Intraocular lens formula calculation in pediatric eyes: Do we have an answer? A retrospective comparison between Sanders–Retzlaff–Kraff II and Barret’s formula

Abstract

Purpose:

The ideal formula for intraocular lens (IOL) power calculation following cataract surgery in pediatric eyes till date has no answer. We compared the predictability of the Sanders–Retzlaff–Kraff (SRK) II and the Barrett Universal (BU) II formula and the effect of axial length, keratometry, and age.

Methods:

This was a retrospective analysis of children who were under eight years of age and who underwent cataract surgery with IOL implantation under general anesthesia between September 2018 and July 2019. The prediction error of SRK II formula was calculated by subtracting the target refraction and the actual postoperative spherical equivalent. Preoperative biometry values were used to calculate the IOL power using the BU II formula with the same target refraction that was used in SRK II. The predicted spherical equivalent of the BU II formula was then back-calculated using the SRK II formula with the IOL power obtained with the BU II formula. The prediction errors of the two formulae were compared for statistical significance.

Results:

Seventy-two eyes of 39 patients were included in the study. The mean age at surgery was 3.8 ± 2 years. The mean axial length was 22.1 ± 1.5 mm, and the mean keratometry was 44.7 ± 1.7 D. The group with an axial length >24 mm showed a significant and strong positive correlation (r = 0.93, P = 0) on comparison mean absolute prediction errors using the SRK II formula. There was a strong negative correlation between the mean prediction error in the overall keratometry group using the BU II formula (r = −0.72, P < 0.000). There was no significant correlation between age and refractive accuracy using the two formulae in any of the subgroups of age.

Conclusion:

There is no perfect answer to an ideal formula for IOL calculation in children. IOL formulae need to be chosen keeping in mind the varying ocular parameters.

The ideal formula, planned under correction and refractive outcome in children following pediatric cataract surgery is a question that has pediatric ophthalmologists still searching for an “ideal” answer. Emmetropia in the immediate postoperative period and a myopic shift later or hyperopia due to undercorrection and emmetropia later on is something that needs to be carefully weighed.

These questions depend on the intraocular lens (IOL) power and the formula chosen to calculate the same. The Sanders–Retzlaff–Kraff (SRK) II is probably the most widely used formula today, and there are studies that have compared prediction errors amongst various formulae and with never tools like the pediatric IOL calculator.[1–3]

The aim of our study was to assess the predictability of the SRK II and the Barrett Universal (BU) II formula and possible effect of axial length, keratometry, and age.

Methods

This was a retrospective analysis of children who were under eight years of age and who underwent cataract surgery with IOL implantation under general anesthesia between September 2018 and July 2019. Initially medical records of 123 children were analyzed and 72 were included in the study. We excluded cataracts following trauma, glaucoma filtration surgery, post-retinal detachment, and those with persistent fetal vasculature and anterior segment developmental anomalies.

After induction of general anesthesia, a detailed examination was performed in all cases. The keratometry readings were recorded using a Nidek KM 500 handheld keratometer (Nidek, Inc., remont, CA) with good centration on the cornea. An average of three readings were taken; thereafter the intraocular pressure was recorded using the Perkins applanation tonometer. Biometry, such as axial length, lens thickness, and anterior chamber depth, was then performed using immersion technique (OcuScan RxP, Alcon laboratories, Inc., Fort Worth, TX). The axial length was recorded till 10 readings of sharp retinal spike followed by low orbital spikes were obtained. An average of these readings within a standard deviation of 0.01 was recorded. Similarly, the anterior chamber depth and lens thickness were recorded. The IOL power was calculated using the SRK II formula on an age-appropriate target hypermetropia, as suggested by Enyedi et al.[4] All surgeries were performed by six fellowship-trained pediatric ophthalmologists.

Postoperatively, topical antibiotics, steroids (weekly tapering), and cycloplegics were prescribed, and patients were evaluated on postoperative day 01, day 02 or day 03, 1 week and then 1 month. Refraction was performed on day 3 postoperatively, and glasses or contact lenses prescribed. If reliable refraction was not obtained on day 3, it was repeated in the first week postoperatively and again performed at the one-month follow up. The refraction noted between 1-3 months post operatively was used to calculate the spherical equivalent in the study.

