During laser in situ keratomileusis (LASIK), surgeons occasionally encounter complications in the interaction between a mechanical microkeratome and a patient's corneal tissue. One of the more common microkeratome complications is a free cap.^{1,2}

A free LASIK cap occurs when the microkeratome creates a free piece of corneal tissue instead of the intended hinged flap. Common causes of free caps may include flat corneas or inadequate microkeratome suction. If fiduciary marks are placed on the cornea before the microkeratome cut, the surgeon usually can replace the free cap in its original position. If the surgeon does not place fiduciary marks or if they rub off during the handling of a free cap, the surgeon may inadvertently replace the cap in a rotated position.

Theoretically, rotating a free LASIK cap should have no effect on refraction if the cap is round, has a uniform thickness, and is well centered on the stromal bed when replaced. This is similar to what occurs optically when spherical contact lens rotates on the eye.

It is reasonable to assume, however, that a free LASIK cap may not have uniform thickness. If the blade passing through stromal tissue is shallow at the beginning and end of its cut, but of relatively normal thickness in the center, the cap would be shaped like a plus-power cylindrical lens (Figure 1, A ).

Figure 1.: A: An irregular free cap may be shaped like a plus-powered cylindrical lens if the microkeratome does not pass through tissues at a constant depth. In this case, the microkeratome blade, passing from temporal to nasal, begins its pass shallowly and travels deeper into the corneal stroma centrally. The blade again becomes shallow toward the end of its pass. The stromal bed has a mirror-image shape and behaves optically like a minus-powered cylindrical lens. B: The irregularly shaped free cap may be inadvertently rotated during surgery. This occurs if the surgeon cannot identify fiduciary marks placed on the cornea at the beginning of the procedure. In this diagram, the cap is rotated 90 degrees. C: The free cap, a plus cylinder, is superimposed on the stromal bed, a minus cylinder of equal but opposite power. The resulting optical effect resembles a Jackson cross-cylinder. Mixed astigmatism develops.

In this case, the matching stromal bed would be deeper centrally and shallower at the ends where the blade entered and exited the cornea, thus having the shape of a minus-power cylinder. If the cap were intended to have a nasal hinge, this cap would be thin nasally and temporally.

If a cylindrical corneal cap is replaced in its original configuration, or if it is rotated exactly 180 degrees, the deep and shallow areas will match (ie, the plus and minus cylinders will cancel each other) and there will be no net effect of the irregular cut. If the cylindrical cap is rotated to some angle other than 180 degrees (Figure 1, B ) and then replaced, however, a new corneal surface shape will result. Figure 1, C , shows an exaggerated view of the new surface shape if the cap is rotated 90 degrees. The corneal cap acts as a plus cylinder, while the stromal bed acts as a minus cylinder of equal but opposite power. Together, they create a cross-cylinder with its power and axis dependent on the angle between the crossed cylinders.

We report 3 cases of a free cap occurring during LASIK. In each case, the planned laser ablation was performed despite the free cap, and the surgeon was unable to identify the fiduciary marks placed on the cornea. The caps were replaced. In each case, after at least 3 weeks of healing, each eye had a reduction of at least 1 line of best corrected visual acuity (BCVA). All 3 eyes had developed mixed astigmatism with a spherical equivalent near zero.

We hypothesized that each eye's free cap had been inadvertently rotated from its original position. We report a method for determining the axis of cap rotation based on the observed cylinder. In these 3 patients, this method allowed us to rotate the cap back to an astigmatically neutral position, resulting in a reduction of astigmatism and improvement of BCVA to 20/20 all 3 patients.

SURGICAL TECHNIQUE
All patients who had a procedure to rotate a free LASIK cap to treat induced postoperative astigmatism were reviewed. In each case, it was necessary to determine the angle of cap rotation. To do this, the following assumptions were made:

The laser ablation eliminated the eye's preexisting astigmatism. Thus, any measured astigmatism was attributable to the cap rotation alone.
The free corneal cap was thinner where the microkeratome blade first entered and exited the cornea (nasally and temporally) and thicker centrally. In the 3 cases described, it was known that all flaps were made with the automated corneal shaper (Bausch & Lomb), which normally makes a nasally hinged flap.
The path of the microkeratome blade passed along the same 0- to 180-degree axis that is used for refraction. In this case, the free cap would have the shape of a plus cylinder with its axis at 90 degrees and power at 0 degrees (Figure 1, A ). If this assumption were not true, as was the case in patient 3, it would be necessary to perform 1 additional procedure to correct the induced astigmatism, using additional calculations to determine the true cap rotation angle.
As a mirror image of the free cap, the stromal bed was deeper centrally and shallower at the nasal and temporal ends, producing a minus cylinder with axis also at 90 degree and power at 0 degree. The power of this minus cylinder (stromal bed) was equal in magnitude but opposite in sign to the power of the plus cylinder (free cap).
The surgeon might have inadvertently rotated the free cap to any angle, clockwise or counterclockwise. The cap behaves optically as a symmetrical cylinder, however, and any angle of cap misalignment has the same optical effect as a counterclockwise cap rotation of less than 180 degrees. Therefore, any angle of cap misalignment can be corrected with a clockwise rotation of the cap of 0 to 180 degrees.
If this free cap were rotated before it was replaced on the stromal bed, optically, it would create the same effect as adding 2 equal but oppositely powered cylindrical lenses. Consider the cap, a plus cylinder, with its power rotated to some angle θ. The stromal bed is a minus cylinder with power at 0 degrees—the original axis of the temporal microkeratome cut. According to Rubin,^{3} the axis that bisects 0 and θ (mathematically represented by θ/2) will be halfway between the steep and flat axes of the clinically observed astigmatism (Figure 2 ). The astigmatism in plus cylinder is found on the same side of the bisector as the original plus-powered cylinder. This same principle can be applied to any angle of cap rotation, even if the angle θ is greater than 90 degrees.

