astigmatic overcorrection. Tilting a toric IOL that was aligned at 180 degrees (ie, greater IOL power along the vertical meridian) decreased the magnitude of the induced WTR astigmatism, resulting in astigmatic undercorrection. For average IOL powers (eg, 22.0 D) with average tilts of 5 to 6 degrees, the induced astigmatism was approximately 0.1 to 0.2 D. When the tilt of these IOLs increased to 10 degrees, the resultant astigmatism increased significantly to 0.4 to 0.5 D. The magnitude of the induced astigmatism increased even more as IOL power increased. In our study evaluating IOL tilt, we found that short eyes tended to have greater degrees of IOL tilt.A Because short eyes also tend to
require higher IOL powers, it might be worthwhile to consider the effect of IOL tilt when formulating a plan for astigmatic correction. Factoring in the effect of IOL tiltinduced astigmatism might have the potential to improve refractive accuracy and image quality in this challenging group of patients. One important finding in this study was the effect of IOL tilt on the actual versus intended level of astigmatic correction achieved with toric IOLs. Tilting toric IOLs horizontally around a vertical meridian resulted in overcorrection of WTR astigmatism when they were aligned at 90 degrees and undercorrection of ATR astigmatism when aligned at 180 degrees. The contribution of posterior corneal astigmatism to total corneal astigmatism has been studies, and it has been shown that ignoring posterior corneal astigmatism can lead to overcorrection in eyes that have WTR corneal astigmatism and undercorrection in eyes that have ATR corneal astigmatism.11 Previous studies12,13 have evaluated the accuracy of total corneal astigmatism calculated from anterior and posterior corneal curvature measurements via Scheimpflug imaging to predict ideal astigmatic correction targets in toric IOL implantation. These studies showed that the use of total
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
Figure 2. Tilt-induced astigmatism in eyes with toric IOLs aligned at 90 degrees and 180 degrees for correction of corneal WTR and ATR astigmatism, respectively (ATR Z against the rule; IOLs Z intraocular lenses; WTR Z with-the-rule).
corneal astigmatism still resulted in overcorrection of eyes with WTR corneal astigmatism and undercorrection of eyes with ATR corneal astigmatism. Based on these findings, the accuracy of posterior corneal astigmatism measurements using Scheimpflug imaging was called into question. However, our findings suggest that astigmatism induced by IOL tilt might help explain the residual astigmatism found with use of total corneal astigmatism measurements. Given these results, consideration of both posterior corneal astigmatism and IOL tilt-induced astigmatism might improve toric IOL calculations and planning. Further studies assessing the effect of IOL tilt on ocular astigmatism in patients with toric IOL implantation are desirable. Our results showed that increasing the amount of toricity in the tilted IOL produced different effects on induced astigmatism depending on the alignment of the toric IOL. When toric IOLs were aligned at 90 degrees to correct corneal WTR astigmatism, higher IOL toricities yielded greater increases in ATR astigmatism. In contrast, when toric IOLs were aligned at 180 degrees to correct corneal ATR astigmatism, the reduction in WTR astigmatism correction decreased as IOL toricity increased. Therefore, when selecting toric IOLs in eyes with greater crystalline lens tilt or in eyes with high IOL powers, consideration of the effect of tilt on ocular astigmatism might improve refractive accuracy.
