Predicting accuracy of spherical equivalent after cataract surgery using the online Zcalc calculator for toric IOLs (2025)

Abstract

Compare Zcalc with other formulas on spherical equivalent prediction errors (PE) and explore the relationship between PE and ocular parameters. Optimize 709 IOL power calculation. 114 eyes with age-related cataract and preoperative regular corneal astigmatism of more than 1.5D were included. They underwent cataract surgery followed by implantation of a toric intraocular lens (Zeiss Torbi 709M) calculated by Zcalc formula. The prediction errors of spherical equivalent (SE) were analysed 3 months post-surgery. The refractive prediction errors of Zcalc, Barrett Universal II, Kane, and K6 formulas were 0.07 ± 0.63D, − 0.36 ± 0.65D, − 0.41 ± 0.67D, and − 0.31 ± 0.66D, respectively. Statistically significant difference were observed between Zcalc and other formulas. The Zcalc was prone to positive deviation, Barrett Universal II, Kane and K6 were prone to negative deviation. When the axial length is greater than 29.0mm, the prediction errors of Kane is higher, and prone to negative deviation. Prediction errors of Zcalc are small in all eyes and prone to positive deviation. For more accurate prediction, we recommend Barrett Universal II formula for 709 IOL power calculation.

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Introduction

In modern cataract surgery, we are not only aiming at cataract extraction, but also focusing on the satisfaction of patients1. Many patients’ satisfaction largely based on refractive outcome. 40% of cataract patients have corneal astigmatism above 1.0D2. If these astigmatism cannot be corrected, it will significantly affect the postoperative vision of patients and reduce their quality of life after surgery3. The methods for correcting corneal astigmatism in cataract patients include corneal incision correction and toric IOL correction4. Toric IOL has the characteristics of better unaided corrected visual acuity(UCVA), and smaller residual astigmatism compared to other methods for correcting astigmatism5. AT TORBI 709M IOL (709 IOL) has been proven to be a predictable and effective Toric IOL with good rotational stability, which had been used for correcting corneal astigmatism in cataract surgery6. 709M IOL uses online computing websites to calculate IOL degrees, with a built-in formula of Zcalc.

The Zcalc online calculation formula is based on the principle of Gaussian thick lens. A Zmatrix model is created to predict the effective lens position (ELP) corresponding to different axial length (AL) and anterior chamber depth (ACD) and Abulafia-Koch formula is applied for toric IOL calculation. To date, the study on the accuracy of Zcalc are rare.

As is known to us, minimizing the prediction error (PE) is a crucial step in achieving the ideal refractive state after surgery7. To accurately predict postoperative refractive outcome, the selection of the IOL calculation formula is of significance. The well-known formulas are Barrett Universal II (especially for normal and long eyes), K6 (especially for short eyes), and Kane (for all eyes)8,9,10,11,12. Currently, there were several studies compared the PE between Barrett Universal II (Barrett) and Zcalc after surgery, but did not consider the rediction error across ocular dimensions such as AL and ACD13,14. In this study, we present refractive outcomes of Zcalc in different AL subgroups and compare it with Barrett Universal II, K6, Kane formula. We aimed to explore the predictive accuracy of Zcalc’s formula, optimize the calculation of 709 IOL SE and provide theoretical basis for its clinical application.

Methods

The protocol for this study was approved by the Medical Ethics Committee of Tongji Medical College, Huazhong University of Science and Technology. All procedures conformed to the Declaration of Helsinki. Patients with age-related cataract and preoperative regular astigmatism of more than 1.5D by topographic Scheimpflug analysis (Sirius) were included in Union Hospital, Tongji medical college, Huazhong university of science and technology between January 2020 and May 2023. Exclusion Criteria were irregular astigmatism, pseudoexfoliation syndrome, glaucoma and corneal pathologies. IOLMaster 700 was used for optical biometry and preoperative Scheimpflug measurement for total corneal astigmatism assessment was carried out in all patients. These devices were daily calibrated with a test eye. The subjects were sorted into 4 groups according to axial length. They are AL ≤  23mm (AL 1), 23mm < AL ≤ 26mm (AL 2), 26mm< AL ≤ 29mm (AL 3), AL>29mm (AL 4). Uneventful cataract surgery was performed by the same surgeon with implantation of 709 IOL. Postoperative refraction was confirmed by using an autorefractometer postoperatively at 3 months by the same optometrist. SE prediction error of Zcalc was analysed and compared with Barrett Universal II, Kane and K6 in SPSS 26.0 software.

