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Purpose: To evaluate the effect of axial length (AL) and the average preoperative keratometry (K) on the A constant in the SRK/T formula. Methods: The retrospective, comparative case series includes 635 eyes from 407 cataract patients from Columbia University Medical Center from January 2006 to August 2010, operated by a single surgeon using a temporal incision and the Acrysof SN60WF IOL (Alcon Laboratories, TX). Using the postoperative manifest refraction and biometry data, we calculated the precise A constant (Ap) necessary to yield the postoperative spherical equivalent for each eye. To optimize the A constant, we developed three regression models (linear, quadratic, and categorical in 7 AL groups) to relate these precise A constants to AL and K. We verified our method with another series of 45 eyes for which we calculated mean errors (defined as the difference between the spherical equivalent of the postoperative refraction and the predicted postoperative refraction) using the optimized and manufacturer’s suggested A constants. Results: There is a statistically significant relationship between AL (P < 0.001), K (P < 0.001) and the A constant. Ap increased as AL increased and as K decreased. In the validation data set, optimizing the A constant reduced mean errors from 0.50 D to 0.25 D and also reduced hyperopic refractive outcomes. Conclusions: The A constant for longer eyes with flatter corneas is larger than the A constant for shorter eyes with steeper corneas. Optimizing A constants using both AL and K improved the predictability of refractive outcomes without modification to the SRK/T formula.

In small incision cataract surgery, an accurate refractive outcome depends on a reliable intraocular lens (IOL) power formula, accurate biometry, and appropriate IOL constants. The SRK/T formula [

Authors of modern formulas have recommended many methods for optimizing IOL constants [

The Institutional Review Board of Columbia University approved this retrospective study of 635 cataract surgery cases (mean age 75 years, with 172 male eyes and 235 female eyes) with at least three consistent preoperative keratometry measurements and a consistent postoperative refraction. The study excludes patients unable to maintain fixation and those whose corneas were irregular due to conditions such as megalocornea or other congenital abnormalities, scars, dystrophies, or edema, or whose cataracts were too dense for accurate AL measurement with the IOLMaster (Carl Zeiss Meditec AG, Jena, Germany).

The surgeon selected the IOL power based on the preoperative biometry using the SRK/T formula. Keratometry measured with the IOLMaster was compared to manual keratometry, but in all cases the IOL calculation was based on the average keratometry values generated by the IOLMaster. A single surgeon (JCM) performed all procedures with local anesthesia and a temporal 2.2 or 2.6 mm clear corneal incision. The surgeon injected an Acrysof SN60WF (Alcon Laboratories, TX) into the capsule and dilated all patients postoperatively to be certain that both haptics of the IOL were within the capsule. The surgeon refracted all patients and entered the spherical equivalent of the stable postoperative manifest refraction into the IOLMaster’s database.

The biometry data for each patient was extracted from the IOLMaster database by Zeiss in Jena, Germany. Using the biometry data and the spherical equivalent of the postoperative manifest refraction, we used the SRK/T formula to back calculate the precise A constant (Ap) for each eye.3 We ran multiple regression analyses to identify three possible models to optimize the A constant based on AL and Kavg 1) as linear variables, 2) AL as a quadratic variable, and 3) AL as a categorical variable with 7 subgroups in 1 mm increments ranging from less than 22 mm to greater than 27 mm. Optimized A constants from each model were used to predict the refractive outcome and the mean absolute error from the achieved refraction for each patient. The extracted data contained measurements from IOLMaster versions 3 and 5. Separate analysis of these two groups showed no significant difference between their Ap (P = 0.91), and the groups were merged for this paper.

Statistical AnalysisMixed linear models were developed to describe the association between Ap and age, gender, AL, and Kavg. Variables with no significant effect on Ap were removed from the regression models, and SAS PROC MIXED (SAS software version 9.2, SAS Inc., Cary, NC) was used to account for the intra-class correlation between eyes of the same patient and to allow for a random intercept. Results were considered statistically significant if the P value was < 0.05.

Variable | Mean + StdDev | Min, Max Maximum | Mean + StdDev | Min, Max | |||
---|---|---|---|---|---|---|---|

Data Set for Developing Formulas (635 eyes) | Data Set for Validating Formulas (45 eyes) | ||||||

Ap (mm) | 119.31 ± 0.51 | 117.44, 122.58 | -- | -- | |||

AL (mm) | 24.1 ± 1.37 | 20.5, 30.0 | 23.9 ± 1.16 | 22.2, 27.5 | |||

Kavg (mm) | 43.7 ± 1.42 | 39.4, 48.3 | 44.1 ± 1.48 | 40.2, 47.1 | |||

mm. The Ap almost always differed from the manufacturer’s A constant of 118.7 mm. Linear regressions indicate that Ap has a significant correlation with both AL and K (P < 0.0001). No correlation is evident between Ap and age (P = 0.92). While a statistically significant relationship was also found between gender and the A-constant (P = 0.005), AL was highly correlated with gender, so gender provided no additional information to the model. Pearson correlation coefficients showed that AL (correlation coefficient 0.39) has a stronger effect than K (correlation coefficient −0.25) on Ap. AL and K are also inversely correlated with one another (correlation coefficient −0.23) (P < 0.0001). ^{2} = 0.25).

