FORMULAS Generations

First Generation

The first IOL power formula was published by Fyodorov²³ in 1967. Colenbrander²⁴ wrote his in 1972 followed by the Hoffer²⁵ formula in 1974. Binkhorst²⁶ published his formula in 1975, which became widely used in America.

In 1978, first Lloyd and Gills^27,28, followed by Retzlaff²⁹ and later Sanders & Kraff³⁰, each developed a regression formula based on analysis of their previous IOL cases.

This work was amalgamated in 1980 to yield the SRK I formula.³¹ All these formulas depended on a single constant for each lens that represented the predicted IOL position (ACD).

Second Generation

In 1982, at the Welsh Cataract Congress in Houston, the author^32,33 showed a direct relationship between the position of a PMMA posterior chamber IOL and the axial length and I presented a formula to better predict ACD.

Others (Binkhorst³⁴, SRK II³⁵ (1988)) developed different mechanisms to apply this predictive relationship which Holladay defined as the second generation.

Third Generation

In 1988, Holladay³⁶ proposed a direct relationship between the steepness of the cornea and the position of the IOL. He modified the Binkhorst formula to incorporate this as well as the axial length relationship. Instead of ACD input, the formula would calculate the predicted distance from the cornea to the iris plane (using a corneal height formula by Fyodorov) and add to it the distance from the iris plane to the IOL. The latter he called the surgeon factor (SF) and it is specific to each lens. Retzlaff³⁷ followed suit and modified the Holladay I formula to allow use of A constants calling it the SRK/T theoretic formula in 1990. It was intended to replace the previous SRK regression formulas, but still 50% of American surgeons use them. In 1992, Hoffer developed the Q formula³⁸ using a tangent function to accomplish the same effect.

Fourth Generation

In 1990, Olsen³⁹ proposed using the preoperative ACD and other factors to better estimate the postoperative IOL position and published algorithms for this. After several studies showed the Holladay I formula not as accurate as

the Hoffer Q in eyes shorter than 22 mm, Holladay used the preoperative ACD measurement as well as corneal diameter, lens thickness, refractive error and age to calculate an estimated scaling factor (ESF) that multiplies the IOL-specific ACD. This Holladay 2 formula has been promulgated since 1996 but has yet to be published.

Fifth Generation

In 1999, Wolfgang Haigis proposed using three constants to predict the position of the IOL based on the characteristics of the eye and the IOL. The formula calculates the predicted PO ELP by:

ELP = a₀ + a₁× ACD + a₂ × AL

Where ELP = predicted IOL position, a₀ = a lens specific constant, a₁ = a constant to be effected by the measured preoperative ACD, and a₂ = a lens specific constant to be effected by the measured preoperative axial length, ACD

= the measured axial distance from the corneal apex to the front surface of the lens and AL = axial length.

As in the Holladay formula, the constants must be optimized (personalized) to each IOL style and surgeon.

Single optimization only optimizes the a₀ and creates accuracy equal to the Hoffer Q and Holladay, but triple optimization of all three constants creates additional accuracy. The problem is that triple optimization requires a series of 500-1000 cases of one lens style and the eyes in the series must statistically cover all axial lengths from very short to very long. This may be quite difficult to achieve for the average surgeon.

Refraction Formula

Holladay⁴⁰ published a formula in 1993 to calculate the power of an IOL for an aphakic eye or ametropic pseudophakic eye (piggyback IOL) or a refractive lens (PRL) for a phakic eye. It does not need the AL but requires the corneal power, preoperative refractive error and desired postoperative refractive error as well as the vertex distance of both. I do not recommend its use in aphakic eyes because the vertex distance is difficult to measure accurately and due to the high power of their refractive error, greater errors can result. It is, however, a good check against the AL formula calculation.

Usage

Based on Axial Length

My study³⁸ of 450 eyes (by one surgeon using one IOL style) (Fig. 14.8) showed that in the normal range (72%) of

axial length (22.0-24.5 mm) almost all formulas function adequately, but that the SRK I formula is the leading cause of poor refractive results in eyes outside this range. It also showed that the Holladay I formula was the most accurate in medium long eyes (24.5-26.0 mm) (15%) and the SRK/

T was more accurate in very long eyes (>26.0 mm) (5%). In short eyes (<22.0 mm) (8%) the Hoffer Q formula was most accurate and this was confirmed (p>0.0001) in an additional large study of 830 short eyes as well as in a multiple-surgeon study by Holladay. Holladay has postulated that the other formulas overestimate the shallowing of the effective lens position (ELP) in these very short eyes.

