An improved universal theoretical formula for intraocular lens power prediction

An improved universal theoretical formula for intraocular lens power prediction Graham D. Barrett, F.R.A.e.O., F.R.A.C.S.

ABSTRACT Although available empirically derived and theoretical formulas perform adequately for eyes of average axial length, both have been shown to be deficient for eyes that have unusually short and long axial lengths. I developed a formula based on a theoretical model eye in which anterior chamber depth is related to axial length and keratometry. A relationship between the A-constant and a "lens factor" is also used to determine anterior chamber depth. The location of the intraocular lens' principle planes of refraction is retained as a relevant variable in the formula, and the user need not know the material and construction of the lens and or its constant. I compared the new formula with the SRK II, Holladay, and SRK/T formulas in a group of 100 unselected patients and in selected subgroups of patients with average, short, and long axial lengths. The new formula was significantly more accurate than the other third-generation formulas and maintained its accuracy in the subgroups. The formula can be described as universal because it can be used for different lens styles and for eyes with short, medium, and long axial lengths. Key Words: A-constant, anterior chamber depth, intraocular lens power calculation, lens factor, prediction, regression formula, theoretical formula

The accurate prediction ofthe postoperative refraction for a patient having cataract extraction and intraocular lens (IOL) implantation remains a challenge. The development of surgical techniques and multifocal IOLs, which reduce induced astigmatism and the need for added reading correction, further increases the importance of choosing the correct IOL for a desired postoperative refraction. Accurate keratometry and axial length determination are vital, and the development of improved formulas is integral to accurate prediction. Although available empirically derived and theoretical formulas perform adequately for eyes of average axial length, both have been shown to be deficient for eyes with unusually short and long axial lengths. 1 This has led to the development of second- and third-generation formulas such as the SRK IV Holladay, 3 and SRK/T.4 The SRK II is a regression formula similar to the SRK formula but adjusts the A-constant in an empirically derived, stepwise fashion for eyes of short and long axial

lengths. The Holladay formula is a theoretical formula that predicts the anterior chamber depth (ACD) on the basis of the corneal height and a lens-related surgeon factor. The ACD is adjusted for eyes with long and short axial lengths by relating the corneal height to the axial length. The SRK/T formula is an optimization of the Holladay formula using empirically derived values for such factors as the corneal diameter, retinal thickness factor, and an offset factor as well as axial length modification of the ACD. I have previously described a theoretical formula based on Gaussian optical principles, including the IOL's thickness, refractive index, and location of the principle planes of refraction as relevant variables. s The formula was described as universal because it could be used for IOLs manufactured from a variety of materials and with different optical configurations. The present formula is an enhancement ofthis formula and seeks to expand the universal description by developing a formula that is not only useful for all lens styles but also for eyes with short, medium, and long axial lengths.

Presented in part at the Symposium on Cataract, IOL and Refractive Surgery, Boston, April 1991. Reprint requests to Graham D. Barrett, F.R.A.C.O., F.R.A.C.S., Lions Eye Institute, 2 Verdun Street, Perth 6009, Western Australia. J CATARACT REFRACT SURG-VOL 19, NOVEMBER 1993

