In refractive surgery, astigmatism corrections have been the subject of numerous discussions since the second half of the 19th century- when it became possible to measure the radius of the cornea. Snellen1 and Lans2 studied the development of corneal astigmatism after incisions in animal experiments. In 1894, Bates3 recommended clinical correction through corneal incisions. Sato4, unaware of the vulnerability of the endothelium, recommended posterior transverse incisions. Troutman and Swinger5 introduced "relaxing incisions," to correct astigmatism following perforating keratoplasty. Troutman6 also recommended wedge resection. Other authors7-9 have published quantitative papers on astigmatism correction.
For several years, arcuate keratotomy has been recommended and performed clinically by Merlin10, who considers arcuate incisions more efficient than transverse incisions. Incisions are made which run either perpendicular to the steep radius or arcuateIy over the steep radius. With the exception of Troutman's wedge resection, the goal of all of these techniques is to flatten the steep radius.
Considering the various factors which are involved in astigmatism, such as corneal rigidity, corneal diameter, or the origins of astigmatism, the initial situation will determine different parameters for incision depth and length as well as for the distance from the corneal center. In May 1992, the authors11 recommended a circular cut based on Gauss' law. The eyes discussed here represent a further development of this procedure. The basic idea is recognition of a natural law whereby all bodies and volumes show a tendency to contain the least possible amount of energy. This principle affects volumes contained in a flexible membrane in such a way that they tend to take on globular form when they are subjected to a hyperbaric pressure. This principle can be observed in everyday things, such as the balloon.
Gauss' law (1777-1855) states that the modification of a radius of a volume in an elastic container results in a corresponding modification of the other radius. Thus, the product of the reciprocal value is constant:
K = 1/Rp 1 + 1/Rp 2
The application of this principle is highly effective when the cornea is cut up to a depth of 90%. The method we describe is a modification of and an improvement over the original procedure.
PATIENTS AND METHODS
A consecutive series of 32 patients (32 eyes) underwent circular keratotomy, and refractive data were obtained prospectively. Before surgery, mean astigmatism was -4.66 D (range -2.25 to -6.00 D). The origin of the corneal astigmatism was, in most instances, idiopathic or due to corneal scarring (from penetrating keratoplasty, corneal injury, etc.). All patients had a comprehensive ophthalmological examination to verify that they were free of ocular or systemic diseases that might affect the eye. A complete written informed consent was obtained from all patients.
We used the first author's guided trephine system12 with a trephine diameter of 7 mm and an obturator (a spherical glass plate inside the trephine) with a concave radius of 7.9 mm (Figs 1 and 2). With the help of a vacuum of 800 mBar, the eye was immobilized in the following way. First, the horizontal and vertical axes were marked with a radial keratotomy marker. The vacuum ring was positioned on the eye according to these markings. The eye was positioned with a squint hook in such a manner that the markings on the ring matched the corneal markings. Then, a suction of 800 mBar was applied, reliably positioning the ring. The construction of the ring permits high suction since the right-angled suction chambers of the ring are filled with triangular segments that prevent the sclera from being sucked into the hollows of the ring. Thus, intraocular pressure remained unchanged while the ring was suctioned onto the eye.
The trephine was than inserted into the ring at its zero position. This pushes the cornea against the sphere of the trephine and presses it into the shape of the sphere. The trephine itself is not a suction trephine. Rather, suction is exerted through the ring so that the suction cannot cause a deformation of the cornea. The trephine can be removed from the ring even during the trephine procedure without interrupting the suction, in order to check the effect of the trephination. The depth of the trephine and the incision procedure are set independently. Thus, rotation does not automatically result in a shift in the depth setting of the trephine.
The zero position of the trephine was set on a drum- a dish over which adhesive foil was tightly stretched- and marked on the depth-setter ring. A second marking determined the desired depth of 300 µt?. After the trephine was positioned, trephination was carried out in increments of 50 µp? per full rotation until the required depth of 300 µt? was reached. Subsequently, the trephine was removed without interrupting the suction. A fine forceps (eg, Paufique) was used to test the effect of the trephination. Next, the keratoscope (Ophthalmic Ventures, Los Angeles, Calif) was projected concentrically to the trephination. Since the effect of the primary 300-µt? deep trephination is commonly insufficient, the trephination must be deepened along the steeper semimeridians. Here, the diamond micrometer knife was set at 550 µt? and the trephination incision was deepened in the area of the hyperopic axis over an arcuate length of 1 to 3 hours (30 to 90°). The resulting sphericity of the cornea was checked through the keratoscope and by radii measurements on the hand-held electronic ophthalmometer (KM-500, Nidek, Tokyo, Japan). Unlike the method described in our first publication11, no suture was needed. Rather, the incision was cleansed thoroughly with an anterior chamber cánula with a downward positioned hole, primarily to remove epithelium possibly present in the wound.
