#### Abstract

To evaluate factors associated with residual astigmatism after toric intraocular lens implantation based on data from an online toric intraocular lens (IOL) back-calculator.

This was a retrospective data review of an online toric IOL back-calculator, which allows users to input preoperative toric planning information and postoperative lens orientation and refractive results. These data were used to determine the optimal orientation of the IOL to minimize residual refractive astigmatism. Aggregate data were extracted from this calculator to investigate factors associated with relative magnitudes of residual astigmatic refractive error after implantation of toric IOLs.

A total of 3,159 validated records with an average reported postoperative refractive astigmatism of 1.85 diopters (D) were analyzed; 566 included data allowing calculation of surgically induced astigmatism. The relative magnitude of reported residual astigmatism appeared similar whether a femtosecond laser system was used or not. Significant differences relative to the use of intraoperative aberrometry were observed, as were differences by toric calculator. Higher measured surgically induced astigmatism was most associated with higher levels of reported residual astigmatism. A significant potential decrease in the mean refractive astigmatism was expected with IOL reorientation; in 1,416 cases (44.8%), the expected residual refractive astigmatism after lens reorientation was less than 0.50 D, with a mean reduction of 56% ± 31%.

When present after cataract surgery, higher levels of residual refractive astigmatism were most associated with large differences in measured preoperative to postoperative keratometry. To a lesser degree, intraoperative aberrometry was associated with lower levels.

**[ J Refract Surg. 2018;34(6):366–371.]**

Although toric intraocular lenses (IOLs) have demonstrated considerable success in reducing astigmatism at the time of cataract surgery, residual refractive astigmatism remains in some patients. With early toric IOL calculators, aggregate results indicated that only approximately 70% of eyes implanted with a toric IOL had 0.50 diopters (D) or less of refractive astigmatism postoperatively.^{1} The advent of toric IOL calculators that incorporated consideration of posterior corneal astigmatism appears to have increased this number to near 80%.^{2,3} Although these percentages are significantly higher than those achieved with non-toric IOLs, it is clear that factors remain that reduce the predictability of toric IOL results. A better understanding of these factors may be helpful to improve overall results. Such factors may include variability in the magnitude and direction of surgically induced astigmatism (SIA), effects of different toric calculators, and apparent rotational stability of different toric IOLs.^{4}

Reorientation of a toric IOL by rotating it can sometimes be helpful in reducing residual refractive astigmatism when it is present after cataract surgery. The optimal orientation of the IOL and the expected residual refraction can be determined through vector analysis. The solution requires knowing the cylinder power of the IOL, its current orientation, and the current refraction of the eye. A web site to assist surgeons with this calculation ( www.astigmatismfix.com) has been used by surgeons for several years. Earlier versions of this online toric back-calculator required surgeons to input only the necessary information above. A description of the original data collected, its filtering, and subsequent analysis has been reported previously.^{5}

The most recent version of the web site includes the capability to allow surgeons to add additional information, such as the toric calculator used and the preoperative and postoperative keratometry data for the eye. These data are not mandatory, but surgeons are encouraged to include them. In an effort to better filter data, there are flags that surgeons may select to indicate the entered calculation is a duplicate or that the entered calculation is for theoretical purposes only.

The purpose of the analysis presented here was to determine whether the additional data from the online toric back-calculator could be used to identify factors associated with residual refractive astigmatism after toric IOL implantation.

### Methods

This analysis was based on data input by users of a web site ( www.astigmatismfix.com) designed to provide surgeons information related to reducing or eliminating residual refractive astigmatism after toric IOL implantation. The University of Iowa Human Subjects Office/Institutional Review Board was contacted to evaluate the need for approval of this retrospective data analysis. They provided a waiver of this requirement because there is no protected health information in the stored data from the web site.

Although the minimum data required for toric back-calculation are the current IOL cylinder power and orientation, along with the current manifest refraction, the site has been revised to request additional data. **Table 1** shows the fields that require a mandatory response from users and those that are optional. Additional data that surgeons may input include the intended orientation of the IOL (from their calculations), the preoperative and postoperative keratometry values, and the device(s) used to measure each. In addition, the surgeon may indicate whether devices such as a femtosecond laser, an image guidance system, or an intraoperative aberrometer were used during the procedure.