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MATERIALS AND METHODS

optic. Lens factors in common use include the ACD and the A-constant for a particular IOL. The A-constant, an empirically derived factor for the Developing the Formula SRK formula,7,8 is the most familiar lens constant Determining a Lens Factor. The previous universal known to ophthalmic surgeons and lens manufacturers. formula contained expressions for the first and second Determining a relationship between the A-constant and principle planes of refraction. The user was required to a lens factor that is used as part of the determination of enter relevant data such as the refractive index, radii of the ACD in the universal theoretical formula would free curvature, and thickness of the IOL in question rather the user from having to know the IOL's material and than assuming standard values. construction and becoming familiar with a new lens I sought to enhance the formula by retaining the constant. The following relationship between A-conexpressions for the principle planes of refraction and lens (A) and lens factor (LF) was found for the unistant thickness in such a way that the user did not have to an average eye with an axial length of versal formula for know these factors to use the formula accurately. This is 23.5 mm and keratometry of 43.8 diopters (D) with a feasible because the measurement of an IOL as defined 6 symmetrical biconvex IOL: by the American National Standards Institute uses the second principle plane as a reference point from which LF = A x 0.5825 - 67.6627 the power of the IOL in aqueous is measured. The relationship between the A-constant and the secThe location of the second principle plane from a ond principle plane will vary minimally if the lens is not relatively fixed anatomical reference plane, such as the biconvex and the optic diameter is not 6.0 mm but plane of the iris in the pseudophakic eye, is primarily calculations of lenses with refractive indices varying determined by characteristics of the IOL that can be from 1.41 to 1.49 and with available optic configurations described as a lens factor. Because the second principle differed by less than 0.1 D from the symmetrical biconplane is used as a reference plane for the lens factor, IOLs vex model. Table 1 lists the lens factor for different IOLs with different optical configurations but with the same with refractive indices varying from 1.41 to 1.49 and lens factor will have the second principle plane of the with different optic diameters and configurations. The optic located in the same plane. This relationship is difference between the lowest lens factor (0.96) and highillustrated in Figure 1, which compares a convex-plano, est lens factor (1.03) obtained is equivalent to an plano-convex, and biconvex IOL with the same lens A-constant difference of 0.1. factor. The major determinants of a lens factor for an The location of the second principle plane from the IOL placed in a constant position such as the capsular iris plane is calculated using this relationship. The lobag are the configuration of the IOL haptic and the cation of the first principle plane can be determined from the second principle plane and the lens thickness. Lens thickness will vary with lens power and can be calculated by the formula assuming a symmetrical biconvex lens with an optic diameter of 6.0 mm.

LF

12

b.

Table I. Comparison of the calculated lens factors for IOLs with different refractive indices, optic diameters and optic configurations. The maximum difference i~ the calculated lens factor resulting from the variation in these parameters is equivalent to a difference in the A-constant of 0.1.

L

LF

12

a•

I

I

I

12

c.

Fig. 1. (Barrett) The first principle plane (I) and second principle plane (2) for a convex-plano (a), planoconvex (b), and biconvex IOL (c). The lens factor is the distance between the iris or ciliary plane (I) and second principle plane. The location of the first principle plane will vary with lens thickness. 714

Material PMMA PMMA PMMA PMMA PMMA PMMA Silicone Silicone Silicone Silicone

Refractive Optic ALens Index Diameter Optic Shape constant Factor 1.69 117 6.00 Biconvex 1.03 1.49 6.00 Convex-plano 117 1.02 1.49 7.00 Convex-plano 117 1.00 1.49 6.00 Plano-convex 117 1.02 1.69 6.00 Asymmetrical 117 1.03 biconvex 1.49 7.00 Biconvex 117 1.00 1.41 117 6.00 Biconvex 1.03 l.41 6.00 Convex-plano 117 l.01 1.41 7.00 Convex-plano 117 0.96 l.41 7.00 Plano-convex 117 0.96

J CATARACT REFRACT SURG-VOL 19, NOVEMBER 1993

T = (RA - SQR(RA 2 - (00/2) 2» + (RP - SQR(RP 2 - 00/2) 2» RA = «N2 - NI) x I,OOO/(Pl/2) A

A

A

A

where T = thickness of IOL, RA = anterior radius of IOL, 00 = optic diameter ofIOL, RP = posterior radius ofIOL, N2 = refractive index of IOL, NI = refractive index of aqueous, PI = predicted power of IOL

Postop ACO = Predicted position of posterior lens capsule - LPCO - IOL thickness where LPCO = central distance between IOL's posterior surface and capsule The corneal height as described by Fyodorov 13 and Bagan and Brubaker l4 and used by Olsen, 15 Holladay et al.,3 and in the SRKjT4 formula regards the cornea as a section of a sphere and calculates the height of the corneal dome from the corneal curvature and corneal radius. The base of the dome is located at the iris plane. The distance between the iris plane and the IOL is referred to as the surgeon factor by Holladay et al. and the offset factor by Olsen and the authors of the SRKjT formula. The general form of the corneal height formula can be expressed as:

