Haigis1 suggests a solution to overcome the problem of a systematic hyperopic outcome of intraocular lens (IOL) calculations with third-generation formulas in very long eyes. He proposes to distinguish between positive and negative IOL powers by different formula constants. For his formula, he proposed a constant of a0 = 2.77 mm for positive power IOLs and of a0 = 1.73 mm for negative power IOLs, corresponding to the SRK/T A-constants of 121.2 and 114.4, respectively. In a subsequent paper with Haigis as a coauthor,2 these A-constants were modified to 126.63 for positive-power MA60MA IOLs (Alcon, Inc.) and 104.43 for negative-power MA60MA IOLs.
This approach is physically misleading, mathematically wrong, and clinically at least questionable.
- A-constants of 126.63 for positive powers and 104.43 for negative powers suggest that there is a physical difference of 22.2 diopters (D) between these IOLs. However, all physical properties of IOLs that change their power from small positive values to small negative values, thereby crossing zero power, are steady, without any gap between positive-power values and negative-power values. Figure 1 in Haigis' article shows the influence of a changing shape factor, not the difference between low power positive and negative IOLs. Power level–dependent shape factors are unfortunately not addressed by IOL formulas, but their impact is on the order of some tenths of a diopter, not 22.0 D.
- Mathematically, the partial derivative of the refraction of the eye with respect to the IOL position has a singularity at zero IOL power. Graphically, this means that a zero power IOL can be positioned at any location on the optical axis without changing the eye's refraction and IOLs with small positive or negative powers can be shifted by large distances with only small influence on the refractive outcome. It is generally a violation of basic mathematical principles to try an adjustment of a target function by a variable in the neighborhood of a singularity of the target function. This mistake is additionally disguised when the variable is called a “constant,” as in case of the so-called formula constants of IOL calculation formulas.
- In clinical application, the resulting A-constants in the proposal by Haigis highly depend on considering the distribution of IOL power levels. The closer these power levels to zero, the higher the differences between the A-constants for positive and negative power levels. On the other hand, these differences between the A-constants raise the prediction errors for power levels farther from zero power. If, for example, the corresponding IOL model would also comprise the power range for normal eyes, the proposed A-constant of 126.63 would result in highly myopic outcomes in these eyes.
- The whole problem reflects the insufficient approach of IOL formulas to minimize to zero the mean prediction error of a patient collective by adjusting a single variable, the so-called effective lens position (ELP). This also applies to the Haigis formula, which uses 3 adjusting parameters; however, all influence only the ELP. The said approach works in normal eyes and is unfortunately extended by Haigis to a range beyond the limits of its applicability. On the other hand, in normal eyes, many parameters beside the IOL position could be used to zeroize the mean prediction error—eg, axial eye length, corneal radius, refractive index of the aqueous humor or of the vitreous—thereby keeping in mind that these parameters may have systematic errors. Historically, the ELP is used for fudging because this parameter cannot be measured preoperatively (and only with great effort postoperatively) and because an error analysis shows that the uncertainty of the postoperative IOL position is currently the largest single error contribution in mean-sized normal eyes.
- Axial eye length errors may be more responsible for a systematic bias of the prediction error in extremely long eyes. Nobody knows the true length of a human eye, and no independent gold standard for this parameter exists. The axial lengths indicated in the IOLMaster (Carl Zeiss Meditec) are based on a transformation proposed by Haigis3,4 to adjust the optically measured data to ultrasound measurements. However, these adjustments may fail in very long eyes, thus explaining the hyperopic outcome in very long eyes as a problem of inaccurately calibrated length measurements rather than assuming different physical properties for positive-power and negative-power IOLs.
1. Haigis W. Intraocular lens calculation in extreme myopia. J Cataract Refract Surg. 2009;35:906-911.
2. Petermeier K, Gekeler F, Messias A, Spitzer MS, Haigis W, Szurman P. Intraocular lens power calculation and optimized constants for highly myopic eyes. J Cataract Refract Surg. 2009;35:1575-1581.
3. Lege BAM, Haigis W., 2000. Erste klinische Erfahrungen mit der optischen Biometrie. In: Kohnen T, Ohrloff C, Wenzel M, editors., 13. Kongress der Deutschsprachigen Gesellschaft für Intraokularlinsen-Implantation und refraktive Chirurgie, Frankfurt am Main, 12 und 13 März 1999. Biermann Verlag, Köln, Germany, pp. 175-179.
4. Haigis W, Lege BAM., 2000. Ultraschallbiometrie und optische Biometrie. In: Kohnen T, Ohrloff C, Wenzel M, editors., 13. Kongress der Deutschsprachigen Gesellschaft für Intraokularlinsen-Implantation und refraktive Chirurgie, Frankfurt am Main, 12 und 13 März 1999. Biermann Verlag, Köln, Germany, pp. 180-186.