Journal of Refractive Surgery

Original Article 

Sources of Error in Toric Intraocular Lens Power Calculation

Nino Hirnschall, MD, PhD; Oliver Findl, MD, MBA; Natascha Bayer, MSc; Christoph Leisser, MD; Sverker Norrby, PhD; Eva Zimper, MD; Peter Hoffmann, MD

Abstract

PURPOSE:

To evaluate the influencing factors on remaining astigmatism after implanting a toric intraocular lens (IOL) during cataract surgery.

METHODS:

This retrospective study included parameters that were considered to have an influence on toric IOL power calculation. Therefore, data from the literature and the authors' own data were used. This included axial eye length, anterior chamber depth, central corneal thickness, corneal radii (anterior and posterior), diurnal changes of the cornea, inter-device differences, rotational misalignment of the IOL, tilt and decentration of the IOL, pupil size, angle kappa, and surgically induced astigmatism. Ray-tracing and Gaussian error propagation analysis was performed to quantify the sources of error.

RESULTS:

In total, 4,949 eyes (4,365 eyes of 42 studies and 584 eyes of retrospectively analyzed study data) were included in the study and the difference vector between aimed and calculated remaining astigmatism was 0.81 diopters (D). The main source of error was the preoperative measurement of the cornea (27%), followed by IOL misalignment (14.4%) and IOL tilt (11.3%). Other factors, such as angle kappa (10.9%), pupil size (8.1%), surgically induced astigmatism (7.8%), anterior chamber depth (7.5%), axial eye length (7.5%), and decentration (5.6%), also contributed to the refractive astigmatic error.

CONCLUSIONS:

The main source of error in toric IOL power calculation is the preoperative corneal measurement followed by IOL misalignment and tilt.

[J Refract Surg. 2020;36(10):646–652.]

Abstract

PURPOSE:

To evaluate the influencing factors on remaining astigmatism after implanting a toric intraocular lens (IOL) during cataract surgery.

METHODS:

This retrospective study included parameters that were considered to have an influence on toric IOL power calculation. Therefore, data from the literature and the authors' own data were used. This included axial eye length, anterior chamber depth, central corneal thickness, corneal radii (anterior and posterior), diurnal changes of the cornea, inter-device differences, rotational misalignment of the IOL, tilt and decentration of the IOL, pupil size, angle kappa, and surgically induced astigmatism. Ray-tracing and Gaussian error propagation analysis was performed to quantify the sources of error.

RESULTS:

In total, 4,949 eyes (4,365 eyes of 42 studies and 584 eyes of retrospectively analyzed study data) were included in the study and the difference vector between aimed and calculated remaining astigmatism was 0.81 diopters (D). The main source of error was the preoperative measurement of the cornea (27%), followed by IOL misalignment (14.4%) and IOL tilt (11.3%). Other factors, such as angle kappa (10.9%), pupil size (8.1%), surgically induced astigmatism (7.8%), anterior chamber depth (7.5%), axial eye length (7.5%), and decentration (5.6%), also contributed to the refractive astigmatic error.

CONCLUSIONS:

The main source of error in toric IOL power calculation is the preoperative corneal measurement followed by IOL misalignment and tilt.

[J Refract Surg. 2020;36(10):646–652.]

Toric intraocular lens (IOL) implantation successfully treats corneal astigmatism and provides independence from distance spectacles in more than 70% of all cases compared to less than 50% in the case of non-toric IOLs.1 However, a moderate number of patients still have relevant remaining astigmatism after toric IOL implantation, resulting in patient dissatisfaction.

One way to evaluate and quantify sources of error in (toric) IOL power calculation is ray-tracing combined with Gaussian error propagation. This error quantification was performed for monofocal IOL power calculation in the past,2,3 but not for toric IOLs. Although a variety of publications focus on single or multiple errors in toric IOL power calculation,4–7 to our knowledge, no error quantification using Gaussian error propagation has been published so far.

The aim of this study was to detect and quantify the most relevant sources of error in toric IOL power calculation, including data from the literature and retrospectively analyzed data.

Patients and Methods

This retrospective ray-tracing and Gaussian error propagation analysis included parameters that were considered to have an influence on toric IOL power calculation from different studies using toric IOLs or related to toric IOL implantation. This included axial eye length, anterior chamber depth, central corneal thickness, keratometry (corneal radii and steep axis of anterior and posterior surface), diurnal changes of the cornea, inter-device differences of different corneal measurement techniques (including the posterior surface of the cornea), rotational misalignment of the IOL, tilt and decentration of the IOL, pupil size, angle kappa (angle between line of sight and pupillary axis), and surgically induced astigmatism.

