IOL Power Calculation for the Unusual Eye

Reprinted with permission from Holladay JT. IOL power calculation for the unusual eye, Chapter 15. In: Gills JP, ed. Cataract Surgery: The State of the Art. 1998:197.

Introduction

Several measurements of the eye are helpful in determining the appropriate intraocular lens (IOL) power to achieve a desired refraction. These measurements include central corneal refractive power (keratometry readings), axial length (biometry), horizontal corneal diameter (horizontal white to white), anterior chamber depth, and lens thickness. The accuracy of predicting the necessary power of an IOL is directly related to the accuracy of these measurements.^1,2

Fyodorov and colleagues first estimated the optical power of an IOL using vergence formulas in 1967.³ Between 1972 and 1975, when accurate ultrasonic A-scan units became commercially available, several investigators derived and published the theoretical vergence formulas.^4-9 All of these formulas were identical¹⁰ except for the form in which they were written and the choice of various constants such as retinal thickness, optical plane of the cornea, and optical plane of the IOL. These slightly different constants accounted for less than 0.50 D in the predicted refraction. The variation in these constants was a result of differences among the investigators in lens styles, A-scan units, keratometers, and surgical techniques.

IOL Calculations Requiring Axial Length

Theoretical Formulas
The theoretical formula for IOL power calculations has six variables. The six variables in the formula are: (1) corneal power (K), (2) axial length (AL), (3) IOL power, (4) effective lens position (ELP), (5) desired refraction (DPostRx), and (6) vertex distance (V). Normally, IOL power is chosen as the dependent variable and solved for using the other five variables, where distances are given in millimeters and refractive powers given in diopters:

The only variable that cannot be chosen or measured preoperatively is the effective lens position (ELP). The improvements in IOL power calculations over the past 30 years are a result of improving the predictability of the variable ELP. Slide 1 illustrates the physical locations of the variables. The term "effective lens position" was adopted by the U.S. Food and Drug Administration (FDA) in 1995 to describe the position of the lens in the eye, because the term anterior chamber depth (ACD) is not anatomically accurate for lenses in the posterior chamber and can lead to confusion for the clinician. The ELP for IOLs before 1980 was a constant of 4 mm for every lens in every patient (first-generation theoretical formula). This value actually worked well in most patients because the majority of lenses implanted were iris clip fixation, in which the principal plane averages approximately 4 mm posterior to the corneal vertex.

In 1981, Binkhorst improved the prediction of ELP by using a single variable predictor, the axial length, as a scaling factor for ELP (second-generation theoretical formula).¹¹ If the patient's axial length was 10% greater than normal (23.45 mm), Binkhorst would increase the ELP by 10%. The average value of ELP was increased to 4.5 mm because the preferred location of an implant was in the ciliary sulcus, approximately 0.5 mm deeper than the iris plane. Also, most lenses were convex-plano, similar to the shape of the iris-supported lenses.

The average ELP in 1996 has increased to 5.25 mm. This increased distance has occurred primarily for two reasons: the majority of implanted IOLs are biconvex, moving the principal plane of the lens even deeper into the eye, and the desired location for the lens is in the capsular bag, which is 0.25 mm deeper than the ciliary sulcus.

In 1988, my colleagues and I proved that using a two-variable predictor - axial length and keratometry - could significantly improve the prediction of ELP, particularly in unusual eyes (third-generation theoretical formula).² The original Holladay 1 formula was based on the geometrical relationships of the anterior segment. Although several investigators have modified the original Holladay two-variable prediction formula, no comprehensive studies have shown any significant improvement using only these two variables.

In 1995, Olsen and colleagues published a four-variable predictor that used axial length, keratometry, preoperative anterior chamber depth, and lens thickness.¹² Their results did show improvement over the current two-variable prediction formulas. The explanation is simple. The more information available about the anterior segment, the better the ELP can be predicted. This explanation is a well-known theorem in prediction theory in which the more variables that can be measured describing an event, the more precisely one can predict the outcome.

