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Theoretical Formulas
All the theoretical formulas used for calculation of lens power are based on a two lens systems, i.e. the cornea and the pseudophakos lens focussing images on the retina.
1. Basic theoretical formulas: These include Colenbrander’s, Fyodorov’s and Van der Heijde’s formula which yield approx. the same IOL powers.
Binkhorst’s formula yield 0.50 D stronger lens power.
2. Modified theoretical formulas: These include Hoffer’s formula, Shamman’s fudged formula and Binkhorst’s adjusted formula. The fudged formula is a modification of Colenbrander’s formula.
The various formulas are described in Table 23.1.
Regression Formulas
These formulas are derived empirically from retrospective computer analysis of data of patients who have undergone surgery before.
The factors on which IOL power calculation depends are:
Table 23.1: For emmetropic IOL power calculations
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1. Axial Length Measurement: This is the most important step in calculation of lens power. The IOL Master is recent method which gives high accuracy in measurement of axial length. An error of 1 mm affects the postoperative refraction by 2.5 D approximately. It is measured in millimeters (mm).
2. Corneal Power: It is measured either in diopters or in mms (radius of curvature).
Keratometer measures the radius of curvature of the central part of anterior corneal surface.
K = 1000 (n – 1) n = corneal index of refraction R 1.3375 for Haag- Streit and Bausch and Lomb.
3. Postoperative anterior chamber depth (ACD): It is least important factor in calculation of lens power. It is important in cases of Haigis formula.
An error of 1 mm affects the post operative refraction by approx. 1.0 D in myopic eye, 1.5 D in emmetropic eye and upto 2.5 D in hyperopic eye.
The recent 3rd generation 2 variable formulas use commonly are given below.
SRK Formula
1. SRK I Formula: It is basic regression formula. It is given by:
P = A – 0.9K – 2.5 L
Where P = IOL power for emmetropia K = Keratometric power reading A = A constant
L = Axial length in mm.
2. SRK II Formula: In this formula, the A constant is adjusted to different axial length ranges. It is given by:
P = A1 – 0.9 K – 2.5 L
A1 = new constant
A1 = A + 3 if axial length (L) < 20 mm A1 = A + 2 if L 20 – 21 mm
A1 = A + 1 if L 21 – 22 mm A1 = A if L = 22 – 24.5 mm A1 = A – 0.5 if L > 24.5 mm
3. SRK III Formula: This is new formula which is used to produce a desired postoperative refraction R.
I = P – cr R
where P = Power which is calculated by SRK II cr = Another empirical constant defined as cr = 1 for P < 14
cr = 1.25 for P > 14 Hoffer Q Formula
The Hoffer Q formula was published in 1993 [Hoffer, 1993], based on the earlier work of Kenneth J Hoffer, MD (cf.
references).
The Hoffer Q IOL power is given by:
P = f (A, K, Rx, pACD) It is a function of A: axial length
K: average corneal refractive power (K-reading) Rx: refraction
pACD: personalized ACD (ACD – constant) Likewise, the Hoffer Q refractive error Rx Rx = f (A, K, P, pACD)
depends on A, K, P and pACD.
For the calculations, the corneal radii, R1C and R2C in [mm] are converted into K in [D] according to:
K = 0.5 (K1 + K2) with K1 = 337.5/R1C and K2 = 337.5/R2C.
The personalized ACD (pACD) is set equal to the manufacturer’s ACD – constant, if the calculation was selected to be based on the ACD – constant. In case the A – constant was chosen, pACD is derived from the A – constant [Hoffer, 1998] according to [Holladay et al, 1988]
pACD = ACD – const = 0.58357 * A – const – 63.896 Haigis Formula
On of the final frontiers in ophthalmology is the consistent accurate calculation of intraocular lens power in all the eyes.
The more recent formula which is developed, to increase the accuracy of lens power calculation is Haigis Formula. This formula was given by Dr. Wolfgang Haigis.
It uses three constants to set both the position and shape of a power prediction curve. The IOL calculation according to Haigis is based on the elementary IOL formula for thin lenses.
d = a0 + [a1 × ACD] + (a2 × AL) where d = the effective lens position
ACD = measured anterior chamber depth of the eye AL = axial length of the eye
a0 constant = same as lens constants for the different formulas given before
a1 constant = tied to anterior chamber depth a2 constant = measured axial length
Thus the value for d is determined by a function rather than a single number.
The a0, a1 and a2 constants area derived by multivariable regression analysis. The Haigis formula IOL constants will appear different than normal as they interact with the ACD and the AL.
The main part of highly accurate IOL power calculation is able to correctly predict ‘d’ for any given patient and IOL.
‘d’ for the five formulas commonly in use are:
SRK/T d = A constant Hoffer Qd = pACD
Holladay 1d = surgeon Factor Holladay 2d = ACD
Haigis d = a0 + (a1 × ACD) + (a2 × AL).
In actual practice, the two eyes with same axial length and keratometric reading may have different lens power.