The following concept was used: for those parameters that are usually included in toric IOL power calculation (axial eye length, anterior chamber depth, and corneal radii [anterior and posterior]), the standard deviation of measurement reproducibility was used. The reason is that the magnitude of error for these parameters depends mainly on the reproducibility of the measurement. For those parameters that are usually not included in toric IOL power calculation (diurnal changes of the cornea, inter-device differences [including posterior surface of the cornea], central corneal thickness, rotational misalignment of the IOL, tilt and decentration of the IOL, pupil size, angle kappa, and surgically induced astigmatism), the standard deviation between patients (inter-patient deviation) was used. The reason is that these factors either are not considered in toric IOL power calculation or a constant factor is used.

Methods of Evaluation

An eye model based on Liou and Brennan8 was developed using Zemax software (version 16) by one of the authors (NB) and a 3.00 diopters (D) astigmatic cornea was simulated.9 For the eye model, 42 studies2,10–51 (and 584 eyes of retrospectively analyzed data) were included in the analysis. Additionally, one study was used to assess the influence of the posterior surface of the cornea52 and three studies to evaluate the influence of surgically induced astigmatism.13,24,53

Ray-tracing was used to calculate the effect of one standard deviation of each parameter quantified as dioptric value. Vector analysis was performed as suggested by Thibos and Horner.54 In the next step, Gaussian error propagation was performed. Microsoft Excel 2011 software version 14.2.3 for Mac (Microsoft Corporation) with a Xlstat 2012 plug-in (Addinsoft) was used for statistical analysis.

Results

In total, 4,949 eyes (4,365 eyes of 42 studies and 584 eyes of retrospectively analyzed data) were included in the analysis. Table 1 summarizes the included values for the eye model. Total error as a vector difference representing astigmatism caused by error with reference to a starting point of no astigmatism was 0.81 D.

Values for Each Eye Model

Table 1:

Values for Each Eye Model

In the next step, the parameter difference between devices (including posterior surface), corneal radii, central corneal thickness, and diurnal changes were merged because they are part of the corneal measurement error. Merging was performed using a sum vector of all parameters. This corneal measurement error was larger compared to all other parameters (27.0% or 0.59 D) and it sums up 44.5% (0.26 D) of differences between devices (including posterior surface of the cornea), 24.0% (0.14 D) of corneal radii, 16.3% (0.10 D) of diurnal changes, and 15.2% (0.09 D) of central corneal thickness, respectively. Table 2 and Figure 1 represent the distribution of error.

Distribution of Error

Table 2:

Distribution of Error

Error distribution in toric intraocular lens (IOL) power calculation (percent) using a combined vector for all corneal measurement errors and other parameters. Calculations are based on ray-tracing and Gaussian error propagation. SICA = surgically induced corneal astigmatism; ACD = anterior chamber depth; AL = axial length

Figure 1.

Error distribution in toric intraocular lens (IOL) power calculation (percent) using a combined vector for all corneal measurement errors and other parameters. Calculations are based on ray-tracing and Gaussian error propagation. SICA = surgically induced corneal astigmatism; ACD = anterior chamber depth; AL = axial length

The posterior surface of the cornea was included in the model as part of the inter-device difference. The estimated average error deriving from neglecting the posterior surface of the cornea is 0.22 D. In other words, neither measuring nor estimating the posterior surface of the cornea results in an error of approximately 0.22 D, or 37.4% of the corneal measurement error. Additionally, the influence of the standard deviation of the posterior surface reproducibility measurements was assessed. Because this value is small (0.03 D), it was not mentioned in the table.

The measurement error of the cornea depends on the measurement technique. Therefore, a subanalysis using difference vectors from Hoffmann et al25 was used.

The corneal measurement error for swept-source optical coherence tomography, automated keratometry, and Scheimpflug imaging was 19.2% (0.42 D), 25.6% (0.56 D), and 32.0% (0.70 D), respectively (Figure 2). These values account for the simulation of a 3.00 D astigmatic cornea. In the case of low astigmatism, the corneal measurement error increases.

Double-angle plot for postoperative refractive astigmatism prediction error on the corneal plane using three different measurement techniques: triangle = swept-source optical coherence tomography technology, circle = autokeratometry, square = Scheimpflug measurement; D = diopters

Figure 2.

Double-angle plot for postoperative refractive astigmatism prediction error on the corneal plane using three different measurement techniques: triangle = swept-source optical coherence tomography technology, circle = autokeratometry, square = Scheimpflug measurement; D = diopters

In this eye model, the influence of the toric IOL would only be expressed by differences in rotational misalignment. Due to the fact that all modern toric IOLs show a mean absolute rotational misalignment below 5°, the difference was found to be negligible.

