Dr. Wolfgang Haigis
Head of the Biometry Department
University of Wurzburg Eye Hospital
Users Group for Laser Interference Biometry (ULIB)
One of the final frontiers in ophthalmology is the consistently accurate calculation of intraocular lens power for all eyes. When correctly “personalized,” any of the modern IOL power calculation formulas will do a good job for eyes with a normal anterior segment. However, for eyes where the anterior segment may be abnormal in some way (influencing the effective lens position), consistently accurate IOL power calculations have remained elusive.
The following link offers a free Excel spreadsheet that you can use to derive your own set of a0, a1, and a2 Haigis formula IOL constants and instructions for submitting this data to Dr. Hill in North America or Dr. Haigis in Europe: Haigis Formula Optimization
IOL Constants and IOL Power Prediction
For most formulas, the shape of their IOL power prediction curve is fixed. For a given lens, constants and a pair of axial length and central corneal power measurements, the IOL power predicted will always be the same. Another equally inflexible feature is that the larger the IOL constant, the more IOL power each formula will recommend for the same set of measurements; the smaller the IOL constant, the less IOL power the same formula will recommend for the same set of measurements. Other than the lens constant, these formulas treat all IOLs as if they were the same and make similar assumptions for all eyes regardless of individual differences.
In reality, two eyes with the same axial length and the same keratometry may require completely different IOL powers for emmetropia. This is due to two additional variables: the actual (not assumed) distance of the lens from the cornea (known as the effective lens position) and the individual geometry of each lens model. Commonly used lens constants do not account for this. These include:
- Hoffer Q Formula uses “Pseudophakic Anterior Chamber Depth”
- Holladay 1 Formula uses “Surgeon Factor”
- Holladay 2 Formula uses “Anterior Chamber Depth”
- SRK/T Formula uses “A-constant”
Knowing one of these lens constants, it is possible to approximate another. In this way, surgeons can move from one formula to another for the same intraocular lens implant. However, the shape of the power prediction curve generated by each formula remains the same no matter which IOL is being used. However, variations in keratometers, ultrasound machine settings, and surgical techniques (such as capsulorrhexis configuration) can all impact the refractive outcome as independent variables. “Personalizing” the lens constant for a given IOL and formula can be used to make global adjustments for a variety of practice-specific variables.
An exception to all of this is the Haigis Formula, which is included in the software packages of many biometers. Rather than moving a fixed, formula-specific IOL power prediction curve up (more IOL power recommended) or down (less IOL power recommended), the Haigis Formula instead uses three constants (a0, a1, and a2) to set both the position and the shape of a power prediction curve. Why is this important?
Why Three Lens Constants?
For the Haigis formula, the a0 constant moves the power prediction curve up or down, in much the same way as the SRK/T A-constant. The a1 constant is tied to the measured anterior chamber depth, and the a2 constant is tied to the measured axial length. Both the a1 and the a2 constants are used to vary the shape of the power prediction curve, changing the power based on the central corneal power, anterior chamber depth, axial length, and individual lens geometry.
One little-appreciated reality is that the geometry of many IOL models may vary for different powers. When this is the case, it would be helpful if a formula could take this information into account. It is not uncommon for some IOLs to have a shift in the lens constant by more than 1.00 D at the low end of the power range. With three lens constants, the Haigis formula can make adjustments, adding or subtracting power when necessary, based on actual observed results for a specific surgeon and the individual geometry of an intraocular lens implant. All of this gives the Haigis Formula a new level of mathematical flexibility not yet seen in ophthalmology.
