The IOLMaster700 (Carl Zeiss Meditec, Jena, Germany) uses swept-source optical coherence tomography to provide a detailed analysis of corneal curvature and power. The significant contribution of posterior corneal astigmatism to total corneal astigmatism is well recognized1 and the ability of this device to measure both anterior and posterior corneal surfaces could potentially simplify surgical planning and improve visual outcomes from cataract surgery. Recently, the manufacturer has incorporated these new measurements of posterior corneal astigmatism and total corneal power or “total keratometry” into the IOLMaster 700 user interface.
Given that this device has produced posterior corneal astigmatism measurements consistent with previous studies,2 one could expect it to measure total corneal astigmatism more accurately than current estimations based on population average statistics. If total keratometry is found to be accurate, it would allow individualized measurement of total corneal power, negating the need for external calculation, adjustment, and potential transcription errors. Total keratometry would be expected to be of most benefit to patients who fall outside the population average in terms of posterior corneal astigmatic power and axis orientation that are not considered in current formulas, calculators, and nomograms that apply population average statistics to individual patients.
Goggin nomogram adjusted anterior keratometry (GNAK) is a population average-based keratometry adjustment algorithm.3 It was chosen as the gold-standard comparison method for total corneal astigmatism estimation in this study for four reasons. First, it is the only method of adjusting keratometry to allow for posterior corneal astigmatism with published, prospective validating data.4 Second, it has recently been confirmed as being accurate in eyes with high levels of astigmatism requiring IOLs of cylinder power greater than 2.50 diopters (D).5 Third, it allows a more direct comparison of keratometric values rather than comparison to the IOL recommendation output of “black-box” formulas that use population average-based statistics to estimate total corneal power. Fourth, it is our currently used method of cataract surgical planning at our surgical centers.
The Goggin nomogram adjusts the magnitude of anterior keratometric astigmatism to estimate total corneal astigmatism, but makes no adjustment to the axis of astigmatism. This latter strategy may be wrong if the posterior corneal astigmatism is not closely aligned with the anterior astigmatism. Toric calculators that do adjust the axis of anterior corneal astigmatism presumably assume that the steep axis of posterior corneal astigmatism is acting at a vertical meridian and make a vector addition accordingly. Although it is correct that most eyes have a steep axis of posterior corneal astigmatism in the vertical range, this covers an arc from 60° to 120° and is not always precisely at 90°. It is apparent that a biometric technique that can measure total corneal astigmatism power and axis accurately should offer more accurate results.
The aim of this study was to provide the first comparison of the new IOLMaster 700 total keratometry measurement of total corneal astigmatism with validated GNAK estimates of total corneal astigmatism. This would determine whether it was safe and reasonable to use total keratometry measurements prospectively to plan cataract surgery. To the best of our knowledge, this will be the first published assessment of the accuracy of total keratometry values.
Patients and Methods
Ethical approval was obtained for this study from the Human Research Ethics Committee of the Central Adelaide Local Health Network, and the study was conducted in accordance with the tenets of the Declaration of Helsinki.
Routine biometric measurements were taken using the IOLMaster 700 on all patients planning to undergo cataract surgery at two sites (The Queen Elizabeth Hospital and Ashford Advanced Eye Care) in Adelaide, Australia. A total of 46 eyes were included in the study. Inclusion criteria consisted of having had biometry measured on the IOLMaster 700 between October 2016 and March 2017 with good quality measurements of all parameters including total keratometry, had cataract surgery with implantation of a toric IOL, and had their final, stable 6-week review. Patients were excluded if there was either a failure to acquire good quality measurement of any biometric parameter, previous laser keratorefractive surgery, previous ocular surgery of any type, or if the patient could not attain an unaided or corrected visual acuity of 20/25 (logMAR 0.1) or better due to any ocular or systemic reason postoperatively.
Each surgery was planned using GNAK derived from the same preoperative biometry measurement on the IOLMaster 700 on the same date as total keratometry acquisition. Adjustments to anterior keratometry measurements were made depending on the steep axis of measured anterior keratometry and the cylinder power of the intended toric IOL to be implanted (see below for a detailed explanation of the principles of the Goggin nomogram). Patients underwent standard microincision phacoemulsification cataract surgery via a 1.9-mm main incision. All eyes were implanted with a Zeiss AT TORBI 709MP monofocal toric IOL (Carl Zeiss Meditec) calculated using the Carl Zeiss Meditec online calculator ( https://zcalc.meditec.zeiss.com/zcalc/) aiming for minimal postoperative residual astigmatism regardless of whether the predicted residual astigmatic axis was flipped from the preoperative state.
