(India)
INTRODUCTION
It is necessary for every ophthalmologist who is working with intraocular lenses to know how to calculate the power of the IOL.
AXIAL LENGTH MEASUREMENT
For IOL implantation, the ultrasonic method affords the best way to calculate the axial length and achieves the desired postoperative refraction. The instruments available to make these measurements are of two basic types:
- Instruments with rigid probe tips
- Instruments with distensible tips or with water baths.
Those instruments with distensible membranes on the front of the probe are approximately 5 percent more accurate in making measurements than those with the rigid tip. The reasons why the distensible tip are better are as follows:
- The distensible tip prevents indenting the cornea when the measurement is made, and does not cause the eye to appear artificially shortened. A rigid tip can cause corneal indentation between 0.1 and 0.3 mm, resulting in error from 0.3 to 1.0 diopters (Fig. 1.1). In other words if one is buying an A-scan, one should get one with a distensible tip.
- The distensible tip helps to separate the corneal reflection from the signal sent out from the front surface of the transducer, i.e. it makes it more accurate to determine exactly where the front surface of the cornea is, and when it is not in direct contact with the transducer.
KERATOMETRIC MEASUREMENTS
The keratometric measurements can be done through a keratometer or through an autokeratometer. Many biometers (Fig. 1.2) have provision for connecting the autokeratometer to their computer so that once the keratometer reading is taken automatically, the value is entered into the biometer, and one does not have to feed it in again.4
IOL FORMULA
There are two major categories of IOL formulae.
Theoretical Formula
Introduction
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 5theoretical 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 algebraically transformed into the following
P = [N/(L–C)] – [NK/(N–KC)]
where,
P | = | Dioptric power of the lens for emmetropia |
N | = | Aqueous and vitreous refractive index |
L | = | Axial length (mm), |
C | = | Estimated postoperative anterior chamber depth (mm), and |
K | = | Corneal curvature [D]. |
Binkhorst Formula
Binkhorst has made a correction in his formula for surgically induced flattening of the cornea, using a corneal index of refraction of 1.333. Binkhorst also corrects for the thickness of the lens implant by subtracting approximately 0.05 mm from the measured axial length. Thus with the Binkhorst formula, 0.25 mm is added to the measured axial length to account for the distance between the vitreoretinal interface and the photoreceptor layer, and 0.05 mm is subtracted for lens thickness, resulting in a net addition of 0.20 mm to the measured axial length. The Binkhorst's formula is:
where,
D | = | Dioptric power of IOL in aqueous humor, |
1336 | = | Index of refraction of vitreous and aqueous, |
r | = | Radius of curvature of the anterior surface of the cornea, |
a | = | Axial length of the globe (mm), and |
d | = | Distance between the anterior cornea and the IOL. |
Disadvantages
The problem in the theoretical formula is in the axial length measurement. The reason why it is difficult to measure the axial length accurately is that one must know the exact velocities of the ultrasound as it travels through the various structures of the eye. Because of the variation of the acoustic density of a cataract, these velocities cannot be known exactly. As a result, when cataractous lenses are much more acoustically dense than the average lens, the sound wave will move more rapidly through the lens and return to the transducer much more quickly than would have been expected for a given axial length. As a result of the velocity error, the eyes appear to be shorter. The formula consequently calculates an IOL power for an axial length which is too short. The patient then becomes overminused (too myopic). Theoretical formulae help the surgeon to anticipate what should result, not what will result from implantation.7
Regression Formula (Empirical Formula)
Introduction
The regression formulae or empirical formulae are derived from empirical data and are 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.
Advantages
Implant power calculations can be made much more accurately through the use of regression formulae that are based on the analysis of the actual results of many uncomplicated IOL implantations in previous cataract surgeries. Since regression analysis is based on the results of actual operations, it includes the vagaries of the eye and measuring devices, vagaries that theoretical formulae attempt to address with correction factors.