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Marcos et al.14 reported an equation to easily estimate the theoretical astigmatism induced by a tilted thin IOL. An ophthalmic lens in air of C22.0 D tilted 10 degrees produced astigmatism of 0.69 D. In our study using the ray-tracing approach, a 22.0 D aspheric IOL immersed in aqueous with tilt of 10 degrees produced astigmatism of 0.44 D. This study has several limitations inherent in its design. First, it was a theoretical study. Evaluation of astigmatism induced by IOL tilt using actual patient data is ongoing. Second, in the toric IOL model, the asphericity and anterior corneal radius of curvature for the Acrysof SN60WF IOL were used (exact toric IOL data for each model was unavailable). Toric IOLs with different optical specifications might produce different amounts of astigmatism with tilt. Third, in this model, only the IOLs were tilted (ie, the cornea was not tilted). In human eyes, the cornea can also manifest tilt and decentration. Fourth, 2nd-order astigmatism data with and without IOL tilt were used to assess the effect of IOL tilt on total ocular astigmatism. Astigmatism from higher-order Zernike terms might have contributed to the astigmatism induced by tilt; however, we believe their contribution is minimal. In conclusion, our study found that induced astigmatism increased with increasing degree of IOL tilt and IOL power. Tilting aspheric IOLs horizontally around a vertical
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
meridian (as seen in previous studies) induced ATR astigmatism. Tilting toric IOLs aligned at 90 degrees in a similar fashion increased the magnitude of induced ATR astigmatism, producing overcorrection of WTR astigmatism. Tilting toric IOLs aligned at 180 degrees decreased the magnitude of induced WTR astigmatism, resulting in undercorrection of ATR astigmatism. Further studies of the effect of IOL tilt on ocular astigmatism in a clinical setting are warranted. WHAT WAS KNOWN Intraocular lenses tilt greatest around a vertical meridian with the nasal border displaced anteriorly and the temporal border displaced posteriorly at average magnitude of 5 to 6 degrees.
WHAT THIS PAPER ADDS Intraocular lens tilt-induced astigmatism assessed using a ray-tracing model showed that ATR astigmatism was induced by aspheric IOLs tilted horizontally around the vertical meridian. The induced astigmatism increased with increasing IOL tilt and power. Tilting toric IOLs aligned at 90 degrees increased ATR astigmatism and resulted in overcorrection. Tilting toric IOLs aligned at 180 degrees decreased WTR astigmatism and produced undercorrection.
REFERENCES 1. Mura JJ, Pavlin CJ, Condon GP, Belovay GW, Kranemann CF, Ishikawa H, Ahmed II. Ultrasound biomicroscopic analysis of iris-sutured foldable posterior chamber intraocular lenses. Am J Ophthalmol 2010; 149:245–252 2. de Castro A, Rosales P, Marcos S. Tilt and decentration of intraocular lenses in vivo from Purkinje and Scheimpflug imaging; validation study. J Cataract Refract Surg 2007; 33:418–429 3. Kumar DA, Agarwal A, Prakash G, Jacob S, Saravanan Y, Agarwal A. Evaluation of intraocular lens tilt with anterior segment optical coherence tomography. Am J Ophthalmol 2011; 151:406–412 4. Holladay JT, Calogero D, Hilmantel G, Glasser A, MacRae S, Masket S, Stark W, Tarver ME, Nguyen T, Eydelman M. Special report: American Academy of Ophthalmology Task Force summary statement for measurement of tilt, decentration, and chord length. Ophthalmology 2017; 124:144–146. Available at: https://www.aaojournal.org/article/S0161-64 20(16)31419-1/pdf. Accessed May 2, 2018