Simulating the surgically induced corneal astigmatism with a standard deviation of 0.31 D (104 eyes from the VIROS database) and 0.37 D resulted in a difference vector of 0.70 D in the ray-tracing model. However, if only the flattening effect of a 2.2-mm temporal incision was used (0.20 ± 0.24 D), the percentage of the total error would be 7.8%. This value was included in the Gaussian error propagation.

Discussion

This ray-tracing and Gaussian error propagation model shows that more than one-quarter of the error in toric IOL power calculation derives from the corneal measurement. It should be mentioned that the calculation would have been slightly different if another toric IOL power had been used. Furthermore, it is difficult to take interactions between different parameters into account, and this is a potential bias of this study. However, the mean difference vector in the eye model used was similar to results from clinical studies.25,55,56 This similarity can be used for validation purposes of the eye model. Hoffmann et al25 showed similar results for conventional measurement techniques, but the difference vector for swept-source optical coherence tomography (OCT) measurements was lower.

Corneal Measurement

Directly quantifying the error of the preoperative corneal measurement is not possible because the “true power” of the cornea is not known and changes over time and even during the day were observed. Therefore, a surrogate parameter was used: the standard deviation of the difference vector between corneal measurement devices. To aim for a real-life scenario, different measurement techniques (eg, keratometry, Placido disc-based topography, and Scheimpflug- and OCT-based tomography) were included in the model and the vector difference between devices was averaged. This means that this value also takes into account the posterior surface of the cornea. As shown by Hoffmann et al,25 modern measurement techniques such as swept-source OCT technology may reduce the prediction error, especially in combination with keratometry and ray-tracing. It should also be mentioned that the measurement error is relatively larger in low astigmatism, especially due to difficulties in meridian detection57 compared to moderate or high corneal astigmatism.24 Additionally, fluctuations of the tear film changes and eye drops58,59 significantly influence measurements of the cornea.

The influence of the posterior surface is relevant and the difference vector between anterior and total astigmatism was 0.30 D, with a maximum of 1.50 D.60

One problem in the ray-tracing and Gaussian error propagation model is that it is difficult to take interactions between parameters into account. Examples of such interactions are reproducibility-based error and diurnal change error. To improve this model, we used a sum vector of all explanatory variables summarized in “corneal measurement” to reduce this problem. In the second part of this analysis, we also calculated the influence of the posterior surface of the cornea on the corneal measurement error. Neglecting (not measuring and not estimating) the posterior surface of the cornea results in approximately one-third of the corneal measurement error.

Misalignment

Misalignment is the second largest source of error in toric IOL power calculation and it is the sum vector of preoperative/intraoperative marking error, implantation error, and postoperative rotation of a toric IOL. Preoperative marking was shown to result in a minor but relevant rotational error and there was a device-dependent difference.38,60 Intraoperative use of augmented reality was shown to reduce misalignment slightly.61 Postoperative rotation was a large source of error in the past, but modern toric IOLs have been shown to have good rotational stability.62 Visser et al63 calculated the combined vector for all steps of mis-alignment and found similar values to our study. Although mean absolute misalignment is usually small, there is a large deviation between patients, resulting in a relevant source of error in toric IOL power calculation. However, this study did not include a comparative analysis between different marking and aligning techniques. Therefore, it is possible that this amount of error differs between different centers.

Tilt and Angle Kappa

Tilt and angle kappa were shown to be relevant sources of error that are usually not considered in toric IOL power calculation. This finding was also confirmed for tilt in a previous study.64 A tilt prediction algorithm was recently introduced using preoperative tilt measurements with swept-source OCT. It was shown that the orientation of the postoperative tilt can be predicted with good precision.65 It is possible that taking angle kappa and tilt prediction into account results in a better toric IOL power calculation.

Pupil Size

Pupil size was shown to be a relatively small source of error. It appears that different designs of toric IOLs are less dependent on pupil size compared to others.66 For the error propagation, a commonly available aspheric toric IOL was used for simulation purposes. Nevertheless, there are case reports suggesting that pupil size can be a relevant cause of remaining astigmatism.67

Surgically Induced Corneal Astigmatism

Surgically induced corneal astigmatism showed the limits of Gaussian error propagation. The reason is that surgically induced corneal astigmatism is on average small, but the standard deviation between patients is large. However, this standard deviation is influenced by a variety of factors, such as corneal measurement error, tear film problems, and diurnal changes. All of these interactions between parameters influence the standard deviation, resulting in an unreliable parameter. Therefore, the flattening effect of a 2.2-mm temporal incision was included in the model. In a previous study using partial least squares regression modelling, it was shown that the influence of surgically induced corneal astigmatism is small with a high amount of unpredictability.4

