Before entering the study, all patients were informed of its purpose and expressed their written consent. The study protocol was approved by the Ethics Committee of the Kermanshah University Medical Sciences and health services, and the study complied with the tenets of the Declaration of Helsinki. Institutional review board approval was obtained for this study. Of the 423 eyes underwent cataract surgery during the study period, Inclusion criteria were met by 250 eyes. 173 eyes were excluded from the study due to inadequate biometry data (N = 136); associated ocular comorbidities and previous intraocular surgeries (N = 19) or postoperative complications (N = 18).
As all eyes were operated by the same surgeon, constant optimization did not have to compensate for different surgical techniques, such as different capsulorhexis size, influencing the postoperative IOL position. On the other hand the postoperative refraction was assessed by the same surgeon, who measured it with the maximum attention.
Patients separated in 3 study groups according to ALs: 135 eyes in normal AL group [AL 22–24.5 mm], 53 eyes in short AL groups [AL < 22 mm], and 62 eyes in long AL groups [AL > 24.5 mm].
The mean age of the study group population was 61.8 ± 2.73 years (range: 59–64 years), with 141 male patients (mean age 61.9 ± 3.45 years; range 61–64 years) and 109 female patients (mean age 60.2 ± 2.82 years; range 59–62 years). The mean age of the study patients in normal AL group was 61.29 ± 2.51 years, short AL group was 62.24 ± 3.78 years, and those in long AL group was 61.19 ± 3.28 years.
The mean preoperative visual acuity was 20/50 ± 20/50 LogMAR units in the whole study population, with 10/50 ± 20/50, 30/50 ± 10/50, and 20/50 ± 30/50 in normal AL group, short AL group, and long AL group, respectively. (P-value > 0.05).
The mean uncorrected visual acuity (UCVA) and mean best corrected visual acuity (BCVA) of the study subjects at 3 month postoperative follow up are summarized in Table 5.
In the entire study sample population, the BU II formula gave the lowest mean absolute error and median absolute error in predicted postoperative refraction. This was noted in the individual groups as well, with mean absolute error of 0.32 ± 0.25 D in normal AL group, 0.45 ± 0.24 D in eyes with AL < 22 mm, and 0.38 ± 0.23 D in eyes with AL > 24.5 mm .
Statistically significant differences were observed between the mean absolute errors in postoperative refraction given by the two formulas (by Freidman test) in normal and short axial length groups. BU II gave the lowest mean absolute prediction error in postoperative refraction and median absolute error in normal and short AL group, respectively.
The mean postoperative refractive error (spherical equivalent) at 3 month was 0.20 ± 0.49D (range: 0.63 D to 1.13 D).
The comparison (by post hoc analysis using Wilcoxon signed ranks test) of the mean absolute prediction errors between the IOL formulas in the 3 study groups is summarized in Table 4. In all the three AL groups, there was statistically significant difference between mean prediction error in postoperative refraction of Barrett and BU II (P value < 0.0005); however, the difference in mean absolute prediction errors between Olsen and BU II formulas was statistically significant in the short AL group (P value < 0.0005), also in the normal AL group (P value < 0.0005). In the long axial length eyes group, there was no statistically significant difference between formula (p = 0.24). No post-hoc analysis was performed because of the lack of statistically significant result.
Eyes with prediction error in postoperative refraction within ± 1 D and ± 0.5 D of the given target by the two formulas was highest with BU II formula with approximately 98% and 71% of the eyes achieving within ± 1D and ± 0.5D of the given target postoperative refraction, respectively.
The mean implanted IOL power was 22.29 D ± 4.23 (SD) (range 10.5 to 31.5 D).
Our study revealed the Barrett Universal II had the lowest MAE. There was a statistically significant difference in absolute error between the two IOL power calculation formulas (P < .001). Compared with the Barrett Universal II formula Olsen ranked worse. The BU II formula provided predictions that were more accurate than those using the Olsen in normal and short AL grupe (P < .001).
Significantly more eyes placed in PE between − .25 D _+.25 D with BU II formula.
This findings emphasized on accuracy of BU II formula except in long AL patient.
Repeated-measures ANOVA did not reveal any statistically significant difference for the mean PE (P = .2738), which was close to zero with all formulas due to constant optimization.
The most interesting finding is the lack of far outliers for Barrett formula.
Table 6 shows the change in biometric variables between preoperatively and postoperatively. The K flat, K steep, and AL values did not change significantly after the IOL implantation; however, there was a significant decrease in the ACD (P Z .008).
The simple linear regression used to predict the pre-operative ACD from the postoperative value found statistically significant regression (P = .002). The correlation coefficient (R2) was 0.373 based on the following equation:
ACD preoperative = 1.95 * 0.505 *ACD postoperative.
The difference between the preoperative and postoperative values was not statistically significant. Thus, if the mean preoperative values were considered as references for IOL power calculation and because the changes in the values (flat K: D; steep K: D; AL: mm) was not significant.
Table 5 showed the refractive errors and visual acuity before and after surgery.
Table 2 shows the characteristics of the study population.
Table 2
Demographic data of the patients by axial length group.
Parameter | short AL < 22 mm | normal AL 22.0–24.5 mm | long AL > 24.5 mm | P Value |
Mean age (year) | 62.24 ± 3.78 | 61.29 ± 2.51 | 61.19 ± 3.28 | .07 |
Sex (Male / Female) | 46/23 | 54/49 | 41/37 | .47 |
Eye (Right / Left) | 33/44 | 45/45 | 41/42 | .52 |
No significant differences were found between demographic data in 3 groups. |
Table 3 revealed Refractive measurements obtained with the formulas investigated between three study groups. Differences between two formulas was significantly lower in BU II group versus Olsen group in normal and short axial length groups.