5. Hirnschall N, Buehren T, Bajramovic F, Trost M, Teuber T, Findl O. Prediction of postoperative intraocular lens tilt using swept-source optical coherence tomography. J Cataract Refract Surg 2017; 43:732–736 €ffler A, Meßner A, Langenbucher A. Effect of decen6. Eppig T, Scholz K, Lo tration and tilt on the image quality of aspheric intraocular lens designs in a model eye. J Cataract Refract Surg 2009; 35:1091–1100 rez-Vives C, Ferrer-Blasco T, Lo pez7. Madrid-Costa D, Ruiz-Alcocer J, Pe s-Mico R. Visual simulation through different intraocular lenses Gil N, Monte using adaptive optics: effect of tilt and decentration. J Cataract Refract Surg 2012; 38:947–958 €hren J, Kohnen T. Tilt and decentration of spherical and 8. Baumeister M, Bu aspheric intraocular lenses: effect on higher-order aberrations. J Cataract Refract Surg 2009; 35:1006–1012 9. Holladay JT, Simpson MJ. Negative dysphotopsia: causes and rationale for prevention and treatment. J Cataract Refract Surg 2017; 43:263–275 10. Applegate RA, Ballentine C, Gross H, Sarver EJ, Sarver CA. Visual acuity as a function of Zernike mode and level of root mean square error. Optom Vis Sci 2003; 80:97–105. Available at: http://journals.lww.com/optvissci/Full text/2003/02000/Visual_Acuity_as_a_Function_of_Zernike_Mode_and.5 .aspx. Accessed May 2, 2018 11. Koch DD, Ali SF, Weikert MP, Shirayama M, Jenkins R, Wang L. Contribution of posterior corneal astigmatism to total corneal astigmatism. J Cataract Refract Surg 2012; 38:2080–2087 12. Koch DD, Jenkins RB, Weikert MP, Yeu E, Wang L. Correcting astigmatism with toric intraocular lenses: effect of posterior corneal astigmatism. J Cataract Refract Surg 2013; 39:1803–1809 13. Savini G, Næser K, Schiano-Lomoriello D, Ducoli P. Optimized keratometry and total corneal astigmatism for toric intraocular lens calculation. J Cataract Refract Surg 2017; 43:1140–1148 14. Marcos S. Special circumstances: effect of IOL tilt on astigmatism. In: Hoffer KJ, ed, IOL Power. Thorofare, NJ, Slack, 2011; 223–230 OTHER CITED MATERIAL A. Wang L, Guimaraes de Souza R, Golla A, Weikert MP, Koch DD, “Evaluation of Crystalline Lens and IOL Tilt using Swept-Source Biometry,” presented at the ASCRS Symposium on Cataract, IOL and Refractive Surgery, Los Angeles, California, USA, May 2017
Disclosures: None of the authors has a financial or proprietary interest in any material or method mentioned.
First author: Mitchell P. Weikert, MD Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine, Houston, Texas, USA
Volume - Issue - - 2018
LABORATORY SCIENCE
Astigmatism induced by intraocular lens tilt evaluated via ray tracing Mitchell P. Weikert, MD, Abhinav Golla, MS, MPH, Li Wang, MD, PhD
Purpose: To evaluate astigmatism induced by aspheric and toric intraocular lens (IOL) tilt using a ray-tracing model.
Setting: Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA. Design: Experimental study.
ATR astigmatism. For 5 degrees of tilt, induced astigmatism was 0.08 D, 0.11 D, and 0.14 D for 16.0 D, 22.0 D, and 28.0 D aspheric IOLs, respectively. Ten degrees of IOL tilt produced 0.33 D, 0.44 D, and 0.56 D of induced astigmatism for 16.0 D, 22.0 D, and 28.0 D aspheric IOLs, respectively. Tilting toric IOLs aligned at 90 degrees around a vertical meridian increased the magnitude of induced ATR astigmatism. Tilting toric IOLs aligned at 180 degrees decreased the magnitude of induced WTR astigmatism.
Methods: Ray-tracing eye models with aspheric IOLs (16.0 diopters [D], 22.0 D, and 28.0 D) and toric IOLs (16.0 D, 22.0 D, and 28.0 D each with toricities of 1.50 D, 3.75 D, and 6.00 D) were used. The IOLs were tilted from 1 to 10 degrees horizontally around a 90-degree vertical meridian. Toric IOLs were aligned at 90 degrees and 180 degrees to correct with-the-rule (WTR) and against-the-rule (ATR) corneal astigmatism, respectively. Astigmatism at the corneal plane induced by IOL tilt was calculated.
Conclusions: Tilting aspheric IOLs horizontally around a vertical meridian induced ATR astigmatism. Tilting toric IOLs aligned at 90 degrees increased ATR astigmatism, resulting in overcorrection. Tilting toric IOLs aligned at 180 degrees decreased WTR astigmatism, producing undercorrection.
