



ORIGINAL ARTICLE 

Year : 2020  Volume
: 2
 Issue : 1  Page : 23 

Comparison of toric intraocular lens calculation using the new corneal curvature measurement methods and the haigis suite, barrett tk, barrett toric, and z calc formulas
Carlos Emiliano Rodriguez Lopez^{1}, Guadalupe Fernando Mora González^{2}, Jorge Rendón Félix^{3}, Gerardo Daniel Jáuregui García^{1}, Miguel Angel Ibañez Hernández^{1}
^{1} Centro Médico Puerta de Hierro, Puerta de Hierro Medical Center, Zapopan, Mexico ^{2} Department of Ophthalmology, Puerta de Hierro Medical Center, Zapopan, Mexico ^{3} Puerta de Hierro Medical Center – Technological Institute of Superior Studies of Monterrey, Zapopan, Mexico
Date of Submission  19Jul2020 
Date of Acceptance  29Jun2020 
Date of Web Publication  19Aug2020 
Correspondence Address: Dr. Carlos Emiliano Rodriguez Lopez Puerta de Hierro Medical Center, Zapopan Mexico
Source of Support: None, Conflict of Interest: None
DOI: 10.4103/PAJO.PAJO_28_20
Background: More than 50% of patients undergoing cataract surgery have corneal astigmatism ≥ 0.75 diopters (D). A fundamental factor for the calculation of the intraocular lens (IOL) is the power of corneal refraction, which can be calculated with different methods and incorporated into different mathematical prediction models. Little information has been written comparing new formulas that take into account posterior keratometry. Aims and Objectives: Compare the prediction of the ideal IOL with different formulas that use anterior keratometry and posterior keratometry measured by different devices. Setting: Private practice, Guadalajara, Jalisco, Mexico. Materials and Methods: A descriptive, observational and retrospective study was carried out where 50 healthy eyes with cataract and a degree of corneal astigmatism >1 D were evaluated, IOL calculation was compared using the anterior and total keratometries measured with the Zeiss IOL master 700 and the total corneal refractive power (TCRP) keratometries of the Oculus Pentacam. The results were also compared with the Haigis Suite, Barrett TK and Z Calc formulas. The IOL used for the analysis was the Zeiss AT TORBI 709M/MP. Results: It was found that the different formulas can generate different predictions in the cylinder power but no significant differences in the sphere power. Measurement of the posterior cornea did not significantly change the selection of the ideal IOL for implantation. Calculations with Haigis Suite and Z Calc are very similar. Barrett TKToric uses less cylindrical power than Haigis Suite and Z calc, regardless of the method chosen to measure corneal power. Conclusion: Our results contribute to clarify the current scenario where the great variety of options for the calculation of IOL generates uncertainty about which method generates better results of postoperative refraction.
Keywords: Astigmatism, Barrett, cataract surgery, Haigis, intraocular lens, toric lens calculation, total corneal refractive power, total keratometry, Z calc
How to cite this article: Rodriguez Lopez CE, Mora González GF, Félix JR, Jáuregui García GD, Ibañez Hernández MA. Comparison of toric intraocular lens calculation using the new corneal curvature measurement methods and the haigis suite, barrett tk, barrett toric, and z calc formulas. Pan Am J Ophthalmol 2020;2:23 
How to cite this URL: Rodriguez Lopez CE, Mora González GF, Félix JR, Jáuregui García GD, Ibañez Hernández MA. Comparison of toric intraocular lens calculation using the new corneal curvature measurement methods and the haigis suite, barrett tk, barrett toric, and z calc formulas. Pan Am J Ophthalmol [serial online] 2020 [cited 2021 Aug 1];2:23. Available from: https://www.thepajo.org/text.asp?2020/2/1/23/292653 
Introduction   
Refractive errors are the most common eye problem, the leading cause of visual impairment and the second leading cause of vision loss worldwide. Approximately 40% of adults have astigmatism. However, the prevalence of astigmatism varies widely in the different World Health Organization regions, being highest in America.^{[1]} Astigmatism (or cylindrical refractive error) is defined as a type of cylindrical ametropia that arises from nonrotational symmetric deformation of the refractive media. Usually, it is caused by deformation of the corneal curvatures (external astigmatism), although it may also be due to deformation of the lens (internal astigmatism), the latter being much less common.^{[2]} More than 50% of patients undergoing cataract surgery have corneal astigmatism ≥0.75 diopters (D), which is within the range of surgically treatable astigmatism and can significantly limit optimal visual outcome if not corrected.
