One of the final frontiers in ophthalmology isthe consistently accurate calculation of intraocularlens (IOL) powers over a wide range of axiallengths. After being properly “personalized,” any ofthe modern IOL power calculation formulas will doan excellent job from 22 mm to 24.5 mm. However,for significantly longer or shorter eyes, a high degreeof accuracy remains elusive.

The present system of IOL constants simplymoves the predicted IOL power curve (determined bythe IOL geometry and the mathematics of the IOLcalculation formula) of the surgeon’s favorite IOLpower calculation program up or down. But thiscurve is mostly fixed. The larger the IOL constant,the more IOL power the formula will recommend forthe same set of measurements. And the smaller thenumber, the less IOL power the same formula willrecommend for the same set of measurements.

Currently, we use these three IOL formulas:� The SRK/T formula, which uses an A-constant� The Holladay 1 formula, which uses a surgeon

factor� The Holladay 2 formula and the Hoffer Q for-

mula, which both use an anterior chamber depth(ACD) factor.

These standard IOL constants are mostly inter-changeable. Knowing one, you can calculate theothers. In this way, surgeons can move from oneformula to another for the same IOL implant. Someformulas, like Holladay 1, work very well for eyes

Using three constants, thisformula can be individuallyadjusted for each surgeon/IOLcombination.

of normal to moderately long axial lengths, whileother formulas, like Hoffer Q, work better forshorter axial lengths. The Holladay 2 formulaworks well over a very wide range of axial lengths.My experience has been that the SRK/T formulatends to underestimate IOL power for shorter axiallengths and overestimate IOL power for longeraxial lengths.

Variations in keratometers, biometry calibra-tion, and surgical technique all can have an effect onrefractive outcomes because they add variables. Bypersonalizing the lens constant, it is possible toadjust for various practice-specific variables toachieve the most predictable refractive results,whatever formula is being used.

Unfortunately, the IOL power curve generatedby each formula remains the same. Changing thelens constant just moves the curve up or down(more power recommended, less power recommened).

Another problem with the commonly used two-variable prediction formulas is that they rely on theaxial length and the central corneal power to predictthe postoperative position of the IOL implant.These formulas assume that the longer the axiallength, the deeper the anterior chamber, and theshorter the axial length, the shallower the anteriorchamber. Holladay and Gills have shown that thisoften is not the case. Eyes with axial lengths of lessthan 20 mm often have large lenses but otherwisecompletely normal anterior chamber anatomy. Thisbasic assumption creates a mathematical limitationand is another reason why these formulas are notaccurate over a wide range of axial lengths. TheHolladay 2 formula has done a good job of over-coming this limitation by using the measured ACDand several other variables, such as lens thicknessand corneal diameter, to better predict the finalposition of the IOL implant.

By Warren E. Hill, M.D., F.A.C.S.Mesa, Ariz.

The Haigis Formula for IOLPower Calculation

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New IOL ConstantsA recent exception to this is the Haigis formula,

which can be found as part of the Zeiss IOLMastersoftware package.

The Haigis formula differs in a very importantway. Rather than simply move a fixed, formula-spe-cific outcomes curve up (more IOL power recom-mended) or down (less IOL power recommended), theHaigis formula uses three constants: a0, a1 and a2,such that:

d = the effective lens position, whered = a0 + (a1 * ACD) + (a2 * AL)

ACD is the measured anterior chamber depth ofthe eye (corneal surface to the anterior lens capsule),and AL is the axial length of the eye (the distance fromthe corneal surface to the vitreoretinal interface).

The a0 constant basically moves the curve up ordown in much the same way that the A-constant, sur-geon factor or ACD does for the Holladay 1,Holladay 2, Hoffer Q and SRK/T formulas.

The a1 constant is tied to the measured ACD. Thea2 constant is tied to the measured axial length.

So, rather than using a single number, the Haigisformula recommends IOL power based on a three-variable (a0, a1 and a2) function.

The a0, a1 and a2 constants are set by optimizinga set of surgeon- and IOL-specific outcomes for a widerange of ALs and ACDs. By double-regression analy-sis, the a0, a1 and a2 constants are adjusted to matchthe results for a specific surgeon and IOL. This meansthat the mathematics of the Haigis formula can beadjusted for each surgeon/IOL combination.

At present, this can be done by requesting a Haigisformula optimization Excel spreadsheet by e-mailfrom Dr. Wolfgang Haigis in Germany(w.haigis@augenklinik.uni-wuerzburg.de) or from mehere in North America (hill@a-scan.net).

Innovative approachDr. Haigis gets very high marks for this innova-

tive approach. Using a three-variable function ratherthan a single number gives the Haigis formula acompletely new level of mathematical flexibility notyet seen in ophthalmology.

As the a0, a1 and a2 Haigis constants for themore commonly used IOLs become established andif the Haigis formula begins to be included with bio-metry devices other than the Zeiss IOLMaster, Iexpect that this formula will gain in popularity herein the United States. OM

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