This meaningful accuracy was not obtained in long axial length group.
Table 3
Refractive outcomes obtained with the formulas investigated and the biometric measurements.
Formula | Mean Absolute Error ± SD (D) | Median Absolute Error (D) | Range (D) | P value |
Entire Study Population |
Olsen | 0.38 ± 0.27 | 0.39 | 1.31to1.63 | < 0.0005 |
BU II | 0.27 ± 0.38 | 0.29 | 1.29to1.38 |
Eyes with Normal Axial Length |
Olsen | 0.35 ± 0.28 | 0.35 | 1.3 to 1.6 | < 0.0005 |
BU II | 0.37 ± 0.25 | 0.30 | 1.31to1.43 |
Eyes with Short Axial Lengths |
Olsen | 0.54 ± 0.38 | 0.59 | 0.80 to 1.6 | < 0.0005 |
BU II | 0.35 ± 0.24 | 0.28 | 0.46 to 1.2 |
Eyes with Long Axial Lengths |
Olsen | 0.39 ± 0.39 | 0.35 | 0.81to0.21 | 0.240 |
BU II | 0.37 ± 0.23 | 0.26 | 0.54to0.75 |
CDVA = corrected distance visual acuity; logMAR = logarithm of the minimum angle of resolution; UDVA = uncorrected distance visual acuity Means ± SD |
Table 4
demonstrated Optimized Constant and Lens constant for both formulas.
formulas | Optimized Constant | Lens constant | PE ± SD | PE ≤ 0.25 D | PE ≤ 0.50 D | PE ≤ 0.75 D | PE ≤ 1.00 D |
Entire study group |
Barrett | 118.5 | Lens factor | 0.005 ± 0.323 | 62.05 | 93.20 | 95.33 | 100.0 |
Olsen | 4.45 | ACD | 0.010 ± 0.326 | 60.58 | 90.33 | 90.00 | 98.04 |
short AL group |
Barrett | 118.5 | Lens factor | 0.015 ± 0.302 | 64.45 | 90.20 | 94.43 | 100.0 |
Olsen | 4.45 | ACD | 0.014 ± 0.325 | 58.58 | 77.33 | 81.88 | 97.11 |
Normal AL group |
Barrett | 118.5 | Lens factor | 0.005 ± 0.311 | 66.15 | 87.21 | 94.31 | 99.89 |
Olsen | 4.45 | ACD | 0.012 ± 0.325 | 59.48 | 84.27 | 88.72 | 95.14 |
Long AL group |
Barrett | 118.5 | Lens factor | 0.005 ± 0.329 | 61.15 | 88.19 | 94.23 | 98.26 |
Olsen | 4.45 | ACD | 0.015 ± 0.317 | 60.56 | 87.29 | 93.20 | 98.14 |
AL = axial length; EVO = Emmetropia Verifying Optical; MAE = mean absolute error; MedAE = median absolute error; PE = prediction error; RBF = Radial Basis Function.
*Significantly different compared with the Barrett Universal II formula (P < 0.05, related-samples Friedman 2-way analysis of variance by rank)
Table 5
Preoperative and postoperative patient characteristics.
Parameter | Mean ± SD | Minimum | Maximum |
Preoperative |
Sphere (D) | 9.89 ± 4.03 | 5.32 | 13.85 |
Cylinder (D) | 2.43 ± 1.59 | 0.00 | 4.23 |
SE (D) | 8.69 ± 3.58 | 3.13 | 12.02 |
BCVA | 40/50 | 30/50 | 20/20 |
CDVA | 30/50 | 20/50 | 20/20 |
UCDVA | 25/50 | 10/50 | 20/20 |
Postoperative |
Sphere (D) | 0.46 ± 0.62 | 1.69 | 0.49 |
Cylinder (D) | 0.59 ± 0.54 | 0.00 | 2.02 |
SE (D) | 0.20 ± 0.49 | 1.13 | 0.63 |
BCVA | 25/30 | 25/30 | 20/20 |
UDCVA | 25/30 | 20/30 | 20/20 |
CDVA | 25/30 | 20/30 | 20/20 |
CDVA = corrected distance visual acuity; SE = spherical equivalent |
Table 6
shows the change in biometric variables between preoperatively and postoperatively. The K flat, K steep, and AL
Parameter | Preoperative | Postoperative | P Value |
Mean ± SD | Range | Mean ± SD | Range |
K flat (D) | 41.48 ± 1.47 | 36.79–44.77 | 41.28 ± 1.56 | 37.12–44.88 | .052 |
K steep (D) | 42.85 ± 1.72 | 41.72–47.60 | 42.92 ± 1.67 | 41.74–48.76 | .53 |
AL (mm) | 23.22 ± 1.71 | 23.12–30.41 | 27.35 ± 2.6 | 22.63–31.53 | .90 |
ACD (mm) | 3.28 ± 0.32 | 2.87–4.52 | 3.31 ± 0.56 | 2.27–4.45 | .008* |
ACD = anterior chamber depth; AL = axial length; K = keratometry
*Statistically significant difference (P < .005)
The ACD was the only biometric parameter that changed significantly after pIOL implantation in our study