Variations in IOL power alter the thickness and the location of the first principle plane. As the second principle plane is used as reference plane in determining the lens factor (Figure 1), this formula will correct for the variation that may occur with different lens powers for an IOL with a given lens factor or A-constant. As in the original universal formula, an iterative analysis described previously is necessary to solve the equations for the principle planes and lens thickness as the predicted Height = radius - SQR(radius 2 - (diameter/2) 2) power ofthe IOL is an unknown variable. A designated power is assigned to the formula and the lens thickness Holladay et a).3 used the corneal height formula and and location of the principle planes are calculated. The a corneal or internal angle diameter of 12.5 mm which predicted power of the IOL is then calculated by the is then adjusted for the axial length. The axial length formula, this value reassigned as the designated power of modification of ACD is limited to a maximum axial the IOL, and the thickness and principle planes recal- length of 25.3 mm for a corneal diameter of 48.31. culated. This process is then repeated several times, thereby solving the two unknown but related variables. AG = 12.5 x AL/23.45 Determining Postoperative ACD. Theoretical formu- If AG > 13.5, then AG = 13.5 las originally used a constant ACD for a particular lens where AG = anterior chamber diameter from angle to angle, style. The postoperative ACD, however, tends to be shalAL = axial length lower in eyes with short axial lengths and deeper in eyes The authors of the SRKjT4 have used the corneal with long axial lengths. The modification of ACD for variations in axial length has been recognized as an height formula with a regression-derived formula to preimportant factor in improving the accuracy of theoret- dict the corneal diameter from the axial length. A modification of the axial length limits the adjustment of ACD ical formulas. Hoffer9 found a positive correlation between the post- for axial lengths in a curvilinear fashion commencing at operative anterior chamber depth (AC) and axial length an axial length of 24.4 mm. (AL) and suggested the theoretical formula be modified Cw = -5.41 + 0.58412 x LCOR + 0.098 according to the derived formula. If L :s 24.4, then LCOR = L AC = (0.292 x AL) - 2.93 IfL> 24.4, then LCOR = 3.446 + 1.716 x L - 0.0237 Binkhorst lO modified the ACD in his formula with a xLxL correction for axial length and assumed a maximum where Cw = corneal width, L = axial length, LCOR = ACD of 4.43 mm. corrected axial length d = 0.17 x a + 0.017 Modification of ACD in the universal formula. The If d > 4.43 mm, then d = 4.43 mm. concept of considering the ACD into an anatomical where d = postoperative ACO, a = modified axial length axial-length-related component and a smaller IOL-related component inherent in the corneal height formula Olsen II has used a combination of preoperative ACD is useful and is retained in the universal formula. The measurements and a regression-derived axial length term lens factor is preferred, for the reasons discussed modification of the ACD to determine postoperative above, to describe the distance between the iris or ciliary ACD. plane and the second principle plane of the IOL. To determine an anatomical component to the ACD Cd(post) = 1.14 + 0.22 x Cd(pre) + 0.10 x Ax that would be dependent on the interaction of the radii where Cd(post) = postoperative ACO, Cd(pre) = preoperof curvature and axial length, a new model eye was ative ACO, Ax = axial length constructed (Figure 2). The model eye was conceived as Naeser and coauthors l2 used the preoperative mea- the intersection of two spheres. An anterior segment or surement of the anterior chamber and the position of the corneal sphere and a posterior segment or global sphere posterior capsule to derive a regression relationship with intersect at a junction located at the iris root. The point the axial length to predict postoperative ACD. of intersection will be determined by the axial length, the peripheral radius of curvature of the posterior cornea, Predicted position of posterior lens capsule = 2.40 + 0.0 II and the radius ofthe globe. The formulas relating these x Patient age + 0.171 x Preop ACO + 0.051 x Axial length measurements follow: A

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A

715

radius of the globe was obtained by comparing the results of the universal theoretical formula and the SRK formula over a range of keratometry values and axial lengths (~22 mm and <24.5 mm) where the latter formula has proved to be accurate. A regression analysis was used to derive the following formula: RG = 0.35066 x AL - 0.06607 x K + 5.70871 where RG = radius of the globe, K = preoperative keratometry

Fig. 2.

(Barrett) The theoretical model eye used to derive a relationship between the anatomical anterior chamber depth (ACD), lens factor (LF), axial length (AL), retinal thickness (RT), radius of the posterior segment of the globe (RG), central radius of the cornea (RC), radius of the peripheral cornea (RCP), and ciliary diameter at the iris root (CD).