In a recent study,¹³ we discovered that the anterior segment and posterior segment of the human eye are often not proportional in size, causing significant error in the prediction of the ELP in extremely short eyes (< 20 mm). We found that even in eyes shorter than 20 mm, the anterior segment was completely normal in the majority of cases. Because the axial lengths were so short, the two-variable prediction formulas severely underestimated the ELP, explaining part of the large hyperopic prediction errors with current two-variable prediction formulas. After recognizing this problem, we began to take additional measurements on extremely short and extremely long eyes to determine if the prediction of ELP could be improved by knowing more about the anterior segment. Table 1 shows the clinical conditions that illustrate the independence of the anterior segment and the axial length.

For the past year, we have been gathering data from 35 investigators around the world. Several additional measurements of the eye have been taken, but only the following seven preoperative variables have been found to be useful for significantly improving the prediction of ELP in eyes ranging from 15 mm to 35 mm.

• axial length
• corneal power
• horizontal corneal diameter
• anterior chamber depth
• lens thickness
• preoperative refraction
• age

The improved prediction of ELP is not totally due to the formula, but is also a function of the technical skills of the surgeons who are consistently implanting the lenses in the capsular bag. A 20 D IOL that is 0.5 mm axially displaced from the predicted ELP will result in approximately a 1 D error in the stabilized postoperative refraction. However, when using piggyback IOLs totaling 60 D, the same axial displacement of 0.5 mm will cause a 3 D refractive surprise; the error is directly proportional to the implanted lens power. This direct relationship to the lens power is why the problem is much less evident in extremely long eyes, because the implanted IOL is either low plus or minus to achieve emmetropia following cataract extraction.

The Holladay 2 formula and the interim results of the 35 investigators were presented at the 1997 meeting of the American Society of Cataract and Refractive Surgeons. Software programs that implement the new formula were available in 1996. Once these additional measurements become routine among clinicians, a new flurry of prediction formulas using seven or more variables will emerge, similar to the activity following our two-variable prediction formula in 1988.³ The standard of care will reach a new level of prediction accuracy for extremely unusual eyes, just as it has for normal eyes. Calculations on patients with axial lengths between 22 mm and 25 mm with corneal powers between 42 D and 46 D will do well with current third-generation formulas (Holladay 1,⁴ SRK/T,¹⁴ and Hoffer Q¹⁵). In cases outside this range, the Holladay 2 should be used to ensure accuracy.

Normal Cornea with No Previous Keratorefractive Surgery

Clear Lensectomy for High Myopia and Hyperopia
The intraocular power calculations for clear lensectomy are no different than the calculations when a cataract is present. The patients are usually much younger, however, and the loss of accommodation should be discussed thoroughly. The actual desired postoperative refraction should also be discussed, because a small degree of myopia (-0.50 D) may be desirable to someone with no accommodation to reduce dependence on spectacles.

Clear lensectomy is usually reserved for patients who are outside the range of other forms of refractive surgery. Consequently, the measurements of axial length or keratometry are usually different from typical cataract patients because of the degree of refractive error. In most of the cases with high myopia, the axial lengths are extremely long (> 26 mm). In cases of high hyperopia, the axial lengths are very short (< 21 mm).

In patients with myopia exceeding 20 D, removing the clear lens often results in postoperative refractions near emmetropia with no implant. The exact result depends on the power of the cornea and the axial length. The recommended lens powers usually range from -10 D to +10 D in the majority of these cases. The correct axial length measurement is difficult to obtain in these cases because of the abnormal anatomy of the posterior pole. Staphylomas are often present in these eyes, and often the macula is not at the location in the posterior pole where the A-scan measures the axial length. In these cases, it is recommended that a B-scan be performed to locate the macula (fovea) and recheck the measurement determined by A-scan. I have personally seen 3 D to 4 D surprises because the macula was on the edge of the staphyloma, and the A-scan measured to the deepest part of the staphyloma. Such an error results in a hyperopic surprise because the distance to the macula is much shorter than the distance to the center of the staphyloma. The third-generation theoretical formulas yield excellent results if the axial length measurement is accurate and stable.