A fundamental factor for the calculation of the intraocular lens (IOL) is the power of corneal refraction. Currently, with the advances in the optics field, it is possible to measure both the anterior and posterior curvatures of the cornea. Several studies have shown that ignoring posterior corneal curvature when calculating an IOL could lead to significant overcorrection or undercorrection, leading to residual refraction errors, even when a cataract surgery is now considered a refractive procedure.^{[3]}
Corneal power has traditionally been calculated using the anterior keratometry. Various technologies have been used for this purpose. These devices measure the radius of curvature (in millimeters) of the anterior corneal surface and convert it to refractive power (in diopters, D).^{[4]} The Pentacam (Oculus ^{®}, Wetzlar, Germany) measures the anterior and posterior corneal surfaces using a Scheimpflug rotary camera. The device uses ray tracing technology to determine the corneal power of the anterior and posterior surfaces, obtaining as a result the socalled total corneal refractive power (TCRP).^{[5]}
Another method of calculating corneal power is the IOL Master 700 with SWEPT Source Technology (Zeiss ^{®} Württemberg, Germany) which uses a scanning optical coherence tomography (OCT) biometer combined with telecentric keratometry technology. This technology allows us to obtain two different keratometric values of the same cornea. The standard keratometry (K) is calculated based on the anterior corneal curvature from the measurement of reflections of 18 lightemitting diodes, combined with telecentric keratometry and the total keratometry (TK) is calculated based on the anterior corneal curvature, posterior corneal curvature, and corneal thickness derived from the combination of telecentric keratometry and OCT technology.^{[6]}
The Barrett TK formula uses the Barrett Universal 2 formula to calculate the effective position of the lens and takes into account posterior corneal astigmatism to predict actual postoperative refractive astigmatism.^{[7]} On the other hand, the Haigis formula uses a regression equation (based on the a0, a1, and a2 constants) to calculate the effective position of the lens.^{[8]}
Our group has observed that the different methods to calculate the power of corneal curvature, together with the diversity of formulas that have been designed to calculate the power of the IOL, lead to an important variation in prediction both in the sphere and cylinder. Our objective is to compare the results obtained from the IOL calculation with different keratometries and formulas to describe the magnitude of the differences and similarities of the different refractive predictions.
Patients and Methods   
This is a descriptive, observational, and retrospective study. Our sample was collected for convenience and corresponds to 50 eyes of adult Mexicans of both sexes with cataract and a degree of corneal astigmatism >1.0 D with all the corneal curvature measurement methods included in this study, which came between November 2019 and May 2020 to IOL calculation at Centro Médico Puerta de Hierro in Guadalajara, Jalisco, Mexico. Exclusion criteria were previous corneal or intraocular surgery, keratoconus, and any other corneal disease. Patients were also excluded when optical biometric measurements were not possible due to cataracts. All patients underwent the measurements with Pentacam and IOL Master 700.
IOL power was calculated according to the Haigis Suite, Barrett TK, and Barrett toric formulas, as well as with the Z Calc online calculator (Zeiss ^{®} Württemberg, Germany) using TK and keratometry standard (K) obtained from IOL master 700 and TCRP keratometry obtained from Pentacam. A refractive index of 1.3375 and a surgically induced astigmatism of 0.00 were considered for all our measurements to prevent bias. When calculating both spherical and cylindrical values using K and TCRP, the Barrett Toric formula was used instead of Barrett TK because it is more suitable. The IOL chosen to perform the calculations was the Zeiss AT TORBI 709M/MP. A 95% confidence interval was used.
Results   
[Table 1] shows the demographics of the study population and average keratometry. Most of the astigmatisms analyzed in our sample are with the rule (WTR) astigmatism (87.5%), and only 10% had an against the rule (ATR) astigmatism; however, this factor was not found to affect the trends in the calculations.
We compared the calculations with Haigis Suite and Barrett TKToric. Choosing Haigis Suite or Barrett TKToric was found not to make a statistically significant difference in spherical results regardless of the keratometry used. Despite the fact that when analyzing individual cases, there is a great variation [Figure 1]. The spherical values varied up to 1.5 D. It was found that in 57%–82.5% of the calculations (depending on the keratometries used), the discordance was due to the fact that Barrett TKToric suggests ≥0.5 D of the sphere than Haigis Suite to reach the first negative residual value. When comparing the difference between the average of the spherical values, we find that Barrett TKToric suggests more sphere than Haigis Suite being with TK: 0.47 D, with K 0.32 D, and with TCRP 0.40 D.  Figure 1: Variation between Haigis Suite and Barrett TKToric using different keratometries
Click here to view 
When comparing the cylinder values using the same formulas, it was found that the spherical results varied significantly (P < 0.005). The variation range of the cylindrical values was from 0 to 1.5 D. In 83%–97% of the cases (depending on the keratometries used), the cylinder value with the Haigis Suite was ≥0.5 D. greater than with Barrett TKToric (not to change the axis of the cylinder). When analyzing the difference between the average of the cylindrical values, we found that Haigis Suite suggests a higher cylinder IOL to be implanted than Barrett TKToric, being the difference with TK 0.9 D, with K 0.8 D, and with TCRP 1 D.
