Vertex distance is an essential component when determining the correct power for contact lenses, excimer laser treatments and phakic IOLs. The measurement should always be included in power calculations, said Jack T. Holladay, MD, MSEE, FACS.
“For prescriptions greater than a magnitude of 4 D, the accuracy of the vertex distance is extremely important in determining the necessary power because there is a significant difference between a glasses prescription and the equivalent power at the corneal plane or phakic IOL plane,” Dr. Holladay told Ocular Surgery News.
Jack T. Holladay

He said that not incorporating the vertex distance – the distance in millimeters from the posterior surface of the spectacle lens to the corneal vertex – into prescription calculations for large refractive errors can lead to incorrect powers at the corneal or phakic IOL plane.
“Neglecting to factor in vertex distance is often a major cause of incorrect power calculations with excimer laser treatments and phakic IOLs. Everyone who fits patients for contact lenses, performs laser ablation or phakic IOL implantation should know about vertex distance and the formulas to calculate the equivalent lens at another plane,” Dr. Holladay said.
For determining correction for errors larger than 4 D, he said, surgeons should perform overrefraction with a soft contact lens in addition to employing formulas that incorporate vertex distance.
“Using a soft contact lens for overrefraction guarantees predictability in your excimer surgery and phakic IOL procedures and rules out the largest source of error — inaccurate vertex distance,” Dr. Holladay said.
Focal length
When fitting a patient for contact lenses or determining treatment values for excimer laser correction, a simple subtraction formula is used to determine the new prescription. In this calculation, the vertex distance (usually about 12 mm) is subtracted from the focal length of the old lens at the spectacle plane to obtain the focal length of the new lens at the corneal plane. This formula is expressed as follows:
Power of any lens = 1000/focal length in mm of lens in air
Focal length of new lens = focal length of old lens in mm – vertex distance in mm
Power of new lens = 1/focal length in mm of new lens
Using this formula, a patient with –4 D of error with a vertex distance of 12 mm (expressed as 0.012 m) would have a focal length of –3.82 D, Dr. Holladay said, as shown here:
Power of any lens = 1000/– 4 = –250 mm
Focal length of new lens = –250 –12 = –262 mm (Note: Focal length and vertex are both negative)
Power of new lens = 1/(–262)= –3.82 D
“So a –4 D patient with 12 mm of vertex distance would need a little less than 0.25 D when moving from a spectacle prescription to a prescription at the corneal plane,” he explained.
(For contact lenses, which are available in 0.25D steps, the patient would be fitted for lenses with a power of –3.75 D, he noted.)
Conversely, a hyperopic patient with a glasses prescription of +4 D would have a new prescription of +4.20 D, as shown here:
Power of any lens = 1000/+4 = ± 250 mm
Focal length of new lens = +250 –12 = ± 238 mm
Power of new lens = 1/(± 238) = +4.20 D
Dr. Holladay pointed out that both myopic and hyperopic spectacle prescriptions become more positive when vertexed to the cornea as a result of these calculations.
“The plus lens becomes a bigger number and the minus lens becomes a smaller number, but both move in a positive direction when vertexed from the spectacle to the cornea,” he said.
Higher powers
Because prescriptions of 4 D or less have less than a 0.25 D difference when vertexed back to the corneal plane, Dr. Holladay said that there is “little concern” among surgeons that the difference in prescription power will be significant. However, he said, with errors above 4 D, getting an exact measurement for vertex distance is crucial to outcomes, although they can be “difficult to obtain.”
He noted that phoropters specify a vertex distance of 13.75 mm when the corneal vertex is aligned properly, but the vertex distance, even when the cornea is aligned properly, can vary significantly because different combinations of lenses are used in the phoropter to get a specific power.
“For higher prescriptions, such as –8 D or –10 D, the combination of lenses within the phoropter changes, and the refraction cannot be trusted. So, the 13.75mm vertex distance is not accurate, even when the corneal vertex is in the correct position,” Dr. Holladay explained. “For this reason, we recommend another method of calculation for the new corneal prescription.”
Soft contact lens method
Calculating the new prescription for patients with higher errors requires placing a soft contact lens of confirmed power on the cornea and performing overrefraction, Dr. Holladay said. The formulas described above are not used. The power obtained in the overrefraction can be added directly to the power of the contact lens used, provided it is less than ± 4 D and the vertex distance is considered to be zero, he said.