This may be due to:
Effective lens position, i.e. distance of the lens from the cornea
Individual geometry of lens model.
Commonly used lens constants in different 3rd generation 2 variable formulas are:
SRK/T Formula – uses A constant Holladay I Formula – uses Surgeon Factor
Holladay II Formula – uses Anterior Chamber Depth (ACD)
Hoffer Q Formula – uses Anterior Chamber Depth (ACD)
These constants are usually interchangeable All the above formula has limited axial length range of accuracy.
Holladay I – works well for normal – moderately long axial length and
Hoffer Q – works better for shorter axial length.
Hoffer Q formula is best for short eyes. Holladay for long eyes and SRK/T is best for very long eyes. Overall SRK/T is probably most accurate in majority of cases.
Holladay Formula
The components of the three part Holladay system are:-1. Data screening criteria to identify improbable axial
length and keratometric measurement.
2. The modified theoretical formula, which predicts the effective position of the IOL based on the axial length and the average corneal curvature.
3. Personalized surgeon factor (PSF) that adjusts for any consistent bias on surgeon from any source. It is advance method, which requires patient refractions.
The initial formula uses the “Basic Surgeon Factor”. It can be calculated from the A constant provided by lens manufacturer.
Intraocular Lens Power Calculation after Corneal Refractive Surgery
Keratorefractive surgeries done to decrease the refractive errors have gained enormous popularity among patients
and the doctors. Most of these techniques permanently and irreversibly alter the corneal shape and its effective power. Thus the routine formula used for IOL power calculation cannot be used these patients.
Increased accuracy has increased both the surgeon and the patient’s expectation for precise outcome and more so in patients having undergone refractive surgery.
The different methods available for IOL power calculations are:
Hard Contact Lens Method
This method uses a hard contact lens of known power and base curve to determine true corneal powers. After refraction is over, a plano hard contact lens is placed on the eye and over refraction is performed. If no differences exist between refraction, then the corneal dietetic power is the same as the contact lens base curve.
If the over refraction is more myopic than refraction without the contact lens, the lens is steeper than the cornea.
The change in refraction is subtracted from the contact lens base curve to yield the corneal power.
If over refraction is more hyperopic than the contact lens refraction, the cornea is steeper than the lens. The change in refraction is then added to the contact lens base curve to calculate corneal power.
In this situation, the clinical relationship:
C base + C power + R cl + R bare = K true Generally holds true, if the following are known:
C base = base curve of the contact lens in diopters, and
C power = spherical power of the contact lens in diopters, and
R cl = spherical equivalent refractive error with the contact lens and
R bare = spherical equivalent refractive error without the contact lens, then
K true = the estimated corneal power after refractive surgery
To give accurate information, the refractive numbers (R cl and R bare) must retain their corresponding plus (hyperopic) and minus (myopic) signs, and be corrected for vertex distance.
Clinical History Method
It was first described by Holladay and later by Hoffer for corneal power estimation as
Kp + Rp – Ra = Ka.
Where,
Kp = the average keratometry power before refractive surgery,
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Rp = the spherical equivalent before refractive surgery, Ra = the stable spherical equivalent after refractive surgery,
Ka = final central corneal power after refractive surgery.
This method requires knowledge of keratometry prior to refractive surgery, as well as induced refractive change, i.e. changes in spherical equivalent (SE) before the development of cataract.
A. For postmyopic procedure patients;
Corneal diopteric powers = prerefractive surgery Ks – change in SE
B. For posthyperopic procedure patients;
Corneal dioptric power = prerefractive surgery + change in SE
Calculated corneal dioptric power is then used for IOL determination.
Feiz and Mannes IOL Power Adjustment Method In this technique, initially the IOL power is calculated using the pre-LASIK corneal power.
The pre-LASIK IOL power is then increased by the amount of refractive change at spectacle plane divided by 0.7
IOL power = (IOL) pre + DD/0.7 DD = the refractive change after LASIK.
Modified Maloney Method
In this method, the central corneal power is obtained by using the Axial Map of Zeiss Humphery Atlas Topographer (Cccp)
(Cccp × 1.114) – 6.10 = post-LASIK adjusted corneal power.
Nomogram-based Correction
The following formula is used to predict IOL power to maintain emmetropia after refractive surgery.
After myopic LASIK;
Post-LASIK IOL = Pre-LASIK IOL + (change in SE/
0.67)
After hyperoic LASIK;
Post-LASIK IOL = Pre-LASIK IOL – (change in SE/
0.67).
IOL Power Calculations in Silicone Filled Eyes Silicone oil in the vitreous causes an error in axial length measurement. This occurs due to change in the velocity of sound through silicone oil. The error may be 3 to 4D. Axial
length measurement should be done prior to injection of silicone oil.
Regarding the spike pattern, it is difficult to get good retinal spikes.
The axial length obtained can be corrected by the following formula:
Axial length = AL × Velocity (corrected)/Velocity (measured)
ACCURACY OF IOL POWER CALCULATION