Table 1: Data Collected From Revised astigmatismfix.com Web Site |

Several variables can be calculated from the input data; details of these calculations are described in a previous publication.^{5} One measure of interest is whether the lens is implanted “as intended”(ie, in the orientation indicated from the toric calculator used by the surgeons in their surgery planning). Another measure of interest is whether the lens is in the ideal orientation, which is the optimal orientation as determined from the toric back-calculator. Residual astigmatism can occur when an IOL is in the ideal position but the cylinder power is incorrect. The difference between the intended and ideal orientation is also calculated because it may reflect inaccuracy in the toric IOL calculation (possibly a function of dry eye or lack of consideration of posterior corneal astigmatism) or variability in SIA. Finally, results are categorized based on the expected residual refractive astigmatism after optimizing the orientation. If the result is 0.50 D or less, the IOL in the eye is considered appropriate. If higher than this, a new IOL or other remedial treatment is indicated. The reason for selecting 0.50 D is that the most common IOL brands provide approximately 0.50 D of refractive cylinder power difference (at the corneal plane) between lens models.

Given the lack of overall use data for intraoperative aberrometry, femtosecond lasers, and image guidance systems for toric IOL implantation, there is no way to determine whether these technologies reduced the number of cases requiring toric back-calculation. However, some insights related to these technologies when residual refractive astigmatism is present may still be gained. The mean presenting residual refractive astigmatism and the mean expected residual refractive astigmatism by technology use can be compared.

In the current data set, SIA was calculated as the vector difference between the preoperative and postoperative keratometry measured, and was calculated only for those eyes where the measurements were made with the same keratometry device or biometer. When the preoperative and postoperative keratometry values were equal, it was presumed that the preoperative data were copied; with most devices measuring to 0.01 D, the statistical likelihood of duplicate readings was considered extremely low.

The data collected from the online web site are stored in a comma-delimited text file. This file was imported into an MS Access (Microsoft Corporation, Redmond, WA) database for data checking, collation, and preliminary analysis. Statistical analyses were performed using the STATISTICA data analysis software system (version 13; TIBCO Software Inc., Palo Alto, CA). Statistical testing was performed using analysis of variance on continuous variables, with a *P* value of .05 considered statistically significant. For categorical data, odds ratio testing with 95% confidence intervals was applied.

### Results

The downloaded data set included all user records input from January 23 to September 2, 2017. A total of 12,285 raw data records were collected from the web site; these records were from an estimated 3,100 different surgeons or sites. Data qualification filters were applied to remove presumed erroneous data (eg, “eye” not right or left, specified axes not between 0° and 180°, and residual refractive cylinder > 6.00 D). Records tagged by the user as “Theoretical” or “Repeat Calculation” were also removed. To reduce the likelihood of retaining repeat data that had not been identified by the user, calculations on a given day for a specific IOL by a given surgeon were collated. The result was a total of 3,159 records. Of these, 2,532 (80.2%) were unique records (only one calculation) and 415 cases (13.1%) included two records; the remaining 212 cases (6.7%) included more than two records for a given eye and given lens on a given date. For all cases where there was more than one record, the final calculation for that day, lens, and surgeon was used, an approach consistent with that adopted in the past for this data set.^{5}

Use of the toric back-calculator suggested a significant decrease in the mean refractive astigmatism could be obtained through IOL reorientation, with an observed mean of 1.85 ± 1.02 D input by surgeons and an expected mean after reorientation of 0.75 ± 0.66 D (*P* < .01). Almost three-quarters (72%, 2,283 of 3,159) of cases had initial residual refractive astigmatism between 0.50 and 2.00 D. In 1,416 cases (44.8%), the expected residual refractive astigmatism after lens reorientation was less than 0.50 D. The mean percentage reduction in refractive astigmatism expected was 56% ± 31% (range: 0% to 100%).