In patients with hyperopia exceeding +8 D, the axial lengths are often less than 21 mm and require lens powers that exceed the normal range (> 34 D). In these cases, piggyback lenses are necessary to achieve emmetropia.15 The only formula available at this time in these eyes is the Holladay 2. If the required lens power is less than or equal to 34 D, then the piggyback lenses are not required and third-generation theoretical formulas may be used.

Piggyback IOLs to Achieve Powers above 34 D
Patients with axial lengths shorter than 21 mm should be calculated using the Holladay 2 formula. In these cases, the size of the anterior segment has been shown to be unrelated to the axial length.15 In many of these cases, the anterior segment size is normal and only the posterior segment is abnormally short. In a few cases, however, the anterior segment is proportionately small to the axial length (nanophthalmos). The differences in the size of the anterior segment in these cases can cause an average of 5 D hyperopic error with third-generation formulas because they predict the depth of the anterior chamber to be very shallow. Using the newer formula can reduce the prediction error in these eyes to less than 1 D.

Accurate measurements of axial length and corneal power are especially important in these cases because any error is magnified by the extreme dioptric powers of the IOLs. Placement of both lenses in the bag with the haptics aligned is essential. Inadvertently placing one lens in the bag and the other in the sulcus can cause a 4 D refractive surprise.

Patients with Previous Keratorefractive Surgery

The number of patients who have had keratorefractive surgery (e.g., radial keratotomy [RK], photorefractive keratectomy [PRK], or laser-assisted in situ keratomileusis [LASIK]) has been steadily increasing over the past 20 years. With the advent of the excimer laser, these numbers are predicted to increase dramatically. Determining patients' corneal power accurately is difficult and usually is the determining factor in the accuracy of the predicted refraction following cataract surgery. Providing this group of patients the same accuracy with IOL power calculations as we have provided our standard cataract patients presents an especially difficult challenge for the clinician.

Methods of Determining Corneal Power
Accurately determining the central corneal refractive power is the most important and difficult part of the entire IOL calculation process. Our current instruments for measuring corneal power make too many incorrect assumptions with corneas that have irregular astigmatism. The cornea can no longer be compared to a sphere centrally, the posterior radius of the cornea is no longer 1.2 mm steeper than the anterior corneal radius. Because of these limitations, the calculated method and the trial hard contact lens method are most accurate, followed by corneal topography, automated keratometry, and finally manual keratometry.

Calculation Method
For the calculation method, three parameters must be known: the keratometry readings and refraction before the keratorefractive procedure, and the stabilized refraction after the keratorefractive procedure. It is important that the stabilized postoperative refraction is measured before any myopic shifts from nuclear sclerotic cataracts occur. It is also possible for posterior subcapsular cataracts to cause an apparent myopic shift, similar to capsular opacification, where the patient wants more minus in the refraction to make the letters appear smaller and darker. The concept that we described in 1989 subtracts the change in refraction due to the keratorefractive procedure at the corneal plane from the original K readings before the procedure, to arrive at a calculated postoperative K reading.16 This method is usually the most accurate because the preoperative K readings and refraction are usually accurate to ± 0.25 D. An example calculation to illustrate the calculation method is given.

Example:

      Mean Preoperative K = 42.50 @ 90° and 41.50 @ 180° = 42.00 D
      Preoperative Refraction = -10.00 + 1.00 X 90°, Vertex = 14 mm
      Postoperative Refraction = -0.25 + 1.00 X 90°, Vertex = 14 mm

Step 1. Calculate the spheroequivalent refraction for refractions at the corneal plane (SEQ[sbc]) from the spheroequivalent refractions at the spectacle plane (SEQ[sbs]) at a given vertex, where
      a. SEQ = sphere + 0.50 (cylinder)
      b.

