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By Stefanie Petrou-Binder

MAINZ — OKULIX, a new biometric computer program to stimulate the whole pseudophakic eye, aims to reduce calculation error and ensure a more reliable estimation of IOL strength.
Up until now, IOL calculations have been largely based on Gaussian optics. These physical principles have been the only means of calculating refraction in systems comprising more than one optical surface — like in the eye. They take into account only those light rays close to the optical axis (small angle assessment).

In reality, however, the entire cornea allows light to enter into the eye, limited only by pupillary size. Gaussian optics do not account for spherical aberrations since they rely only on axial measurements — a weak-point in precise IOL calculation. In fact, what we know as refractive power is a measurement determined by these very principles that do not reflect the eye in real terms.

The OKULIX computer program package overcomes the limitations of Gaussian optics by using numerical ray-tracing. Ray-tracing employs an adapted usage of Snell’s Law, which is itself fundamental to Gaussian optics. Snell’s Law calculates single rays on all optical surfaces. The numerical results of one surface are the input for the next one, and so on.

Together, these values provide a complete refractive picture. An advantage of today’s computer technology is that it allows us to numerically approximate ray refraction for all distances from the optical axis.

This software calculates single rays exactly, according to Paul-Rolf Preussner MD, inventor and developer of OKULIX. Individual ray refraction is measured at each optic surface, not only along the optic axis, but also throughout the light-transparent cornea.

Separating measurement and calculation errors
“The main difference between this approach and others is that we clearly separate between measuring and calculating errors. We cannot avoid measuring errors, for example, in axial length, and it is particularly difficult to avoid estimation errors in post-operative ACD (anterior chamber depth).

“What we can do, however, is make the error contributions clear to the user of our software, and try to limit them. We can also make calculation errors negligible, especially in ‘odd’ eyes. These eyes benefit most, while our results for mean eyes match the results seen in other methods,” he said.
Dr Preussner analyzed the major potential error contributors as the basis for improving his IOL calculations. These included calculation errors; measurement errors of biometrical data; manufacturer IOL data and fabrication error limits; and errors in estimation of ACD.

The ACD presents a particular challenge. It is often incorrectly estimated since it varies from person to person. ACD is a parameter that changes after lens extraction and IOL implantation.

The crystalline lens is generally more space-occupying than the implanted IOL and it exerts a certain amount of tension on the zonula fibers. Its removal from the eye, therefore, tends to widen the chamber angle, deepen the anterior chamber and slacken the over-all capsular tension.

The axial position of the implanted IOL is therefore frequently different than expected, requiring over- and under-corrections of unpredictable strengths.

Empirical SRK formulas measure overall refraction using corneal refraction and axial length values in linear approximation, together with an A-constant that incorporates the ACD-value as determined by the IOL manufacturer. These measurements are frequently unreliable, particularly in long and short eyes, as the errors encountered in linear approximation are increased in such cases. Also, manufacturers have at times overestimated ACD-values by 2 D.

OKULIX software proposes the ACD by recalculating it from A-constants using numerical methods. A joint study with a Viennese research group revealed unexpectedly high accuracy of ACD values confirmed by their laser measurements. With the ACD determined through ray-tracing, OKULIX obtains the same IOL values as in the SRK-formulae for the “mean eye”, Dr Preussner pointed out.

OKULIX and the IOL Master
“As with all other power calculation formulas, OKULIX will only perform well with exact measurements of axial length, corneal power and a good estimation of the postoperative IOL position. With the introduction of the IOL Master, which uses the principle of laser interferometry for axial length measurement, together with ray-tracing for IOL power calculation, we have powerful tools to significantly improve refractive outcome after cataract surgery.

“This leaves us with two main points to focus on: improved corneal power assessment and better prediction of postoperative IOL position,” Oliver Findl MD, Department of Ophthalmology, University of Vienna, told EuroTimes.

Another distinguishing function of OKULIX is the assessment of corneal refraction. While current methods measure rays along the optical axis, OKULIX approximates the cornea for off-axis rays. This measurement is much more accurate and realistic.

Of the two models studied in this approximation, the “simple model”, given only by two radii on perpendicular meridians and their orientation angle together with a unique numerical eccentricity, revealed less approximation error than the approximation of Zernicke polynomials, and is incorporated into OKULIX calculations.

Following corneal surgery for myopia correction, the refraction in the oblate cornea is difficult to measure. It has an altered curvature radius, inverted from the normally steeper centre and flatter periphery. OKULIX software incorporates the tools which include this shape change from sphere to asphere.

Precise steps also permit a customised IOL calculation, including measurements regarding spherical aberrations and astigmatisms. Residual errors are taken into account. A topographic map of the “best fit model cornea” is derived. Refraction maps and a retinal image are calculated for the customised IOL. The IOL can be decentred and/or rotated to visualise any blurring caused by these additional errors.

Customised corneal refractive surgery can also be applied to this software using algorithms similar to those used in IOL calculations. The ablation profile is simply the difference between the target-profile calculated and the original height-profile of the cornea. Unfortunately, this procedure may be very sensitive to even small misalignment errors.

Three papers on this subject currently in press to be published in the Journal of Cataract and Refractive Surgery will disclose preliminary clinical experiences with OKULIX. Two other papers are underway, regarding ACD measurements and topometry-based IOL adaptation.

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