Results: Induced astigmatism increased with increasing IOL tilt and power. Horizontal tilt around a vertical meridian induced
J Cataract Refract Surg 2018; -:-–- Q 2018 ASCRS and ESCRS
I
ntraocular lens (IOL) tilt has the potential to induce astigmatism. Until now, IOL tilt could not be measured routinely in the clinical setting because a separate device, such as the ultrasound biomicroscope, Purkinje reflection device, Scheimpflug camera system, or anterior segment optical coherence tomography (OCT), was needed.1–4 Recently, swept-source OCT (SS-OCT) biometers were introduced; these include the IOLMaster 700 (Carl Zeiss Meditec AG), Argos (Movu, Inc.), and OA-2000 (Tomey Corp.). Recent studies using the IOLMaster 700 SS-OCTA,5 reported that this device can measure crystalline lens tilt, and preoperative phakic lens tilt can be used to predict postoperative IOL tilt. This makes it possible to obtain crystalline lens or IOL tilt information during optical biometry and perhaps factor its effect into the selection of IOL toricity. The impact of tilted or decentered IOLs on retinal image quality has been investigated using an optical bench, adaptive optics, and in clinical patients.6–8 However, data on the
effect of IOL tilt on induced astigmatism are scarce. The purpose of this study was to evaluate the astigmatism induced by aspheric and toric IOL tilt in a theoretical model constructed using optical design software. MATERIALS AND METHODS Eye Model Opticstudio (Zemax, LLC) generates ray tracing models of optical systems from user-designed specifications. With this software, theoretical eye models were constructed using the parameters outlined below. Corneal Data The cornea was modeled as 2 aspheric surfaces with a central thickness of 0.550 mm. Detailed parameters are listed in Table 1 and are the same as those used in the study by Holladay and Simpson.9 Pupil Plane The pupillary aperture was set at 6.00 mm and was placed 4.05 mm behind the anterior corneal surface. Intraocular Lens Data The anterior IOL surface was placed 0.50 mm behind the pupil plane or 4.55 mm posterior to the
Submitted: February 7, 2018 | Final revision submitted: March 22, 2018 | Accepted: April 1, 2018 From Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine, Houston, Texas, USA. Supported in part by an unrestricted grant from Research to Prevent Blindness, New York, New York, USA. Corresponding author: Mitchell P. Weikert, MD, Cullen Eye Institute, Baylor College of Medicine, 6565 Fannin, NC 205, Houston, Texas 77030, USA. Email: mweikert@ bcm.edu. Q 2018 ASCRS and ESCRS Published by Elsevier Inc.
0886-3350/$ - see frontmatter https://doi.org/10.1016/j.jcrs.2018.04.035
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
anterior corneal surface. Aspheric IOLs and toric IOLs were included in the eye models. For aspheric IOLs, the specific optical parameters for the Acrysof IQ monofocal IOL (SN60WF) were provided by the manufacturer, Alcon Laboratories, Inc. The parameters included the anterior and posterior curvatures, asphericity, and thickness. Eye models with powers of 16.0 diopters (D), 22.0 D, and 28.0 D were constructed. For toric IOLs, specific optical parameters were not available for the Acrysof IQ. Thus, general optical parameters for the SN60WF, including the lens asphericity conic constant and lens thickness, were used for toric IOL construction. To create a toric IOL with a specific lens power, the anterior radius of curvature of a SN60WF IOL with the same refractive power was used. The radii of curvature for the steep and flat meridians of the posterior surface were then determined using OpticStudio optical design software to produce the desired overall IOL power. For example, to create a 22.0 D lens with a cylinder power of 6.0 D, the radius of curvature on the anterior surface was the same as the radius of curvature on the anterior surface for a 22.0 D aspheric IOL and radii of curvature to produce equivalent power of 19.0 D and 25.0 D were determined and used for the flat meridian and steep meridian on the back surface. Eye models were constructed using 16.0 D, 22.0 D, and 28.0 D toric IOLs with cylinder powers of 1.50 D (SN6AT3), 3.75 D (SN6AT6), and 6.00 D (SN6AT9). Intraocular Lens Tilt Previous studiesA,4 have reported that IOLs were tilted greatest in a nasal direction. In the model used, aspheric IOLs and toric IOLs were tilted horizontally around a vertical meridian with the nasal border tilted anteriorly and the temporal border tilted posteriorly in 1-degree steps up to 10 degrees. For the toric IOLs, horizontal lens tilt was performed with the IOLs aligned at 90 degrees (as if correcting with-the-rule [WTR] corneal astigmatism) and at 180 degrees (as if correcting against-the-rule [ATR] corneal astigmatism). Data Analysis For each eye model and IOL power, the ray-tracing software was used to optimize the vitreous cavity length before the IOL was titled. Wavefront aberrations at the corneal plane up to the 7th order were calculated for a 6.0 mm pupil and IOL tilt from 0 to 10 degrees. Second-order astigmatism data without and with IOL tilt were evaluated. Because the IOL was tilted horizontally, only the astigmatism term Z(2,2) was relevant in this study. For easy comprehension, Zernike coefficient values of the 2nd-order astigmatism Z(2,2) ðC22 Þ in micrometers were converted to diopters (D) using the following equation: pffiffiffi C Z 4 6 C22 R2
where C is the dioptric power of the cylinder and R is the radius of the pupil in mm. This equation pffiffiffiis a modification of the original conversion equation CZ 4 6 C22 =R2 described by Applegate et al.10 In this study, the equivalent dioptric power of C22 in micrometers, not the traditional cylinder correction format, was calculated. The 2nd-order astigmatism induced by IOL tilt at corneal plane was calculated.