GNAK and total keratometry astigmatism values were derived and compared to assess whether there was any significant difference in power and steep axis orientation. Eyes were further divided into three subgroups for analysis: “with the-rule” (WTR) if the anterior keratometric steep meridian was oriented between 60° and 120° (n = 15), “against-the-rule” (ATR) if the steep meridian was oriented between 0°and 30° or 150° and 180° (n = 20), and “oblique” if the steep meridian was oriented between 31° and 59° or 121° and 149° (n = 11).
Given that this study has real life implications and we aimed to provide a practical analysis of whether new planning techniques incorporating total keratometry will be safe and accurate to use, we also considered clinical significance in our analysis. We chose an astigmatic value of 0.25 D as a threshold for clinical significance because this is typically the smallest step used in subjective refraction. We chose an axis difference of 10° or greater to signify clinical significance because toric IOL misalignment by 10° or more is considered to cause significant loss of astigmatic correction and is a threshold above which IOL re-rotation is most commonly considered.6
Measurements taken between October 2016 and March 2017 also included data about the shape and power of the posterior corneal surface, although this additional information was not accessible to the surgeons and did not influence surgical planning. These measurements were de-identified and analyzed by Carl Zeiss Meditec using proprietary methods to provide a value for total corneal power. This value has since been named “total keratometry” and is now available for use on the IOLMaster 700.
Although precise total keratometry values were derived using proprietary methods and undisclosed refractive indices, the basic principles of total keratometry calculation appear to be relatively straightforward. To the best of our knowledge, swept-source optical coherence tomography provides keratometry measurements and pachymetry from points around the clock-face of the cornea to describe the shape of the posterior cornea. The combination of anterior and posterior corneal surface shapes along with pachymetry then allows calculation of total corneal power and total corneal astigmatism. The two principal total keratometry axes (flat and steep) can be used to plan surgery and make IOL choices. Total corneal astigmatism values used for analysis were derived from the difference between the steep and flat total keratometry axes. Given that total keratometry is a measured value rather than an estimate, the steep axis of total keratometry may differ from that of anterior keratometry alone.
All patients undergoing cataract surgery at both research sites had their procedures planned using the Goggin nomogram.3 This method makes adjustments to anterior keratometry values to allow for the contribution of population average posterior corneal astigmatism, which has been shown consistently to have a steep vertical axis in most eyes.1,2,7,8 The Goggin nomogram was initially developed by analyzing the refractive outcomes of a large number of patients who had undergone cataract surgery with implantation of a toric IOL.3 Vector analysis showed a consistent, systematic error where eyes with ATR anterior corneal astigmatism on average had their astigmatism undercorrected and eyes that had WTR anterior corneal astigmatism were overcorrected. Posterior corneal astigmatism with a vertically orientated steep axis in most cases was the cause of this error. The average undercorrection and overcorrection of ATR and WTR eyes, respectively, was used to create a correction coefficient for each group of eyes. To keep this adjustment as simple to use and transparent as possible, adjusted keratometry values rather than changes in IOL cylinder power are provided by the nomogram. The prescribed increase or decrease in astigmatic power provides the surgeon with new steep and flat keratometry values that can be used in any standard toric IOL calculator if required.
The Goggin nomogram originally recommended that such keratometry adjustments be made when a toric IOL cylinder power of 2.00 D or less was required following IOL calculation with unadjusted keratometry values. It was found that there was no significant astigmatic refractive error in outcome based on the rule of the corneal astigmatism in eyes receiving IOLs of 2.50 D cylinder or greater.3 In view of this finding, a recommendation that such eyes should not undergo adjustment was made. This initial Goggin nomogram was subsequently validated in a prospective study.4 More recently, using a greater number of patients, a statistically significant result confirmed that eyes requiring a toric IOL cylinder power of 2.50 D or greater should not undergo adjustment of their keratometry.5 The relatively small effect of posterior corneal astigmatism on these greater magnitudes of anterior astigmatism was found to be neither statistically or clinically significant.
