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Improving IOL power calculations


An advanced, self-validating method is providing a new approach to IOL power selection, explains Warren E. Hill, MD, FACS.

Take-home message: An advanced, self-validating method is providing a new approach to IOL power selection, explains Warren E. Hill, MD, FACS.

 Reviewed by Warren E. Hill, MD, FACS

Mesa, AZ-Every time ophthalmologists implant a multifocal lens, a toric lens, or even a monofocal lens-“where we absolutely positively have to get the power right”-the selection of IOL power is always playing in the background, said Warren E. Hill, MD, FACS.

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The continued emphasis on improving outcomes is to increase patient safety and reduce the many burdens associated with a refractive surprise, said Dr. Hill, in private practice, East Valley Ophthalmology, Mesa, AZ.

“If a patient ends up –4 D, it’s an annoyance for us, but can be a life-changing event for the patient,” he said.

Even with the most advanced metrics and the use of multiple theoretical formulas, there can still be problems with the selection of IOL power, according to Dr. Hill.

The simple fact is that no one gets the calculations right all the time, he noted. Refractive targets within 1 D are usually achieved, but the discrepancy between what was expected and what is reached for ± 0.50-D accuracy remains problematic.

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For more than a decade, Dr. Hill has reviewed physician databases for lens constant optimization from surgeons around the world, totaling now more than 260,000 optical biometry cases. Each physician submits between 200 and 300 cases, which typically represents their best work.

Less than 1% of surgeons have a refractive accuracy of 92% or better within ± 0.5D 92%. Six percent reach that level of accuracy 84% of the time, and the vast majority reaches that level of accuracy only 78% of the time, he noted.

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“If we’re in the business of putting in lens-based refractive IOLs, this is probably not good enough,” he said.

The “mathematical backbone” of all theoretical formulas is basically the same: Lens vergence equals image vergence minus object vergence.

Reoccuring difficulty


“The recurring difficulty with this approach is the power of the IOL inside the eye is relative and not absolute,” Dr. Hill said. “Inside the eye, a 21 D lens only acts as a 21 D lens a certain distance from the cornea.”

Place it a bit more anterior or posterior, and it will have a different relative power-that distance is more commonly referred to as the “effective lens position” (ELP) of an IOL, and represents a “significant part” of the accuracy of any theoretical formula calculations.

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“Theoretical formulas have to first estimate the position of the IOL inside the eye before performing the rest of the calculation,” Dr. Hill said. “And with regrets, the ELP is an unknowable quantity-something that can only be estimated and not directly measured.”

So, ophthalmologists are faced with the problem that preoperative measurements and the actual postoperative ELP are not always correlated.

Using that same 21 D example, a 0.5 mm mis-estimation of the ELP is a 1 D error at the plane of the capsular bag.

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“Try holding your fingers 0.50 mm apart and it’s easy to see how sensitive all of this can be,” Dr. Hill said. “The ELP remains a major limiting factor for all theoretical formulas.”

Changing calculations

Almost 20 years ago, Gerald Clarke, MD, an ophthalmologist in Wisconsin, showed that by using a completely different approach for IOL power selection, the accuracy could be improved by more than 80% over a conventional theoretical formula of the day-and this was before optical biometry and sophisticated keratometry were introduced, Dr. Hill said.

“That paper should have been a wake-up call, but it did not gain the attention it should have,” Dr. Hill said. “Looking back-it was a wonderful idea, but way ahead of its time.

However, Dr. Clark’s insights did lay the groundwork for a closer look at the concept of adaptive learning, by which a method for IOL power selection can be developed that is based solely on data and independent of what was previously known, Dr. Hill explained.

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“Such a method is well suited to the task of pattern recognition and complex nonlinear relationships,” he said.

With the sophisticated mathematical tools currently available, clinicians have the ability to think about lens calculations as a pattern, Dr. Hill noted.

“For any axial length, anterior chamber depth, central corneal power and IOL power producing a given post-operative spherical equivalent, we can approach this as pattern,” he said.

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Dr. Hill provided an example in which 1,000 seemingly random points were placed within a box, although these points were not actually random, but created using a “Manhattan distance” generator. In layman’s terms, imagine the city blocks of Manhattan as little squares.

Using a concept of feature extraction and feature matching, Dr. Hill described how a neural network was able to begin with a seemingly chaotic collection of points and demonstrate that it actually has a pattern.