Calculation for preoperative spheroequivalent refraction at corneal plane

      a. SEQ(sbR) = -10.00 + 0.50 3 (1.00) = -9.50 D
      b.

Calculation for postoperative spheroequivalent refraction at corneal plane
      a. SEQ(sbR) = -0.25 + 0.5 3 (1.00) = +0.25 D
      b.

Step 2. Calculate the change in refraction at the corneal plane.

      Change in refraction = Preoperative SEQ(sbc) - postoperative SEQ(sbc)
      Change in refraction = -8.38 - (+.025) = -8.68 D

Step 3. Determine calculated postoperative corneal refractive power.

      Mean postoperative K = Mean preoperative K - change in refraction at corneal
      plane
      Mean postoperative K = 42.00 - 8.68 = 33.32 D

This value is the calculated central power of the cornea following the keratorefractive procedure. For IOL programs requiring two K readings, this value would be entered twice.

Trial Hard Contact Lens Method
The trial hard contact lens method requires a plano hard contact lens with a known base curve and patients whose cataract does not prevent them from being refracted to approximately ±0.5 D. This tolerance usually requires a visual acuity of better than 20/80. The patient's spheroequivalent refraction is determined by normal refraction. The refraction is then repeated with the hard contact lens in place. If the spheroequivalent refraction does not change with the contact lens, then the patient's cornea must have the same power as the base curve of the plano contact lens. If the patient has a myopic shift in the refraction with the contact lens, then the base curve of the contact lens is stronger than the cornea by the amount of the shift. If there is a hyperopic shift in the refraction with the contact lens, then the base curve of the contact lens is weaker than the cornea by the amount of the shift.

Example: The patient has a current spheroequivalent refraction of +0.25 D. With a plano hard contact lens with a base curve of 35 D placed on the cornea, the spherical refraction changes to -2 D. Because the patient had a myopic shift with the contact lens, the cornea must be weaker than the base curve of the contact by 2.25 D. Therefore, the cornea must be 32.75 D (35 - 2.25), which is slightly different than the value obtained by the calculation method. In equation form, we have

      SEQ refraction without hard contact lens = +0.25 D
      Base curve of plano hard contact lens = 35.00 D
      SEQ refraction with hard contact lens = -2.00 D
      Change in refraction = -2.00 - (+0.25) = -2.25 D (myopic shift)
      Mean corneal power = Base curve of plano HCL + change in refraction
      Mean corneal power = 35.00 + (-2.25)
      Mean corneal power = 32.75 D

This method is limited by the accuracy of the refractions which may be limited by the cataract.

Corneal Topography
Current corneal topography units measure more than 5000 points over the entire cornea and more than 1000 points within the central 3 mm. This additional information provides greater accuracy in determining the power of corneas with irregular astigmatism compared to keratometers. The computer in topography units allows the measurement to account for the Stiles-Crawford effect, actual pupil size, etc. These algorithms allow an accurate determination of the anterior surface of the cornea. The algorithms provide no information, however, about the posterior surface of the cornea. To accurately determine the total power of the cornea, the power of both surfaces must be known.

In normal corneas that have not undergone keratorefractive surgery, the posterior radius of curvature of the cornea averages 1.2 mm less than the anterior surface.17 In a patient with an anterior corneal radius of 7.5 mm, using the Standardized Keratometric Index of Refraction of 1.3375, the corneal power would be 45 D. Several studies have shown that this power overestimates the total power of the cornea by approximately 0.56 D. Hence, most IOL calculations today used a net index of refraction of 1.3333 (4/3) and the anterior radius of the cornea to calculate the net power of the cornea. Using this lower value, the total power of a cornea with an anterior radius of 7.5 mm would be 44.44 D. This index of refraction has provided excellent results in normal corneas for IOL calculations.