ACD = AL - 0.593 + 0.13 - RG - SQR(RG 2 - RCP 2 + (RCP - ACD) 2) where ACD = anatomical chamber depth, AL = axial length, RG = radius of curvature of the globe's posterior segment, RCP = radius ofcurvature of the peripheral cornea

An alternative would have been to use actual postoperative results to derive a similar relationship between RG, axial length, and K-readings. The equation for ACD once again requires an iterative solution; in this instance, a bisection method was used. Parameters that predict an ACD less than 0 (AL < 2 x RG + 0.593 - 0.13) or greater than the posterior radius (Rep) of the cornea (AL > RG + 0.593 - 0.13 + SQR(RG 2 - RCP 2) + RCP) are beyond the theoreticallimits of the model eye and are excluded from calculation. The refractive index of the cornea is an assumption and several different values have been used for theoretical formulas. The ratio of the posterior central radius of curvature of the cornea to the anterior central radius of curvature has been estimated by Gullstrand to be 0.883. If this value is used, the corneal power can be calculated using an optical formula as follows: A

A

A

A

A

The peripheral curvature of the cornea is unknown. The shape of the cornea can be considered as an ellipse and the peripheral curvature of the cornea has been shown to relate to the central anterior curvature. 16 RCP = (SQR(RC 2 + (1 - PZ) x 5 2» 3/RC 2 where RCP = peripheral radius of cornea, RC = central radius of cornea, PZ = P-factor of cornea A

A

A

A

The P-factor relates to the shape of the peripheral zone, which is generally flatter than the central zone and has been shown to be equal in myopes and hyperopes. Yet many eyes do not follow this shape and in some the peripheral zone may be steeper. The intersection of the two spheres defines a ciliary diameter at the iris root. The internal diameter is known to vary only slightly, about a mean value similar to the corneal diameter, and therefore limits of 11.5 mm and 13.5 mm are accepted for this dimension. If the calculation of the anatomical chamber depth (i.e., corneal vertex to plane of the pseudophakic iris) indicates a ciliary diameter beyond this range, the P-factor is adjusted until this is corrected. The radius of the globe or posterior segment is unknown. Initially an attempt was made to measure this diameter with A-scan ultrasound but this was found to be unreliable due to variation in the conjunctival thickness and difficulty in aligning the probe correctly. A relationship between keratometry, axial length, and 716

KC = (376/RC) - (40/RCC) + (0.00052/1.376) x (376/RC) x 40/RCC) where KC = power of the cornea, RC = central anterior radius of the cornea, RCC = central posterior radius of the cornea (=RC x 0.883)

This solution has been proposed by Olsen 17 and is equivalent to assuming a refractive index of 1.3315 for the cornea. Additions to the axial length varying from 0.15 to 0.25 have been proposed by various authors to account for the difference in reflection from the vitreoretinal interface to the true location of the photoreceptors. Rather than derive an empirical factor, the actual thickness of the retina at the fovea (i.e., 0.13 mm)18 is used in this formula. The factor is used in the formula and in the prediction of the ACD.

Evaluating the Formula

The performance of the formula was evaluated retrospectively in a series of consecutive patients who had extracapsular cataract extraction and an IOL implanted into the capsular bag performed by the author. The cases were from a group of 150 patients who had surgery performed in 1988. The lens was a three-piece posterior chamber IOL with either a modified C-Ioop or J-Ioop polypropylene haptic and a convex-plano 6.00 mm poly(methyl methacrylate) (PMMA) optic. The manufacturer's recommended A-constant for this IOL was 116.9, and a retrospective analysis confirmed that there was no significant difference between the A-constant of the two haptic styles.

