• 25/10/2021
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Lens power calculation formulas have evolved over the past 30 years, since the first theoretical formula for iris-supported lenses was published by Fyodorov and Kolonko in 1967.

A. First Generation

Initial formulas were based largely on axial length, but with the availability of posterior chamber implants, consideration had to be given to the distance from the cornea to the implant (anterior chamber depth). By studying large numbers of cases, linear regression techniques were used to determine a formula for predicting emmetropic implant power. The most widely used regression formula was developed by Sanders, Retzlaff, and Kraff in 1980 and is known as the SRK formula.

– (2.5 × AL) – (0.9 × K)

where is the lens implant power (diopters), AL is the axial length (mm), is average keratometry (diopters), and is the constant (no units), a theoretical value that relates the lens power to axial length and keratometry. It is specific to the design of the IOL and its intended position inside the eye. This number is specified by the IOL manufacturer.

B. Second Generation

The SRK formula is a linear equation derived by fitting collected data to a straight line. However, the optical system is nonlinear and begins to produce significant error with short or long eyes. To improve accuracy, the formula was modified, taking into consideration variation in axial length. This enhancement is known as the SRK II formula in which the A-constant is defined at different axial lengths:

+ 3 (AL < 21 mm)
+ 2 (20 mm < AL < 21 mm) + 1 (21 mm < AL < 22 mm) (22 mm < AL < 24.5 mm) – 0.5 (24.5 mm < AL)

Although the SRK II formula was an improvement, there was a push to increase accuracy and design formulas based on both empirical and theoretical data. These second-generation formulas include those pioneered by Binkhorst and Hoffer, which included different approaches for predicting the anterior chamber depth (ACD constant).

C. Third Generation

In 1988, Holladay et al further refined the theoretical formulas by proposing a relationship between the steepness of the cornea and the position of the IOL. Instead of factoring in the anterior chamber depth, the formula would calculate the distance from the cornea to the iris plane and add the distance from the iris plane to the IOL. This second variable was termed the surgeon factor, was specific to each lens, and had the ability to be personalized and adjust for any consistent bias in the surgeon’s results. Hoffer achieved the same effect via another approach in his Hoffer Q formula. Retzlaff followed suit to take into consideration not only the position of the implant, but also incorporated a correction for the retinal thickness, thus developing the SRK/T formula in 1990.

D. Fourth Generation

In the early 1990s, Haigis presented the notion that the individual geometry of each IOL model also should be considered in determining which formula to use. The geometry for a particular IOL model is not the same at all powers; therefore, the Haigis formula utilizes 3 lens constants to address these issues:

a0 constant moves the power prediction curve up or down

a1 constant is tied to the measured anterior chamber depth

a2 constant is tied to the measured axial length

Optimization of the Haigis formula requires collecting pre- and postoperative data from over 200 patients in order to allow surgeon-specific optimization, which is available online.

In the late 1990s, the Holladay 2 IOL consultant software was introduced to attempt to improve upon predictability by incorporating additional optical data points. It requires 7 measurements including white-to-white corneal diameter, anterior chamber depth, lens thickness, patient’s age, preoperative refraction, keratometry, and axial length. This formula may be more precise in unusual eyes such as those that have undergone refractive surgery.

One or more of the third-generation formulas (SRK/T, Holladay 1, and Hoffer Q) are generally programmed into A-scan biometers sold today. The optical biometers are now incorporating the fourth-generation formulas (Haigis and Holladay 2).

Over time, some trends have emerged regarding which formulas to use in general categories of patients:

<22 mm: Hoffer Q
22 to 23 mm: Hoffer Q or Holladay 1
24 to 26 mm: Holladay 1
>26 mm: SRK/T or Holladay 2
It is essential to use the appropriate power calculation constant (A-constant, ACD-constant, surgeon factor) specified by the IOL manufacturer for the specific formula, chosen IOL style, and personalized as warranted by the surgeon.

E. Intraocular Lens Calculation After Refractive Surgery

The complex scenario of a patient undergoing cataract surgery after refractive surgery is becoming increasingly common. Determining the proper IOL power in these patients is a challenge for the surgeon, and while dozens of formulas have been published to address this issue, here we will focus on the basic sources of error that can contribute to a refractive surprise.

1. Error in corneal curvature

This error is due to the fact that keratometric measurements are not taken centrally, but slightly peripherally, where the curvature may be steeper or flatter than it is in the center after a myopic or hyperopic ablation, respectively.

2. Error in corneal power

To measure true corneal power, both the anterior and posterior surfaces must be considered. Classic keratometry, however, derives the refractive power of the cornea from the anterior surface alone and assumes a fixed ratio between the anterior and posterior corneal surface. Naturally this relationship has been altered in any refractive surgery, and therefore leads to an incorrect power calculation.

3. Error from the Intraocular Lens formula

Several IOL formulas assume the effective lens position based on the corneal power, which is reasonable in normal eyes. However, after refractive surgery, the new corneal curvature does not reflect the eye’s original geometry. Therefore the resulting effective lens position will be calculated incorrectly, resulting in a hyperopic error after myopic refractive surgery.

Once the source of these errors is understood, steps can be taken to minimize the possibility of a refractive surprise.

  1. To address the issue of corneal curvature: With the increased optical zones of refractive laser treatment, this error is becoming less of an issue. Measurements from the internal ring of the LENSTAR may contribute to more accurate data.
  2. To address the issue of corneal power: Classically, this can be achieved using the refractive history method. Recent advancements in instrumentation have allowed direct measurements of both the anterior and posterior corneal surfaces that can overcome this error.
  3. To address the issue of the IOL formula: A formula should be selected that does not use keratometric readings to predict the effective lens position, such as the Haigis formula.

The IOLMaster and the LENSTAR include software to address the postrefractive patient, and there are a number of free online IOL calculators that can be used, including on the ASCRS Web site:


Although emmetropia is often desirable, it may not always be the ideal postoperative refraction for all patients undergoing cataract extraction with IOL implantation. A thoughtful decision-making process should involve discussion with the patient, with adequate time to confirm the desired target refraction. A number of factors should be considered.

A. Visual Acuity and Refraction of the Other Eye

Consideration must be given to the refraction of the fellow eye particularly when surgery is being performed on only one eye, to avoid significant postoperative anisometropia (usually no more than 2 to 3 D difference).

B. The Refraction the Patient Has Been Accustomed to for Most of His or Her Life

It might be anticipated that a patient who is +6.00 or –6.00 would appreciate being plano OU after surgery. However, there are many patients who would not want to be changed from –2.50 to plano OU, necessitating reading glasses when they never needed them before.

C. The Lifestyle and Desires of the Patient, Including Occupational and Recreational Needs

Attention must be given to the patient’s most frequent vision needs. For example, an attorney who reads many hours a day may prefer a myopic target refraction. Certain patients may also prefer monovision or blended vision, with a slightly higher power IOL in the nondominant eye to eliminate the need to wear glasses for most daily activities.

D. Availability of Premium Intraocular Lenses

There are now a number of IOLs that can address issues of presbyopia and astigmatism. These require an in-depth evaluation and counseling to determine the ideal candidate for these specialized implants.

*Dikutip dari Buku Essentials of Cataract Surgery 2nd Ed, halaman 161-165

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