The eye was closed after the application of cortisone/antibiotic drops. Eye ointment was not used, since it results in less transparent scars and delayed healing. The eye may remain open the next day, since in most cases an epithelial closure has by then taken place. Application of eye drops (such as Maxitrol), four times a day for 3 days, and subsequently three times a day for another 14 days is a routine measure.
In 32 consecutive eyes, no complications occurred during or after surgery. Patients rarely complained of discomfort after surgery. Analgesics were generally not needed. Visual acuity was restored by the first postoperative examination and patients returned to work within a few days.
Figure 1: The guided trephine system placed on the recipient side. A suction ring that does not increase the intraocular pressure fixates the globe with 800 mBar of suction. The trephine is locked into the ring and the trephine, carrying a central, sphericallyshaped obturator, is moved forward. Rotation of the blade and progression of the cut are indepedent, allowing individual trephine settings.
Although sutures were not employed in this series, wound gaping was not observed. At the 1year follow-up examination, scar formation was stable and no wound retreatment was necessary.
Figure 3 shows refractive results after circular keratotomy at different follow-up examinations. Correction of corneal astigmatism was reached almost immediately. The keratometric powers measured during surgery with a hand-held electronic keratometer were similar to the ones measured 1 day after surgery, and 1 week, respectively. Since the intrastromal incision did not affect the inner 7 mm of the corneal center, measurements were not precluded by irregular light reflexes due to epithelial distortions.
Corneal astigmatism measured between 1.00 and 5.50 D at the 1-week postoperative examination (Tables 1 and 2). The mean preoperative cylinder of -4.66 D was decreased to -1.72 D at 1 week, - 1.77 D at 1 month, -1.69 D at 6 months, and -1.78 D at 1 year (Fig 4). Spherical equivalent and amount of corneal astigmatism measured at 1 week remained stable in subsequent follow-up examinations, except for two eyes (6%) that had an increase of astigmatism more than or equal to 1.00 D, compared to the 1-week amount. One eye (3%) had a late improvement of 1. 00 D at the 1-year follow-up examination, compared to the 1-week amount. However, paired i-tests revealed no statistically significant differences between the mean keratometric power at 1 week, 6 months, and 1 year.
Clinically, there was no significant correlation between arcuate incision length and amount of refractive correction. Two eyes (6.3%) were corrected by the circular incision alone, as indicated by the intraoperative keratometric measurements, and did not require additional deepening. Deepening over the steep semimeridians was performed in 14 eyes (43.8%) for 1 hour, in 12 eyes (37.5%) for 2 hours, but in four eyes (12.4%) for 3 hours. Due to the insufficient number of eyes and heterogeneous indications, a statistical analysis was not meaningful. The data were not appropriate from which to derive any kind of nomogram that could predict which arcuate length would produce a particular refractive correction.
Figure 2: Radius changes due to the trephine obturator. The aspherical surface of the recipient cornea is pressed against the spherical surface of the obturator, thus leaving its distorted shape. Rounding of the anterior corneal surface allows an evenly deep and perfectly symmetrical cut to be made through Bowman's layer.
Vector analysis of the refractive changes showed overcorrection in 5 of 32 eyes. However, the amount of corneal astigmatism was significantly reduced in all of these eyes. Patients with mixed astigmatism and preoperative spherical equivalents of within ± 0.50 D of emmetropia were the most satisfied; they stated that they carried out most of their daily work without corrective spectacles. As predicted by Gauss' law, the preoperative spherical equivalent remained unchanged by the procedure. The preexisting hyperopia consequently was reduced by half of the cylinder value, by which corneal astigmatism was reduced.
The majority of patients reported improved quality of vision due to reduction of astigmatism. Furthermore, 40% (13 eyes) of the patients gained one or more lines of spectacle-corrected visual acuity. No patient lost one or more lines of spectaclecorrected visual acuity.