Overall, there was no statistically significant difference between GNAK and total keratometry at assessing magnitude of total corneal astigmatism in all eyes (Table 1). This similarity remained in the ATR and oblique subgroups, but there was a statistically significant difference in mean magnitude in the WTR subgroup. All comparisons of mean and median astigmatic values for GNAK and total keratometry were clinically significant within 0.25 D, except for median values in WTR eyes that fell just outside this value at 0.26 D after rounding to two decimal places (Table 1).
Comparison of GNAK and TK Including Test of Statistical Significance for Difference in Mean Value (D)
It is difficult to assess the difference in astigmatic magnitude in the absence of any assessment of directionality. Vector analysis combines both of these factors. Analysis of the vector differences between GNAK and total keratometry values and the summated vector mean (0.10 D at 138°) of this difference provides a clearer overview of individual contributions (Figure 1). There does not appear to be any perceptible difference in the tightness of the spread of data or a clear directional bias when all eyes are looked at together. The WTR and ATR eyes appear to have a similar tightness of spread and no particular directional bias. However, the oblique subgroup does appear to be more tightly grouped to one side of the centroid chart, indicating a consistent difference in measurement of these eyes between GNAK and total keratometry in terms of both magnitude and orientation of astigmatism.
Centroid plot of vector differences between Goggin nomogram adjusted anterior keratometry and total keratometry values for each eye separated into anterior keratometry subgroups. WTR = with-the-rule astigmatism; ATR = against-the-rule astigmatism; SVM = summated vector mean
The difference in steep axis identification between GNAK and total keratometry is the same as the difference between the anterior keratometric steep axis and total keratometry because GNAK makes no change to the axis. Signed axis difference was analyzed using a one-sample t test comparing to the null hypothesis that there was no difference in mean axis measurements. The absolute axis difference data were highly skewed, and a signed rank test was used instead of a t test, comparing to the null hypothesis that there was no difference in median absolute axis (Table 2).
Analysis of Axis Difference Between GNAK and TK Measurements in Degrees
There was a statistically significant difference in steep axis assessment of GNAK and total keratometry when considering absolute axis differences in all eyes and all subgroups. Results were similar when comparing signed axis difference other than in the WTR subgroup, where the 95% confidence interval just straddled zero difference between the mean axes (Table 2).
Posterior corneal astigmatism is currently one of the most important factors determining postoperative refractive error following cataract surgery with toric IOL implantation.9 Nearly half of ophthalmologists responding to the most recent clinical survey by the American Society of Cataract and Refractive Surgeons stated that they did not factor posterior corneal astigmatism into their IOL calculations because they do not think there is a good way to measure it.6 Clearly, many ophthalmologists find the currently available techniques to estimate or measure posterior corneal astigmatism inadequate in some respect. Physically measuring the posterior cornea has indeed proven difficult and often unreliable in terms of repeatability between devices10 and sessions.11
Methods that estimate the effects of the posterior cornea using population-derived statistics have always had a limited lifespan while we await accurate measurement of total corneal astigmatism. Population-based methods have performed well and continue to do so for most cases. Many current methods can be used to incorporate posterior corneal astigmatism into IOL calculations. Nomograms allow adjustment of keratometry (GNAK) or IOL choice (Baylor nomogram).12 Regression formulas based on anterior keratometry have also been developed to estimate the effects of the posterior cornea.13 Calculators, both online and in device software, have evolved to incorporate such formulas and be able to make similar estimations, although it can be difficult to know exactly how these adjustments are made.14,15
Interestingly, these estimation methods have outperformed actual measurement of total corneal power when comparing prediction error for toric IOL implantation in a retrospective study.16 In our study, total keratometry using actual measurement of the posterior cornea provided measurements of total corneal astigmatism magnitude similar to the validated GNAK estimation method. Overall, there was no statistically or clinically significant difference between the two methods. Subgroup analysis of WTR eyes did show a statistically significant difference in magnitude and the median difference did just breach our threshold for clinical significance. Overall, it is promising that total keratometry provides a good comparative measure to GNAK. The WTR result is surprising because it is generally considered that the steep axis of posterior corneal astigmatism is more consistently aligned with anterior astigmatism in WTR and less correlated in ATR.1 We would have assumed that this would make estimations of total corneal astigmatism in WTR eyes using GNAK more similar to measured total keratometry results and have perhaps expected this significant difference in the ATR subgroup instead. One interpretation of this result would be that total keratometry is providing a measure of total corneal astigmatism more accurately than GNAK has estimated and that the difference is that the steep axis of the posterior cornea is not aligned vertically as often as previously thought. This theory does have some merit given that exactly this finding was recently reported using the same device in a large number of eyes.2 However, GNAK has consistently been shown to be accurate, and this result may indicate that the IOLMaster 700 is less accurate at assessing the magnitude of total corneal astigmatism in WTR eyes. This matter will likely be resolved by larger, future studies.