Following keratorefractive surgery, the assumptions that the central cornea can be approximated by a sphere (no significant irregular astigmatism or asphericity) and that the posterior corneal radius of curvature is 1.2 mm less than the anterior radius are no longer true. Corneal topography instruments can account for the changes in the anterior surface, but are unable to account for any differences in the relationship to the posterior radius of curvature. In RK, the mechanism of having a peripheral bulge and central flattening apparently causes similar changes in both the anterior and posterior radius of curvature so that using the net index of refraction for the cornea (4/3) usually gives fairly accurate results, particularly for optical zones larger than 4 mm to 5 mm. In patients who have had RKs with optical zones of 3 mm or less, the accuracy of the predicted corneal power diminishes. Whether this inaccuracy is due to the additional central irregularity with small optical zones or the difference in the relationship between the front and back radius of the cornea is unknown at this time. Studies measuring the posterior radius of the cornea in these patients will be necessary to answer this question.

In PRK and LASIK, the inaccuracies of these instruments to measure the net corneal power is almost entirely due to the change in the relationship of the radii of the front and back of the cornea, because the irregular astigmatism in the central 3 mm zone is usually minimal. In these two procedures, the anterior surface of the cornea is flattened with little or no effect on the posterior radius. Using a net index of refraction (4/3) will overestimate the power of cornea by 14% of the change induced by the PRK or LASIK, that is, if a patient had a 7 D change in the refraction at the corneal plane from a PRK or LASIK with spherical preoperative K readings of 44 D, the actual power of the cornea is 37 D and the topography units will give 38 D. If a 14 D change in the refraction has occurred at the corneal plane, the topography units will overestimate the power of the cornea by 2 D.

In summary, the corneal topography units do not provide accurate central corneal power following PRK and LASIK, and in RK cases with optical zones of 3 mm or less. In RKs with larger optical zones the topography units become more reliable. The calculation method and hard contact lens trial are always more reliable.

Automated Keratometry
Automated keratometers are usually more accurate than manual keratometers in corneas with small optical zone ( 3 mm) RKs because automated keratometers sample a smaller central area of the cornea (nominally 2.6 mm). In addition, the automated instruments often have additional eccentric fixation targets that provide more information about the paracentral cornea. When a measurement error on an RK cornea is made, the instrument almost always gives a central corneal power that is greater than the true refractive power of the cornea. This error occurs because the samples at 2.6 mm are very close to the paracentral knee of the RK. The smaller the optical zone and the greater the number of the RK incisions, the greater the probability and magnitude of the error. Most of the automated instruments have reliability factors that are given for each measurement helping the clinician decide on the reliability in the measurement.

Automated keratometry measurements following LASIK or PRK yield accurate measurements of the front radius of the cornea because the transition areas are far outside the 2.6 mm zone that is measured. The measurements are still not accurate, however, because the assumed net index of refraction (4/3) is no longer appropriate for the new relationship of the front and back radius of the cornea after PRK or LASIK, just as with the topographic instruments. The change in central corneal power as measured by the keratometer from PRK or LASIK must be increased by 14% to determine the actual refractive change at the plane of the cornea. Hence, the automated keratometer will overestimate the power of the cornea proportional to the amount of PRK or LASIK performed.

Manual Keratometry
Manual keratometers are the least accurate in measuring central corneal power following keratorefractive procedures, because the area that they measure is usually larger than automated at 3.2 mm in diameter. Therefore, measurements in this area are extremely unreliable for RK corneas with optical zones of 4 mm or less. The one advantage with the manual keratometer is that the examiner is actually able to see the reflected mires and the amount of irregularity present. Seeing the mires does not help get a better measurement, but does allow the observer to discount the measurement as unreliable. The manual keratometer has the same problem with PRK and LASIK as topographers and automated keratometers, and is therefore no less accurate. The manual keratometer will overestimate the change in the central refractive power of the cornea by 14% following PRK and LASIK.