RESULTS Aspheric Intraocular Lens Tilt
Figure 1 shows the aspheric IOL tilt-induced ATR astigmatism. Table 2 shows the induced 2nd-order astigmatism by degree of tilt. The astigmatism induced by IOL tilt increased as both IOL tilt and power were increased. Toric Intraocular Lens Tilt
Toric IOL tilt induced astigmatism that was dependent on IOL alignment and power (Figure 2 and Table 2). When the toric IOLs were aligned at 90 degrees, IOL tilt increased the ATR astigmatic effect at the corneal plane. The induced ATR astigmatism also increased as tilt increased. When the toric IOLs were aligned at 180 degrees, IOL tilt decreased the WTR astigmatic effect at the corneal plane. The deduction in WTR astigmatism increased as tilt increased and decreased as toricity increased. DISCUSSION In a previous study using the IOLMaster 700 SS-OCT biometer to examine postoperative IOL position, Hirnschall et al.5 found IOL tilt was greatest in a horizontal direction (around a vertical meridian) with the nasal border displaced anteriorly and the temporal border displaced posteriorly at an average magnitude of 6.2 degrees. Tilt direction and magnitude were similar in right eyes and left eyes. In a comparable study at our institution,A we found similar tilt directions and magnitudes, with a mean IOL tilt of 4.9 degrees (range 2 to 10 degrees). In this study, which used OpticStudio ray-tracing software, we evaluated the astigmatism induced by aspheric and toric IOL tilts ranging from 0 to 10 degrees. We also investigated the effect of IOL power, IOL toricity, and toric
Table 1. Nominal values used in the eye model. Parameter Corneal anterior surface radius (mm) Corneal anterior surface Q value Corneal index of refraction @555 nm Corneal thickness (mm) Corneal posterior surface radius (mm) Corneal posterior surface Q value Pupil plane behind anterior corneal surface (mm) IOL anterior surface plane behind anterior corneal surface (mm) IOL Z intraocular lens; Q value Z asphericity
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Value 7.76 0.26 1.376 0.55 6.36 0.24 4.05 4.55
Figure 1. Tilt-induced ATR astigmatism (D) in eyes with aspheric IOLs (ATR Z against-the-rule; IOL Z intraocular lens).