Anterior Chamber Depth and Axial Eye Length

Anterior chamber depth and axial eye length had a minor impact on toric IOL power calculation. Both parameters are important to predict the axial position of a toric IOL. Although this mainly influences the spherical equivalent, it also has an influence on residual astigmatism, especially in the case of high-powered toric IOLs.20

Decentration

Contrary to tilt, decentration plays a minor role in the case of toric IOLs in terms of residual astigmatism. This was also shown in a previous study on the optic bench.66

Limitations

There are several limitations of this study. First, the different parameters had to be simplified to be used for Gaussian error propagation. This is especially the case for the factor “corneal measurement.” Depending on the measurement method, the error distribution changes. We added a subanalysis in this study, but a more detailed comparison in a prospective trial including the influence of the posterior surface of the cornea in Gaussian error propagation would be useful. Another limitation is that the influence of each parameter changes depending on the astigmatic correction. In case of low corneal astigmatism, the influence of the corneal measurement increases, whereas misalignment is more relevant in correction of high corneal astigmatism.

A second minor limitation is the choice of the eye model. The Liou and Brennan eye model was chosen because it is a “finite” eye model instead of a paraxial model. Therefore, this model allows better simulation of optical imaging farther from the visual axis and simulation of a larger pupil size. This suggestion was taken from a publication from Atchison and Thibos.68 However, other eye models would have performed slightly differently.

The main source of error in toric IOL power calculation is the preoperative corneal measurement, followed by misalignment and tilt of the IOL. These findings suggest that measurement techniques should be improved to increase the predictability of toric IOL power calculation, which includes the measurement of the posterior surface of the cornea. Furthermore, angle kappa and tilt should be used in toric IOL power calculation in the future.

