Ординатура / Офтальмология / Английские материалы / Wavefront Analysis Aberrometers and Corneal Topography_Boyd_2003

Flying Spot Lasers and Eye Tracking

Before getting in more details about custom refractive surgery we should get more familiar with the state of the art technology that is allowing this subject to evolve so rapidly. As we mentioned earlier, the first excimer lasers for refractive surgery had simple and symmetric beam profile and a diaphragm to change its spot size. With these kinds of lasers the aberrations that could be corrected through refractive surgery were very limited, and it was useful for basically eyes with approximately spherical corneas and low myopia, with no astigmatism.

Recent excimer lasers, like the Nidek EC-5000[36], have a scanning slit delivery system that can treat over 7.5 mm of the cornea in myopia and up to 10 mm in hyperopic, using a 10 to 40 Hz frequency. A larger area ablation can be combined with a small area (1.0 mm) over a 10 mm diameter of the cornea.

Authors like Ronald Krueger (SummitAutonomous Custom Cornea) argue that effective wave-front based customized ablations require small scanning spot gaussian beams[37]. In essence, Krueger states that small gaussian beams allow for very smooth ablation profiles, which directly affect post surgical visual acuity. The other aspect to consider is the size of the spot. If we have high-resolu- tion corneal topographers and wave-front devices, the size of the laser beam has to be proportional to that resolution. Unpublished mathematical calculations[37] show that to correct up to fourth order aberrations a spot size of less than 1 mm is necessary and therefore lasers with greater beam profiles would fail to correct common high order aberrations, like coma and spherical aberration. Studies with a 2 mm profile beam have shown poor performance[38].

Because of the involuntary constant movements of the eye (called saccadic movements)

There are basically two types of eye tracking systems in the market: the CCD based systems and radar sys-

tems. The CCD based systems work with image processing algorithms to find eye position and input feedback to mirror micro-motors; they have tracking frequencies that are limited by the CCD frequency and range from 30 to 300 Hz. Radar based systems work with retro-reflected diode laser light and may obtain even higher frequencies [37].

Algorithms for Customized Ablations

With the advances in laser and eye-tracking technology, customized surgeries with the goal of maximizing visual acuity for specific patient based data, is becoming a non science fiction possibility. Recently, with the advances of HS sensors for human eyes we’re even closer to this technology. Authors have developed algorithms to calculate the exact amount of corneal tissue for each surface point that should be ablated in order to obtain the highest quality of vision, that is, in order to eliminate low and high order aberrations. Stanley Klein[40], Jim Schwiengerling and Robert Snyder[41] have described very interesting algorithms for corneal ablations based on VKS and HS data. The basic idea behind these algorithms is that with the VKS data we have corneal elevation information and with the HS data we have the aberration data, so it’s possible to calculate the exact corneal surface profile that would minimize optical aberration. With this information at hand for any measured eye, what would be the ablation profile? That’s the question that these algorithms attempt to answer.

A Look Into the Future of

Refractive Surgery

In this section we’ll make brief comments with references about certain aspects that, in our point of view, have yet to be considered in order to maximize refractive surgery efficiency.

Simulation of Refractive Surgery

Results

Most people who have undergone refractive surgery didn’t actually have a precise notion of how much improvement they would get from surgery. They probably had to make a decision based on other people’s experience and their own doctor’s opinion. In fact, this is probably the single most important question when a candidate is about to make a decision. Now, with adaptive optics, there is a way of actually showing the patient the benefits of low and high order aberration correction.

As we have seen in section (2), HartmannShack sensors have been originally used for use in adaptive optics [42] components of astronomical telescopes. In astronomy the HS sensor is usually attached to a computer that sends practically real time information to a deformable mirror, and then the mirror’s surface is molded for aberration correction. This real time process is called a "closed loop" adaptive optics system because the process aberration measurement-correction is practically instantaneous. Based on this idea some authors have used closed loop systems to simulate refractive surgery outcomes [43] such that the subject can experiment with supernormal vision [27, 44]. This is certainly one of the most interesting applications of the technologies we have discussed up to now, and it will certainly change the way doctors and patients come to the decision of having or not refractive surgery.

The Need for Better Refractive Surgery

Models

Another interesting issue is the discussion of better refractive surgery computer models, recently discussed by Cynthia Roberts. Better refractive surgery models have yet to be developed in order for custom surgeries become truly effective. Current ablation algorithms are optimized to the mean population response. However customization requires

Section IV: Aberrations and Aberrometer Systems

prediction of individual rather than mean corneal response. Cynthia Roberts and colleagues have been developing a model for the biochemical consequences of laser refractive surgery [45] and hopefully this model will help understand how individual physiological aspects influence on refractive surgery outcome. If we understand these aspects, than we’ll be able to design algorithms that take into account personal physiological data and accurately predict optimal ablations.

Physiological Limitations to Visual Acuity

Although most people in the refractive surgery community show excitement with supernormal vision possibilities, we must consider the physiological limitations of the eye. No matter how well we can measure and correct low and high order aberrations, there is a clear limitation imposed by the human photoreceptor configuration and dimensions. The region of the retina where images are formed is the foveola, an approximately 0.35mm disk. In the foveola the cones are very packed and have a mean diameter of 2 µm. Just like the number and size of photo sensitive cells in a CCD camera imposes limitation to the camera’s resolution, so does the number and size of cones in our eyes. Seeing with higher acuity essentially means seeing more detail at longer distances. It is easy to understand by simple image formation principles from geometric optics, that smaller objects in the outer world will form smaller images at the retina. The question is: how small can an image formed at the retina still be interpreted? If it gets too small it will unavoidably be interpreted as a single point. Assuming eye model parameters (see figure 14), a simple calculation may be done to show that visual acuity is limited in the retina to about 20/08. But there are certainly many other aspects that have to be considered in an individual basis, such as receptor sampling [46].