Choosing the Desired Postoperative Refraction Target
Determining the desired postoperative refractive target is no different than in other patients with cataracts in which the refractive status and the presence of a cataract in the other eye are the major determining factors. A complete discussion of avoiding refractive problems with cataract surgery is beyond the scope of this text, and is thoroughly discussed in the reference given.18 A short discussion of the major factors will follow.

If the patient has binocular cataracts, the decision is much easier because the refractive status of both eyes can be changed. The most important decision is whether the patient prefers to be myopic and read without glasses, or near emmetropic and drive without glasses. In some cases the surgeon and patient may choose the intermediate distance (-1 D) for the best compromise. Targeting for monovision is certainly acceptable, provided the patient has successfully utilized monovision in the past. Trying to produce monovision in a patient who has never experienced this condition may cause intolerable anisometropia and require further surgery.

Monocular cataracts allow fewer choices for the desired postoperative refraction, because the refractive status of the other eye is fixed. The general rule is that the operative eye must be within 2 D of the nonoperative eye to avoid intolerable anisometropia. In most cases, this means matching the other eye or targeting for up to 2 D nearer emmetropia (i.e., if the nonoperative eye is -5 D, then the target would be -3 D for the operative eye). If the patient is successfully wearing a contact lens in the nonoperative eye or has already demonstrated his ability to accept monovision, then an exception can be made to the general rule. However, should the patient be unable to continue wearing a contact lens, the necessary glasses for binocular correction may be intolerable, and additional refractive surgery may be required.

Special Limitations of IOL Power Calculation Formulas
As discussed previously, the third-generation formulas (Holladay 1, Hoffer Q, and SRK/T) and the new Holladay 2 are much more accurate than previous formulas for the more unusual the eye. Older formulas such as the SRK1, SRK2, and Binkhorst 1 should not be used in these cases. None of these formulas will give the desired result if the central corneal power is measured incorrectly. The resulting errors are almost always in the hyperopic direction following keratorefractive surgery, because the measured corneal powers are usually greater than the true refractive power of the cornea.

To further complicate matters, the newer formulas often use keratometry as one of the predictors to estimate the ELP of the IOL. In patients who have had keratorefractive surgery, the corneal power is usually much flatter than normal and certainly flatter than before the keratorefractive procedure. In short, a patient with a 38 D cornea without keratorefractive surgery would not be expected to be similar to a patient with a 38 D cornea with keratorefractive surgery. Newer IOL calculation programs are now being developed to handle these situations and will improve our predictability in these cases.

Intraoperative Visualization and Corneal Protection
Intraoperative visualization is usually more difficult in patients with previous RK than in the normal cataract patient and is somewhat similar to severe arcus senilis or other conditions that cause peripheral corneal haze. The surgeon should be prepared for this additional difficulty by making sure that the patient is lined up to visualize the cataract through the optical zone. This usually means lining the microscope perpendicular to the center of the cornea, so that the surgeon is looking directly through the optical zone at the center of the cataract. When removing the peripheral cortex, the eye can be rotated so that visualization of the periphery is through the central optical zone. It is also prudent to coat the endothelium with viscoelastic to minimize any endothelial cell loss, since the keratorefractive procedure may have caused some prior loss.

Intraoperative Autorefractor/Retinoscopy
Large refractive surprises can be avoided by intraoperative retinoscopy or handheld autorefractors. These refractions should not be relied upon, however, for fine-tuning the IOL power because there are many factors at surgery that may change in the postoperative period. Factors such as the pressure from the lid speculum, axial position of the IOL, intraocular pressure may cause the intraoperative refraction to be different than the final stabilized postoperative refraction. If the intraoperative refraction is within 2 D of the target refraction, no lens exchanges should be considered unless intraoperative keratometry can also be performed.