Regression analysis identified a linear model to describe the relationship between the A constant and both AL and K.

In the linear model, an AL of 24 mm and K of 43.7 mm yield an optimized A constant of 119.22; and an AL of 27 mm and K of 43.7 m yield an A constant of 119.55.

In contrast, the quadratic model incorporates a quadratic AL term to allow for curvature to improve the fit.

In the quadratic model, an AL of 24 mm and K of 43.7 mm yield an optimized A constant of 119.19; and an AL of 27 mm and K of 43.7 mm yield an A constant of 119.73.

Finally, the categorical model employs seven AL subgroups as categorical variables (in 1 mm increments from less than 22 mm to greater than 27 mm) with an AL correction factor X that adjusts the A constant for each AL subgroup (

In the categorical model, an AL of 24 mm and K of 43.7 mm and an AL factor of −0.64 result in an optimized A constant of 119.31 mm; and an AL of 27 mm and K of 43.7 mm and an AL factor of 0 result in an A constant of 119.95. For the same eye with AL 24 mm and K of 43.7 mm, all three regression models produce similar optimized A’s that differ from the manufacturer’s A. For eyes with the same AL, a steeper cornea would yield a smaller A value, and vice versa. For example, for eyes with AL of 24 mm and mean K of 42.0 and 47.0 mm, the categorical model yields an A of 119.47 and 119.01, respectively. In summary, both AL and K influence the A constant, which increases with increasing AL and decreasing K. In other words, a larger A is needed for longer eyes with flatter corneas.

We used a data set of 45 eyes to evaluate the accuracy of the predicted postoperative refraction with the optimized A constants. With A constants derived from our three models, the ULIB website^{1}, and the manufacturer, the absolute value of the ME ranged from 0.00 to 1.25 D. The absolute value of the ME decreased from 0.50 D when using the manufacturer’s A to 0.25 D when using optimized As from any of the three models. Furthermore,

Axial Length (mm) | Number | X Frequency |
---|---|---|

<22.0 | 25 | −0.59 |

22.0 to <23.0 | 80 | −0.70 |

23.0 to <24.0 | 260 | −0.76 |

24.0 to <25.0 | 142 | −0.64 |

25.0 to <26.0 | 71 | −0.57 |

26.0 and <27.0 | 32 | −0.44 |

AL ≥ 27.0 | 25 | 0 |

greater than +0.5 D. Using optimized A constants, none of the eyes from the three optimization models had hyperopic MEs greater than +0.5 D.

Cataract surgery is a refractive procedure, and suboptimal refractive outcomes may temper patient satisfaction [

Eom and colleagues examined the relationship between K, AL and predicted refractive error in 637 patients and found that the A constants decreased as K increased, consistent with our results. However, they concluded AL did not have a significant effect on postoperative error [

Clinicians may use the authors’ A constants as a point of reference for each AL subgroup in the IOLMaster. A prior study found that optimizing IOL constants for the IOLMaster substantially improved refractive outcomes, far exceeding any additional benefit of personalizing IOL constants for individual surgeons [

Low myopia after surgery may work as a substitute for accommodation and make patients more spectacle- independent [

The range of acceptable error depends on the clinical significance of the refractive error. With a large data base of 8108 eyes, Aristodemou et al. analyzed the benefits of IOL constant optimization based on refractive outcomes using manufacturers’ and optimized IOL constants for the Hoffer Q, Holladay 1, and SRK/T formulas. They found that an A constant error exceeding 0.15 produced up to a 2.0% reduction in the percentage of eyes within ±0.50 D deviation from target refraction with the SRK/T formula [

It has been suggested that different IOL formulas may be used for different ALs. Aristodemou compared the Hoffer Q, Holladay 1, and SRK/T formulas in 8108 eyes. They found that while all three tend to work equally well for medium length eyes, the Hoffer Q performed best in eyes with AL less than 22 mm and the SRK/T in eyes with AL > 27 mm [

We would like to thank Stephen DeVience, PhD, for his support.

John C.Merriam,EvaNong,LeiZheng,MalkaStohl, (2015) Optimization of the A Constant for the SRK/T Formula. Open Journal of Ophthalmology,05,108-114. doi: 10.4236/ojoph.2015.53017