References

  1. Kessel L, Andresen J, Tendal B, Erngaard D, Flesner P, Hjortdal J. Toric intraocular lenses in the correction of astigmatism during cataract surgery: a systematic review and meta-analysis. Ophthalmology. 2016;123(2):275–286. doi:10.1016/j.ophtha.2015.10.002 [CrossRef]
  2. Norrby S. Sources of error in intraocular lens power calculation. J Cataract Refract Surg. 2008;34(3):368–376. doi:10.1016/j.jcrs.2007.10.031 [CrossRef]
  3. Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg. 1992;18(2):125–129. doi:10.1016/S0886-3350(13)80917-0 [CrossRef]
  4. Hirnschall N, Hoffmann PC, Draschl P, Maedel S, Findl O. Evaluation of factors influencing the remaining astigmatism after toric intraocular lens implantation. J Refract Surg. 2014;30(6):394–400. doi:10.3928/1081597X-20140429-01 [CrossRef]
  5. Kaur M, Shaikh F, Falera R, Titiyal JS. Optimizing outcomes with toric intraocular lenses. Indian J Ophthalmol. 2017;65(12):1301–1313. doi:10.4103/ijo.IJO_810_17 [CrossRef]
  6. Kramer BA, Berdahl JP, Hardten DR, Potvin R. Residual astigmatism after toric intraocular lens implantation: analysis of data from an online toric intraocular lens back-calculator. J Cataract Refract Surg. 2016;42(11):1595–1601. doi:10.1016/j.jcrs.2016.09.017 [CrossRef]
  7. Potvin R, Kramer BA, Hardten DR, Berdahl JP. Toric intraocular lens orientation and residual refractive astigmatism: an analysis. Clin Ophthalmol. 2016;10:1829–1836. doi:10.2147/OPTH.S114118 [CrossRef]
  8. Liou HL, Brennan NA. Anatomically accurate, finite model eye for optical modeling. J Opt Soc Am A Opt Image Sci Vis. 1997;14(8):1684–1695. doi:10.1364/JOSAA.14.001684 [CrossRef]
  9. Bayer N, Hirnschall N, Traxler L, et al. Analysing the impact of a misaligned toric intraocular lens on wave front aberrations. Presented as a poster at the Association for Research in Vision and Ophthalmology meeting. ; May 6–11, 2017. ; Baltimore, Maryland. .
  10. Abulafia A, Barrett GD, Kleinmann G, et al. Prediction of refractive outcomes with toric intraocular lens implantation. J Cataract Refract Surg. 2015;41(5):936–944. doi:10.1016/j.jcrs.2014.08.036 [CrossRef]
  11. Ahmed II, Rocha G, Slomovic AR, et al. Canadian Toric Study Group. Visual function and patient experience after bilateral implantation of toric intraocular lenses. J Cataract Refract Surg. 2010;36(4):609–616. doi:10.1016/j.jcrs.2009.10.044 [CrossRef]
  12. Akman A, Asena L, Güngör SG. Evaluation and comparison of the new swept source OCT-based IOLMaster 700 with the IOLMaster 500. Br J Ophthalmol. 2016;100(9):1201–1205. doi:10.1136/bjophthalmol-2015-307779 [CrossRef]
  13. Alió JL, Piñero DP, Tomás J, Alesón A. Vector analysis of astigmatic changes after cataract surgery with toric intraocular lens implantation. J Cataract Refract Surg. 2011;37(6):1038–1049. doi:10.1016/j.jcrs.2010.12.053 [CrossRef]
  14. Aramberri J, Araiz L, Garcia A, et al. Dual versus single Scheimpflug camera for anterior segment analysis: precision and agreement. J Cataract Refract Surg. 2012;38(11):1934–1949. doi:10.1016/j.jcrs.2012.06.049 [CrossRef]
  15. Bauer NJ, de Vries NE, Webers CA, Hendrikse F, Nuijts RM. Astigmatism management in cataract surgery with the AcrySof toric intraocular lens. J Cataract Refract Surg. 2008;34(9):1483–1488. doi:10.1016/j.jcrs.2008.05.031 [CrossRef]
  16. Bjelos Roncevic M, Busic M, Cima I, Kuzmanovic Elabjer B, Bosnar D, Miletic D. Comparison of optical low-coherence reflectometry and applanation ultrasound biometry on intraocular lens power calculation. Graefes Arch Clin Exp Ophthalmol. 2011;249(1):69–75. doi:10.1007/s00417-010-1509-4 [CrossRef]
  17. Bullimore MA, Buehren T, Bissmann W. Agreement between a partial coherence interferometer and 2 manual keratometers. J Cataract Refract Surg. 2013;39(10):1550–1560. doi:10.1016/j.jcrs.2013.03.034 [CrossRef]
  18. Chang DF. Comparative rotational stability of single-piece open-loop acrylic and plate-haptic silicone toric intraocular lenses. J Cataract Refract Surg. 2008;34(11):1842–1847. doi:10.1016/j.jcrs.2008.07.012 [CrossRef]
  19. Chen W, McAlinden C, Pesudovs K, et al. Scheimpflug-Placido topographer and optical low-coherence reflectometry biometer: repeatability and agreement. J Cataract Refract Surg. 2012;38(9):1626–1632. doi:10.1016/j.jcrs.2012.04.031 [CrossRef]
  20. Goggin M, Moore S, Esterman A. Toric intraocular lens outcome using the manufacturer's prediction of corneal plane equivalent intraocular lens cylinder power. Arch Ophthalmol. 2011;129(8):1004–1008. doi:10.1001/archophthalmol.2011.178 [CrossRef]
  21. Güler E, Kulak AE, Totan Y, Yuvarlak A, Hepsen IF. Comparison of a new optical biometry with an optical low-coherence reflectometry for ocular biometry. Cont Lens Anterior Eye. 2016;39(5):336–341. doi:10.1016/j.clae.2016.06.001 [CrossRef]
  22. Harrer A, Hirnschall N, Tabernero J, et al. Variability in angle kappa and its influence on higher-order aberrations in pseudophakic eyes. J Cataract Refract Surg. 2017;43(8):1015–1019. doi:10.1016/j.jcrs.2017.05.028 [CrossRef]
  23. Hill W. Expected effects of surgically induced astigmatism on AcrySof toric intraocular lens results. J Cataract Refract Surg. 2008;34(3):364–367. doi:10.1016/j.jcrs.2007.10.024 [CrossRef]
