IOL calculation according to HAIGIS

Like all other popular theoretical formulas, IOL calculation according to HAIGIS is based on the elementary IOL formula for thin lenses [for details cf eg HAIGIS 1991, 1996]. As for the German speaking scientific community, this formula has first been published as early as 1970 by GERNET, OSTHOLT and WERNER (today also denoted as GOW70 formula [GERNET, 1998]): 

                       n          n 
                DL = -----  -  -------                          (1)
                     L - d     n/z - d                          
                                                               
                       ref                       nC - 1        
    with  z = DC + -----------     and     DC =  ------        
                   1 - ref dBC                      RC

D : refractive power of IOL
DC : refractive corneal power
RC : corneal radius
nC : (fictitious) refractive index of cornea
ref : desired refraction
dBC : vertex distance between cornea and glasses
d : optical ACD
L : axial length
n : refractive index of aequeous and vitreous (1.336)

Whereas the physics behind (thin lens geometrical optics) and thus the very formula describing the eye model is identical for nearly all popular theoretical authors, differences between existing 'IOL formulas' are due to different meanings and different numerical values attributed to the individual formula parameters.

The calculation according to HAIGIS is given by:
nC = 1.3315
dBC = 12 mm
L : axial length as measured by ultrasound

with the optical ACD d obtained by regression from preoperatively measured acoustical data: 

              d = a0 + a1 VKpr + a2 ALpr                        (2)

    with     a0 = ACD-Konst - a1 MW(VKpr) - a2 MW(ALpr)         (3)
VKpr : preop. anterior chamber depth measured ultrasonically
ALpr : (=L) preop. axial length from ultrasound
MW(..) : means of VKpr(=3.37) mm and ALpr(=23.39) mm
ACD-Konst : ACD constant of manufacturer

Using preoperative biometric data to determine postoperative 'ACD's has first been described by LEPPER & TRIER in 1983.

The ACD constant as well as the A-constant are given by the manufacturers to characterize a given lens. They can be calculated from each other according to [RETZLAFF et al, 1990]:

A-Const = (ACD-Konst + 68.747) / 0.62467

Whereas the constant a0 is directly related to the lens makers' ACD-constant through eq. (3), the following default values are used for a1 and a2: a1=0.4, a2=0.1 [HAIGIS, 1995]. These parameters may be optimized by analyzing postoperatively the refractive outcomes. For each patient the value of d leading to the actually achieved postoperative refraction ref is determined from eq. (1). The individual optical ACDs thus obtained are then correlated with the preoperative ultrasound data for the anterior chamber depth and the axial length according to eq. (2). From this regression analysis, the optimized constants a0, a1 and a2 are readily obtained. These statistical fit parameters are different for each given lens and may therefore be used as independent IOL constants to characterize the individual lens model.

References

GERNET H, OSTHOLT H, WERNER H: Die praeoperative Berechnung intraocularer Binkhorst-Linsen. 122. Vers. d. Ver. Rhein.-Westfäl. Augenärzte. Balve, Verlag Zimmermann. S. 54-55, 1970

GERNET H: personal communication, 1998.

HAIGIS W: Strahldurchrechnung in Gauß'scher Optik zur Beschreibung des Systems Brille-Kontaktlinse-Hornhaut-Augenlinse (IOL), 4. Kongreß d. Deutschen Ges. f. Intraokularlinsen Implant., Essen 1990 , hrsg.v. K Schott, KW Jacobi, H Freyler, Springer Berlin, 233-246, 1991

HAIGIS W: Biometrie, in: Jahrbuch der Augenheilkunde 1995, Optik und Refraktion, Kampik A (Hrsg), Biermann-Verlag, Zülpich, 123-140, 1995

HAIGIS W: Einfluß der Optikform auf die individuelle Anpassung von Linsenkonstanten zur IOL-Berechnung. In: 9. Kongreß d. Deutschen Ges. f. Intraokularlinsen Implant., Kiel 1995 , hrsg.v. R Rochels, GIW Duncker, Ch Hartmann, Springer Heidelberg, 183-189, 1996

LEPPER RD, TRIER HG: Refraction after intraocular lens implantation: Results with a computerized system for ultrasonic biometry and for implant lens power calculation, Doc Ophthal Proc Ser 38:243-248. Junk, The Hague, 1983

RETZLAFF J, SANDERS DR, KRAFF MC (1990): Lens Implant Power Calculation - A manual for ophthalmologists & biometrists, 3rd edition, Slack Inc, Thorofare NJ, USA

SANDERS DR, RETZLAFF J, KRAFF MC: Comparison of the SRK II formula and other second generation formulas. J Cataract Refract Surg 14: 136-141, 1988

(C) W.Haigis. Last Revision: Dec.07, 1998

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