Sanders-Retzlaff-Kraff (SRK) Formula
The most popular regression formula is the SRK formula which was developed by Sanders, Retzlaff and Kraff in 1980. This is:
where,
P | = | Implant power to produce emmetropia, |
L | = | Axial length (mm), |
K | = | Average keratometer reading, and |
A | = | Specific constant for each lens type and manufacture. |
The SRK formula calculates the IOL power by linearly regressing the results of previous implants. As this is a linear formula, it will underestimate the power of high-powered lenses and it will overestimate the power of the low-powered lenses compared to the theoretical calculation. For example, if the Binkhorst formula predicts that a 28-diopter lens should be used, the SRK formula will predict that a 26-diopter lens should be used. In lenses with low power, if the Binkhorst formula predicts that a 10-diopter lens is necessary, the SRK will predict that a 12-diopter lens should be used.
RELATION OF EQUIPMENT TO SPECIFIC FORMULAE
Most of the instruments calculate the desired power for the IOL at least by three different methods including a regression formula and a theoretical formula. It is the responsibility of the doctor to select which of the formulae he or she wants to use. Rarely, between 18 and 22 diopters, is there a significant difference between the calculated lens powers. But outside this range, there will be a progressive increase in difference between that determined by the theoretical formula and the one calculated by the regression formula. Since the regression formula has 9turned out to be statistically more accurate, 5 percent at these extremes, it is presently more reliable than the theoretical formulae. The manufacturers vary as to which programs they provide. One should anyway make sure that both the regression and theoretical formulae are included so that one has the opportunity to personally select the most reliable technique for one's surgery.
TARGETING IOL POSTOPERATIVE REFRACTION
The question that comes to one's mind next is “How to predetermine what postoperative refraction the patient should have?” This is the one parameter which the doctor has to decide upon and feed into the computer. The other parameters like axial length, etc. we have no control over. The answer depends on whether we are doing a monocular or binocular correction.
Monocular Correction
If we are considering only one eye (i.e. if the other eye has cataract or is amblyopic), targeting the postoperative refraction for approximately −1.00 diopter is probably the best choice. This is usually best because most people have visual needs for both distance and near. This means that the patient wants to be able to drive and to read without wearing glasses. If we target the postoperative refraction to −1.00D, it will allow the patient to perform most tasks with no glasses. At times, when they need finer acuity, they can wear regular bifocals, which will correct them for distance and near.10
The second reason for targeting the postoperative refraction to −1.00D is that statistically, between 70 and 90 percent of the patients will fall within +1.00D error of the desired postoperative refraction. The errors, as mentioned earlier are due to our inexact measurements. Therefore, the patient will fall between plano and −2.00D 90 percent of the time. This will assure most patients of useful vision without glasses. Hence, the error of the ultrasound is best handled by choosing the postoperative refraction to −1.00D. If we would target for plano, then 90 percent of the patients will be between −1.00 and +1.00D. When the patient's refraction is on the +1 side he or she has no useful vision at any distance because he or she is hyperopic and does not have the ability to accommodate. Consequently, because it is very undesirable to have a hyperopic correction, targeting for −1.00D not only optimizes the best vision at all distances, but also minimizes the chance for hyperopia that can result from inaccurate ultrasonic measurements.
Binocular Correction
When the vision in the other eye is good, its refraction must be considered for binocular vision. One overriding rule when prescribing glasses is that one should never prescribe spectacles which gives the patient a difference in the power between the right and left lens greater than 3D. The reason for this is that even though the patient may have 6/6 vision in primary gaze, when the patient looks up or down, the induced vertical prism difference in the two eyes is so great that it will create double vision. In a patient who has good vision in the nonoperative eye, 11one must target the IOL power for a refraction within 2D of his or her present prescription in the nonoperative eye. Two diopters, not three, due to our 1D A-scan variability. For example, if we have a patient who is hyperopic and has +5D correction in each eye, we cannot target the IOL for a postoperative refraction of −1.00D because this would produce a 6D difference between the two lenses resulting in double vision. We must therefore select the IOL power to obtain a refraction which is approximately 2D less than the nonoperative eye. Consequently, on our patient who is +5D in both eyes, we should target the postoperative refraction in the eye with the cataract for +3D, so that there is a 90 percent probability that there will be less than a 3D difference.
