Corneal Refractive Surgery

This part of the program is an option, i.e., it is not included in all installations. Corneal profiles can be either read in as topographic data (see previous section), or they can be generated as "model" data.

Corneal Model

For the corneal model, it is assumed that the cornea can be approximated by the rotation of a cartesian curve (circle, ellipsis, parabola, hyperbola), i.e. a conicoid, which is then compressed in one dimension ⁶. Thereby, two different vertex radii perpendicular to each other are generated, corresponding to the axes of the classical spherocylinder. In addition, the whole three-dimensional body can be shifted in an arbitrary direction. Altogether, the cornea is defined in the model by two radii, their angle to the horizontal, the numerical eccentricity e and a shift vector. In the images shown, only the absolute value of the shift vector d is displayed. However, internally it is represented as a two-dimensional vector. If the sign of the numerical eccentricity is set negative, this has only a formal meaning (negative numerical eccentricities are mathematically nonsense). In such a case, an oblate cornea is described which is approximated by an ellipsis, for which the minor axis is parallel to the optical axis. This model defined by the parameters R1,R2, α, e is the "standard" within OKULIX. A simplified possibility is given by entering the Refraction, i.e. sphere, cylinder and axis without asphericity. If corneal topographic data are already present (either from an input file or generated as a model), another model approximation can be calculated by Zernike polynomials. This is provided particularly for didactic purposes. Zernike approximations can be calculated for different radial orders n (3 ≤ n ≤ 12). The number of series elements is then (n + 1)(n + 2)/2 e.g. 45 for the 8-th radial order. The quality of the model approximation in a single case can be estimated by Diff. to Model. The difference between real cornea and model cornea is displayed either as a height profile or as a profile of the refraction or wavefront difference. This difference is calculated for the unshifted coordinates. Chosing Difference to.. the difference between the actual cornea and another cornea, defined by its topographic data is calculated. This difference is again displayed either as height profile or as a profile of the refraction or wavefront difference. If a model cornea is generated, the model parameters displayed after that might have little differences to the input data. This results from the fact that these parameters are always re-calculated from the two-dimensional data. The small differences mentioned show the limits of the model approximation. Corneal thickness is internally treated as a two-dimensional data field. Unfortunately, there is so far no input possibility for these data, because the interfaces to corresponding hardware equipment are not yet available.

Calculation Method for Corneal Ablation

In the calculation of Lasik / PRK ablation profiles, in principle all refraction errors (myopia, hyperopia, astigmatism, irregular regions) can be corrected. As target profile, a spherical cornea, an aspherical cornea with user-defined numerical eccentricity or an aspherical cornea, for which numerical eccentricity is optimized in such a way, that spherical aberration of the eye is minimized, can be chosen ⁷. In addition, the ablation profile can be numerically "smoothed" in order to eliminate high frequency errors. In the calculation of ablation profiles for Lasik / PRK it is always tried to minimize the ablation depth. In case of a mixed astigmatism, the steepest meridian undergoes a myopic correction, the flattest one a hyperopic correction ("cross-cylinder ablation"). In some cases the optical outcome may be nevertheless unsatifying. This can be verified by the two-dimensional refraction map, or, better, by simulated Landolt’s rings. The suboptimal outcome is caused by the primary data quality. They can either contain too many missing data points or the approximation by the model parameters is too poor.

Export of ablation profiles

The calculated profiles to be ablated during treatment are converted into so-called "shot-files". They contain the coordinates of the positions of flying spot lasers, which are processed by the corresponding laser machines. The spot sizes must be in the range between 0.6mm and 2.0mm. Such shotfiles can be generated for the Schwind ESIRIS. If the data file to control the laser, the "shot file" shall be generated, a name has to be entered if the corresponding window appears. If no name is entered, no shot file is generated. The file can be directly written on diskette if the drive mnemonic is entered additionally, e.g. A:\EAGLE-EYE.SHT
OKULIX generates the shot-files fulfilling the following requirements:

• Approximate the theoretical profile with maximum accuracy .
• Minimise surface roughness .
• Avoid local overheating .
• Avoid shooting into the vapor of the last shots.
• Minimize scanner movement amplitudes.