The prediction error of SRK II formula was calculated by subtracting the target refraction and the actual postoperative spherical equivalent. Absolute prediction error was calculated by subtracting the target refraction from the postoperative spherical equivalent, and it represents the absolute difference. The preoperative biometric values were then used to calculate the IOL power using the BU II formula with the same target refraction as used in SRK II. The predicted spherical equivalent of the BU II formula was then back-calculated using the SRK II formula with the IOL power obtained by using BU II formula. The difference between the target refraction and this back-calculated spherical equivalent was the back-calculated prediction error for the BU II formula. The prediction errors of the two formulae were then compared for statistical significance.

Statistical analysis was performed using IBM SPSS Statistics (version 21.0, SPSS, Inc.). The differences in prediction error (PE) and mean absolute prediction error (APE) in postoperative refraction between the formulae were assessed by post hoc analysis using the Wilcoxon signed-rank test. A P-value less than 0.05 was considered significant. The Pearson correlation coefficient was used to analyze the effect of axial length, keratometry, and age on PE and APE for the two formulae.

Results

Seventy-two eyes of 39 patients were included in the study. The mean age at surgery was 3.8 ± 2 years. The mean axial length was 22.1 ± 1.5 mm, and the mean keratometry was 44.7 ± 1.7 D. For data analysis, we divided the subjects into two main groups based on age, axial length, and keratometry [Table 1].

Table 1.

The number of eyes in different subgroups

Criteria	Subgroups	Number of eyes
Axial length (mm)	18-21	16
	22-24	50
	>24	6
Keratometry (D)	≤45	44
	>45	28
Age (years; range: 1-8 years)	≤2	23
	3-5	30
	6-8	19

In our cohort, we found that the BU II formula gave a lower mean prediction error (0.094 ± 1.41 D) compared to that given by SRK II (−0.60 ± 1.11; P < 0.05). There was no statistically significant difference (P = 0.6) between the mean absolute prediction error of SRK II (0.97 ± 0.81 D) and that of BU II (0.95 ± 1.04 D) (D= dioptres).

There was a significant difference in the prediction errors when using the SRK II formula (P = 0.007) across the subgroups of axial length. Across the subgroups, there was a significant difference in the prediction error (P = 0) and the absolute prediction error (P = 0.008) when using the BU II formula.

While the overall average PE using the SRK II and BU II formulae were comparable, the PE (1.37 ± 1.45) and APE for BU II (1.5 ± 1.31) was higher than the PE (−0.06 ± 0.95) and APE (0.75 ± 0.56) for SRK in eyes with axial length between 18 and 21 mm [Table 2].

Table 2.

Comparison of prediction error and absolute prediction error using SRK II and BU II formulae in the axial length group

Axial length	PE_SRK II	APE_SRK II	PE_BU II	APE_BU II
18-21 mm n=16	−0.06±0.95	0.75±0.56	1.37±1.45	1.5±1.31
21-24 mm n=50	−0.63±1.05	0.94±0.78	−0.11±1.05	0.70±0.78
>24 mm n=6	−1.83±1.18	1.83±1.18	−1.62±1.35	1.62±1.35
P	0.007	0.119	0	0.008

PE: Prediction error; APE: Absolute prediction error. The values of PE and APE are expressed as mean±standard deviation

There was a significant difference in prediction errors when using the SRK II formula (P = 0.013) across the subgroups of keratometry. The PE (0.04 ± 1.15) and APE (0.79 ± 0.83) for BU II was lower compared to the PE (−0.90 ± 1.04) and APE (1.04 ± 0.91) for SRK II in eyes with keratometry ≤45 D [Table 3].

Table 3.

Comparison of prediction error and absolute prediction error using SRK II and BU II formulae in the keratometry group

Groups	PE_SRK II	APE_SRK II	PE_BU II	APE_BU II
≤45 D n=44	−0.90±1.04	1.04±0.91	0.04±1.15	0.79±0.83
>45 D n=28	−0.13±1.07	0.85±0.63	0.16±1.75	1.2±1.26
P	0.013	0.698	0.722	0.102

K=Keratometry; PE: Prediction error; APE: Absolute prediction error. The values of PE and APE are expressed as mean±standard deviation

Across age groups, there was a significant difference in prediction error (P = 0.02) and absolute prediction error (P = 0.017) when using the SRK II formula, with the prediction error being the highest (−0.99 ± 1.29) in the age group of 3–5 years and the lowest (−0.15 ± 0.84) in the age group of ≤ 2 years. The BU II formula showed a lower prediction error of 0.09 ± 1.41 in the overall group and was lower across all age groups when compared with SRK II [Table 4].