In contrast, if the patient were highly myopic in each eye, for example, −10D in both eyes, we should target the IOL power to produce refraction of approximately −8D. Again, we have limited the difference in the spectacles lenses to a 2D difference in the final prescription. Again, target, for a 2D difference not a 3D, because there is approximately a 1D tolerance in the accuracy of the ultrasonic measurement.
If the operation on the second eye is to be done shortly after the first, the preoperative spectacles refraction can be ignored, and the patient is treated as if he or she were monocular.
FACTORS AFFECTING ACCURACY OF IOL POWER CALCULATION
Keratometry
Keratometers only measure the radius of curvature of the anterior corneal surface. This measurement must be converted to an estimate of the refracting power of the cornea in diopters, using a fictitious index (the true corneal refractive index of 1.376 could be used only if both the anterior and posterior corneal radii of curvature were known). The variability can alter calculated corneal dioptric power by 0.7D.
Axial Length Measurement
As explained earlier, indentation of the cornea by the A scan instrument tip can alter the axial length affecting the accuracy of the power of the IOL.
Axial Length Correction Factor
The distance from the vitreoretinal interface to the photoreceptor layer has been estimated to be about 0.15 to 0.5 mm. This distance can affect the accuracy of the IOL power calculated.
Site of Loop Implantation
Posterior chamber IOLs may be implanted with both loops in the ciliary sulcus or in the capsular bag, or with one loop in the sulcus and one loop in the capsular bag. Positioning the implants within the capsular bag places the implant further back in the eye and decreases the effective power of the lens. There is usually a 0.5 to 1.5D loss of effectivity by placing the implant 13in the capsular bag as opposed to the ciliary sulcus. A higher power lens should therefore be used when the implant is placed in the capsular bag.
Orientation of Planoconvex Implants
Some surgeons implant planoconvex posterior chamber lenses with the plano surface forward. Such flipping of the implant decreases the effective power of the lens by 0.75D even if the position of the lens is unchanged. An additional 0.5D loss of effectivity occurs because the principal plane of the lens is usually displaced further back into the eye. Thus, a total loss in effectivity of 1.25D is expected by turning the lens around.
Postoperative Change in Corneal Curvature
Suturing of a cataract incision has a tendency to steepen the vertical meridian. These changes affect the postoperative refraction of the patient.
Density of the Cataract
The density of the cataract also makes a difference. In a dense cataract (Fig. 1.3), the ultrasonic waves travel faster whereas in an early cataract (Fig. 1.4) the ultrasonic waves travel slower.
IOL Tilt and Decentration
When a lens is tilted, its effective power increases and plus cylinder astigmatism is induced about the axis of the lens tilt.14
The tilting of the lens occurs if one loop is in the capsular bag and the other in the sulcus (Fig. 1.5). Alternatively, residual cortex being left behind can cause an inflammatory response which causes contraction and pulling unequally on parts of the loops and the optic.
PSEUDOPHAKIC LASIK
If a patient has had a wrong biometry then the solution can be to remove the IOL and replace it with a correct powered IOL. Another alternative is to perform LASIK and correct the problem. Figure 1.6 is the topograph before LASIK of a patient who had a power of −10.0 diopters after IOL implantation.
Fig. 1.7: Topograph of the same patient as in Figure 1.6 after LASIK
If a patient has had a The patient was referred to us and we did a LASIK as the patient was operated a year back. We felt that the IOL might be fixed firmly in the bag. Figure 1.7 is the topograph after LASIK.