INTRODUCTION
When the manufacturer or the surgeon uses a new IOL without a designated constant A. We want to give you how to calculate a constance A after a few cases for the new implant. The first step it’s to use a constant A approching the type of implant we use with a table then after having used 20 or more implants, the manufacturer should personalize the constant by back-calculating the constant for each case. It is best for the initial implants to be used in average eyes between 23 and 24 mm to obtain only minimal variation in the personalized constant for the new implant.
It is necessary for every one who is working with intraocular lenses to know how to calculate the power of the IOL.
All available formulas aim to calculate the exact power of an intraocular lens (IOL) that will be placed inside the eye after cataract extraction and that will produce postoperative emmetropia. After surgery, the two major refracting elements inside the eye would be the cornea and the IOL. Both act as plus lenses and these curved surfaces will refract the incoming rays of light, focusing them on the retina, thus reaching emmetropia.
OPTICS OF THE THIN PLUS LENS1
A thin plus lens is characterized by its power, expressed in diopters (D). It indicates the amount of vergence produced by the lens. Each lens has a primary focal point and a secondary focal point. The distance between each of the primary and secondary focal points and the center of the lens is the focal distance. The relationship between the lens power (D) and the focal distance (f) in meters is : D = 1 / f
THE TWO-LENS SYSTEM
In the presence of a two-lens system, it becomes a little bit more difficult to calculate the object-image relationship.
The vergences have to be calculate in succession, dealing first with the first lens to encounter the incident light. The image position created by first lens will then be the object position for the second.
IOL FORMULA 2,3
There are two major categories of IOL formulae.
Theoretical Formula
This formula is based on an optical model of the eye. An optics equation is solved to determine the IOL power needed to focus light from a distant object onto the retina.
In the different formulae, different assumptions are made about the refractive index of the cornea, the distance of the cornea to the IOL, the distance of the IOL to the retina as well as other factors. These are called theoretical formulae because they are based on a theoretical optical model of the eye. All of these theoretical equations make simplifying assumptions about the optics of the eye, and hence, provide a good (but not perfect) prediction of IOL power.
The most popular formula in this group is the Binkhorst formula. This is based on sound theory. All the theoretical formulae can be algebrically transformed into the following :
P = [N / (L – C)] – [N * K / (N – K * C)]
Where
P = Dioptric power of the lens for emmetropia N = Aqueous and vitreous refractive index
How to Calculate the Constant A
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L = Axial length (mm)
C = Estimated postoperative anterior chamber depth (mm)
K = Corneal curvature (D)
Regression Formula (Empirical Formula)
The regression formulae or empirical formulae are derived from empirical data and based on retrospective analysis of postoperative refraction after IOL implantation. The results of a large number of IOL implantations are plotted with respect to the corneal power, axial length of the eye, and emmetropic IOL power. The best-fit equation is then determined by the statistical procedure of regression analysis of the data. Unlike the theoretical formulae, no assumptions are made about the optics of the eye. These regression equations are only as good as the accuracy of the data used to derive them.
The Modern Theoretical Formulas4
The modern theoretical formulas are more complete than the original and modified formulas. The most striking difference is the manner in which the estimated lens position (ELP), also known as the estimated postopera-tive anterior chamber depth (ACD), is calculed :
• In the original formulas, ELP is a constant value.
• In the modified formulas, ELP varies with the axial length (ALX). It decreases in the shorter eye and increases in the longer eye.
• In the modern formulas, ELP varies, not only with the ALX, but with the corneal curvature as well. The anterior chamber is deeper in the presence of a steep cornea and shallower in the presence of a flat cornea.
It is important to note that the postoperative ACD does not correlate with the preoperative ACD. Instead, it correlates with the placement of the intraocular lens (IOL), whether it is in the anterior chamber, in the sulcus, or in the capsular bag. The ELP also varies with the implant’s
configuration and the location of its optical center. The use of a meniscus lens with its anteriorly located optical center calls for a smaller value than a biconvex IOL, where the optical center is more posteriorly located.