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All patients had at least three months follow-up and timate, and percentage of patients with refractive errors cases with less than 20/40 corrected visual acuity were less than 1.00 D. These parameters have previously been excluded as were cases with more than 3.00 D of post- used as valid criteria for comparison. 19 operative astigmatism. The A-scan units were applanation style and the K-readings were recorded in diopters. Keratometry and axial length measurements were perRESULTS formed by the same personnel for all patients studied. The universal formula was the most accurate in a To evaluate the formula in more detail, this group of patients was divided into 50 patients with average axial comparison of errors in prediction of the formulas in the lengths (axial lengths greater than or equal to 22.5 mm 100 unselected cases (Group 1). The errors in prediction and less than or equal to 24.5 mm), short axial lengths for the different formulas and the percentage of patients (axial lengths less than 22.5 mm), and long axial lengths with predicted errors less than 1.00 D, 2.00 D, and (axial lengths greater than 24.5 mm). Additional cases 3.00 D are listed in Table 2. The universal formula had were added to the short and long axial length groups for the lowest mean absolute error, standard deviation, and a total of 25 patients in each group and a total of standard error of the estimate. A higher percentage of patients were predicted to within 1.00 D of spherical 100 patients overall. The performance of the different formulas was com- equivalent refractive error for the universal formula pared in the four groups: (1) un selected group of 100 than for the other formulas. patients, (2) selected group of25 patients with short axial The universal formula was the most accurate in a lengths «22.5 mm), (3) selected group of 25 patients comparison of errors in prediction of the formulas in the with long axial lengths (>24.5 mm), and (4) selected 25 selected cases with axial lengths less than 22.5 mm group of 50 patients with average axial lengths (Group 2). The errors in prediction for the different formulas and the percentage of patients with predicted (~22 . 5 mm and :524.5 mm). The prediction accuracy of the universal formula was errors less than 1.00 D, 2.00 D, and 3.00 D are listed in compared with the SRK II, the Holladay, and the Table 3. The universal formula had the lowest mean SRK/T formulas. These formulas were considered rep- absolute error, standard deviation, and standard error of resentative of current state-of-the-art regression and the- the estimate. A higher percentage of patients were preoretical formulas. The expected postoperative refraction dicted to within 1.00 D of spherical equivalent refractive was calculated for each IOL according to the formulas error for the universal formula than the other formulas. The universal formula was the most accurate in a published by each of the authors. The predicted refraction was compared with actual comparison of errors in prediction ofthe formulas in the measured postoperative refraction to obtain the error in 25 selected cases with axial lengths greater than 24.5 mm prediction of the different formulas. Each formula was (Group 3). The errors in prediction for the different optimized for the series of patients by adjusting the formulas and the percentage of patients with predicted constants to achieve a mean prediction error of zero. The errors less than 1.00 D, 2.00 D, and 3.00 D are listed in optimized constants were used in all comparisons. De- Table 4. The universal formula had the lowest mean riving an optimal A-constant for each formula improves absolute error, standard deviation, and standard error of the accuracy but not the variability of the different for- the estimate. A higher percentage of patients were premulas. The new formula was not developed from the dicted to be within 1.00 D of spherical equivalent resame data set of patients used in the evaluation and fractive error for the universal formula than the other formulas. comparison of the different formulas. The parameters used to compare the different forThe universal formula was the most accurate in a mulas were mean ~bsolute error, standard error of es- comparison of errors in prediction of the formulas in the

Table 2. Table listing the mean error, SD, mean absolute error, 2 x SEM of the mean absolute error, and standard estimate of the error of prediction for the universal, SRK II, Holladay, and SRK/T formula in the 100 cases unselected on the basis of axial length. The percentages of cases predicted to be within 1.00 D, 2.00 D, and 3.00 D of spherical refractive error are listed. Mean Error

Mean Absolute Error

Standard Error of Estimate·

2 x SEM Formula SD :::;1.00 D Universal 0.00 0.88 0.71 om 0.88 74 SRK II 0.00 1.04 0.81 0.01 1.03 69 Holladay 0.00 0.96 0.78 0.01 0.95 70 0.00 0.94 SRK/T om 0.75 0.93 69 • Standard error of estimate (in diopters) = Sqr (sum(actual refraction - predicted refraction/n)2) ] CATARACT REFRACT SURG-VOL 19. NOVEMBER 1993

