Accurate lens position, corneal power needed for calculations in post-refractive surgery patients

Surgeons implanting IOLs in patients who have undergone corneal refractive surgery must be precise in their measurements and calculations.

Calculating the correct IOL power for a patient who has undergone previous corneal refractive surgery is a challenge. Miscalculations in these patients have led in some cases to large “refractive surprises” requiring lens exchange or a secondary piggyback IOL, said Jack T. Holladay, MD, MSEE, FACS.

To prevent these surprises from occurring, surgeons must be precise in obtaining preoperative measurements and exact in their prediction of the effective lens position (ELP) in order to achieve the best surgical outcome, Dr. Holladay said.

“Carrying out successful cataract surgery, refractive lens exchange or phakic IOL implantation after LASIK, PRK, RK or LASEK requires the right ingredients,” he said. “You need to know the ELP and the net corneal power. These two variables are the most difficult to determine precisely of the four preoperative variables (axial length, keratometry, ELP and desired postoperative refraction) necessary to calculate the proper IOL power.”

Average ELP

The average ELP, or manufacturer’s lens constant, for each IOL is listed on the product packaging, along with the A-constant and the surgeon factor. Dr. Holladay noted that most IOL manufacturers misleadingly refer to the ELP as the “anterior chamber depth,” or ACD. He said this label is an antiquated misnomer because it refers to the anterior chamber depth of the eye, when the measurement actually represents the effective lens position of the IOL relative to the corneal vertex.

The ELP measurement provided by lens manufacturers is the average value of the position of the IOL within the eye when measured from the corneal vertex, Dr. Holladay said. The ELP value for each lens model or style is averaged from data collected from thousands of patients, he said.

The ELP and surgeon factor measurements are expressed in millimeters, while A-constants are expressed in diopters. Although these factors are measured in different units of measurement, all are equivalent in value. Each can be converted to the other types of measurements, like a linear distance converted from feet to meters, Dr. Holladay said.

Conversion formulas from A-constant to ELP and surgeon factor are as follows:

ELP =	(Aconst * 0.5663) – 65.600 + 3.595
	0.9704

SF = (Aconst * 0.5663) – 65.600

Dr. Holladay noted that inconsistent values for A-constant and ELP occasionally appear on IOL packaging because the manufacturer has not updated the lens constants with a conversion formula that he developed in 1997.

“When the converted lens constants are inconsistent, it is usually because one value (usually ACD/ELP) is for in-the-sulcus positioning and the other is for in-the-bag. If you find a set of lens constants for an IOL that are not consistent, then the higher value is usually the best value and is for in-the-bag placement,” he said.

Determining individual ELP

IOL power calculation formulas use the manufacturer’s ELP to help predict the specific ELP for each patient, he said. Individual ELP is determined by starting with the manufacturer’s ELP for the average patient and then using preoperative biometric measurements to determine the value for the specific patient.

The Holladay II formula, a fifth-generation IOL formula introduced by Dr. Holladay in 2000, factors in the patient’s axial length, keratometry, horizontal corneal diameter, lens thickness, preoperative refraction and age, in addition to the lens model’s ELP, to determine the individual ELP for the patient.

In the course of developing the Holladay II formula, Dr. Holladay found that the horizontal corneal diameter (commonly called the white-to-white measurement) is a key anatomical factor that is helpful in predicting individual ELP.

“The corneal white-to-white measurement is probably the most important element in judging the size of the anterior segment and indicating the depth of the IOL within the eye,” Dr. Holladay said.

The average horizontal white-to-white measurement in a normal eye is 11.7 mm, he said.

“Ninety-five percent of people have a white-to-white measurement between 12.5 mm and 10.8 mm,” Dr. Holladay said. “Patients with a measurement of 12.5 or greater have a large anterior segment, while patients with 10.5 mm or less have a small anterior segment.”

Nine types of eyes

In doing the research that led to the Holladay II formula, Dr. Holladay found that there is little correlation between the size of the anterior segment – small, normal or large – and the patient’s axial length.

“We used to think that these two factors, anterior segment and axial length, were proportional,” Dr. Holladay said. “But we determined that the size of the anterior segment and the length of the eye in the posterior compartment are far enough apart that they only correlate about 10% to 20% of the time.”

This finding led to the conclusion that, instead of three types of eyes (small, normal or large), there are nine possible types of eyes, with three sizes of anterior chamber and the additional independent variable of short, normal or long axial length. (See accompanying chart above.)

“With this system, we determined that 80% of short eyes and 90% of long eyes have normal anterior segment sizes,” Dr. Holladay noted.

