Module 2 Section 3

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Module 2:

Section 3:

Introduction

Types of formulas

• Regression

• Theoretical

• Holladay

• Hoffer Q

• SRK/T

Regression formula calculations

Regression formula compensation

• Table

Emmetropia and ammetropia

Post RK calculations

• History method

• Contact lens method

Introduction

When intraocular lenses were first becoming a viable alternative to aphakic after cataract removal, back in the 1970's,  the IOL power was estimated by consulting a chart of expected outcomes given a patient's refractive history.  It soon became obvious that this method was inadequate and formulas were developed based on keratometry readings, axial length, and past results.  Formulas continue to improve and are now based on theoretical optical models.

Types of formulas

Regression:   Regression formulas are based upon mathematical analysis of a large sampling of post-operative results.  The most familiar regression formula is the SRK formula. The basic SRK formula  works well for eyes in the "average" measurement range; 22.5 to 25.0 mm in axial length, with certain combinations of K readings.  The formula does not work well for "long" (>25 mm) or "short" (<22.5 mm) eyes. 

The advantage of a simple regression formula is that it is relatively simple to calculate.  A factor can be added to a simple regression formula to compensate for a long or a short eye.

Theoretical:   Theoretical formulas are optical formulas based on the optical properties of the eye.  They do a better job of predicting post-op outcomes for long and short eyes.

There are three widely used theoretical formulas, each with their own strengths and weaknesses.  These formulas are included in various combinations  with many A-scan instruments.  They are also  available in software products.

Holladay -- Produced by Jack Holladay MD.  It has been considered to be most accurate for eyes with an axial length between 22 and 26mm.  Available in Holladay IOL Consultant (HIC) V2.2 software.  This software has the other two major formulas and will perform calculations with all three. The software will also do calculations for piggyback IOLs, post-refractive surgery patients, and personal constants for the surgeon.  The latest version of the software, called Holladay II, requires the pre-op refraction, the anterior chamber depth, the lens thickness, and the "horizontal white-to-white"  (corneal diameter), as well as the K's and axial length.  The software claims that the additional information improves accuracy. The anterior chamber depth and the lens thickness can be obtained from most A-scan instruments in the process of obtaining the axial length measurement. The software costs $995 and can be ordered by phone (713-668-6828)

Hoffer Q -- Produced by Kenneth Hoffer MD.  It has been considered to be the most accurate formula for short eyes and does well for eyes shorter than 24.5mm.  Available in Hoffer Programs V2.2 software.  This software also has the other two major formulas and will perform calculations with all three.  It recommends the best calculation based on axial length.  It will also calculate a personal constant for the surgeon.   The software costs $750 and is available by phone (310-451-2020) or over the internet at icatmall.com/eyelab.

SRK/T --   Produced by Donald Sanders MD.  It has been considered to do a good job at predicting the outcome for long eyes (>26mm).  An updated version is on the way.   The current version is available with the other two packages.

Calculations with the SRK (regression) formula

As stated earlier, the advantage of the old SRK formula is its simplicity.  Of course, that is its downfall too, when dealing with long and short eyes.  Knowing how to work the formula can come in handy if you are in a situation in which you are without access to a theoretical formula.  The SRK formula is accurate on eyes in the "average" range, and it can have good accuracy on long and short eyes if a compensating factor is used.  The basic formula is:

A-2.5L-.9K

A = IOL constant,  L = axial length,  K = average K reading

Example calculation --  IOL constant = 118.0, axial length = 23.2,   K1 = 44.50, K2 = 42.25.

2.5 x the axial length is 23.2 x 2.5 = 58

The average K is 43.37.     43.37 x .9 = 39.03

118.0 - 58.0 = 60.0       60.0 - 39.03 = 20.97

The recommended IOL power for emmetropia would be +21.  The formula can be used un-modified with good success for a large percentage of patients.  A compensation factor should be added for eyes that are out of the "normal" range.

Compensation for long and short eyes -- Take a look at the table below.  This is a table of the approximate divergences between the SRK regression formula and the  theoretical formulas. For axial lengths greater than 26mm, the deviations are from the SRK/T formula. For axial lengths less than 23.5mm, the deviations are from the Hoffer Q formula, and for axial lengths between 23.5mm and 26mm, the deviations are from the Holloday I formula. Axial lengths from 20mm to 30mm are listed in the left column.   Average K readings from 40.00 to 47.00 are listed across the top.  Example:   for a 26 mm, 43.0 K eye you would subtract 1.25 D from the SRK calculation to approximate the Holladay calculation.