Percentage of Cases :::;2.00 D

:::;3.00 D

97

100

95

100

97

100

97

100

717

Table 3. Mean error, SD, mean absolute error, 2 x SEM of the mean absolute error, and standard estimate of the error of prediction for the universal, SRK II, Holladay, and SRK/T formula in the 25 cases selected with short axial lengths less than 22.5 mm. The percentages of cases predicted to be within 1.00 D, 2.00 D, and 3.00 D of spherical refractive error are listed. Mean Standard Percentage of Cases Error of Mean Standard Absolute 2 x SEM ::51.00 D Estimate· ::53.00 D Error Deviation Error ::52.00 D Formula 1.01 76 0.98 0.75 0.06 88 100 Universal 0.21 0.07 1.02 0.81 1.18 72 84 100 SRKII 0.58 0.78 0.06 1.08 72 Holladay 0.42 0.99 88 100 0.77 0.06 1.04 72 0.98 88 100 0.35 SRK/T • Standard error of estimate (in diopters) = Sqr (sum(actual refraction - predicted refraction/nf) Table 4. Mean error, SD, mean absolute error, 2 X SEM of the mean absolute error, and standard estimate of the error of prediction for the universal, SRK II, Holladay, and SRK/T formula in the 25 cases selected with axial lengths greater than 24.5 mm. The percentages of cases predicted to be within 1.00 D, 2.00 D, and 3.00 D of spherical refractive error are listed for each formula. Mean Standard Percentage of Cases Absolute Error of Mean 2 X SEM SD Error Estimate· ::51.00 D ::52.00 D Formula Error ::53.00 D 0.03 0.76 0.73 80 Universal -0.21 0.64 100 100 -0.76 0.76 0.91 0.05 1.07 64 SRKII 96 100 -0.42 0.71 0.70 0.04 76 Holladay 0.83 100 100 0.04 -0.42 0.75 0.71 72 0.87 SRK/T 100 100 • Standard error of estimate (in diopters) = Sqr (sum(actual refraction - predicted refraction/n)2)

50 selected cases with average axial lengths (Group 4). The errors in prediction for the different formulas and the percentage of patients with predicted errors less than 1.00 D, 2.00 D, and 3.00 D are listed in Table 5. The universal formula had the lowest mean absolute error, standard deviation, and standard error of the estimate. A higher percentage of patients was predicted to be within 1.00 D of spherical equivalent refractive error for the universal and SRK II formulas than the other formulas. The universal formula was more accurate in predicting refractive error for patients in the unselected, short, long, and average axial length groups. The differences in

the mean absolute error are presented in Figure 3, and the percentage of cases predicted to be within 1.00 D of spherical equivalent refractive error are presented in Figure 4 for the different formulas and groups. The improved accuracy of prediction of the universal formula was maintained regardless of axial length, and the overall performance of the universal formula appeared superior. To determine whether the difference in prediction accuracy of the universal formula when compared with the other formulas was significant, the absolute errors of the entire group of 100 patients were subjected to statistical analysis using a paired-sample t-test. The uni-

Table 5. Mean error, SD, mean absolute error, 2 X SEM of the mean absolute error, and standard estimate of the error of prediction for the universal, SRK II, Holladay, and SRK/T formulas in the 50 cases selected with average axial lengths greater than or equal to 22.5 mm and less than or equal to 24.5 mm. The percentages of cases predicted to be within 1.00 D, 2.00 D, and 3.00 D of spherical refractive error are listed. Mean Standard Percentage of Cases Mean Absolute Error of Error 2 X SEM Estimate· Error SD Formula ::51.00 D ::52.00 D ::53.00D Universal 0.87 0.00 0.72 0.02 0.87 70 100 100 0.76 SRKII 0.09 0.02 0.93 0.94 70 100 100 Holladay 0.00 0.95 0.81 0.02 0.95 66 100 100 SRK/T 0.03 0.92 0.77 0.02 66 100 0.92 100 • Standard error of estimate (in diopters) = Sqr (sum(actual refraction - predicted refraction/n)2) 718

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MEAN ABSOLUTE ERROR

" CASES 100,-------------------------------~

0,9

90

0,8

0,7 0,6 0,5 UN SELECTED

<22.5 MM

• UNIVERSAL

Fig. 3.

III SRKII 0

>24.5 MM

22.5<>24.5

UNSELECTED

HOLLADAY ~ SRK-T

<22.5 MM

• UNIVERSAL

(Barrett) The mean absolute error of the universal, SRK II, Holladay, and SRK/T formulas in all 100 patients as well as subgroups selected on the basis of axial length.

Fig. 4.