Postoperative Evaluation

Refraction on the First Postoperative Day On the first postoperative day following cataract surgery, patients who previously have had RK usually have a hyperopic shift, similar to the first postoperative day following their RK. This phenomenon is primarily due to the transient corneal edema that usually exaggerates the RK effect. These patients also exhibit the same daily fluctuations during the early postoperative period after their cataract surgery as they did after the RK. Usually, this daily shift is in a myopic direction during the day due to the regression of corneal edema after awakening in the morning.¹⁹ Because the refractive changes are expected and vary significantly among patients, no lens exchange should be contemplated until after the first postoperative week or until after the refraction has stabilized, whichever is longer.

Very few results of cataract surgery following PRK and LASIK are available. In the few cases that have been performed, the hyperopic shift on the first day and daily fluctuations appear to be much less, similar to the early postoperative period following these procedures. In most cases, the stability of the cornea makes these cases no different than patients who have not had keratorefractive surgery.

Long-term Results
Long-term results of cataract surgery following RK are very good. The long-term hyperopic shifts and development of against-the-rule astigmatism over time following cataract surgery should be the same as in the long-term studies following RK. The problems with glare and starburst patterns are usually minimal because the patients have had to adjust to these unwanted optical images following the initial RK. If the patient's primary complaint before cataract surgery is glare and starbursts, it should be made clear to the patient that only the glare due to the cataract will be eliminated by surgery, and the symptoms that are due to the RK will remain unchanged.

Long-term results following PRK and LASIK are nonexistent. Because there are no signs of hyperopic drifts or development of against-the-rule astigmatism in the 5-year studies following PRK, one would not expect to see these changes. However, the early studies following RK did not suggest any of these long-term changes either. Only time will indicate whether complications such as central haze or irregular astigmatism will develop in the future.

IOL Calculations Using Keratometry Readings and Preoperative Refraction

Formula and Rationale for Using Preoperative Refraction versus Axial Length
In a standard cataract removal with IOL implantation, the preoperative refraction is not helpful in calculating the power of the implant because the crystalline lens will be removed; dioptric power is being removed and then replaced. In cases in which no power is being removed from the eye, such as secondary implant in aphakia, piggyback IOL in pseudophakia, or a minus IOL in the anterior chamber of a phakic patient, the necessary IOL power for a desired postoperative refraction can be calculated from the corneal power and preoperative refraction - the axial length is not necessary. The formula for calculating the necessary IOL power is given below²⁰:

where ELP = expected lens position in mm (distance from corneal vertex to principal plane of intraocular lens), IOL = intraocular lens power in diopters, K = net corneal power in diopters, PreRx = preoperative refraction in diopters, DPostRx = desired postoperative refraction in diopters, and V = vertex distance in mm of refraction.

Calculation From Preoperative Refraction
As mentioned above, the appropriate cases for using the preoperative refraction and corneal power include secondary implant in aphakia, secondary piggyback IOL in pseudophakia, and a minus anterior chamber IOL in a high myopic phakic patient. In each of these cases, no dioptric power is being removed from the eye, so the problem is simply to find the IOL at a given distance behind the cornea ELP that is equivalent to the spectacle lens at a given vertex distance in front of the cornea. If emmetropia is not desired, then an additional term, the desired postoperative refraction (DPostRx), must be included. The formulas for calculating the predicted refraction and the back-calculation of the effective lens position ELP are given in the reference and will not be repeated here.²⁰

Example: Secondary Implant for Aphakia
The patient is 72 years old and is aphakic in the right eye and pseudophakic in the left eye. The right eye can no longer tolerate an aphakic contact lens. The capsule in the right eye is intact and a posterior chamber IOL is desired. The patient is -0.5 D in the left eye and would prefer to be the same in the right eye.