Building these differentiations in the types of eyes into the Holladay II enabled the formula to predict ELP more accurately in shorter eyes, Dr. Holladay said. This helped surgeons avoid the“5 D surprise” that was often caused by ELP formulas that preceded the Holladay II formula, he said.

The ELP, the predicted position of the IOL within the eye, is an important factor in modern IOL formulas because it is the only variable that cannot be measured or chosen by the surgeon, Dr. Holladay said. The surgeon has no control over the prediction of the ELP for a specific patient other than choosing the formula for the calculation, he said.

The Holladay II formula uses seven variables to predict the ELP (axial length, keratometry, horizontal white-to-white, anterior chamber depth, lens thickness, age and current refraction of the patient). The original Holladay I uses two (axial length and keratometry) as do other third-generation formulas such as the Hoffer Q and SRK/T, he said.

The additional five measurements are especially helpful in precisely predicting the ELP in short eyes (< 22 mm), he said.

Once the IOL formula has been chosen; the corneal power, axial length, white-to-white, ACD and lens thickness have been measured; age and current refraction have been determined; and the desired postoperative refraction chosen, all of the necessary ingredients are ready to be entered into the vergence formula. The accurate determination of the net corneal power of the front and back surfaces of the cornea can be achieved with tomography and calculations detailed in this article.

“The vergence formula (shown below), relating the targeted refraction, IOL, corneal power, individual ELP and the retina is more than 140 years old,” Dr. Holladay said. “The only difference in today’s theoretical formulas is the method of predicting the ELP.”

Axial length in long eyes

Dr. Holladay said the surgeon must be “extra cautious” in measuring axial length in long eyes.

“Eyes with axial lengths that are 26 mm or longer can have a myopic staphyloma. This means that the scleral fibers in the back of the sclera, where the fovea is, are weakened and bulge out,” he said.

Traditional ultrasonic measurements, which measure axial length to the deepest point where the ultrasound wave is perpendicular to the retina, can scan deep into a staphyloma and may miss the fovea completely, he said.

“In highly myopic patients with staphyloma, the fovea can be mid-way up the staphyloma or on the rim,” Dr. Holladay said. As a result, he said, the anatomic axial length (at the posterior pole) can be up to 3 mm longer than the optical axial length (at the fovea).

“For every millimeter difference between the optical axial length and the anatomic axial length we make a 2.5 D to 3 D surprise,” Dr. Holladay said.

In the Journal of Cataract and Refractive Surgery in 2000, Dr. Holladay and Roberto Zaldivar, MD, reported on this finding. They found that patients with axial length measurements greater than 26.5 mm (up to 35 mm) had anatomic and optical axial lengths that differed by up to 3 mm, which would cause a 9 D error in the power of their IOL.

To avoid this problem, Drs. Holladay and Zaldivar said surgeons should measure patients with long eyes (26 mm or more in length) with light instead of ultrasound. A partial interferometry device such as the Carl Zeiss Meditec IOLMaster can accurately measure axial length to the fovea by allowing patients to fixate on a target, he said.

“It is crucial that you measure highly myopic long eyes with light. The IOLMaster is the only currently available technology that uses light and not ultrasound,” Dr. Holladay said. He noted, however, that the IOLMaster cannot measure eyes with dense cataract, because opacification prevents the coherent light from forming a measurable interference pattern. In these patients, ultrasound is the only option.

Central corneal measurement

After the anatomic factors explained above have been accurately measured, corneal power must be determined before the IOL power can be calculated correctly, Dr. Holladay said. He said it is particularly difficult to determine the corneal power of an eye that has undergone corneal refractive surgery such as LASIK, PRK, or RK because the traditional tools surgeons have to measure corneal power are inadequate; they were originally created to measure the corneal power of an unaltered cornea.

“Our current instruments don’t give us an accurate measurement of corneal power,” Dr. Holladay said. Keratometers and topographers are limited in their ability to measure surgically treated corneas because they take paracentral measurements and do not truly measure the center of the cornea.

“There is very little correlation between the paracentral measurement and what’s going on in the center of the cornea,” Dr. Holladay said. “Topographers and keratometers have a central scotoma from 1.5 to 3 mm in diameter where no measurements are taken, and this central area is the most important in the patient’s vision and the true corneal power.”

The center of the cornea is the most critical area for calculating the corneal power of a patient who has had refractive surgery, he said, and yet it is the one area that is not truly measured by the available technologies. These tools miss this critical zone, which increases in size with the amount of refractive surgical correction.