The refractive prediction error was calculated as the difference between the actual and predicted postoperative refractive spherical equivalent. Before the analysis of mean absolute error(MAE) and median absolute error(MedAE), we zero out the arithmetic mean error by adjusting the refractive prediction error for each eye. The Kolmogorov-Smirnov test was applied to determin whether the data are normally distributed. The non-parametric Wilcoxon signed rank test and Friedman test were used to compare the differences in refractive prediction error and absolute prediction errors for between formulas respectively, The Cochran’s Q test was utilized to compare percentage of eyes between formulas within different PE groups. Multiple linear regression was applied to examine the linear relationship between biological parameters and absolute prediction errors of different formulas. A P value less than 0.05 was considered statistically significant.

Availability of formulas

Barrett Universal II formulas were included in the biometer.The remaining formulas were accessed from their respective web sites in the following: Zcalc (https://zcalc.meditec.zeiss.com), Kane (https://www.iolformula.com/) and K6 (https://www.cookeformula.com/).

Results

A total of 114 patients (114 eyes) were recruited between January 10, 2020, and January 20, 2023. The age of the study participants ranged from 20 to 88 years. Table1 shows the measured parameters of the eyes and demographic characteristics and measured ocular parameters of the study group. Of the 114 observed patients, 48 were male and 66 were female. There was no significant difference in the sex and cylinder among the four groups (P > 0.05 for all). The measured parameters of the eyes and demographic characteristics of the patients were shown in Table1.

Full size table

Refractive prediction errors of Zcalc compared with that of Barrett Universal II, Kane and K6

As shown in Fig.1, the refractive prediction errors, without adjusting the refractive prediction error to zero, produced by Zcalc, Barrett Universal II, Kane, and K6 formulas were 0.07 ± 0.63D, − 0.36 ± 0.65D, − 0.41 ± 0.67D, and − 0.31 ± 0.66D, respectively. The difference between Zcalc and other formulas was statistically significant (in all subgroups) (P < 0.01). The results showed that Zcalc is prone to positive deviation, Barrett Universal II, Kane, K6, and is prone to negative deviation (Fig.1).

Refractive prediction errors of formulas before adjusting.

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Absolute prediction errors of formulas

MAEs and MedAEs of four formulas in four subgroups are showed in Figs.2 and 3. Barrett was the best generally giving rise to an MAE ± SD (MedAE) of 0.41 ± 0.51 D (0.29 D). Subgroup analysis showed that when the axial length was less than 29.0mm, there was no statistically significant error in the four formulas. When the axial length s greater than 29.0mm, Kane emerged as the less accurate formula with a prediction error within 0.45 ± 0.50 D (0.35 D) (P < 0.05).

Mean absolute errors of formulas after adjusting (the asterisk indicates significant differences between groups).

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Box plot graph of the median absolute errors of formulas in total and subgroups.

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Percentage of eyes within different prediction error groups were shown in Figs.4 and 73.68% of the eyes had a absolute predition error within ± 0.5 D with the Barrett and K6 formula, 67.54% with the Kane formula and 72.81% with the Zcalc formula. The percentage of eyes with a PE within ± 1.0 D ranged from 91.23% (Zcalc) to 92.98% (Barrett, Kane and K6). Percentage differences betweent formulas did not reach statistical significance.

Percentage of eyes within different prediction errors.

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Formula performance across ocular dimensions

Line graphs with points representing the sample mean of the refractive prediction errors and absolute prediction errors of formulas for several ocular dimensions were displayed in Figs.5 and 6. Multiple linear regression analysis with above 6 ocular dimensions revealed that refractive prediction errors of Kane formula were negative related to AL (P < 0.001, r = − 0.1).

Line graphs of refractive prediction error after adjusting versus ocular dimensions.

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Line graphs of absolute prediction error versus ocular dimensions.