Table 4.

Comparison of prediction error and absolute prediction error using SRK II and BU II formulae in the age group

Groups	PE_SRK II	APE_SRK II	PE_BU II	APE_BU II
≤2 years n=23	−0.15±0.84	0.67±0.50	−0.07±1.71	1.20±1.19
3-5 years n=30	−0.99±1.29	1.32±0.94	0.1±1.51	1±1.11
5-8 years n=19	−0.54±0.9	0.76±0.71	0.09±0.74	0.56±0.47
P	0.02	0.017	0.311	0.104

PE: Prediction error; APE: Absolute prediction error. The values of PE and APE are expressed as mean±standard deviation

Subgroup analysis

Prediction error and axial length

There was a significant negative correlation between the mean prediction error and the axial length across the subgroups using the SRK II formula and the BU II formula. However, there was a strong and significant correlation between prediction error and axial length in eyes with axial length >24 mm when using both SRK II (−0.93, P = 0) and BU II (−0.82, P = 0) formulae.

The group with axial lengths >24 mm showed a significant and strong positive correlation (r = 0.93, P = 0) on comparison of the mean absolute prediction errors using the SRK II formula [Table 5].

Table 5.

Correlation between axial length and prediction error for SRK II and BU II formulae

Groups	PE_SRK II	APE_SRK II	PE_BU II	APE_BU II
Overall AXL (mm) n=72	−0.5 (0)	0.39 (0)	−0.72 (0)	−0.16 (0.17)
18-21 mm n=16	−0.54 (0.02)	−0.01 (0.95)	−0.77 (0)	−0.18 (0.49)
21-24 mm n=50	−0.27 (0.05)	0.26 (0.06)	−0.46 (0)	−0.07 (0.6)
>24 mm n=6	−0.93 (0)	0.93 (0)	−0.82 (0)	0.82 (0.04)

AXL: Axial length; PE: Prediction error; APE: Absolute prediction error. The correlation values are expressed as correlation coefficient r (P)

When the mean PE were compared in the >24 mm axial length group, there was a significant negative correlation (r = -0.82, P < 0.00) of post-operative refraction using Barrett’s formula. [Table 5].

Prediction error and keratometry

We found a strong and significant negative correlation between the mean prediction error in the overall keratometry group when using the BU II formula (r = −0.72, P < .000) and a significant but weak positive correlation (r = 0.3, P = 0.01) using the SRK II formula [Table 6].

Table 6.

Correlation between keratometry and prediction error for SRK II and BU II formulae

Groups	PE_SRK II	APE_SRK II	PE_BU II	APE_BU II
Overall K (D) n=72	0.3 (0.01)	−0.1 (0.37)	−0.72 (0)	−0.16 (0.17)
K <45 D n=44	0.04 (0.76)	0.01 (0.94)	−0.24 (0.11)	−0.04 (0.75)
K >45 D n=28	0.07 (0.7)	−0.12 (0.52)	0.36 (0.05)	0.07 (0.69)

K=Keratometry; PE: Prediction error; APE: Absolute prediction error. The correlation values are expressed as correlation coefficient r (P)

Prediction error and age

There was no significant correlation between age and refractive accuracy when using the two formulae in any of the age subgroups [Table 7].

Table 7.

Correlation between age group and prediction error for SRK II and BU II formulae

Groups	PE SRK II	APE SRK II	PE BU II	APE BU II
Overall age (years)	−0.09 (0.46)	0.01 (0.93)	−0.03 (0.83)	−0.24 (0.048)
≤2 years n=23	−0.02 (0.25)	0.09 (0.66)	−0.27 (0.2)	−0.07 (0.75)
3-5 years n=30	0.15 (0.41)	−0.04 (0.81)	−0.07 (0.69)	0.06 (0.72)
5-8 years n=19	0.31 (0.18)	−0.25 (0.29)	0.15 (0.53)	0.29 (0.22)

PE: Prediction error; APE: Absolute prediction error. The correlation values are expressed as correlation coefficient r (P)

Discussion

We aimed to study the predictability of the SRK II and BU II formulae for calculating IOL power and the effect of axial length, keratometry, and age on prediction error.