  24. Hoffmann PC, Auel S, Hütz WW. Results of higher power toric intraocular lens implantation. J Cataract Refract Surg. 2011;37(8):1411–1418. doi:10.1016/j.jcrs.2011.02.028 [CrossRef]
  25. Hoffmann PC, Abraham M, Hirnschall N, Findl O. Prediction of residual astigmatism after cataract surgery using swept source Fourier domain optical coherence tomography. Curr Eye Res. 2014;39(12):1178–1186. doi:10.3109/02713683.2014.898376 [CrossRef]
  26. Kim MH, Chung TY, Chung ES. Long-term efficacy and rotational stability of AcrySof toric intraocular lens implantation in cataract surgery. Korean J Ophthalmol. 2010;24(4):207–212. doi:10.3341/kjo.2010.24.4.207 [CrossRef]
  27. 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(12):2080–2087. doi:10.1016/j.jcrs.2012.08.036 [CrossRef]
  28. Koshy JJ, Nishi Y, Hirnschall N, et al. Rotational stability of a single-piece toric acrylic intraocular lens. J Cataract Refract Surg. 2010;36(10):1665–1670. doi:10.1016/j.jcrs.2010.05.018 [CrossRef]
  29. Kunert KS, Peter M, Blum M, et al. Repeatability and agreement in optical biometry of a new swept-source optical coherence tomography-based biometer versus partial coherence interferometry and optical low-coherence reflectometry. J Cataract Refract Surg. 2016;42(1):76–83. doi:10.1016/j.jcrs.2015.07.039 [CrossRef]
  30. Kurian M, Negalur N, Das S, et al. Biometry with a new swept-source optical coherence tomography biometer: repeatability and agreement with an optical low-coherence reflectometry device. J Cataract Refract Surg. 2016;42(4):577–581. doi:10.1016/j.jcrs.2016.01.038 [CrossRef]
  31. Lam AK, Chan R, Pang PC. The repeatability and accuracy of axial length and anterior chamber depth measurements from the IOLMaster. Ophthalmic Physiol Opt. 2001;21(6):477–483. doi:10.1046/j.1475-1313.2001.00611.x [CrossRef]
  32. Mao X, Savini G, Zhuo Z, et al. Repeatability, reproducibility, and agreement of corneal power measurements obtained with a new corneal topographer. J Cataract Refract Surg. 2013;39(10):1561–1569. doi:10.1016/j.jcrs.2013.04.029 [CrossRef]
  33. McAlinden C, Khadka J, Pesudovs K. A comprehensive evaluation of the precision (repeatability and reproducibility) of the Oculus Pentacam HR. Invest Ophthalmol Vis Sci. 2011;52(10):7731–7737. doi:10.1167/iovs.10-7093 [CrossRef]
  34. Mendicute J, Irigoyen C, Aramberri J, Ondarra A, Montés-Micó R. Foldable toric intraocular lens for astigmatism correction in cataract patients. J Cataract Refract Surg. 2008;34(4):601–607. doi:10.1016/j.jcrs.2007.11.033 [CrossRef]
  35. Mendicute J, Irigoyen C, Ruiz M, Illarramendi I, Ferrer-Blasco T, Montés-Micó R. Toric intraocular lens versus opposite clear corneal incisions to correct astigmatism in eyes having cataract surgery. J Cataract Refract Surg. 2009;35(3):451–458. doi:10.1016/j.jcrs.2008.11.043 [CrossRef]
  36. Mingo-Botín D, Muñoz-Negrete FJ, Won Kim HR, Morcillo-Laiz R, Rebolleda G, Oblanca N. Comparison of toric intraocular lenses and peripheral corneal relaxing incisions to treat astigmatism during cataract surgery. J Cataract Refract Surg. 2010;36(10):1700–1708. doi:10.1016/j.jcrs.2010.04.043 [CrossRef]
  37. Módis L Jr, Szalai E, Kolozsvári B, Németh G, Vajas A, Berta A. Keratometry evaluations with the Pentacam high resolution in comparison with the automated keratometry and conventional corneal topography. Cornea. 2012;31(1):36–41. doi:10.1097/ICO.0b013e318204c666 [CrossRef]
  38. Popp N, Hirnschall N, Maedel S, Findl O. Evaluation of 4 corneal astigmatic marking methods. J Cataract Refract Surg. 2012;38:2094–9. 32. doi:10.1016/j.jcrs.2012.07.039 [CrossRef]
  39. 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(9):1140–1148. doi:10.1016/j.jcrs.2017.06.040 [CrossRef]
  40. Schulle KL, Berntsen DA. Repeatability of on- and off-axis eye length measurements using the Lenstar. Optom Vis Sci. 2013;90(1):16–22. doi:10.1097/OPX.0b013e3182780bfd [CrossRef]
  41. Shammas HJ, Hoffer KJ. Repeatability and reproducibility of biometry and keratometry measurements using a noncontact optical low-coherence reflectometer and keratometer. Am J Ophthalmol. 2012;153:55–61.e2. doi:10.1016/j.ajo.2011.06.012 [CrossRef]
  42. Shammas HJ, Ortiz S, Shammas MC, Kim SH, Chong C. Biometry measurements using a new large-coherence-length swept-source optical coherence tomographer. J Cataract Refract Surg. 2016;42(1):50–61. doi:10.1016/j.jcrs.2015.07.042 [CrossRef]
  43. Shankar H, Taranath D, Santhirathelagan CT, Pesudovs K. Anterior segment biometry with the Pentacam: comprehensive assessment of repeatability of automated measurements. J Cataract Refract Surg. 2008;34(1):103–113. doi:10.1016/j.jcrs.2007.09.013 [CrossRef]
  44. Srivannaboon S, Chirapapaisan C, Chonpimai P, Loket S. Clinical comparison of a new swept-source optical coherence tomography-based optical biometer and a time-domain optical coherence tomography-based optical biometer. J Cataract Refract Surg. 2015;41(10):2224–2232. doi:10.1016/j.jcrs.2015.03.019 [CrossRef]
  45. Srivannaboon S, Chirapapaisan C. Consistency analysis of surgically induced astigmatism. J Cataract Refract Surg. 2017;43(8):1117–1118. doi:10.1016/j.jcrs.2017.05.037 [CrossRef]