        Mean keratometric K = 45 D
        Aphakic refraction = +12 sphere @ vertex of 14 mm
        Manufacturers ACD lens constant = 5.25 mm
        Desired postoperative refraction = -0.5 D

Each of the values above can be substituted in the refraction formula except for the Manufacturers ACD and the measured K reading. The labeled values on IOL boxes are primarily for lenses implanted in the bag. Because this lens is intended for implantation in the sulcus, 0.25 mm should be subtracted from 5.25 mm to arrive at the equivalent constant for the sulcus. The ELP is therefore 5 mm. The K reading must be converted from the measured keratometric K reading (n = 1.3375) to the net K reading (n = 4/3), for the reasons described previously under corneal topography. The conversion is performed by multiplying the measured K reading by the following fraction:

        Mean refractive K = Mean keratometric K 3 fraction
        Mean refractive K = 45.00 3 0.98765 = 44.44 D

Using the mean refractive K, aphakic refraction, vertex distance, ELP for the sulcus, and the desired postoperative refraction, the patient needs a 22.9 D IOL. A 23 D IOL would yield a predicted refraction of -0.57 D.20

Example: Secondary Piggyback IOL for Pseudophakia In patients with a significant residual refractive error following the primary IOL implant, it is often easier surgically and more predictable optically to leave the primary implant in place and calculate the secondary piggyback IOL power to achieve the desired refraction. This method does not require knowledge of the power of the primary implant or the axial length. This method is particularly important in cases where the primary implant is thought to be mislabeled. The formula works for plus or minus lenses, but negative lenses are just becoming available at this time.

The patient is 55 years old and had a refractive surprise after the primary cataract surgery and was left with a +5 D spherical refraction in the right eye. There is no cataract in the left eye and he is plano. The desired postoperative result is -0.5 D, which was the target for the primary implant. The refractive surprise is believed to be from a mislabeled IOL, which is centered in the bag and would be difficult to remove. The secondary piggyback IOL will be placed in the sulcus, because trying to place the second lens in the bag several weeks after the primary surgery is difficult. More importantly, it may displace the primary lens posteriorly, reducing its effective power and leaving the patient with a hyperopic error. Placing the lens in the sulcus minimizes this posterior displacement.

        Mean keratometric K = 45 D
        Pseudophakic refraction = +5 sphere @ vertex of 14 mm
        Manufacturers ACD lens constant = 5.25 mm
        Desired postoperative refraction = -0.50 D

Using the same style lens and constant as the previous example and modifying the K reading to net power, the formula yields a +8.64 D IOL for a -0.50 D target. The nearest available lens is +9.0 D which would result in -0.76 D. In these cases, extreme care should be taken to ensure that the two lenses are well centered with respect to one another. Decentration of either lens can result in poor image quality and can be the limiting factor in the patient's vision.

Example: Primary Minus Anterior Chamber IOL in a High Myopic Phakic Patient
The calculation of a minus IOL in the anterior chamber is no different than the aphakic calculation of an anterior chamber lens, except the power of the lens is negative. In the past, these lenses have been reserved for high myopia that could not be corrected by RK or PRK. Because most of these lenses fixate in the anterior chamber angle, concerns of iritis and glaucoma have been raised. Nevertheless, several successful cases have been performed with good refractive results. Because successful LASIK procedures have been performed in myopias up to -20 D, these lenses may be reserved for myopia exceeding this power in the future. Interestingly, the power of the negative anterior chamber implant is very close to the spectacle refraction for normal vertex distances.

        Mean keratometric K = 45 D
        Phakic refraction = -20 sphere @ vertex of 14 mm
        Manufacturers ACD lens constant = 3.50 mm
        Desired postoperative refraction = -0.50 D

Using an ELP of 3.5 and modifying the K reading to net corneal power yields -18.49 D for a desired refraction of -0.5 D. If a -19 D lens is used, the patient would have a predicted postoperative refraction of -0.1 D.

References

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