**Table 2** summarizes the findings related to the use of femtosecond laser systems, intraoperative aberrometry, and image guidance systems as reported by users of the site. The totals do not add up to 3,159 because early iterations of the software did not require entering these data. For each technology, the mean presenting residual refractive astigmatism and the expected residual refractive astigmatism (after IOL reorientation) are shown. The number of eyes where an IOL rotation is sufficient to reduce the expected residual refractive astigmatism is also indicated, along with the number that would appear to require a change in IOL cylinder power. There were no differences in the residual refractive astigmatism values associated with use or non-use of the femtosecond laser system; the 95% confidence interval of the odds ratio related to rotation or a new IOL spans 1.0. This indicates that, for the current data set, the femtosecond laser system does not appear to be a significant factor. For the image guidance systems, the presenting residual refractive cylinder and the expected residual refractive cylinder were both statistically significantly lower (approximately 0.15 D) when the guidance system was used (*P* < .01). The odds ratio indicates that use of the image guidance systems did not affect the likelihood of success regarding rotation or needing a new IOL. Similarly, the use of intraoperative aberrometry was associated with significantly lower refractive cylinder values (approximately 0.20 D, *P* < .01). The odds ratio indicated that there was a 29% higher likelihood of needing a new IOL rather than being able to successfully rotate the current IOL when intraoperative aberrometry was not used.

Table 2: Categorization of Clinical Data With Identified Technologies |

The effects of intraoperative aberrometry and image guidance systems on the difference between the intended and ideal IOL orientations were evaluated with an analysis of variance test. There was no statistically significant difference in the absolute angular difference between the ideal and intended orientations of the IOL between the eyes where intraoperative aberrometry was used and the eyes for which it was not used (*P* = .29), and none between the eyes where an image guidance system was used and the eyes for which it was not used (*P* = .98).

There were 566 records available (17.9%) that included the necessary data for calculating the magnitude of SIA. **Figure 1** shows the distribution of SIA magnitude found in the data set, which ranged from 0.03 to 7.99 D. As can be seen, more than one-third of eyes (37.5%, 212 of 566) had an SIA magnitude greater than 0.75 D, with seven records (1.2%) greater than 4.00 D. Using 0.75 D as a nominal cut-off, the odds ratio of needing a new lens versus successful rotation of the lens in the eye was 2.07, with a 95% confidence interval of 1.46 to 2.96. This indicates that residual refractive astigmatism of greater than 0.50 D after ideal orientation of the IOL in the eye was more than twice as likely when SIA was greater than 0.75 D. Box-whisker plots of the presenting refractive cylinder and the optimized (after reorientation) cylinder by level of SIA are shown in **Figure 2**.

Figure 1. Histogram of calculated surgically induced astigmatism (SIA). D = diopters |

Figure 2. Box-whisker plot of the distribution of refractive cylinder by surgically induced astigmatism (SIA) level. D = diopters; IOL = intraocular lens |

The effectiveness of different toric calculators cannot be specifically determined with the data here because overall use cannot be reliably determined; cases here include only those where residual refractive astigmatism is present. However, 60% (1,909 of 3,159) of all calculations involved two specific manufacturer/toric calculator combinations, with 42% using the Tecnis/AMO calculator and 18% using the AcrySof Toric/Alcon-Barrett calculator; both now include compensation for posterior corneal astigmatism. **Figure 3** shows the expected residual refractive astigmatism when the IOL is at the ideal orientation for these two combinations when compared at various levels of toric IOL cylinder power at the corneal plane. The expected residual refractive astigmatism was statistically significantly higher for higher IOL cylinder powers and statistically significantly higher with the AcrySof Toric/Alcon calculator combination (*P* < .01 in both cases). The clinical significance of the mean difference between IOL/calculators appears nominal at less than 0.16 D in all cases. The odds ratio of needing a new IOL to reduce astigmatism, rather than being able to reorient the existing IOL to a sufficient degree, is 1.39, with a 95% confidence interval of 1.14 to 1.69. This suggests that when residual refractive astigmatism occurs using the Acrysof Toric/Alcon calculator, the likelihood of requiring a lens exchange is 39% higher than if residual refractive astigmatism occurs using the Tecnis/AMO calculator.