  46. Szalai E, Berta A, Hassan Z, Módis L Jr, . Reliability and repeatability of swept-source Fourier-domain optical coherence tomography and Scheimpflug imaging in keratoconus. J Cataract Refract Surg. 2012;38(3):485–494. doi:10.1016/j.jcrs.2011.10.027 [CrossRef]
  47. Tsinopoulos IT, Tsaousis KT, Tsakpinis D, Ziakas NG, Dimitrakos SA. Acrylic toric intraocular lens implantation: a single center experience concerning clinical outcomes and postoperative rotation. Clin Ophthalmol. 2010;4:137–142.
  48. Visser N, Berendschot TT, Verbakel F, de Brabander J, Nuijts RM. Comparability and repeatability of corneal astigmatism measurements using different measurement technologies. J Cataract Refract Surg. 2012;38(10):1764–1770. doi:10.1016/j.jcrs.2012.05.036 [CrossRef]
  49. Visser N, Ruíz-Mesa R, Pastor F, Bauer NJ, Nuijts RM, Montés-Micó R. Cataract surgery with toric intraocular lens implantation in patients with high corneal astigmatism. J Cataract Refract Surg. 2011;37(8):1403–1410. doi:10.1016/j.jcrs.2011.03.034 [CrossRef]
  50. Zarranz-Ventura J, Moreno-Montañés J, Caire Y, González-Jáuregui J, de Nova Fernández-Yáñez E, Sádaba-Echarri LM. [Acrysof(®) toric intraocular lens implantation in cataract surgery]. Arch Soc Esp Oftalmol. 2010;85(8):274–277. doi:10.1016/j.oftal.2010.09.002 [CrossRef]
  51. Zuberbuhler B, Signer T, Gale R, Haefliger E. Rotational stability of the AcrySof SA60TT toric intraocular lenses: a cohort study. BMC Ophthalmol. 2008;8(1):8. doi:10.1186/1471-2415-8-8 [CrossRef]
  52. Bao F, Savini G, Shu B, et al. Repeatability, reproducibility, and agreement of two Scheimpflug-Placido anterior corneal analyzers for posterior corneal surface measurement. J Refract Surg. 2017;33(8):524–530. doi:10.3928/1081597X-20170606-01 [CrossRef]
  53. Savini G, Næser K. An analysis of the factors influencing the residual refractive astigmatism after cataract surgery with toric intraocular lenses. Invest Ophthalmol Vis Sci. 2015;56(2):827–835. doi:10.1167/iovs.14-15903 [CrossRef]
  54. Thibos LN, Horner D. Power vector analysis of the optical outcome of refractive surgery. J Cataract Refract Surg. 2001;27(1):80–85. doi:10.1016/S0886-3350(00)00797-5 [CrossRef]
  55. Kawahara A, Takayanagi Y. Vector analysis investigation of toric intraocular lens with no deviation from the intended axis. Clin Ophthalmol. 2016;10:2199–2203. doi:10.2147/OPTH.S119755 [CrossRef]
  56. Visser N, Beckers HJ, Bauer NJ, et al. Toric vs aspherical control intraocular lenses in patients with cataract and corneal astigmatism: a randomized clinical trial. JAMA Ophthalmol. 2014;132(12):1462–1468. doi:10.1001/jamaophthalmol.2014.3602 [CrossRef]
  57. Norrby S, Hirnschall N, Nishi Y, Findl O. Fluctuations in corneal curvature limit predictability of intraocular lens power calculations. J Cataract Refract Surg. 2013;39(2):174–179. doi:10.1016/j.jcrs.2012.09.014 [CrossRef]
  58. Hirnschall N, Crnej A, Gangwani V, Findl O. Effect of fluorescein dye staining of the tear film on Scheimpflug measurements of central corneal thickness. Cornea. 2012;31(1):18–20. doi:10.1097/ICO.0b013e31821eea97 [CrossRef]
  59. Licznerski TJ, Kasprzak HT, Kowalik W. Analysis of shearing interferograms of tear film using fast fourier transforms. J Biomed Opt. 1998;3(1):32–37. doi:10.1117/1.429886 [CrossRef]
  60. Preussner PR, Hoffmann P, Wahl J. Impact of posterior corneal surface on toric intraocular lens (IOL) calculation. Curr Eye Res. 2015;40(8):809–814. doi:10.3109/02713683.2014.959708 [CrossRef]
  61. Webers VSC, Bauer NJC, Visser N, Berendschot TTJM, van den Biggelaar FJHM, Nuijts RMMA. Image-guided system versus manual marking for toric intraocular lens alignment in cataract surgery. J Cataract Refract Surg. 2017;43(6):781–788. doi:10.1016/j.jcrs.2017.03.041 [CrossRef]
  62. Visser N, Bauer NJ, Nuijts RM. Toric intraocular lenses: historical overview, patient selection, IOL calculation, surgical techniques, clinical outcomes, and complications. J Cataract Refract Surg. 2013;39(4):624–637. doi:10.1016/j.jcrs.2013.02.020 [CrossRef]
  63. Visser N, Berendschot TT, Bauer NJ, Jurich J, Kersting O, Nuijts RM. Accuracy of toric intraocular lens implantation in cataract and refractive surgery. J Cataract Refract Surg. 2011;37(8):1394–1402. doi:10.1016/j.jcrs.2011.02.024 [CrossRef]
  64. Felipe A, Artigas JM, Díez-Ajenjo A, García-Domene C, Peris C. Modulation transfer function of a toric intraocular lens: evaluation of the changes produced by rotation and tilt. J Refract Surg. 2012;28(5):335–340. doi:10.3928/1081597X-20120321-01 [CrossRef]
  65. 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(6):732–736. doi:10.1016/j.jcrs.2017.01.026 [CrossRef]
  66. Kim MJ, Yoo YS, Joo CK, Yoon G. Evaluation of optical performance of 4 aspheric toric intraocular lenses using an optical bench system: influence of pupil size, decentration, and rotation. J Cataract Refract Surg. 2015;41(10):2274–2282. doi:10.1016/j.jcrs.2015.10.059 [CrossRef]
  67. Visser N, Bauer NJ, Nuijts RM. Residual astigmatism following toric intraocular lens implantation related to pupil size. J Refract Surg. 2012;28(10):729–732. doi:10.3928/1081597X-20120911-02 [CrossRef]
  68. Atchison DA, Thibos LN. Optical models of the human eye. Clin Exp Optom. 2016;99(2):99–106. doi:10.1111/cxo.12352 [CrossRef]