“The neural network was able to establish this and create a self-organizing map,” he said.

Improving upon the original neural network concept from the 1940s is a somewhat different mathematical model, known as a radial basis function, Dr. Hill said. This concept handles nonlinear relationships and it does the best with the fewest amounts of necessary inputs, “which means it thinks for itself.”

New paradigm


And for the task of IOL power selection, this sophisticated form of data interpretation becomes an enormously powerful tool, he noted.

Though the terminology is novel for most ophthalmologists, the use of the radial basis function model is not-it is used for fingerprint recognition, in the automotive industry to calibrate engines, in facial recognition software by law enforcement agencies, and for EKG interpretation.

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Dr. Hill-along with his team of physician investigators, and the mathematicians and engineers at MathWorks-developed a study protocol to evaluate the data to determine the best measurement parameters (factors) to be used. Axial length, central corneal power, and anterior chamber depth were deemed the most important factors, in that order.

“Developing this, we didn’t want to have something encumbered by too much data,” Dr. Hill said. “In this case, the more variables we used, the less accurate the IOL power selection method became.”

The new paradigm

Realizing all formulas have limitations, the difference between conventional formulas and RBF pattern recognition is there is no calculation bias, Dr. Hill noted.

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“The RBF method does not know that a 21 mm eye is very short or that a 28 mm is very long eye,” he said. “All it knows is a pattern of data produces a particular result.”

This new IOL power selection method also incorporates a feature commonly employed in engineering-but new to ophthalmology-known as a “boundary model.”

One of the more powerful features of pattern recognition based in artificial intelligence is that the limits, or “boundary” of calculation accuracy, can be identified. Within such a boundary clinicians can anticipate a predicted accuracy outside of which they may not have enough data to for accurate interpolation.

When using the RBF calculator, an IOL power is identified as being “In Bounds,” or “Out of Bounds.” The implications of this added level of security are significant and are meant to enhance patient safety and physician confidence. With conventional theoretical formulas, data is entered and the user hopes for the best.

The RBF model is, at its heart, a “big data” exercise, Dr. Hill explained.

When the dataset used to fit the RBF model was expanded from 681 cases to 3,445 Lenstar cases, the depth of calculation accuracy dramatically improved. For the boundary model of axial length versus ACD, across an enormous range of values, the RBF model was unable to resolve the question in only 12 cases.

For retrospective testing, looking at 3,212 independent cases from 13 surgeons in 8 countries, the outcomes have been impressive with a weighted mean ± 0.50 D accuracy of 95%.

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“No one’s ever seen numbers like this,” he said.

What is even more impressive than the accuracy is the consistency from one beta test site to the next across Europe, the Middle East, Africa, North and South America, Asia, India, and Australia. This level of consistency tells clinicians that the outcomes are technology driven, Dr. Hill noted.

New approach


“In summary, this is a new approach based on pattern-recognition, data interpolation, and a validating boundary model, but just adds an additional level of confidence, and the accuracy of this methodology is due to an increase in flexibility,” Dr. Hill said.

The RBF calculation method is optimized for use with the Haag-Streit Lenstar EyeSuite biometry software. The Hill-RBF calculator may be found under “Online Tools at www.ascrs.org at RBFCalculator.com.

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Dr. Hill is quick to share accolades, and noted Peter Maloney (MathWorks) did “all the heavy lifting for algorithm development, model-fitting, and accuracy testing.”

Li Wang, MD, PhD, and Doug Koch, MD, from Baylor College of Medicine are “a powerhouse research team,” he said. Dr. Wang’s axial length adjustment for high myopia “took that out of the picture as a source of error.”

Dr. Koch’s insights on posterior cornea and its relevance in toric IOL calculations are exemplary, he said.

Adi Abulafia, MD, has “a gift for analysis and did much of the beta testing and guidance for how this program should move forward,” Dr. Hill said.

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Sheridan Lam, MD, and Johnny Gayton, MD, did most of the cataract surgeries early at this course of this project, allowing it to move forward, he added.

Dr. Hill also expressed gratitude to the many beta-testers around the world who participated in this project, which has been under way for the past 6 years.


Warren E. Hill, MD, FACS

E: hill@doctor-hill.com

This article was adapted from Dr. Hill’s delivery of the Charles D. Kelman Lecture at the 2015 meeting of the American Academy of Ophthalmology. Dr. Hill is a consultant for Alcon Laboratories and Haag-Streit.


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