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
Table 2. Induced 2nd-order astigmatism Z(2,2) in dioptric power by tilt ( ). IOL Model and Power Aspheric IOL: increased ATR astigmatism 16.0 D 22.0 D 28.0 D 16.0 D toric IOL @90: increased ATR astigmatism SN6AT3 SN6AT6 SN6AT9 @180: decreased WTR astigmatism SN6AT3 SN6AT6 SN6AT9 22.0 D toric IOL @90: increased ATR astigmatism SN6AT3 SN6AT6 SN6AT9 @180: decreased WTR astigmatism SN6AT3 SN6AT6 SN6AT9 28.0 D toric IOL @90: increased ATR astigmatism SN6AT3 SN6AT6 SN6AT9 @180: decreased WTR astigmatism SN6AT3 SN6AT6 SN6AT9
1
2
3
4
5
6
7
8
9
10
0.00 0.00 0.01
0.01 0.02 0.02
0.03 0.04 0.05
0.05 0.07 0.09
0.08 0.11 0.14
0.11 0.16 0.20
0.16 0.21 0.27
0.21 0.28 0.35
0.26 0.36 0.45
0.33 0.44 0.56
0.00 0.00 0.00
0.01 0.02 0.02
0.03 0.04 0.04
0.06 0.06 0.07
0.09 0.10 0.11
0.13 0.14 0.16
0.17 0.20 0.22
0.23 0.26 0.29
0.29 0.33 0.36
0.36 0.41 0.45
0.00 0.00 0.00
0.01 0.01 0.01
0.03 0.02 0.02
0.05 0.04 0.03
0.07 0.06 0.05
0.10 0.09 0.07
0.14 0.12 0.10
0.19 0.16 0.13
0.24 0.20 0.16
0.30 0.25 0.20
0.00 0.01 0.01
0.02 0.02 0.02
0.04 0.05 0.05
0.07 0.08 0.09
0.12 0.13 0.14
0.17 0.18 0.20
0.23 0.25 0.27
0.30 0.33 0.36
0.38 0.42 0.46
0.47 0.52 0.57
0.00 0.00 0.00
0.02 0.01 0.01
0.04 0.03 0.03
0.06 0.06 0.05
0.10 0.09 0.08
0.15 0.13 0.11
0.20 0.18 0.16
0.26 0.23 0.20
0.33 0.30 0.26
0.41 0.37 0.32
0.01 0.01 0.01
0.02 0.02 0.03
0.05 0.05 0.06
0.09 0.10 0.10
0.14 0.15 0.16
0.21 0.22 0.24
0.28 0.30 0.32
0.37 0.40 0.42
0.47 0.50 0.54
0.58 0.63 0.67
0.01 0.00 0.00
0.02 0.02 0.02
0.05 0.04 0.04
0.08 0.07 0.07
0.13 0.12 0.11
0.18 0.17 0.15
0.25 0.23 0.21
0.33 0.30 0.27
0.42 0.39 0.35
0.52 0.48 0.43
ATR Z against-the-rule; IOL Z intraocular lens; WTR Z with-the-rule
IOL alignment at 90 degrees and at 180 degrees on the magnitude of tilt-induced astigmatism. Our results showed that IOL tilt induced astigmatism and the resultant astigmatism increased with increasing degree of tilt and IOL power. Horizontal aspheric IOL tilt around a vertical meridian (ie, tilt around 90 degrees meridian with the nasal border of the IOL displaced anteriorly and the temporal border displaced posteriorly) induced ATR astigmatism. Tilting a toric IOL that was aligned at 90 degrees (ie, greater IOL power along the horizontal meridian) in this manner increased the magnitude of the induced ATR astigmatism, resulting in astigmatic overcorrection. Tilting a toric IOL that was aligned at 180 degrees (ie, greater IOL power along the vertical meridian) decreased the magnitude of the induced WTR astigmatism, resulting in astigmatic undercorrection. For average IOL powers (eg, 22.0 D) with average tilts of 5 to 6 degrees, the induced astigmatism was approximately 0.1 to 0.2 D. When the tilt of these IOLs increased to 10 degrees, the resultant astigmatism increased significantly to 0.4 to 0.5 D. The magnitude of the induced astigmatism increased even more as IOL power increased. In our study evaluating IOL tilt, we found that short eyes tended to have greater degrees of IOL tilt.A Because short eyes also tend to
require higher IOL powers, it might be worthwhile to consider the effect of IOL tilt when formulating a plan for astigmatic correction. Factoring in the effect of IOL tiltinduced astigmatism might have the potential to improve refractive accuracy and image quality in this challenging group of patients. One important finding in this study was the effect of IOL tilt on the actual versus intended level of astigmatic correction achieved with toric IOLs. Tilting toric IOLs horizontally around a vertical meridian resulted in overcorrection of WTR astigmatism when they were aligned at 90 degrees and undercorrection of ATR astigmatism when aligned at 180 degrees. The contribution of posterior corneal astigmatism to total corneal astigmatism has been studies, and it has been shown that ignoring posterior corneal astigmatism can lead to overcorrection in eyes that have WTR corneal astigmatism and undercorrection in eyes that have ATR corneal astigmatism.11 Previous studies12,13 have evaluated the accuracy of total corneal astigmatism calculated from anterior and posterior corneal curvature measurements via Scheimpflug imaging to predict ideal astigmatic correction targets in toric IOL implantation. These studies showed that the use of total
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
Figure 2. Tilt-induced astigmatism in eyes with toric IOLs aligned at 90 degrees and 180 degrees for correction of corneal WTR and ATR astigmatism, respectively (ATR Z against the rule; IOLs Z intraocular lenses; WTR Z with-the-rule).