Values for Each Eye Model

Source of ErrorSD
Difference between devices (including posterior surface of the cornea)0.24 D12,25,29,42,48,+unpublished
Misalignment3.1°11,13,15,18,20,26,28,34–36,38,47,49,50,51
Keratometry reading0.11 D14,16,17,32,33,37,39,41,43,46,48,+unpublished
Tilt2.3°22
Kappa2.6°22
Pupil size0.76 mmref2
Diurnal changes0.04 D (unpublished)
SICA (temporal 2.2 mm)0.20 D (SD: 0.24) (unpublished)
Anterior chamber depth0.03 mm29,30,44
Central corneal thickness0.00432 mm29,44
Axial length0.02 mm21,29,30,31,40,44
Decentration0.2 mm22

Distribution of Error

Source of Error (3.00 D Corneal Astigmatism)% of Total Error Deriving From Gaussian Error Propagation
Corneal measurement (including posterior surface of the cornea)27.0 (of this, 37.4% deriving from the posterior surface of the cornea)
Misalignment14.4
Tilt11.3
Kappa10.9
Pupil size8.1
SICA (temporal incision)7.8
Anterior chamber depth7.5
Axial length7.5
Decentration5.6
Authors

From Vienna Institute for Research in Ocular Surgery, A Karl Landsteiner Institute, Hanusch Hospital, Vienna, Austria (NH, OF, NB, CL, EZ); Retired, Eindhoven, The Netherlands (SN); Eye & Laser Clinic, Castrop-Rauxel, Germany (PH); and Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom (OF).

Dr. Hirnschall is a research consultant for Carl Zeiss Meditec AG and Hoya Surgical. Dr. Findl is a research consultant for Carl Zeiss Meditec AG, Alcon Laboratories, Inc, Croma Pharma, Johnson & Johnson, and Merck. Dr. Norrby is a former employee of Johnson & Johnson. The remaining authors have no financial or proprietary interest in the materials presented herein.

AUTHOR CONTRIBUTIONS

Study concept and design (NH, OF, SN); data collection (NH, NB, CL, EZ); analysis and interpretation of data (NH, OF, PH); writing the manuscript (NH); critical revision of the manuscript (NH, OF, NB, CL, SN, EZ, PH); statistical expertise (NH, PH); administrative, technical, or material support (EZ); supervision (NH, OF)

Correspondence: Nino Hirnschall, MD, PhD, Hanusch Hospital, Heinrich-Collin-Strasse 30, 1140-Vienna, Austria. Email: nino@hirnschall.at

Received: December 21, 2019
Accepted: July 21, 2020

10.3928/1081597X-20200729-03

Sign up to receive

Journal E-contents