Astigmatism may be either genetic in origin or acquired through trauma, scarring, or after surgery, as a consequence of poor coaptation of scleral or corneal wounds. To correct corneal astigmatism, different techniques of corneal surgery have been suggested and performed.13
Astigmatic correction by surgery to the cornea has been carried out since 1892. Pioneers in this field have been Bates,4 Lans,5 Krwawicz,6 and Merlin.7 The basis for the majority of the techniques used is to flatten the steeper radius of the cornea. The only exception is Troutman's wedge resection2 in which the aim is to steepen the flatter radius. For a variety of reasons, there are many different nomograms and recommendations for the correction of any given astigmatic error. Factors that play a role in the flattening effect include different corneal rigidity, diameter, thickness, intraocular pressure (IOP), the perpendicularity of the cut performed, and its depth.*-12
Arcuate keratotomies as suggested by Merlin,7,13 or straight cuts perpendicular to a radial cut as so-called "flag incisions" are widely used. Mathematically, astigmatism is caused by a difference of two radii 90° opposite to one another, measured in millimeters or converted to diopters (Fig 1).
Gauss5 (1777-1855) law is cited to be the basis of the mechanism of astigmatic correction:
"In a perfectly deformable surface, the modification of one radius results in an opposite modification of the other radius. The product of the reciprocal value constant."
K = 1/r1 × 1/r2
Gauss' law applies typically to the elastic properties of the cornea. The shape of the anterior segment is formed by the limbus and the cornea, whereas the IOP is responsible for the final spherical curve in the emmetropic eye. The force exerted by the aqueous is opposed to the elastic tension of the cornea. In a uniformly elastic tissue, an IOP higher than atmosphericpressure automatically creates a spherical form.
Figure 1: (A1B) Astigmatic comea with agalnst-the-rule astigmatism = Hatter radius in 90°.
This phenomenon can be ascribed to the principle by which all bodies in nature tend to possess the least energy possible. This principle can be observed in daily life in a soap bubble or a balloon. Shortening one radius of a spherical surface means enlarging the smaller radius 90° away from the greater one and vice versa, whereby the product of both radii's reciprocal remain constant. The content of energy of the eye consists of two components:
1. Energy of tension of the elastic tissue.
2. Energy of volume of the pressurized fluid.
For any given volume, the body with the smallest surface area is optimal. Some examples of the surface area of a body containing 4 m L are: a tetrahedron - surface area 18.15 mmp 2, a cube - 15.12 mmp 2, a dodecahedron - 13.38 mmp 2, and a sphere - 12.18 mmp 2.
Since the value of the IOP is positive, ie higher than atmospheric pressure, the prerequisite for forming a spherical surface is present. Astigmatism of the cornea is caused by a longer arc length of one radius as compared to the one lying at 90° to it (Fig 1).
Clinically, all procedures performed for astigmatic correction up until now have not allowed Gauss' law to come fully into play In most instances, a larger radius becomes only a little smaller than before and does not follow the mathematical relationship expressed in Gauss' law.
For instance, a patient with +6.00 D Sph, -5.00 diopters CyI × 90°, changed to +5.00 D Sph, - 1.00 D CyI × 90° instead of +4.00 D Sph, - 1.00 D CyI × 90°, considering the residual cylinder to be the same. We felt, therefore, that present methods used to correct astigmatism have several disadvantages:
* The unpredictability of such surgery since it could not be performed according to mathematical prediction, regardless of the procedure used.1-3
* The appearance of the cuts seemed unacceptable in cases of high astigmatism ("corneal graffiti").14
* The results of the procedure applied indicate that the larger radius keeps its shape probably because it does not have the chance to shorten, due to its connection to the rest of the globe.3,14 The inference from this is that one has to create a perfectly round cut around the optical center. In this cut, all distances from the central point must be the same. The cut must be even and perpendicular to the limbal plane. Any deviation from its perpendicularity could result in its being oval in shape.
To perform such a cut, the aspheric cornea would have to be pushed against a spherical surface along which a circular cut into the cornea could be performed (Figs 2-4). Cutting through Bowman's membrane and the stroma would allow the IOP to generate a sphere from the remaining elastic tissue of the posterior layers. Thus, the correction of astigmatism would be achieved in two ways:
Figure 2: Rounding inside the Guided Trephine System®.