When comparing Haigis Suite and Barrett TK against Z Calc Zeiss online calculator, there were no statistically significant differences in the sphere with Z Calc and Haigis Suite, and it varied more than >5 D in only two cases. On the other hand, there were no statistically significant differences in the cylinder, but it varied ≥0.5 D in 42% of the cases, although these variations were never greater than 0.5 D. Most of the variations in the cylinder occurred because the Haigis Suite formula suggested a higher cylinder (42% of the cases), while the opposite only happened in 2% of the measurements.
When analyzing the calculated sphere with Z Calc and Barrett TK, there were no statistically significant differences. It varied ≥0.5 D in 70% of the cases, the variations were from 0 to 1.5 D. Barrett TK suggested ≥0.5 D of the sphere than Z Calc in 63% of calculations. Cylinder between Z Calc and Barrett did show a significant variation (P < 0.005), there was a difference of ≥0.5 D in 88% of the cases. All variations were because Z Calc suggested more cylinder than Barrett TK but never happening the opposite. The magnitude of the variation was from 0 to 1.5 D.
Proceeding to show how the spherical results behaved when comparing different methods of measuring corneal power. No statistically significant differences were found in the spherical results when using K1 and K2 or TK1 and TK2 with the Barret Suite and Haigis TK  Toric formulas. The averages of both similar keratometries are shown in [Figure 2].  Figure 2: Average corneal power obtained with intraocular lens master 700 and Pentacam
Click here to view 
The spherical and cylindrical values obtained with K and TK were not significantly different. The discrepancy between the means of the sphere was 0.02 with Haigis and 0.1 with Barrett. On the other hand, the difference between the means of the cylinder was 0.06 with Haigis and 0.15 with Barrett. However, when the cases were individually analyzed, a variation ≥0.5 D was found in 42% of the cases with both the formulas, although this variation was only ≥0.1 D in 3%–7% of the cases. No keratometry had a tendency to suggest more or less sphere. The cylindrical values varied ≥0.5 D in 35% of cases with Haigis Suite and in 37.5% of cases with Barrett TKToric. Cylinder variations range from 0 to 0.5 D. Most of the variations were due to the fact that K suggested ≥0.5 cylinder D than TK being with Haigis Suite in 28% and with Barrett TKToric in 32.5% of the cases, the opposite happened only in 2% of the cases.
Comparing the cylinder results using the TCRP and K did not differ significantly. There was a difference ≥0.5 D in 45% of the cases with Haigis Suite and in 50% with Barrett TKToric.
Finally, a comparison of the calculated values when using two ways to measure the posterior cornea TK and TCRP is presented. The keratometries obtained with both the methods were not significantly different. The discrepancy between the means of the sphere was 0.01 with Haigis and 0.05 with Barrett. On the other hand, the difference between the means of the cylinder was 0.61 with Haigis and 0.26 with Barrett. If individual cases were analyzed, a cylindrical difference of ≥0.5 D in 65% of Haigis Suite calculations and 53% with Barrett TK was found. The magnitude of the variations was 0 to 2 D. When analyzing the variation in the sphere, it was not found that any keratometry had a tendency to suggest more or less sphere. The cylindrical results of TK and TCRP varied ≥0.5 D in 67% of the calculations with both the formulas. Cylinder variations range from 0 to 1.5 D. TCRP recommended ≥0.5 D of the cylinder than TK at 45% with Haigis Suite and 50% with Barrett TK.