corneal astigmatism still resulted in overcorrection of eyes with WTR corneal astigmatism and undercorrection of eyes with ATR corneal astigmatism. Based on these findings, the accuracy of posterior corneal astigmatism measurements using Scheimpflug imaging was called into question. However, our findings suggest that astigmatism induced by IOL tilt might help explain the residual astigmatism found with use of total corneal astigmatism measurements. Given these results, consideration of both posterior corneal astigmatism and IOL tilt-induced astigmatism might improve toric IOL calculations and planning. Further studies assessing the effect of IOL tilt on ocular astigmatism in patients with toric IOL implantation are desirable. Our results showed that increasing the amount of toricity in the tilted IOL produced different effects on induced astigmatism depending on the alignment of the toric IOL. When toric IOLs were aligned at 90 degrees to correct corneal WTR astigmatism, higher IOL toricities yielded greater increases in ATR astigmatism. In contrast, when toric IOLs were aligned at 180 degrees to correct corneal ATR astigmatism, the reduction in WTR astigmatism correction decreased as IOL toricity increased. Therefore, when selecting toric IOLs in eyes with greater crystalline lens tilt or in eyes with high IOL powers, consideration of the effect of tilt on ocular astigmatism might improve refractive accuracy.
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Marcos et al.14 reported an equation to easily estimate the theoretical astigmatism induced by a tilted thin IOL. An ophthalmic lens in air of C22.0 D tilted 10 degrees produced astigmatism of 0.69 D. In our study using the ray-tracing approach, a 22.0 D aspheric IOL immersed in aqueous with tilt of 10 degrees produced astigmatism of 0.44 D. This study has several limitations inherent in its design. First, it was a theoretical study. Evaluation of astigmatism induced by IOL tilt using actual patient data is ongoing. Second, in the toric IOL model, the asphericity and anterior corneal radius of curvature for the Acrysof SN60WF IOL were used (exact toric IOL data for each model was unavailable). Toric IOLs with different optical specifications might produce different amounts of astigmatism with tilt. Third, in this model, only the IOLs were tilted (ie, the cornea was not tilted). In human eyes, the cornea can also manifest tilt and decentration. Fourth, 2nd-order astigmatism data with and without IOL tilt were used to assess the effect of IOL tilt on total ocular astigmatism. Astigmatism from higher-order Zernike terms might have contributed to the astigmatism induced by tilt; however, we believe their contribution is minimal. In conclusion, our study found that induced astigmatism increased with increasing degree of IOL tilt and IOL power. Tilting aspheric IOLs horizontally around a vertical
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LABORATORY SCIENCE: ASTIGMATISM INDUCED BY IOL TILT
meridian (as seen in previous studies) induced ATR astigmatism. Tilting toric IOLs aligned at 90 degrees in a similar fashion increased the magnitude of induced ATR astigmatism, producing overcorrection of WTR astigmatism. Tilting toric IOLs aligned at 180 degrees decreased the magnitude of induced WTR astigmatism, resulting in undercorrection of ATR astigmatism. Further studies of the effect of IOL tilt on ocular astigmatism in a clinical setting are warranted. WHAT WAS KNOWN Intraocular lenses tilt greatest around a vertical meridian with the nasal border displaced anteriorly and the temporal border displaced posteriorly at average magnitude of 5 to 6 degrees.
WHAT THIS PAPER ADDS Intraocular lens tilt-induced astigmatism assessed using a ray-tracing model showed that ATR astigmatism was induced by aspheric IOLs tilted horizontally around the vertical meridian. The induced astigmatism increased with increasing IOL tilt and power. Tilting toric IOLs aligned at 90 degrees increased ATR astigmatism and resulted in overcorrection. Tilting toric IOLs aligned at 180 degrees decreased WTR astigmatism and produced undercorrection.