Although it would be somewhat inaccurate to compare total keratometry directly to other predictive methods used in other studies, summated vector mean values for total keratometry versus GNAK difference could be considered similar enough to summated vector mean values for predictive error of residual astigmatism in previous studies. In which case, the overall summated vector mean power of 0.10 D compares favorably with published centroid errors in predicted residual astigmatism where the best method achieved was 0.17 D (Barrett calculator) and the next best was 0.19 D (Alcon calculator).17
The accuracy of astigmatism axis identification should be considered as important as magnitude when analyzing a biometry device. Anecdotally, uncertainty about steep axis location, inconsistency between devices, and subsequent fear of managing an astigmatic refractive surprise may inhibit toric IOL uptake by some surgeons. As expected, there was a statistically significant difference in the absolute and signed axis between GNAK and total keratometry in all analyses other than for WTR signed axis difference. This is understandable given that GNAK makes no change to the anterior keratometric steep axis. The more important question is whether this is of clinical significance and would affect visual outcomes for patients. Overall, the difference was small and could be considered insignificant. However, the upper range of the overall 95% confidence interval for median absolute axis difference does reach 5°. Although this difference in itself is not clinically significant, an error of toric IOL alignment on top of this difference of just 5° could reach a clinically significant level. Even with perfect intraoperative alignment, rotation, particularly in the first hour postoperatively, commonly reaches close to 5°.18 Both signed and absolute axis difference 95% confidence intervals for oblique eyes reached a clinically significant level. These findings combined suggest that the difference between GNAK and total keratometry identification of steep axis of total corneal astigmatism is statistically significantly different and could be considered of clinical significance in certain circumstances.
We are aware that our study is limited by low numbers. However, we believed that it was important for this first comparison to be done to assess whether it would be safe and reasonable to proceed with a prospective comparison. Overall, it appears that total keratometry compares well to the validated GNAK method of assessing total corneal astigmatism. The similarities of magnitude of astigmatism are comforting and the differences in axis seem logical. This combination of findings appears adequate evidence to consider using total keratometry in a prospective trial. Total keratometry analysis on the IOLMaster 700 offers benefits in terms of time efficiency, decreased risk of transcription error, and potentially more precise individual refractive outcomes. It provides an easy-to-use measure of total corneal astigmatism that will add no more complexity than a standard IOL calculation using anterior keratometry. Prospective total keratometry users will, of course, have to use toric IOL calculators that do not already employ another form of posterior corneal astigmatism adjustment. Adoption of this technology should be a step toward reducing residual astigmatism and providing more patients with excellent unaided visual acuity.
- 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. doi:10.1016/j.jcrs.2012.08.036 [CrossRef]
- LaHood B, Goggin M. Measurement of posterior corneal astigmatism by the IOLMaster 700. J Refract Surg. 2018;34:331–336. doi:10.3928/1081597X-20180214-02 [CrossRef]
- Goggin M, Zamora-Alejo K, Esterman A, van Zyl L. Adjustment of anterior corneal astigmatism values to incorporate the likely effect of posterior corneal curvature for toric intraocular lens calculation. J Refract Surg. 2015;31:98–102. doi:10.3928/1081597X-20150122-04 [CrossRef]