Discussion   
Little information has been written comparing new formulas that take into account posterior keratometry. The results presented show the calculations with Haigis Suite and Z Calc which are very similar. It is also important to note that Barrett TKToric uses less cylindrical power than Haigis Suite and Z Calc, regardless of the method chosen to measure corneal power. Higher spherical values can also be observed with Barrett TKtoric compared to Haigis Suite and Z Calc in most cases, but these are not statistically significant. However, it is possible that such small differences can change the final refractive result in an undercorrection, in an era where any factor that improves the accuracy of IOL calculation counts [Figure 3] and [Figure 4].  Figure 3: Comparison of spherical power calculation with Haigis Suite, Barrett TK and Z Calc in the 50 eyes studied
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 Figure 4: Comparison of the calculation of toric power with Haigis Suite, Barrett TK Y Z Calc in the 50 eyes studied
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A study similar to ours that confronted different formulas was conducted in Korea using the Acrysof toric IOL to compare the SRK/T and Haigis formulas, finding that Haigis is more accurate in predicting cylindrical and spherical refraction results.^{[9]}
The importance of measuring the anterior and posterior keratometry has been controversial. A research by Srivannaboon andChirapapaisan analyzed the IOL calculation in 60 patients, where the spherical power was compared using K and TK with SRK/T, Hoffer Q, Haigis, Holladay 1/2, and Barrett TK Universal II formulas, where the power with anterior K was slightly higher than using TK; however, the difference was small, and there was no statistically difference between powers of IOLs selected by the surgeon.^{[10]}
We found that the averages of corneal astigmatism with different keratometries did not show great modifications. In fact, the mean of astigmatism with TCRP and K was the same [Figure 5]. However, when analyzing the differences by individual cases, important differences were found, although not significant, that could change the final refractive result. In an article by Ho with 493 subjects, corneal astigmatism was compared with anterior keratometry against Pentacam's TCRP, differing ≥0.5 D in 28.8% of the eyes and concluding that not taking into account the corneal surface significantly modifies the estimation of corneal astigmatism.^{[11]} Another similar article of 64 eyes using the Barrett Suite formula on the IOL Zeiss Torbi 709M reached similar conclusions.^{[12]}
A Hoshikawa study compared keratometry measured with the automatic keratometer and TK with the Scheimpflug camera in 50 ophthalmologically normal subjects. The difference between the means of conventional keratometry and TCRP was 0.7 D. It was concluded that there was no statistically significant difference in keratometric data between the two devices.^{[13]}
Recently in Germany, 93 eyes were analyzed comparing astigmatism measured with TK and TCRP, showing a difference of >0.5 D in many cases and a significant difference between the total corneal measurements of optical biometers and Scheimpflug devices. This finding agrees with our analysis where we also found a difference of >0.5 D in many cases and even found that TCRP increased the cylinder measurement in half of the cases; however, this difference was not significant.^{[14]}
Abulafia et al. carried out a study in 68 eyes, calculating astigmatism with IOL Master 500, optical lowcoherence reflectometrybased Lenstar LS 900, and Atlas ^{More Details} topographer, and subsequently comparing it with the postsurgical refractive result. They found that the use of devices that measure only the anterior cornea tends to result in insufficient eye correction with WTR astigmatism and overcorrection in ATR astigmatism.^{[15]} Along this same line of investigation, Skrzypecki carried out a study comparing the refractive result of eyes calculated with the Barrett Suite formula with and without the posterior curvature using the IOL master 700. They found no statistically significant differences in the mean absolute error and centroid error in the predicted residual astigmatism and also found no statistically significant differences in WTR and ATR astigmatisms.^{[16]} The behavior mentioned by Abulafia et al. in WTR and ATR astigmatism was not found in our study when our results agree more with the results of Skrzypecki.
It is also worth mentioning that this particular line of study has decreased on recent years due to the advent of intraoperative aberrometer devices (such as the optiwave refractive analysis [Alcon ^{®}, Fort Worth, TX, USA]) where a change of the IOL spherical or cylindrical power is suggested based on actual surgery measurements, making the use of these formulas more of a preoperative guide, rather than a law, with excellent postopearative outcomes,^{[17]} but it is also worth mentioning that, even when some of the cataract and refractive care clinics worldwide have it at their disposal (including our clinic), there is still insufficient access to meet the needs of the population based on the high prevalence of corneal astigmatism, so the need for an even better formula is still essential most of the time.^{[18]}
Conclusions   
Advances in technology have allowed us to find various ways to measure eye biometry and keratometry. This has led us to develop technologies that compete to perform the ideal IOL calculation based on different principles. This has generated great variability in the prediction of IOL power.^{[19]} In the current scenario, there are a variety of options for calculating the ideal IOL, generating uncertainty about which is the best method. We must be aware that clinical optimization is still necessary to have the ideal refractive result regardless of the keratometry or formula used to calculate the IOL.
Although the results of the study are limited by the group size, they showed to be prominent and consistent to expand the patient sample and include postsurgical results (and even a comparison with the intraoperative aberrometer). More prospective research is needed to evaluate the performance of different formulas and the use of posterior corneal astigmatism in clinical practice, allowing perfect adjustment of the power and axis of the toric IOL.^{[20]}
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1]