The postoperative ACD does not correlate with the preoperative ACD. Instead, it correlate with the IOL placement within the eye.
The best known modern formulas are the Holladay II formulas,5 the SRKT6 formula, the Hoffer Q formula7 and Haigis formula,8 and we will confine our discussion to these four formulas. Each formula comprises multiple equations and instead of listing these equations, we will relate the rationale of these formulas. These formulas are readily available on calculators, computer diskettes, and ultrasound units.
Each modern formula use a constant related to the A-constant
The ELP appeared in each of the four formulas with differents name and differents formula :
SRKT A-constant
Holladay II s-factor
Haigis a0, a1, a2
Hoffer Q pACD
The A-constant encompasses multiple variables that include the implant manufacturer, implant style, surgeon’s technique, implant placement within the eye, and measuring equipment.
A-constant, s-factor, a0 and pACD are all related. If we know one of these constants, we can calculate the other one.
There are many manners to calculate the constant A.
Starting with the formula of Holladays 1, We give you the following steps:
With the Holladay’s formula5, we have one formula for the IOL and one formula for the target (Ref) corresponding at this specific IOL.
Formula Type Variables Constant Formula used for which ALX9
Hoffer Q Théorique alx, K, Rx pACD = 0.58357*A-63.896 Little
Haigis Théorique Alx, K d = a0 + (a1*ACD) + (a2*alx) Normal and high Holladay II Théorique Alx, K S-factor = 0.58357*A-63.896 Normal and very high
SRKT Théorique Alx,K A = A-constant Normal and very high
Little: ALX < 22 Normal : 22 < ALX< 24.5 High : 24.5 < ALX < 26 Very high : ALX > 26
The formula of the Ref depending only from the variable IOL, K, ACD, SF.
To calculate the SF we use only variable like Aref, ALX, K, and ACD, the other are fix number .
We give you all the formula that you can calculate our own, the variables are printed with different colors.
Here is the formula :
Ref = (1000 * na * (na * R – (nc – 1 ) * Alm – IOL * ( Alm –
Then we want that the target is as near as possible from zero and we find:
SF = ((((-(Aref *0.001 * (( Alm * V * (nc – 1)) – (R*(Alm- (V * Aref *((V*((na*R)-((nc-1)*Alm))) + (Alm * R)))))/l)))))/
(2*((nc-1) – (0.001 * Aref*(( V (nc-1)) – R)))))-ACD) (337.5/K))))))-ACD)) + 65.6) / 0.5663
With :
ALX : axial length
K : keratometry
ACD anterior chamber depth
Aref : stabilited refraction after 1 month nc = 4/3
V = 12 (vertex) na = 1.336 CONCLUSION
We still have to perfect all the new formulas which don’t give us enough accurate results for the expectation of the patient.
Each modern formula use a constant related to the A-constant which is calculated with the postoperative results and therefore, the A-constant become more accurate with the number of procedures.
We hope this modified formula will be useful for manufacturer and surgeon which use new implants without the A-constant.
REFERENCES
1. Smith ME, Kincaid MC,West CE. Basic Science, Refraction and pathology St Louis MO: Mosby 2002;87-89.
2. Shammas HJ in Intraocular Lens Power calculations. Slack inc. Thorofare NJ,USA 2004.
3. Garg A in Mastering the Techniques of IOL Power calculations. Jaypee Brothers Medical Publishers, New Delhi India 2005.
4. Retzlaff J, Sanders DR, Kraff MC. Lens Implant Power Calculation A manual for ophthalmologists and Biometrists 3rd edition Slack inc. Thorofare NJ, USA 1990.
5. JT Holladay, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:
17-24.
6. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/
T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333-40.
7. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formula. J Cataract and Refract Surg 1993;
19:700-12.
8. Haigis W. IOL calculation according to Haigis 1997. Available at http//www.augenklinik.uni-wuerzburg.de/uslab/ioltxt/
haie.htm.Accessed September 2003.
9. Hill WE. Chossing the right formula Available at http//
www.doctor-hill.com/formula.htm.Retrieved January 2003.
Axial Length Dependence of IOL Constants