Figure 3: Principle of circular keratotomy: trephine cutting after alignment of an aspherical surface to a spherical obturator.
1. Adaptation in height.
2. Adaptation in the circumference.
For example, consider a patient with + 5.00 sph - 6.00 cyl. The corneal radii might be 7.03 mm or 47.80 D for the smaller radius in the vertical direction and 8.03 mm or 41.80 D for the greater radius in the horizontal direction. If a trephine of 7.00 mm is used and the cornea is pushed against the spherical surface of an obturator of a radius of 7.5 mm, there will be a circular island of 7.283-millimeter arch length. To the reference of the 7.00-millimeter trephine, the formerly smaller radius of 7.03 mm had an arch length of 7.327 mm, ie on both sides of the island there will be a surplus of 0.022 mm. The formerly greater radius of 8.03 mm calculates to an arch length of 7.243 mm, thereby forming a gap of 0.020 on both sides of the island. The island, therefore, must be adjusted to both sides by the small amounts of 0.022 and 0.020 mm for a correction of 6.00 D.
The calculation for using a 6-millimeter trephine with the same obturator of radius 7.5 mm and preoperative radii of 7.03 mm and 8.03 mm results respectively in a surplus of 0.013 mm and a gap of 0.012 mm. By these mathematical analyses, one can see that only minute adaptations of arc lengths are needed to correct high astigmatism. The smaller the trephine radius, the smaller the change of radius necessary to correct the same amount of astigmatism. Looked at in another way, the greater the astigmatism to correct, the more advantageous it is to use a smaller trephine. From these considerations, it became clear that we needed to approach the problem in the following manner.
MATERIALS AND METHODS
1. A trephine that remained perpendicular to the limbal plane during the cut;
2. A trephine that could be cut down with an accuracy of a few hundredths of a millimeter with reference to the level of the limbal plane;
3. The trephine to be fixated at right angles to the limbal plane, so that the cut can be performed parallel to the visual axis;
4. The trephine not to be hollow - a suction trephine would not necessarily be applied perpendicular to the limbus and would not maintain vertical cutting due to its suction properties as consequence of the climinishing resistance of the sclera during the cut; and
5. Fixation of the achieved spherical surface to be preferably carried out, particularly in cases with high astigmatism - the suturing technique of choice for these cases was the double-running antitorque suture (Fig 5).
Figure 4: Guided Trephine System® in use for circular keratotomy. Steeper radius in 0° flattens; flatter radius in 90° steepens.
We felt that the ideal instrument to use was the Guided Trephine System® (Fig 6). With this instrument the eye is held by a suction ring that does not increase the IOP despite the application of 800 mbar vacuum. The trephine is locked onto the vacuum ring and remains vertical to the limbal plane. An obturator inside the trephine prevents the oval corneal surface from protruding into the round of the blade. The descent of the trephine can be controlled in relation to the limbal plane (Figs 4-5).
In a laboratory test set-up, seven donor eyes were pressurized to 20 mm Hg. Astigmatism was created by two 7 × "0" sutures placed 1 mm in from the limbus. The astigmatism ranged from between 5.00 D and 7.00 D as measured by the keratoscope. Corneal thickness was measured optically with the Haag-Streit slit-lamp; ultrasonic pachometry was tried but seemed unreliable as the corneal edema caused variable results.
Figure 5: Double-running anti-torque suture to form a round island.
Figure 6: Cross-section of Guided Trephine System® on the eye.
Change in Refraction After Circular Keratotomy*
Next, the Guided Trephine System® with a 7millimeter blade was used with an obturator. The GTS suction ring was applied and the power set of the Barraquer-Krumeieh-Swinger unit was used to produce 800 mbar vacuum. The intraocular pressure was verified with a surgical tonometer and remained unchanged by the suction provided that downward pressure was not exerted.
The trephine rod was locked onto the suction ring and the trephine cut down to 90% of the thickness, as previously measured in the zone to be trephined. A double-running antitorque suture was applied and, before knotting, the intraocular pressure was rechecked and, if necessary, restored to 20 mm Hg (Fig 5). Tension of the sutures was adjusted under the keratoscope to produce optimal rounding despite the continued presence of the sutures that induced the astigmatism. Since the individual induction of the astigmatism did not allow for a reliable standardization, we did not attempt to quantify the measurements.