The calculation of the shot-file as described needs the exact knowledge of the ablated volume per shot. Instead of that, often the central depth assuming a Gaussian profile for the laser fluence is used. The ablation profile as a function of the location inside the spot is then calculated by folding the Gaussian function with the ablation per fluence above the ablation threshold, which is approximately logarithmic. A disadvantage of this approach is the large number of errors and uncertainties influencing the results, among them deviations from the Gaussian profile for the fluence as well as measuring or calibration errors of the ablation curve. In contrast, the volume per shot as used in OKULIX can be determined without an exact knowledge of the laser profile or of the ablation curve just by ablating a large volume e.g. by 10000 shots, and then simply dividing the measured volume by the number of shots. For this approach, the diameter of the laser beam profile only has to be much larger than the underlying raster. The volume per shot has been determined in the described manner. It may vary e.g. if the laser hardware is modified by the manufacturer. Clearing and setup of the individual laser machine to be used with OKULIX is under the responsibility of the laser manufacturer.

Application to Patients

The following points are important for an individual Lasik or PRK based on corneal topography:

1. It is normally dissuaded to use the measured corneal profile directly for the calculation of the ablation profile. This would result in the most accurate correction, but, unfortunately, only theoretically. It requires an error-free laser ablation. This is completely unrealistic due to the misalignment between topography and laser ablation.

2. Instead of that, the measured profile should be used to construct a model. The OKULIX standard model defined by R1,R2, α, e should be used, not the Zernike approximation. The model should reconstruct the full zone as the recorded data often are incomplete. The model results in the same maximum ablation depth and corrects astigmatism and spherical aberration in the same manner as the original profile. It does not, however, contain additional high frequency components. Just these are mostly sensitive against minimal misalignment errors between measurement and laser ablation.

3. If - in case of a highly irregular cornea - model and original topograpy differ too much, so that the model cannot be used instead of the original data, the option Smooth ablation profile should be activated.

4. For a pseudophakic eye all data (axial length, IOL type, ACD) should be entered in OKULIX, if known.

5. In case of a phakic eye the optical parameters of the crystalline lens are not known and are not constant in time (accommodation, age). It is recommended to keep the standard parameters for the IOL in OKULIX. The preoperative ("old") refraction as calculated with these values is therefore always wrong. The known refraction of the patient has to be entered. OKULIX then adjusts the axial length to achieve consistency again. All following calculations are based on this new axial length. The adjustment of the axial length is indicated to the user.

6. The astigmatism is corrected exclusively based on the topography. This is exact for pseudophakic eyes since the IOL has a zero astigmatism. An IOL decentration may be compensated in part by a cylinder correction, but it is strongly dissuadet to induce a corneal astigmatism for that purpose, since this always induces additional errors. The coma caused by an IOL decentration can never be corrected exactly on the cornea. Therefore, no additional tool is provided in OKULIX for that. In case of a phakic eye the lens astigmatism depends on accommodation and age.

7. Spherical aberration can be nearly corrected to zero in a pseudophakic eye if the IOL parameters are known. This results in an "ideal" eye, particularly under mesopic conditions. For the cornea the best fitting numerical eccentricity can be calculated. To choose this option, first the standard keep corneal asphericity has to be disabled, and after that, the next question minimize spherical aberration has to answered affirmatively. This approach, however, is much more sensitive against decentrations compared to ablation profiles in which a spherical cornea is intended. In the individual case it should be tested by simulated Landolt’s rings if there is a net win in visual outcome under realistic assumptions for the amount of decentration. If the option minimize spherical aberration is disabled, a target numerical accentricity can be entered, e.g. 0.0 for a sphere. In a phakic eye, the target numerical eccentricity should have at least the preoperative value (provided, the decentration error is sufficiently low). If a cataract surgery is planned for the next future, e can be increased to 0.7 or 0.8 (prolate cornea). With the most biconvex-symmetrical IOL ideal values for e are close to 0.9 (with a weak additional dependence on the other optical parameters).

8. After writing the shot-file to diskette it is read again to control the data. If the window "Control of shot-file" appears, first the medium has to be removed from the drive and then reinserted before confirming "ok". Otherwise, the operating system would use the image of the file stored in the intermediate storage instead of reading the data from the drive. An ablation is re-calculated and again displayed in pseudocolors. Normally, it is more coarse, and also the maximum ablation depth is somewhat different from the original one. However, these differences should be only a few micrometers. The are caused by the finite extension of the spot (e.g., diameter of 1.0mm), and by the finite position accuracy (e.g. 25μm). The surgeon must check this re-calculated profile for plausibility.