Because our study involved 32 consecutive eyes, undifferentiated as to indication, the question remains whether this procedure can be applied to all eyes with astigmatism and to what extent the results obtained remain stable. Because of the heterogeneous origin of the astigmatism, we do not consider means and standard deviations meaningful.
Reduction of Corneal Astigmatism in 32 Eyes after Circular Keratotomy
Reduction of Corneal Astigmatism in 32 Eyes as a Percentage of Preoperative Cylinder Values
The effectiveness of the circular keratotomy procedure, whereby only Bowman's membrane is cut and deepened over the hyperopic radii, is comparable to the results of a trephination of 90% of corneal thickness. In the surface trephination procedure, only Bowman's membrane is severed and any necessary supplemental deepening is carried out under the keratoscope, over the steep semimerdians. Due to the broad variance in the nature of the astigmatism, tables are meaningful only for gross orientation. We had the impression that there were different origins of astigmatism, due to different locations inside the cornea. The correction of equal amounts of corneal astigmatism required different arcuate lengths of deepening incisions, depending on the origin of the astigmatism. Fine tuning was done with the aid of a keratoscope. Different effects in individual eyes doubtless result from the fact that final controls could not be carried out precisely enough during the operation, since the interpretation possibilities on the keratoscope rings were within ± 2.00 D. Variant corrections result from the depth of the supplemental incisions over the steep semimeridians and from the length of the incisions. The operation was performed only if mixed astigmatism was present and the mathematical goal did not vary more than 1.50 D from 0 (sphere -0.50 cylinder). An improvement in technology relating to incision depth is expected so that the radial keratotomy micrometer blade will be guided along an insert on the guided trephine system ring. Such a procedure prevents uneven applications of the radial keratotomy blade and thus variant depths of this second incision.
Figure 3: Circular keratotomy in 32 consecutive eyes undifferentiated for indication. A) Preoperative cylinder values; B) cylinder values at 1 month after surgery.
Figure 3: (continued) C) Cylinder values 6 months after surgery. D) cylinder values 1 year after surgery.
The success achieved regularly with this procedure shows that the Gauss principle applies to the cornea even when Bowman's membrane only, and the smaller radii in the parenchyma, are severed. The same principle underlies the efficiency of arcuate keratotomy and transverse incision procedures. Unlike these techniques, however, in circular keratotomy the flat radius can follow the mathematical facts of Gauss' law since the circular cut into Bowman's membrane enables the cornea to change its steep and flat radii at the same time. This appears to be a prerequisite for the mathematical predictability of the procedure. As shown clinically, circular keratotomy allows for safe correction of up to 10.00 D of astigmatism (Fig 5). This eye was treated recently for congenital astigmatism and is not included in this series. The correction was achieved by a trephination at 300 µt? and deepening over the steep semimeridians with an arcuate length of 1.5 hours. Again, this example emphasizes the limited predictability that may be provided by nomograms that are undifferentiated for indications. The low number of operations thus far and nonstandardized procedures preclude analysis of longer or shorter, or shallower or deeper incisions. What can be concluded, however, is that the procedure is effective even in penetrating keratoplasty, if the incision is made in the transplanted tissue. Compared to the original claim that 90% incision depth is necessary, with the resultant proximity to the endothelium and the necessity of a circular suture, the procedure is more universally applicable. The procedure is, however, fully effective only if a trephine is used which allows the cornea to be cut while it is pressed against a spherical obturator and which permits a predetermined depth to be set- as in the guided trephine system or the Hanna trephine (Moria, Paris, France). The use of a hollow trephine results in non-identical incision depths and non-calculable radii, especially if it is used free-hand.
Figure 4: Mean corneal cylinder values in 32 eyes (± 1 SD) following circular keratotomy.
Figure 5: Preoperative and postoperative corneal astigmatism in a patient with severe congenital corneal astigmatism. Preoperative refraction: -1.00 -10.00 ? 120°; 20/100; keratometric power: 37.00/49.00. Postoperative refraction: -4.50 -2.75 ? 110°; 20/40; keratometric power: 40.00/43.60.
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Reduction of Corneal Astigmatism in 32 Eyes after Circular Keratotomy
Reduction of Corneal Astigmatism in 32 Eyes as a Percentage of Preoperative Cylinder Values