Figure 3. Expected residual refractive astigmatism by intraocular lens (IOL)/calculator combination and IOL cylinder power at the corneal plane. D = diopters |

### Discussion

Input data and expected clinical outcomes related to use of the web site appear reasonably consistent with those observed in a previous analysis. Seventy percent of cases in the previous analysis involved residual refractive astigmatism between 0.50 and 2.00 D, compared to 72% in the current data set. The mean refractive astigmatism was 1.86 D in the previous data set and 1.85 D in the current data set. The mean calculated percentage reduction in residual refractive cylinder after reorientation was 50% (compared to 56% in the current data set) and the magnitude of residual astigmatism after IOL reorientation was expected to be 0.50 D or less in 37% of eyes (compared to 44.8% in the current data set).^{5}

The magnitude of surgically induced astigmatism could be calculated for almost 1 in 5 eyes in this data set. Higher SIA was significantly associated with the likelihood of requiring a lens cylinder power change to reduce residual refractive astigmatism to less than 0.50 D. With the current data, there is no reliable way to determine whether the measured SIA was real or whether it was related to variability in keratometry measurement preoperatively and/or postoperatively, although values higher than 1.00 D would appear suspect. Data on incision size and location were not requested, so a detailed review of SIA was not possible. Hashemi et al.^{6} reported SIA magnitudes to vary from 0.10 (using a 3.5-mm temporal incision) to 1.92 (using a 6-mm superior incision) D, with most of the temporal incisions being below 1.00 D. In case it is real, this variability associated with any eye's response to cataract incisions would appear unpredictable at present. Variability in observed values supports this notion.^{7,8} It has been suggested that the more traumatic the surgery and/or the greater the decrease in endothelial cell counts, the more unpredictable SIA may be^{9}; this appears especially true in cases of complicated cataract surgery, where multiple procedures (eg, pars plana vitrectomy)^{10} or the use of sutures are required.11 However, if the high SIA for a given eye is related primarily to a measurement error, then reducing the potential for such error would appear prudent. Of particular importance in this regard would be identifying and treating dry eye before final keratometry measurements are made because hyperosmolar tears have a demonstrable effect on variability in keratometry.^{12} In addition, several measurements to verify results, perhaps with several instruments, may at least reduce the likelihood of significant errors in preoperative keratometry.

The use of intraoperative aberrometry was associated with significantly lower refractive cylinder values (approximately 0.20 D). It is not clear to what extent the information from intraoperative aberrometry was used. We have presumed that results from intraoperative aberrometry were taken into account, but there is no way to know to what degree this affected the implanted lens power and position.

The use of a femtosecond laser system was noted in 15% of cases; results with and without use of such a system appeared equivalent. The input form does not indicate whether corneal arcuate incisions were created; presumably this would only be the case where such incisions were used to augment the effect of a toric IOL because all calculations included use of a toric IOL. It would seem more likely that the femtosecond laser system was used for all surgical incisions, but not to perform corneal arcuate incisions. However, this cannot be confirmed without a modification to the input form.

There are other ways to analyze the effects of the various factors discussed in the current study, but odds ratio testing with 95% confidence intervals was considered most appropriate because it allowed a determination of how much each factor contributed to greater residual refractive astigmatism (requiring a proposed IOL cylinder power change, rather than simply IOL rotation). Additionally, the relative impact of the different factors could be compared based on their relative odds ratios.

There are limitations to the current analysis, the most important of which may be the fact that only data from eyes with significant residual refractive astigmatism are collected by the online toric back-calculator. This means that rates of significant refractive astigmatism associated with factors such as femtosecond laser system or imaging system use cannot be determined. In addition, surgeons have other options to investigate residual refractive astigmatism; the data here are therefore only a percentage, although there is no reason to suspect any particular bias.

Higher levels of residual refractive astigmatism when present after cataract surgery were most associated with large measured differences in preoperative to postoperative keratometry (presumed SIA); to a lesser degree, the use of intraoperative aberrometry was associated with lower levels of residual refractive astigmatism.

