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Refractive Vergence Formula.

When both patient and surgeon are unhappy with the postoperative refraction following cataract surgery, removing the original intraocular lens may not always be the best approach. When the first IOL is within the capsular bag, an ideal solution may be to place another IOL in the ciliary sulcus. This second lens has come to be known as a "piggyback" IOL.

According to Holladay, there are several reasons why this approach may be better than a lens exchange. First, removing the original lens may rupture the capsule and/or loosen zonules. Second, inserting a piggyback lens is technically much easier than attempting a lens exchange. And third, the true cause of the refractive error is usually unknown. If the original lens was mislabeled, then a lens exchange may further compound the refractive problem.

Piggyback IOL

In 1993, Holladay elegantly described a method for pseudophakic and aphakic intraocular lens power calculations, independent of axial length.

Holladay JT:  Refractive Power Calculations for Intraocular Lenses in the Phakic Eye. AJO 1993; 116: 63-66

When significant refractive deviations are seen, the Refractive Vergence Formula is very helpful in understanding how much optical power must be added to, or subtracted from, an eye at the level of the anterior chamber, ciliary sulcus, or capsular bag. This formula also works well for the phakic and aphakic eye.

The power of the IOL to be implanted is determined by the following:

Holladay Formula

ELP o = effective lens position.
K o = net corneal power.
IOL e = IOL power.
V = vertex distance.
PreRx = pre-op refraction.
DPostRx = desired post-op refraction.

The Effective Lens Position (ELPo) is the distance from the secondary principal plane of the cornea to the principal plane of the thin-IOL equivalent. The keratometric power of the cornea (Kk) is converted to the net optical power of the cornea (Ko) as follows: Ko = Kk * 0.98765431

If the keratometric power (Kk) is 44.50 D, then...

Ko = 44.50 D * 0.98765431 = 43.95 D

The net optical power of the cornea (Ko) would then be 43.95 D

The following links will take you to our Physician Downloads, for an Excel spreadsheet used for calculating the Refractive Vergence Formula.


Let's say that during cataract surgery, the operating room staff mistakenly handed you a +22.00 D posterior chamber lens when the calculations called for a +18.00 D lens to be placed in the capsular bag (ELPo = 5.55 mm).

Not a surprise, the patient is now -3.25 D more myopic than planned. In spite of aniseikonic bases curves, the smallest eye-size possible and a very close vertex distance, the image disparity cannot be tolerated and she is requesting that you find some other solution.

With postoperative keratometry of 44.25/44.75 x 090, the Refractive Vergence Formula would tell you that a -4.00 D posterior chamber lens, placed in the ciliary sulcus (ELPo = 4.80), will achieve a postoperative refraction close to -0.25 D.

Another example. If an aphakic patient had a refraction of +12.50 D sphere (vertex distance of 10 mm) and keratometry of 45.00/45.00 x 090, it would take a +19.50 D anterior chamber IOL (ELPo = 3.50 mm) to achieve a postoperative refraction of approximately -0.25 D.

In our practice, we typically use the Refractive Vergence Formula for this type of IOL calculation.

The Holladay IOL Consultant has a much more sophisticated form of the Refractive Vergence Formula (known as Holladay R), which is highly recommended.


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Intraocular Lens Power Calculations

East Valley Ophthalmology
5620 East Broadway Road
Mesa, Arizona 85206

Tel: +1-480-981-6111
FAX: +1-480-985-2426

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