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Choosing the Proper Formula for Accurate IOL Calculations
BY FARRELL "TOBY" TYSON, M.D.

Accurate and reproducible axial length (AL) measurements are only the first step to IOL power selection. IOL calculation formulas have now become the limiting factor to achieving predictable postoperative outcomes. We have quite a menu of formulas to choose from, but how do we choose the right one?

First, we must understand how these formulas have evolved. The original formulas were mathematical-regression formulas. The most well known of the first-generation formulas are the SRK I by Sanders, Retzlaff and Kraff and the Binkhorst II.

The SRK I is well known for its simplicity and ease of use where P = A – 0.9K – 2.5L.

P = the IOL power for emmetropia
K = the corneal refractive power
L = the axial length
A = the A-constant

This formula works well for average ALs but is less accurate for long and short eyes.

To increase predictability, the SRK II formula emerged as a second-generation formula, where P = A₁ – 0.9K – 2.5L. The A constant was then modified into 6 subtypes based on AL. This resulted in:

A₁ =(A–0.5) for axial lengths greater than 24.5
A₁ =A for axial lengths between 22 and 24.5
A₁ =(A+1) for axial lengths between 21 and 22
A₁ =(A+2) for axial lengths between 20 and 21
and A₁ =(A+3) for axial lengths less than 20

Predictability improved markedly, but spectacle correction was still necessary.

The Holladay I, Hoffer Q and the SRK/T emerged as the third-generation formulas. These formulas were a merger of the linear regression methods with theoretical eye models. This allowed for greater accuracy, but the reliance on theoretical assumptions led to the differences between the three formulas. These formulas work best near schematic eye measurements and are based on central corneal power and AL.

Over time, it became apparent that the Hoffer Q formula was best for eyes shorter than 22 mm, the Holladay I formula performed best with eyes between 24 mm and 26 mm and the SRK/T formula was best for eyes longer than 26 mm. The assumption that the anterior chamber depth (ACD) was a proportion of the AL and not a true measurement, led to IOL surprises with post-refractive patients. This is because the third-generation formulas do not account for effective lens position.

All three formulas allowed for optimization by adjusting a factor of the formula. This factor is called the "Surgeon Factor" for the Holladay I formula, the "ACD" for the Hoffer Q formula and the "A Constant" for the SRK/T formula. Advances in computer technology allow for the quick optimization of these formulas for a surgeon's patient population. Most immersion ultrasound systems and the IOLMaster allow for optimization after approximately 25 cases.

On the surface, optimization of one's cases sounds ideal, but one has to remember "garbage in equals garbage out." To correctly optimize any of the formulas, no complicated cases should be entered. Ideally, you should leave out any cases that have concurrent limbal relaxing or astigmatic incisions. This basic optimization will provide you with excellent results the majority of the time.

Optimization brings any of the three formulas to your population average. For example, if your patient population was primarily small hyperopic eyes, you would expect that the Hoffer Q would be the ideal formula. After optimization of the Holladay and SRK/T formulas for the same population, the results would be extremely similar to the Hoffer Q. The downside of the optimization in this scenario would be that the three optimized formulas for the small AL population would not be as accurate as the unoptimized SRK/T formula when dealing with large ALs. So, effectively, optimization raises or lowers the curve but does not affect its shape. Ideally, one would have separate optimizations for separate AL subgroups.

The Haigis Formula

In 1991, the Haigis formula evolved as one of two fourth-generation formulas in order to overcome these shortcomings. The Haigis formula does not depend on assumptions for the ACD and requires real measurement of it. In addition, the Haigis formula does not have just one "a Constant" but three (a₀, a₁, a₂) derived by multi-variable regression analysis.

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

By using three adjustable constants, the surgeon can not only raise or lower the prediction curve, but also adjust its shape. This allows for optimization over a larger range of ALs. This also requires a much larger number of cases for optimization – 200 eyes. A note of caution: Most built-in optimization programs in immersion units and the IOLMaster only optimize a₀, making it effectively a third-generation formula. These units usually allow for manual adjustment of a₀, a₁ and a₂. The optimization of all three constants can be performed on an Excel spreadsheet easily found on the Internet.

The inclusion of measured ACD into the Haigis formula has allowed for potentially increased accuracy. On my Accusonic A-Scan, I always use the Haigis formula because I know that my ACD measurements are precise. The optically-measured ACD on the IOLMaster is usually very accurate, but a little less reproducible. Therefore, I use an optimized third-generation formula on my IOLMaster.

The Holladay II Formula

The Holladay II formula, derived in 1998, is the other fourth-generation formula. It attempts to be a predictable formula for AL axial lengths by incorporating as much measured information as possible. It requires seven different variables to be measured (white to white, corneal diameter, ACD, lens thickness, patient's age, preop Rx and axial length). This information effectively works as a pattern-recognition system. This formula has also been found to be highly accurate for a large variety of patient eyes.

The use of immersion A-scan or the IOLMaster has become the standard of care in cataract surgery, and so has the use of third-generation formulas. In order to make the leap into refractive cataract surgery and lens exchange optimization, adoption of third-generation formulas is necessary, and use of fourth-generation formulas is preferable. The time spent optimizing your formula of choice will be well spent and leads to happy patients and fewer surprises.

Farrell Tyson, M.D., practices refractive cataract and glaucoma surgery in Cape Coral, Fla. He obtained his biomedical engineering degree from Johns Hopkins University and completed his ophthalmology residency at the Storm Eye Institute in Charleston, S.C.