“To minimize the power of the overrefraction, surgeons should choose a myopic soft contact lens that is about 80% to 90% of the power of the patient’s prescription for minus lenses at the spectacle plane. The minus contact lens power is always less by about 10% to 20%,” Dr. Holladay explained. “For hyperopic powers, choose a plus soft contact lens that is 110% to 120% of the spectacle prescription. The power for a plus contact lens will always be greater by about 10% to 20%. Because the corneal vertex distance is zero, you can be sure your vertex distance is correct.”
Dr. Holladay said that determining the exact prescription for a patient with a spectacle prescription of –10.00 + 4.00 × 90 would be done as follows:
Place a –9 D soft contact lens on the patient’s eye (90% of –10 D). The only requirement for fit is that it centers well.
“The overrefraction is +0.25 +3.25 × 90, and the final prescription at vertex zero is therefore –8.75 D +3.25 × 90 (–9 added to +0.25 + 3.25 × 90º). Notice that both sphere and cylinder changed,” he said.
“This example raises the question of how to vertex a spherocylindric prescription,” Dr. Holladay continued. “In the above example, let us assume that the vertex is 14 mm for the spectacle prescription of –10.00 +4.00 × 90º. Can we vertex the –10 D and +4 D? No. In spherocylindrical prescriptions, it must be remembered that the cylindrical component is the difference in the principal powers, not the actual power in each meridian. In this example, the actual prescription in crosscylinder form is actually –10 D axis 180º and –6.00 axis 90º. Vertexing the –10 D through 14 mm we get –8.77 D, and vertexing the –6.00 D through 14 mm we get –5.53 D.”
These calculations can be written in three forms, he said:
Crosscylinder = –8.77 × 180º + –5.53 × 90º
Plus cylinder = –8.77 + 3.24 × 90º
Minus cylinder = –5.53 – 3.24 × 180º
Dr. Holladay said the three forms are all equivalent, but only the crosscylinder form has actual powers, and it is the only one that can be vertexed.
He noted that the above example illustrates why “assuming” the measurement of vertex distance is not wise.
“In this example, after performing all calculations, surgeons who did not use the soft contact lens and overrefraction can expect to have sizeable refractive surprises in their outcomes with corneal refractive surgery,” he said.
Phakic IOLs
Calculating the power for a phakic IOL is slightly more difficult than calculating higher powers at the corneal plane because the surgeon must begin with a prescription at the spectacle plane and vertex back through the corneal plane to the phakic IOL plane, whether in the anterior chamber, at the iris plane or in the posterior chamber.
“For phakic IOLs, a more complicated vertex calculation formula is necessary, which cannot be done by hand,” Dr. Holladay noted. The formula, which is reproduced in the accompanying box, was explained in full in an article by Dr. Holladay in the American Journal of Ophthalmology in 1993. Like many of the articles referenced in this series, the article is available on Dr. Holladay’s Web site.
The soft contact lens method with overrefraction can also be used to determine phakic IOL powers, Dr. Holladay said.
“It’s even more important to have accurate vertex measurements when dealing with extremely high refractive errors, up to ± 25 D, such as we see in candidates for phakic IOLs,” he said. “You must be exact.”
If a patient has a –25 D spectacle prescription at exactly 14 mm, the soft contact lens power would be –18.52 D (74% of the power at the spectacle plane). If a –20 D soft contact lens was used, the overrefraction would have been approximately ± 1.50, resulting in –18.50 D.
“Surgeons would then input the vertexed refraction at the corneal plane into their phakic IOL programs, noting zero as the vertex distance, and end up with their new IOL power (phakic IOL power would be approximately between –23.50 and –24.50, depending on the lens constant of the phakic IOL — close to the original spectacle refraction, but not close enough),” Dr. Holladay said.
He added that this method of calculation can also be used for determining power in secondary piggyback IOLs, which are placed in front of the primary IOL.
For Your Information: Jack T. Holladay, MD, MSEE, FACS, can be reached at the Holladay LASIK Institure, Bellaire Triangle Building, 6802 Mapleridge, Suite 200, Bellaire, TX 77401; (713) 6687337; (713) 6687336; email: docholladay@docholladay.com, Web: www.docholladay.com.
Reference:
 Holladay JT. Refractive power calculations for intraocular lenses in the phakic eye. Am J Ophthalmol. 1993;116:636.
 Nicole Nader is an OSN Staff Writer who covers all aspects of ophthalmology, specializing in QOV, pediatrics/strabismus and neuroophthalmology.