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Discussion

Postoperative residual astigmatism affects postoperative unaided vision, thereby influencing the outcomes of cataract surgery15. Toric IOL can effectively and stably correct corneal astigmatism in cataract patients, providing higher spectacle independence and contributing to an improved postoperative quality of life for patients16. Zcalc is the online calculation formula for toric IOL (709MP IOL). To date, a few studies has been carried on about the prediction accuracy of Zcalc formula. Kern et al. compared the Zcalc and Barratt University II and found that Barrett delivered better refractive outcomes when calculate with anterior corneal astigmatism. Less residual postoperative SE, sphere, and cylinder was observed for the Barrett calculator by the same team13,14. However, they did not specify the difference on different biometric dimensions. Wang L.et al. did some research on calculation accuracy of Zcalc and Barrett. However they compared only the above two formulas17. A lot of researches had demonstrated that the new-generation formulas had superior accuracy over the 3rd and 4th generation formulas8,9,10,11,12. Nevertheless, they were mostly about PE accuracy on non-toric IOLs. As we all known, the two meridians of toric IOLs were different. Thus, the calculation of ELP might differ from that of non-toric IOLs, which contribute to different refractive effect of formulas for toric IOLs. Shi J. et al.has evaluated the accuracy of the new-generation formulas on intraocular lens (IOL) power formulas for calculating spherical equivalent (SE) of toric IOL.Whereas, they did not contain Zcalc formula18.

This study compared prediction errors of Zcalc with that of Barrett Universal II, K6, and Kane. Zcalc shows a positive deviation, indicating a hyperopic refractive error of Zcalc. According to our analysis on absolute prediction errors, the Barrett formula has the lowest absolute prediction error. The difference between Kane and Barrett formula is of significance (P < 0.05). Zcalc and K6 formula exhibited slightly higher absolute errors, though the difference was not statistic significant. The Kane has the greatest absolute prediction error for extra long eyes (AL ≥ 29mm). The results on kane formula was different from research by Shi J.et al., As our concern, we used different IOLs. Their IOLs were AcrySof SN6AT (2–9) IOL, and our IOLs were 709 IOL.Different dimensions of IOLs may affect ELP and result in different refractive results. In addition, we included less patients compared to them, which may also contribute to the difference between the two studies. What’s more, multiple linear regression analysis with ocular dimensions indicates that with the increase of AL, PE of Kane formula is prone to decrease and prone to negative deviation, which is similar to studies by Kern et al. It is encouraging that more than 90% of patients had a spherical equivalent result within 1.00 D of the predicted outcome with any of the formulas studied. Moreover, the 4 formulas did vary in having from 67.54 to 72.81% of eyes within 0.50 D, which is often accepted as the value for which the blur allows spectacle independence19,20,21,22.

Conclusion

Prediction errors of Zcalc are small in all eyes and prone to positive deviation. For more accurate prediction, we recommend Barrett Universal II formula for 709 IOL power calculation. This study investigated the predictive accuracy of the Zcalc formula and optimize the calculation of 709 IOL power, providing a theoretical basis for its clinical application.

Data availability

Data is provided within the supplementary information files.

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Authors and Affiliations

  1. Department of Ophthalmology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, 430022, China

    Ling Jin,Yamin Mao,Xuan Yu,Mengyan Wen,Junjie Yang&Yukan Huang

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  1. Ling Jin

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  2. Yamin Mao

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  3. Xuan Yu

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Contributions

Conceptualization, Yukan Huang; methodology, Ling Jin.; software, Yamin Mao.; validation, Junjie Yang; formal analysis, Xuan Yu.; investigation, Mengyan Wen.; data curation, Ling Jin; writing—original draft preparation, Ling Jin.; writing—review and editing, Yukan Huang.; project administration, Yukan Huang. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Yukan Huang.

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The authors declare no competing interests.

Institutional review Board Statement

The study was conducted in accordance with the Declaration of Helsinki, and approved by the Medical Ethics Committee of Tongji Medical College, Huazhong University of Science and Technology (protocol code UHCT-IEC-SOP-016-03-01 and date of approval: Jan 31th, 2024).

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Written informed consent was obtained from all subjects involved in the study.

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Predicting accuracy of spherical equivalent after cataract surgery using the online Zcalc calculator for toric IOLs (10)

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Jin, L., Mao, Y., Yu, X. et al. Predicting accuracy of spherical equivalent after cataract surgery using the online Zcalc calculator for toric IOLs. Sci Rep 14, 27547 (2024). https://doi.org/10.1038/s41598-024-78667-x

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Keywords

  • Zcalc
  • Formula
  • Toric IOL
  • Prediction error
Predicting accuracy of spherical equivalent after cataract surgery using the online Zcalc calculator for toric IOLs (2025)
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