In our cohort, we found that the BU II formula gave the lowest mean prediction error (0.094 ± 1.41 D) compared to SRK II (−0.60 ± 1.11D; P = 0.00). However, even though the mean absolute prediction errors were similar (SRK II: 0.97 ± 0.81, BU II: 0.95 ± 1.04), this was not found to be statistically significant (P = 0.6).

We attempted to study the effects of axial length, keratometry, and age on prediction errors using these two formulae. We further subdivided our cohort into categories, as mentioned in Table 1.

The SRK II formula showed better predictability results in the eyes with axial lengths of 18–21 mm, and the BU II formula gave a lower prediction error in eyes with axial lengths between 21 and 24 mm. In eyes with longer axial lengths (>24 mm), both formulae gave a comparable and higher prediction error. There was a strong and significant negative correlation between prediction error and axial length in eyes with axial length >24 mm when using both SRK II and BU II formulae.

For steeper corneas of >45 D, the SRK II and BU II formulae showed predictable results when compated to the flat corneas ≤45 D where only the BU II showed predictable outcomes. There was a strong and significant negative correlation (r = −0.73, P = 0) between keratometry and prediction errors using the BU II formula.

The BU II formula showed a smaller prediction error of 0.09 ± 1.41 across the subgroups of age and was lesser across all age groups when compared with SRK II.

The ideal formula for calculating IOL power—if there is one—has been the subject of research in many studies. While multiple studies have reported on the safety, feasibility, and benefits of IOL in children,[5,6] which formula gives the most predictable outcomes is something that remains unanswered. The uncertainty and unpredictability come from the fact that pediatric ophthalmologists deal with a growing eye ball and that often biometry has to be done under general anesthesia, which may influence centration.[2] There are studies comparing the various formulae and also those that have compared these formulae with IOL calculators.[2,3,7,8]

Chang et al.[7] reported on the predictability of eight IOL formulae in pediatric eyes. They reported that for smaller eyes (axial length <21 mm) Hoffer-Q and SRK-T had the most predictable outcomes. For larger eyes (axial length >21 mm) and in children older than two years, BU II and Haigis formulae had predictable outcomes. For younger children with smaller eyes, though none of the formulae did well, SRK-T had the most predictable outcomes.

Jasman et al.[1] compared the prediction errors of SRK II formula and the pediatric IOL calculator. Although they felt that prediction errors were comparable, the SRK II formula showed lower prediction errors. Although they analyzed results in children older than three years, they reported that irrespective of age, axial length, and keratometry, the SRK II formula and the IOL calculator gave similar results.[1] Though our grouping was similar, our cohort had children under two years of age.

Kekunnaya et al.[2] compared the prediction errors in children aged under two years, with SRK II, SRK-T, Holladay, and Hoffer-Q formulae. They reported that SRK II gave predictable results compared to the other three formulae. Further the same group has also reported that axial length and keratometry influence prediction errors with the Holladay, Hoffer Q and the SRK-T. Prediction errors tended to be high with flat corneas and the SRK T. In our cohort, the BU II formula gave predictable results in flatter corneas and those with normal keratometry.

The BU II formula seems to be a robust formula to use, with predictable outcomes observed in children aged under two years and above 5 years, in eyes with axial length between 21 and 24 mm, and in eyes with flat corneas.

Our study has limitations. It was retrospective in nature. Among the subgroups, subjects were too few in number for us to make meaningful comparisons. Despite this, we feel that although some of the correlations did not reach statistical significance, a trend can be seen especially in those eyes with extremes of axial length and keratometry.

Conclusion

There is no perfect answer to an ideal formula for IOL calculation in children. IOL formulae need to be chosen keeping in mind various ocular parameters. The BU II formula seems to give predictable outcomes in younger age groups, flatter corneas, and in axial lengths between 21 and 24 mm.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.