III SRKII 0

>24.5 MM

22.5<>24.5

HOLLADAY ~ SRK-T

(Barrett) The percentage of cases predicted to be within 1.00 D of spherical equivalent refractive error for the universal, SRK II, Holladay, and SRK{f formulas. The percentage of cases is illustrated for all 100 patients as well as for subgroups selected on the basis of axial length.

Table 6. Statistical results of paired sample t-tests of the absolute errors in prediction for all 100 cases. Statistic Hypothesized mean difference I-statistic One-sided significance Two-sided significance Mean difference Standard deviation

Universal Versus SRKII

Universal Versus Holladay

Universal Versus

0 -2.950 0.002 0.004 -0.105 0.355

0 -2.644 0.005

0 -2.425 0.009 0.017 -0.044 0.179 0.Ql8

0.036

Standard error

99 -0.175 to -0.034

Degrees of freedom

95% confidence interval

versal formula was compared with the other formulas (Table 6). The improved prediction accuracy of the universal formula as compared with the other formulas was statistically significant using this method of analysis with a two-sided P-value less than .05 and a one-sided P-value less than .01. Although the performance of the formula is not expected to vary with IOLs that have different optical configurations to the convex-plano IOL evaluated in this series, this should be confirmed in further studies.

DISCUSSION This article outlines a new IOL formula that relates ACD to axial length and keratometry. The formula can

0.010 -0.066 0.249 0.025 99 -0.115 to -0.016

SRK/T

99 -0.079 to -0.008

be used with a variety of IOLs without the surgeon knowing details of the IOL required in the original formula. The theoretical model eye introduced has been demonstrated to be useful and the formula performed accurately in eyes with short, medium, and long axial lengths. The enhanced formula can therefore be referred to as universal in a wider sense than originally proposed. The formula is complex in that it contains several equations with interdependent variables that require more than one iterative solution. I have developed a program for IBM-compatible computers for the formula. The program provides a printout ofthe predicted power for emmetropia for IOLs with A-constants from 114.5 to 119.0 in 0.5 increments. The printout provides the predicted power for desired postoperative refractions

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from -3.00 D to +3.00 D in 0.50 D increments. An increment in A-constant of I unit does not necessarily translate to an increment in IOL power of I D but is related to such factors as axial length. Similarly, the relationship between predicted refractive error and predicted IOL power is also nonlinear and varies with axial length and keratometry. Retaining the A-constant as an expression in this formula is useful because it eliminates the need for surgeons to become familiar with a new lens constant. Despite encouragement for surgeons to develop their own constants, most rely on the A-constant recommended by the manufacturers. Manufacturers tend to monitor the clinical data received from surgeons and update the IOL's A-constant when necessary. Nevertheless, optimizing the A-constant or lens factor for individual surgeons will provide more accurate results and is recommended. A program to calculate a personalized A-constant based on this formula is available for this purpose. Errors in measurements of K-readings and axial length are of major importance and confuse the evaluation of different formulas.2° All the formulas in this comparison performed better in eyes with long axial lengths than short axial lengths. The same error in axial length determination would be proportionally larger in an eye with a short axial length than an eye with a long axial length. This factor and anatomical variation may be responsible for difficulties encountered in predicting IOL power accurately in eyes with short axiallengths. 21 The philosophy ofthe universal formula was to maintain theoretical accuracy where feasible while maintaining ease of use. The formula allows the user to select a particular optic configuration and index of refraction. As noted, however, calculations did not indicate a significant difference from the symmetrical biconvex optic used in the theoretical model, and this option is not used in the current program. Future refinements would be to develop a more accurate relationship between the posterior radius of the globe and the axial length and keratometry. These factors could be optimized by conducting a retrospective study of a larger database of patients. In the meantime, using data compatible with our present state of knowledge for such measurements as the peripheral radii of the cornea and retinal thickness, I developed a formula that performed more accurately than other third-generation formulas.

3. 4. 5. 6.

7. 8. 9. 10. II.

12.

13. 14. 15. 16. 17. 18. 19. 20.

REFERENCES 1. Drews RC. Reliability of lens implant power formulas in hyperopes and myopes. Ophthalmic Surg 1988; 19: 11-15 2. Sanders DR, Retzlaff J, Kraff Me. Comparison of the

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21.

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