Considering Cyclotorsion

Another interesting question that we think worthwhile is the consideration of cyclotorsion factors in refractive surgery procedures. Most pre and post surgery eye examinations are done in the vertical position of the head. But surgery takes place in the horizontal position. Our question is: how important is the cyclotorcion movements of the eye and head misalignment in cases of refractive surgery for cases of medium to high astigmatisms?

To answer this question we’ll make some theoretical calculations. Suppose a patient with 4 degrees of astigmatism with the rule (40D (8.43 mm of radius) at the horizontal meridian and 44D (7.67mm of radius) at the vertical meridian) undergoes refractive surgery and an accumulated meridian angle error of 5 diopters is caused by cyclotorsion and 5 more degrees because of head misalignment. For simplicity, let’s describe each hemimeridian as a circle of equation:

(8)

where represents elevation and x represents radial distance along a meridian. Because we have an astigmatic eye, each hemimeridian has a different radius (r ) that may be calculated by the following formula:

(9)

Where is the radius of curvature of the meridian at angle θ, rh is the horizontal radius of curvature, and rv is the vertical radius of curvature.

Let’s suppose that the simple refractive procedure would be to ablate the cornea in such a way as to flatten the steeper meridian, that is, the vertical meridian. So we know that the correct radius of curvature at the vertical meridian would be 8.43 mm. Simple geometrical calculations show that, for a radial distance of 1.0 mm from the apex of the cornea (which means 2 mm central region of the cornea) up to 0.2D errors may occur. Although theoretical, these simple calculations show that the head alignment and cyclotorcion are important aspects in customized ablations, since the precision of all instruments involved are much higher than 0.2D.

Effectiveness of the Hartmann-Shack

Sensor

In recent poster presented at an European adaptive optics meeting [47] we have shown that it’s important to consider optical design optimizations when using HS sensors to measure optical aberrations of the eye. Because the HS sensor was originally conceived for application in astronomy and aberrations in this field differ from those of human eyes, we believe some studies have to be made in this sense. We have developed simulations of HS patterns for real and artificial corneal topography data of eyes with astigmatism, keratocone, and uniform curvature corneas, all these attached to a Le Grand eye model [31] (see figure 14). The basic principle of HS simulation using ray tracing may be seen in figure 15.

Illustration of simulated HS patterns obtained for three interesting cases are shown in figure 16. In general we notice that for eyes with little corneal irregularities ("smooth" corneas) the spots have a quite well behaved distribution; on the other hand for eyes with high astigmatism, keratocone or other severe corneal irregularities (such as post RK), there is a superposition of the HS spots.

Our HS patterns are in agreement with the corneal elevation data and for most cases of regular ("smooth") corneas, small and medium astigmatisms,

there was no spot overlap (see figure 17). But for cases of severe keratocone (simulated), we observed overlapping (see figure 17). Other types of irregularities should be investigated, such as post-cataract, post-RK, and post-Keratoplasty. We believe there will be overlapping for these types of irregular corneas.

In figure 17 we may see examples of HS patterns obtained for artificial corneas generated using ellipsoids and spheres of different sizes and parameters. It is important to notice how the HS pattern varies with small changes in parameters such as radius of curvature, entrance pupil, HS image plane distance, number and size of micro-lenses, CCD res-

olution and scaling, and so on. Our objective here is to show a qualitative view of how these parameters affect the HS patterns. Further work should be done in order to quantify these factors, and possibly suggest HS sensor setups that will generate less superposition in cases of highly distorted corneas.

We have found that the actual HS sensor systems used for ocular aberration measurements may generate spot superposition in certain cases of high corneal irregularities. This happens because the corneal slopes at some points vary rapidly, causing refraction at certain regions to differ considerably from neighbor regions. Once this happens the image processing technique for recovering centroide information becomes challenging. Our finding suggests that further research is necessary in the HS apparatus, it’s optical components, associated distances and dimensions, in order to obtain the best optical design for such a device. Further study should simulate different optical materials and optical diagrams in order

to account for very irregular corneas. The results of such a study will allow manufactures and laboratories to build better wave-front measuring devices for the eye. This in turn will certainly contribute to more accurate refractive surgeries, since corneal ablation algorithms use data from such measurements[40, 41].

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_____________________

L. A. Carvalho, MD.

Instituto de Física de São Carlos (IFSC - USP), Brazil lavcf@ifsc.sc.usp.br

J. C. Castro, MD.

Instituto de Física de São Carlos (IFSC - USP), Brazil lavcf@ifsc.sc.usp.br

W. Chamon, MD.

Escola Paulista de Medicina (EPM), Universidade Federal de São Paulo, Brazil

P. Schor, MD.

Escola Paulista de Medicina (EPM), Universidade Federal de São Paulo, Brazil

L. A. V. Carvalho, Ph.D.

Instituto de Ciências Matemáticas e de Computação de São Carlos (ICMC-USP), Brazil