You can see from the table that you get into big problems with the regression formula as you go to the extremes.  For example, the SRK calculated power for a 41.00 K, 21 mm eye would be 4 D under-powered as compared to the Hoffer Q calculation.  The fact that there is not a one-to-one relationship between IOL power and refractive power tends to reduce the error rather than compound it.  That 4 D error in IOL power would result in a +2.75 D refractive error.

Emmetropia and ammetropia

Emmetropia (plano) is not always the desired result after cataract surgery.  Some people want to be nearsighted in one or both eyes.  Sometimes one eye has a cataract and the other does not.  Sometimes the fellow eye has already had surgery and has a significant refractive error.  If the the fellow eye has a significant refractive error, the surgeon may want to balance the operative result with the fellow eye.  For example, if the fellow eye has a -3.00 D refractive error,   the IOL power of the operated eye might be adjusted to give a -1.50 D post-op result.

Most IOL calculators will give you the IOL power needed for an ammetropic result of up to 1.5 D.  Notice that there is not a one-to-one relationship between IOL power and the refractive result.  If you want to make a 1.0 D change in refractive power, you will need to make about a 1.5 D change in the IOL power.  Adding IOL power makes the refractive result less plus, or more minus.  Subtracting IOL power makes the refractive result more plus, or less minus.  For example:

Suppose the calculator tells us that a +22.0 D IOL is needed for emmetropia.  We want the patient to be -2.00 after surgery.  Since we want the patient to be nearsighted, we will have to add power to the IOL.  Multiply 2 D by 1.5 to get 3.0.  We will add the 3 D to the +22.0 to get a +25.0 recommended IOL power for a -2.00 D refractive result.

Post Radial Keratotomy IOL calculations

Keratometry readings on the post-RK patient have proven to provide erroneous results when used with current IOL formulas. Calculating K readings by the "History Method" and the "Contact Lens Method" have provided improved accuracy. Almost all of the older RK patients are now significantly hyperopic. The cornea and refraction may be unstable for months after cataract surgery because of edema around the RK incisions.  Some of these patients may require a lens exchange.

These calculations are fairly complicated.  A software version is available with the Holladay IOL Consultant software as discussed above.

The History Method requires the following information:

1. Pre-RK refraction
2. Pre-RK K readings
3. Post-RK refraction (preferably current, but before significant cataract formation).

Procedure with example:

• Pre-RK refraction -6.00-1.00 x 90
• Pre-RK K readings  K1= 44.00  K2= 43.00
• Current refraction  +3.00-1.00 x 75

1. Convert the refractions to the spherical equivalent.  Pre-RK = -6.50, Post-RK = +2.50.
2. Adjust the refractions for zero vertex distance.  Pre-RK = -6.00, Post-RK = +2.50.
3. Calculate the change in refraction.  -6.00 to +2.50 equals a 8.50 D change.
4. Figure the average Pre-RK K reading.  43.50.
5. Calculate the corrected K reading.  Subtract the refractive change from the average K reading.  43.50 - 8.5 = 35.0.

The average K reading used in your IOL calculation would be 35.0.    Because of edema around the incisions, your patient may still be hyperopic post-op, even with the above adjustment. 

The Contact Lens Method can be used if Pre-RK information is not available.  The History Method is considered to be more accurate.  Requirements:

1. A current refraction. An accurate refraction is important.  This may be difficult if a significant cataract is present.
2. A hard contact lens is needed with a known power and a known base curve.  Preferably with a power close to plano and a base curve close to the patient's current K reading.
3. Over-refract with the contact lens on the cornea.

Procedure with example:

• Current refraction:  +2.00-1.00 x 180
• Over-refraction:  -2.00-0.50 x 180
• CL power +1.00
• CL base curve 40.00

1. Convert refraction to spherical equivalent: +1.50 and -2.25.
2. Calculate change in refraction: +1.50 to -2.25 is a -3.75 D change.
3. Algebraically add the change in refraction to the base curve of the contact lens: 40.00 - 3.75 = 36.25.
4. Adjust for the contact lens power.  Add a minus contact lens power to the result.  Subtract a plus contact lens power from the result.  36.25 - 1.0 = 35.25.

The average K reading in the IOL power calculation would be 35.25. 

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