Based on these experiments, 14 cases of severe traumatic and/or surgically-induced astigmatism, and five cases of congenital astigmatism were treated (1 to 14 and 15 to 19, respectively in Table 1). The same 7-millimeter Guided Trephine System® was used in all cases. Descent of the trephine was set to 90% of the corneal thickness at the 7-millimeter optic zone size. The cut was washed out with McCarey-Kaufman solution in case of astigmatism more than 5.00 D and then sutured using the double-running antitorque suture under the Ophthalmic Ventures Keratoscope®, using the two concentric rings, tying the knot in accordance to the white reflected ring and the reference circle which is produced in red. If astigmatism was 5.00 D or less, only two single sutures were used at the circular cut over the flat axes.
Additional arcuate incisions of 3 clock hours in length at a 5.00- to 5.50-rnillimeter radius were placed in 5 of the 19 cases at different time intervals after the initial surgery (Table 1). Surgery was performed on an out-patient basis under local anesthesia with 2% Xylocaine 5 mL and 4 mL Bupivicaine-HCl.
Postoperative treatment consisted of Maxitrol four times daily for 4 days, then three times daily, discontinuing all treatment after 3 to 4 weeks. In some instances pure antibiotic drops were used for a short time (chloramphenicol 0.4% three times a day).
Ophthalmometer Values Before and After Circular Keratotomy
Results are outlined in Table 1 and show a consistently significant reduction of cylinder which improved further in some cases during the first 3 months. Thereafter, little change was noted. Taking out the sutures after 3 to 6 months resulted neither in appreciable further improvement nor worsening, except in one case which showed regression (case 6, old penetrating keratoplasty). Arcuate incisions performed with sutures in (cases 5,7,19), or after suture removal (cases 3,18), reduced the remaining astigmatism further. There was some reduction of the central island's sensitivity, but in no case was there any indication of trophic changes as a result.
The purpose of using the Guided Trephine System® to perform circular keratotomy is to create a defined round island within an aspheric surface. By mathematical and physical considerations, it is apparent that sphericalization of the island is independent of the preexisting astigmatism, so long as the change in shape is allowed by an appropriate depth of cut and sufficient IOP. This means that a table of instructions for the use of the Guided Trephine System® to perform this operation should not be necessary. For higher degrees of astigmatism, the procedure could be applied using a smaller trephine of 6 mm in diameter. Results indicate that traumatic or postpenetrating keratoplasty astigmatism respond more readily to this procedure than postcataract or congenital astigmatism.
There is no strict correlation between cylinder measured by refraction and that measured by keratometry. Astigmatism of the lens, or intracorneal astigmatism due to scars, may still be present even if the surface is as spherical as possible (Table 2, cases 6,11, etc). Also, there are subjectively and objectively differing cylinders from the keratometry readings (Table 2, case 9). Possibly, in postcataract astigmatism, the inner corneal layers are pulled into the wound and so do not have the physical possibility of achieving sphericalization. In congenital astigmatism, the reduction in cylinder is not quite so obvious as in the traumatic cases. The factors causing this reduced effect may be insufficient depth of the cut or insufficient counter pressure against the single size of obturator employed (7.8 mm). When used in this way, the adaptation of the cornea to the spherical shape of the obturator is, therefore, possibly not optimal.
In general, the method seems applicable independent of the origin of the astigmatism as long as there is no scarring lying within the trephined zone which might hinder the sphericalization. Small arcuate incisions can be used to enhance the effect of the circular trephination before or after suture removal. With a follow up of up to 1 year, a stable refractive result is observed.
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14. Maguire LJ, Bourne WM. Topographical analysis of the effects of corneal relaxing incisions on high post keratoplasty astigmatism. In: Draeger J, Winter R, eds. New Microsurgical Concepts II. Cornea, Posterior Segment, External Microsurgery. Series Ed. W. Straub, Karger, Basel Dev Ophthalmol, 1989;18:197-220.
Change in Refraction After Circular Keratotomy*
Ophthalmometer Values Before and After Circular Keratotomy