REFERENCES 1. Mura JJ, Pavlin CJ, Condon GP, Belovay GW, Kranemann CF, Ishikawa H, Ahmed II. Ultrasound biomicroscopic analysis of iris-sutured foldable posterior chamber intraocular lenses. Am J Ophthalmol 2010; 149:245–252 2. de Castro A, Rosales P, Marcos S. Tilt and decentration of intraocular lenses in vivo from Purkinje and Scheimpflug imaging; validation study. J Cataract Refract Surg 2007; 33:418–429 3. Kumar DA, Agarwal A, Prakash G, Jacob S, Saravanan Y, Agarwal A. Evaluation of intraocular lens tilt with anterior segment optical coherence tomography. Am J Ophthalmol 2011; 151:406–412 4. Holladay JT, Calogero D, Hilmantel G, Glasser A, MacRae S, Masket S, Stark W, Tarver ME, Nguyen T, Eydelman M. Special report: American Academy of Ophthalmology Task Force summary statement for measurement of tilt, decentration, and chord length. Ophthalmology 2017; 124:144–146. Available at: https://www.aaojournal.org/article/S0161-64 20(16)31419-1/pdf. Accessed May 2, 2018
5. Hirnschall N, Buehren T, Bajramovic F, Trost M, Teuber T, Findl O. Prediction of postoperative intraocular lens tilt using swept-source optical coherence tomography. J Cataract Refract Surg 2017; 43:732–736 €ffler A, Meßner A, Langenbucher A. Effect of decen6. Eppig T, Scholz K, Lo tration and tilt on the image quality of aspheric intraocular lens designs in a model eye. J Cataract Refract Surg 2009; 35:1091–1100 rez-Vives C, Ferrer-Blasco T, Lo pez7. Madrid-Costa D, Ruiz-Alcocer J, Pe s-Mico R. Visual simulation through different intraocular lenses Gil N, Monte using adaptive optics: effect of tilt and decentration. J Cataract Refract Surg 2012; 38:947–958 €hren J, Kohnen T. Tilt and decentration of spherical and 8. Baumeister M, Bu aspheric intraocular lenses: effect on higher-order aberrations. J Cataract Refract Surg 2009; 35:1006–1012 9. Holladay JT, Simpson MJ. Negative dysphotopsia: causes and rationale for prevention and treatment. J Cataract Refract Surg 2017; 43:263–275 10. Applegate RA, Ballentine C, Gross H, Sarver EJ, Sarver CA. Visual acuity as a function of Zernike mode and level of root mean square error. Optom Vis Sci 2003; 80:97–105. Available at: http://journals.lww.com/optvissci/Full text/2003/02000/Visual_Acuity_as_a_Function_of_Zernike_Mode_and.5 .aspx. Accessed May 2, 2018 11. Koch DD, Ali SF, Weikert MP, Shirayama M, Jenkins R, Wang L. Contribution of posterior corneal astigmatism to total corneal astigmatism. J Cataract Refract Surg 2012; 38:2080–2087 12. Koch DD, Jenkins RB, Weikert MP, Yeu E, Wang L. Correcting astigmatism with toric intraocular lenses: effect of posterior corneal astigmatism. J Cataract Refract Surg 2013; 39:1803–1809 13. Savini G, Næser K, Schiano-Lomoriello D, Ducoli P. Optimized keratometry and total corneal astigmatism for toric intraocular lens calculation. J Cataract Refract Surg 2017; 43:1140–1148 14. Marcos S. Special circumstances: effect of IOL tilt on astigmatism. In: Hoffer KJ, ed, IOL Power. Thorofare, NJ, Slack, 2011; 223–230 OTHER CITED MATERIAL A. Wang L, Guimaraes de Souza R, Golla A, Weikert MP, Koch DD, “Evaluation of Crystalline Lens and IOL Tilt using Swept-Source Biometry,” presented at the ASCRS Symposium on Cataract, IOL and Refractive Surgery, Los Angeles, California, USA, May 2017
Disclosures: None of the authors has a financial or proprietary interest in any material or method mentioned.
First author: Mitchell P. Weikert, MD Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine, Houston, Texas, USA
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