“On the average patient with a 44 D cornea, the keratometer measures 3.2 mm apart in diameter,” Dr. Holladay said. “This means, at the corneal center, everything less than 3.2 mm in diameter is lost. This isn’t a problem in a patient who hasn’t had corneal refractive surgery, but in a refractive patient not measuring the central area causes a significant error.”

For example, he said, a patient with a cornea that measures at 36.5 D after –10 D laser surgery actually has a central anterior corneal power that is 15% of his refractive change flatter (–10 × 15% = –1.5 D) than a patient with a 36.5 D cornea who has not had surgery. The refractive surgery patient who has had the –10 D LASIK and measures 36.5 D is actually about 35 D (36.5 – 1.5) in the center of the anterior cornea, Dr. Holladay said.

Deriving net power

A second limitation of keratometers and topographers is that they fail to measure the posterior surface of the cornea, which is needed for calculating net corneal power.

“Topographers and keratometers only measure the front surface of the cornea,” Dr. Holladay said. “They assume that the back and front surface power of the cornea are equal. This isn’t true, of course. The back radius of the cornea is steeper than the front, approximately 82% of the front radius of the cornea.”

Most IOL formulas and programs use a keratometric index of 1.3375 when converting from corneal power to radius using the keratometric formula below:

337.5/radius of curvature of the
cornea (in mm) = power of the cornea

Being aware of net power, the authors of IOL formulas have compensated for the front-and-back corneal ratio by reducing the keratometric power (1.3375) of the cornea to a net power by using a “net” index of refraction, Dr. Holladay said.

“Unfortunately, there is no exact agreed-upon value for this,” he said, “so the net index refraction varies from 1.3315 to 1.3333 depending on the IOL formula.”

This results in reducing the keratometric power of the cornea by 0.3315/0.3375 or 0.3333/0.3375, depending on the formula, to 98.22% or 98.76% of the measured power. For a keratometric power of 44 D, the net value would be from 43.22 to 43.45 D, which is 0.55 to 0.78 D less than the measured keratometric power, he said.

“The power has to be reduced, otherwise the power of the cornea will be overestimated,” Dr. Holladay said.

After corneal refractive surgery, the back surface of the cornea is no longer 82% of the front surface, as it is in a normal cornea. Therefore, there is a second error in the net corneal power, which is 10% of the refractive change (from the above example, –10 D × 10% = 1 D).

The peripheral sampling error outlined above equals 15% of the refractive surgery treatment, and the change in the ratio of the back to front surface adds another 10%, so the total error in the keratometric reading is 25% (15% + 10%) of the effect of the refractive surgery. So a patient with a keratometry reading of 36.5 D after a –10 D LASIK is actually 34 D (36.5 – 25% × –10).

Corneal power calculations

Because, on their own, keratometric and topographic measurements of the cornea are inadequate after corneal refractive surgery, Dr. Holladay has published four mathematical methods to determine and validate the true power of the cornea in these patients.

“The four methods are the historical method, two modified historical methods and the hard contact lens method,” Dr. Holladay said. “While none of these is perfect, they are better than using the keratometric or topographic reading.”

In the examples that follow, the same corneal power measurement (39.50 D) is derived as the answer by each of the four methods. In a “perfect world,” Dr. Holladay said, the answers would always be equivalent, thereby making it easy for the surgeon to choose the corneal power to plug into the vergence formula. However, he said, in real life the corneal powers derived from the historical and contact lens methods are “rarely” the same numeric value when calculated for a single patient.

“After myopic surgery, the corneal measurements are never the same,” he said. “So you should always use the flattest power that you get. This avoids getting a refractive surprise later on, because you avoided believing that the cornea was steeper than it really was.” After hyperopic refractive surgery the opposite is true, because the true corneal power is higher than the measured value, he said.

Historical methods

Using the historical method, the surgeon subtracts the patient’s surgically induced refractive change from the preoperative keratometry reading to determine the current corneal power.

“So if the patient was a –4 D myope with 44 D of corneal power before surgery and turned out to be +0.50 D after surgery, he underwent a –4.5 D change,” Dr. Holladay explained. “You should be able to subtract this change from the preoperative K-reading, which would give you a corneal power of 39.50 D.”

In the first modified historical method, the keratometry reading is used, along with the surgeon’s “best guess” at the refractive change, if preop keratometry readings are not available. As in the example above, where 25% of the power of the refractive change was used to compensate for paracentral sampling and the change in front and back ratio of the corneal surfaces, Dr. Holladay said 25% of the power of the refractive change is subtracted from the keratometric measurement.