A more recent study⁴¹ I performed on 317 eyes, showed that the Holladay 2 formula equaled the Hoffer Q in short eyes but was not as accurate as the Holladay I or Hoffer Q in average and medium long eyes (Table 14.4). Eyes shorter than 19 mm are extremely rare (0.1 %) and may well be benefited by using the Holladay 2 formula. It appears that in attempting to improve the accuracy of the Holladay formula, the addition of more biometric data input has improved the Holladay II formula in the extremes of axial length but deteriorated its excellent performance in the normal and medium long range of eyes (22.0-26.0 mm) which is 82% of the population.

Methodology

There are several means by which to use these newer formulas including A-scan instruments, handheld calculators and computer programs that run on DOS, Windows and Macintosh systems as well as for the handheld Palm PDA operating system (Fig. 14.9). You can also program the published ones yourself on a spreadsheet program. It is important to check the errata Fig. 14.8: Error Range. Range of IOL power error in 450 eye study using regression formulas compared to modern theoretic formulas.

IOL Power Calculations

85

Table 14.4: Results of accuracy of 4 theoretical formulas on 317 eyes using the Holladay IOL consultant for analysis (Shaded = recommended formulas)⁴¹

MEAN ABSOLUTE ERROR ALL 317 EYES

Formula Short Normal M-long V-long Long All MAX >± 2D

<22.0 22.0-24.5 24.5-26.0 >26.0 <24.5 Eyes ERROR ERROR

Holladay II 0.72 0.56 0.51 0.49 0.50 0.55 -1.60 0%

Holladay I 0.85 0.42 0.37 0.56 0.43 0.43 -1.44 0%

Hoffer Q 0.72 0.43 0.47 0.58 0.50 0.45 -1.61 0%

SRK/T 0.83 0.46 0.35 0.44 0.36 0.44 -1.45 0%

AVERAGE 0.78 0.47 0.42 0.52 0.45 0.47

BEST H-Q H-2 H-Q H-1 S/T H-1 S/T S/T

Where M-Long = medium long, V-Long = very long, Long = all long eyes, Max = maximum.

Figs 14.9A to D

Figs 14.9A to F: Hoffer Programs IOL power program on a palm personal digital assistant; A. Main calculation screen using Hoffer Q, Holladay and SRK/T formulas, B. Next screen showing refractive results of different IOL powers, C. Clinical History method screen, D. Contact Lens method screen, E. Personalization screen for adding new PO eyes, F. Personalization screen for various IOLs.

in references 37 and 38. The most popular commercial programs are the Hoffer Programs System* (1994) and the Holladay IOL Consultant* (1997), which include several formulas and the ability to personalize them as well as routines to deal with odd clinical situations.

(*Available from EyeLab, Inc. 1605 San Vicente Blvd, Santa Monica, CA 90402, 310-451-2020, KHofferMD@AOL.com).

Personalization

The concept of personalizing a formula based on a surgeon’s past experience and data was introduced by Retzlaff ⁴² using the A constant to refine the formula.

Holladay incorporated this concept into backsolving for the Surgeon Factor and Hoffer backsolved for his personalized ACD. Several studies have proved that formula personalization definitely improves formula accuracy significantly.

The following parameters are required from postoperative eyes:

1 Axial length (Pre-op) 2 Corneal power (Pre-op) 3 IOL power

4 Postoperative refractive error (Stable)

The eyes should all contain the same lens style by one manufacturer implanted by one surgeon. The same biometry instruments and technician should also have been used. Eyes with postoperative surprises or acuity

worse than 20/40 should not be included due to poor accuracy in obtaining refractive error. Personalization involves backsolving for the exact IOL position that would produce the resultant refractive error with that AL and K.

Then all the “ideal” IOL positions are averaged to arrive at the personalized value to use in the future.

Personalization can be easily performed using the Hoffer Programs or Holladay IOL Consultant computer programs.

CLINICAL VARIABLES