- Goggin M, van Zyl L, Caputo S, Esterman A. Outcome of adjustment for posterior corneal curvature in toric intraocular lens calculation and selection. J Cataract Refract Surg. 2016;42:1441–1448. doi:10.1016/j.jcrs.2016.10.004 [CrossRef]
- LaHood BR, Goggin M, Esterman A. Assessing the likely effect of posterior corneal curvature on toric IOL calculation for IOLs of 2.50 D or greater cylinder power. J Refract Surg. 2017;33:730–734. doi:10.3928/1081597X-20170829-03 [CrossRef]
- American Society of Cataract and Refractive Surgeons. 2017 ASCRS Clinical Survey. Available from: http://supplements.eyeworld.org/h/i/377037466-ascrs-clinical-survey-2017
- Ho J-D, Tsai C-Y, Liou S-W. Accuracy of corneal astigmatism estimation by neglecting the posterior corneal surface measurement. Am J Ophthalmol. 2009;147:788–795. doi:10.1016/j.ajo.2008.12.020 [CrossRef]
- Miyake T, Shimizu K, Kamiya K. Distribution of posterior corneal astigmatism according to axis orientation of anterior corneal astigmatism. PLoS One. 2015;10:e0117194. doi:10.1371/journal.pone.0117194 [CrossRef]
- 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]
- An Y, Kim H, Joo C-K. Comparison of anterior segment measurements between dual and single Scheimpflug camera. Journal of the Korean Ophthalmological Society. 2016;57:1056–1062. doi:10.3341/jkos.2016.57.7.1056 [CrossRef]
- Chen D, Lam AK. Intrasession and intersession repeatability of the Pentacam system on posterior corneal assessment in the normal human eye. J Cataract Refract Surg. 2007;33:448–454. doi:10.1016/j.jcrs.2006.11.008 [CrossRef]
- 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. doi:10.1016/j.jcrs.2013.06.027 [CrossRef]
- Abulafia A, Koch DD, Wang L, et al. New regression formula for toric intraocular lens calculations. J Cataract Refract Surg. 2016;42:663–671. doi:10.1016/j.jcrs.2016.02.038 [CrossRef]
- Barrett GD. An improved universal theoretical formula for intraocular lens power prediction. J Cataract Refract Surg. 1993;19:713–720. doi:10.1016/S0886-3350(13)80339-2 [CrossRef]
- Laboratories A. Alcon Toric Calculator. Available from: https://www.myalcon-toriccalc.com.
- Ferreira TB, Ribeiro P, Ribeiro FJ, O'Neill JG. Comparison of methodologies using estimated or measured values of total corneal astigmatism for toric intraocular lens power calculation. J Refract Surg. 2017;33:794–800. doi:10.3928/1081597X-20171004-03 [CrossRef]
- Ferreira TB, Ribeiro P, Ribeiro FJ, O'Neill JG. Comparison of astigmatic prediction errors associated with new calculation methods for toric intraocular lenses. J Cataract Refract Surg. 2017;43:340–347. doi:10.1016/j.jcrs.2016.12.031 [CrossRef]
- Inoue Y, Takehara H, Oshika T. Axis misalignment of toric intraocular lens: placement error and postoperative rotation. Ophthalmology. 2017;124:1424–1425. doi:10.1016/j.ophtha.2017.05.025 [CrossRef]
Comparison of GNAK and TK Including Test of Statistical Significance for Difference in Mean Value (D)
|All eyes (N = 46)|
| 95% CI of median||0.89 to 1.32||1.08 to 1.31|
| Mean difference||−0.012|
| 95% CI of difference||−0.086 to 0.062|
|ATR eyes (n = 20)|
| 95% CI of median||1.27 to 1.96||1.18 to 1.81|
| Mean difference||0.122|
| 95% CI of difference||−0.009 to 0.253|
|WTR eyes (n = 15)|
| 95% CI of median||0.68 to 1.00||0.89 to 1.31|
| Mean difference||−0.179|
| 95% CI of difference||−0.273 to −0.085|
|Oblique eyes (n = 11)|
| 95% CI of median||0.85 to 1.05||0.80 to 1.18|
| Mean difference||−0.028|
| 95% CI of difference||−0.106 to 0.050|
Analysis of Axis Difference Between GNAK and TK Measurements in Degreesa
|Rule||Measure||No.||Mean/Median Difference||95% CI||P|
|Overall||Signed axis difference||46||1.654||0.173 to 3.134||.029|
|Overall||Absolute axis difference||46||3.611||1.724 to 5.497||< .001|
|ATR||Signed axis difference||20||1.721||0.615 to 2.827||.004|
|ATR||Absolute axis difference||20||1.589||0.187 to 2.990||< .001|
|Oblique||Signed axis difference||11||5.941||1.427 to 10.456||.015|
|Oblique||Absolute axis difference||11||8.896||6.111 to 11.681||< .001|
|WTR||Signed axis difference||15||−1.580||−3.680 to 0.519||.129|
|WTR||Absolute axis difference||15||1.273||0.000 to 4.431||< .001|