“The keratometer after myopic refractive surgery makes an overestimate of the corneal power by 25% of the refractive change,” he said. “If you get a measurement of 40.58, with 4.5 D as the refractive change, you take 25% of that value, which is 1.08. Subtract this value from 40.58 and you again get 39.50 D,” Dr. Holladay said. “This is the corneal power that you enter into your IOL program.”

In the second modified historical method, topography is used instead of keratometry.

“Topography gets closer to the center of the cornea than does keratometry, so the topographer reading needs to be reduced by only 15% of the refractive change rather than 25%,” Dr. Holladay said. “Therefore, if the topographer central refractive power were 40.18, then 15% of the –4.50 D refractive change is –0.68 D, so the calculated power would be 39.50 D.”

When obtaining the topography measurements, Dr. Holladay said, the surgeon should be careful not to use the simulated Ks from the topographer. These measurements are identical to keratometry measurements.

“Use the central refractive power as reported by the topographer,” he said. “Even though it doesn’t truly know what the central corneal measurements are, it extrapolates them. If the measurements don’t automatically come up on the map, click on the central area with your mouse a few times and take an average of those values.”

Contact lens method

In the fourth calculation method, a rigid contact lens is used. Dr. Holladay gave the example of a patient whose refraction is ì0.50 after refractive surgery. If this changes to a refraction of –0.5 D with a 41 D contact lens in place on the cornea, the front corneal curvature must be 1 D flatter than 41 D or 40 D (41 D – 1 D = 40 D).

The contact lens method does not compensate for the change in back-to-front surface ratio, Dr. Holladay said, “so once you get this sum, you still need to reduce by about 10%, just like with topography, because the back surface of the cornea is not consistent with the front. This leaves you with a value of 39.55. That’s the calculated power.”

Measuring front and back

Until better ways of measuring and calculating the total net power of the cornea are available, surgeons must rely on one or more of these calculations to determine corneal power. But Dr. Holladay said that in the very near future surgeons may have a tool available that will eliminate the need for calculations by accurately measuring the front and back surfaces of the cornea.

The Pentacam, from Oculus, “has the potential to be four to five times more accurate in measuring corneal power than any of the historical or contact lens methods, because it measures the back radius curvature of the cornea as well as the front,” Dr. Holladay said.

The Pentacam measures the tomography of the cornea by taking 50 meridional Scheimpflug images. Dr. Holladay explained.

“The device eliminates eye movement by having a consistent central point, so it makes the precision of the instrument far more accurate than any other tomographer I’ve ever seen,” he said.

In a study he conducted, Dr. Holladay determined that the net power of the cornea can be measured by the Pentacam to within ±0.55 D.

“We can measure a cornea that has undergone corneal refractive surgery to within ±0.5 D of its actual power,” he said.

Dr. Holladay is currently working with Oculus to incorporate a display into the Pentacam called the Holladay Report, which he said will accurately calculate the front and back surface powers of the cornea, adjust for any power overestimate, and report a term called the equivalent keratometric reading, or EKR.

When this report is incorporated into the Pentacam software, he said, surgeons will be able to use the EKR in IOL calculation software just as they would a standard keratometry reading.

For Your Information:

• Jack T. Holladay, MD, MSEE, FACS, can be reached at Holladay LASIK Institute, Bellaire Triangle Building, 6802 Mapleridge, Suite 200, Bellaire, TX 77401; 713-668-7337; 713-668-7336; e-mail: docholladay@docholladay.com; www.docholladay.com.

References:

• Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg. 1997;23(9):1356-1370.
• Zaldivar R, Shultz MC, et al. Intraocular lens power calculations in patients with extreme myopia. J Cataract Refract Surg. 2000;26; 668-674.
• Holladay JT. Intraocular lens power calculations for the refractive surgeon. Operative Techniques in Cataract and Refractive Surgery. 1998;1:105-117.

• Carl Zeiss Meditec, maker of the IOLMaster, can be reached at 5160 Hacienda Drive, Dublin CA 94568; 877-486-7473; fax: 925-557-4778; Web site: humphrey.com.
• Oculus Inc., maker of the Pentacam, can be reached at Oculus Optikgeräte GmbH, Münchholzhäuser Str. 29, D-35549 Wetzlar, Germany; 49-641-2005-0; fax: 49-641-2005-255; e-mail: sales@oculus.de.

• Nicole Nader is an OSN Correspondent based in Philadelphia, who is writing the QOV series.