Double-angle plots permit optimal understanding for

Toric IOL outcomes

Use of double-angle plots for displaying astigmatism data permits optimal understanding. Cheryl Guttman Krader reports

Analysis of astigmatism values using double-angle plots is highly informative and easily accessible to cataract surgeons through an online tool, reported Douglas D Koch, MD, at the 2020 ASCRS Virtual Annual Meeting.

“Analysing astigmatism outcomes can be complicated because it involves two variables, power (magnitude) and meridian (axis), and their values cannot be simply added or subtracted. Instead, the analysis requires doubling the angle to convert the data into a true Euclidean vector, performing vector algebra and then halving the angles to return them to standard format that we are accustomed to using,” said Dr Koch, Allen, Mosbacher, and Law Chair in Ophthalmology, Baylor College of Medicine, Houston, TX, USA.

“Single-angle or double-angle plots can be used to display astigmatism data combining both power and meridian. I believe that the double-angle plots are optimal because they are clearer visually and numerically.”

Dr Koch explained that a single-angle plot of astigmatism data is attractive because it resembles phoropters in that eyes having withthe-rule (WTR) astigmatism are oriented vertically and eyes that have against-the-rule (ATR) astigmatism lie to the right or the left.

“With this display, however, it can be harder to know what the data show,” he said.

A single-angle plot is converted into a double-angle plot by doubling the angle for each datapoint. As a result, the datapoints for all WTR eyes are grouped together on the left of the double-angle plot, and the datapoints for all ATR eyes are clustered to the right.

Dr Koch and colleagues reviewed the advantages of displaying astigmatism data using double-angle plots in a guest editorial that was published in the October 2018 issue of the Journal of Cataract and Refractive Surgery (JCRS). The article also proposes simple terminology to use for astigmatism analysis in toric IOL surgery and describes a set of figures, including various double-angle plots, that best display astigmatic outcomes of toric IOL surgery. In addition, the journal article introduces a downloadable Excel spreadsheet that allows surgeons to generate the latter figures using their personal data. The spreadsheet is available on the JCRS, ESCRS, and ASCRS websites.

The figures for depicting toric IOL surgery outcomes include a cumulative histogram of the magnitude of the preoperative corneal astigmatism and postoperative refractive astigmatism data that shows the percentages of eyes falling within different dioptric ranges before and after surgery. Vector analysis is presented on double-angle plots that include text and graphical information on the data means and spread.

The centroid in each plot represents the vectoral centre of the data, with its standard deviation. The data spread is appreciated graphically with an ellipse that surrounds 95% of the values in the dataset, and statistical analysis can readily be performed on these data, Dr Koch explained.

The third type of figure generated from the spreadsheet is a double-angle plot of the postoperative refractive astigmatism prediction error for eyes in the dataset. This outcome provides insight into the accuracy of toric IOL calculation formulas.

Dr Koch illustrated the latter point by comparing a figure created from a set of eyes having toric IOL power calculations done using anterior keratometry (K) data alone versus with the Abulafia-Koch formula that takes into account posterior corneal astigmatism. The

This illustrates what occurs in double-angle plots. The with-the-rule eyes are grouped on the left, and the against-the-rule eyes, which are split apart in single-angle plots, now are grouped together to the right, allowing appropriate display of centroids and confidence ellipses

centroid values for the two datasets were 0.55D @ 180° ±0.47D and 0.05D @ 174°±0.44D, respectively, showing superiority of the method that incorporates posterior corneal astigmatism. Its benefit was also seen clearly on the double-angle plots.

“On the plot for the calculations done using anterior K only, the centroid is located to the right of the vertical meridian, indicating an ATR prediction error,” Dr Koch said. “In contrast, the centroid for the prediction error using the Abulafia-Koch formula is almost at the 0 point, which indicates there is no particular bias in the results for WTR astigmatism, ATR astigmatism, or along any oblique meridian.”

DATA ACQUISITION AND INPUT Although the online tool facilitates analysis of toric IOL surgery outcomes, hopefully the task will become even easier in the future with introduction of a method that will automatically populate data into the spreadsheet.

“Currently, the data need to be input manually, but I am looking forward to the development of a system that will allow for electronic data entry,” Dr Koch said.

He noted that he is currently using both the IOLMaster 700 (Carl Zeiss Meditec) and Lenstar LS 900 (Haag-Streit) for measuring keratometry and is analysing the data from each device separately.

“I find that results are excellent with both of these devices. However, I would remind surgeons that different devices can give different measurements, and any one device can give an erroneous measurement in a given patient. Therefore, it is important to use more than one device for measuring the cornea, or, if only one device is available, consider getting two sets of measurements with that device,” Dr Koch said.

Douglas D Koch: dkoch@bcm.edu

Reference:

Abulafia A, Koch DD, Holladay JT, Wang L, Hill W. Pursuing perfection in IOL calculations. IV. Rethinking astigmatism analysis for intraocular lens-based surgery: Suggested Terminology, analysis, and standards for outcome reports. J Cataract Refract Surg. 2018; Oct;44(10):1169-1174