### References

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*J Cataract Refract Surg*. 2013;39:624–637. doi:10.1016/j.jcrs.2013.02.020 [CrossRef] - Gundersen KG, Potvin R. Clinical outcomes with toric intraocular lenses planned using an optical low coherence reflectometry ocular biometer with a new toric calculator.
*Clin Ophthalmol*. 2016;10:2141–2147. doi:10.2147/OPTH.S120414 [CrossRef] - Davison JA, Potvin R. Refractive cylinder outcomes after calculating toric intraocular lens cylinder power using total corneal refractive power.
*Clin Ophthalmol*. 2015;9:1511–1517. - 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;56:827–835. doi:10.1167/iovs.14-15903 [CrossRef] - 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;42:1595–1601. doi:10.1016/j.jcrs.2016.09.017 [CrossRef] - Hashemi H, Khabazkhoob M, Soroush S, Shariati R, Miraftab M, Yekta A. The location of incision in cataract surgery and its impact on induced astigmatism.
*Curr Opin Ophthalmol*. 2016;27:58–64. doi:10.1097/ICU.0000000000000223 [CrossRef] - Srivannaboon S, Chirapapaisan C. Consistency analysis of surgically induced astigmatism.
*J Cataract Refract Surg*. 2017;43:1117–1118. doi:10.1016/j.jcrs.2017.05.037 [CrossRef] - Theodoulidou S, Asproudis I, Kalogeropoulos C, Athanasiadis A, Aspiotis M. Corneal diameter as a factor influencing corneal astigmatism after cataract surgery.
*Cornea*. 2016;35:132–136. doi:10.1097/ICO.0000000000000668 [CrossRef] - Du X, Zhao G, Wang Q, et al. Preliminary study of the association between corneal histocytological changes and surgically induced astigmatism after phacoemulsification.
*BMC Ophthalmol*. 2014;14:134. doi:10.1186/1471-2415-14-134 [CrossRef] - Park DH, Shin JP, Kim SY. Surgically induced astigmatism in combined phacoemulsification and vitrectomy; 23-gauge transconjunctival sutureless vitrectomy versus 20-gauge standard vitrectomy.
*Graefes Arch Clin Exp Ophthalmol*. 2009;247:1331–1337. doi:10.1007/s00417-009-1109-3 [CrossRef] - Eslami Y, Mirmohammadsadeghi A. Comparison of surgically induced astigmatism between horizontal and X-pattern sutures in the scleral tunnel incisions for manual small incision cataract surgery.
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*J Cataract Refract Surg*. 2015;41:1672–1677. doi:10.1016/j.jcrs.2015.01.016 [CrossRef]

Data Collected From Revised

Mandatory |

Current refractive data |

Current lens parameters |

Intended orientation (“originally calculated IOL axis”) |

UDVA/CDVA^{a} |

Prior corneal surgery |

Toric calculator used |

Source of SIA (calculated or assumed) |

Manual posterior keratometry adjustment |

Intraoperative aberrometry used |

Femtosecond laser system used |

Surgical image guidance system used |

Optional |

Access to excimer laser |

OVD removal |

Time for haptics to unfold |

Preoperative/postoperative keratometry values |

Anterior chamber depth |

Axial length |

Categorization of Clinical Data With Identified Technologies

Femtosecond laser system | ||||||

Used | 448 (15%) | 1.83 ± 1.04 | 0.74 ± 0.67 | 205 | 243 | 1.03 (0.84 to 1.26) |

Not used | 2,603 (85%) | 1.86 ± 1.02 | 0.75 ± 0.65 | 1,170 | 1,433 | |

| .69 | .82 | ||||

Intraoperative aberrometry | ||||||

Used | 537 (17%) | 1.72 ± 0.88 | 0.64 ± 0.53 | 269 | 268 | 1.29 (1.07 to 1.56) |

Not used | 2,614 (83%) | 1.88 ± 1.05 | 0.77 ± 0.68 | 1,142 | 1,472 | |

| < .01 | < .01 | ||||

Image guidance system | ||||||

Used | 566 (23%) | 1.76 ± 0.94 | 0.67 ± 0.55 | 273 | 293 | 1.15 (0.95 to 1.39) |

Not used | 1,931 (77%) | 1.90 ± 1.06 | 0.76 ± 0.68 | 864 | 1,067 | |

| < .01 | < .01 |