Figure 2.:
A cylindrical free cap can be rotated to any angle θ from its stromal bed. According to Rubin,^{3} the eye's induced astigmatism will have its steep and flat axes 90 degrees apart. The bisector between the steep and flat axes of the refractive astigmatism will be the same as the bisector of the angle θ between the rotated cylinder and the opposite-powered (unrotated) cylinder. One can use this principle to determine the angle of cap misalignment from the axis of the observed astigmatism.

In the clinical setting of a patient with a LASIK flap that has been inadvertently rotated to some unknown angle θ, it is necessary to calculate θ from the refractive astigmatism. To do this, following the same assumptions and method above, the following algorithm was developed:

Subtract 45 degrees from the axis of observed refractive astigmatism (in plus-cylinder notation) to find the bisector of the angle between the plus and minus cylinders.
Multiply this number by 2 to yield the angle of counterclockwise cap rotation.
Using this algorithm, the angle of inadvertent cap rotation in 3 patients was calculated and treated accordingly. The surgical technique involved marking the cornea with a radial keratotomy marker before lifting the flap. These marks allowed exact measurement of how much to rotate the cap because there is a known angle between each mark (eg, 60 degrees for a 6-incision marker, 45 degrees for an 8-incision marker). Each cap was lifted with a hook and a Maloney LASIK spatula (American Surgical Instruments Corporation). Once free, the cap was rotated clockwise to the desired angle. The cap was then smoothed with a sponge and allowed to dry. A bandage contact lens was placed, and the eye was patched.

RESULTS
Patient 1
A 43-year-old woman had LASIK in the right eye to correct preoperative myopia of −5.00 diopters (D) sphere. During the procedure, there was a free cap and the surgeon could not identify the fiduciary marks made on the cornea. He then replaced the cap in what he felt was the proper orientation. Surgery was not performed in the left eye. Three weeks postoperatively, uncorrected visual acuity (UCVA) in the right eye was 20/70. The refraction in the right eye was −0.50 +3.00 × 062, correcting the eye to 20/30. Topography showed bow-tie astigmatism consistent with the manifest refraction (Figure 3, A ). To solve for the angle of cap rotation, 45 degrees was subtracted from the observed axis of 62 degrees, giving a bisector angle of 17 degrees. Multiplying 17 degrees by 2 yielded 34 degrees, the angle of counterclockwise cap rotation. The corneal cap was marked with a 6-incision radial keratotomy marker, which had adjacent marks exactly 60 degrees apart. The cap was lifted with a hook and a Maloney LASIK spatula. Once free, it was rotated 34 degrees clockwise, slightly more than one half the distance between adjacent marks from the radial keratotomy marker. The flap was smoothed with a sponge and allowed to dry. The eye was patched over a bandage contact lens. Three weeks later the UCVA in the right eye was 20/30, the topography showed a marked reduction in astigmatism (Figure 3, B ), and the manifest refraction was −0.75 +0.50 × 34 correcting to 20/20.

Figure 3.: A: Patient 1. After laser ablation for myopia of −5.0 D, the surgeon was unable to identify realignment marks and replaced the cap in a random position. Astigmatism with −0.50 +3.00 × 062 correcting the eye to 20/30 developed, and topography showed corneal astigmatism. B: Patient 1. After calculating the angle of cap misalignment, the cap was lifted and rotated 34 degrees clockwise. Three weeks later, UCVA was 20/30; manifest refraction was −0.75 +0.50 × 34 correcting to 20/20, and topography showed significantly less astigmatism.

Patient 2
A 47-year-old man had LASIK in each eye. The preoperative manifest refraction in the left eye was −3.50 +1.00 × 30, correcting the eye to 20/20. A free cap occurred in the left eye. After the laser ablation, it was replaced by the surgeon using his best judgment because the corneal fiduciary marks were not visible. Four weeks later, the UCVA was 20/200 and manifest refraction was −3.50 +6.50 × 90, correcting to 20/25. Topography showed with-the-rule bow-tie astigmatism (Figure 4, A ). Forty-five degrees were subtracted from the observed steep axis of 90 degrees, giving 45 degrees. This bisector angle was multiplied by 2 to yield the angle of counterclockwise cap rotation, θ, at 90 degrees. This patient's free cap was lifted in a similar manner to in patient 1, and the cap was rotated clockwise 90 degrees before being replaced. Four weeks later, the UCVA was 20/30. There was a significant reduction in topographic astigmatism (Figure 4, B ), and refraction was −0.75 +0.75 × 165, correcting the eye to 20/20.

Figure 4.: A: Patient 2. After this eye's free LASIK cap occurred, the surgeon performed laser ablation to correct the preoperative refraction of −3.50 +1.00 × 30 correcting the eye to 20/20. The surgeon was not certain that the cap had been realigned properly. After 4 weeks, the patient had 20/200 UCVA and refraction was −3.50 +6.50 × 90 correcting the eye to 20/25. Topography showed with-the-rule astigmatism. B: Patient 2. Calculations were performed to determine that the cap had been rotated 90 degrees counterclockwise. The cap was lifted, rotated 90 degrees clockwise and replaced. Four weeks later, the eye's UCVA was 20/30, and refraction was −0.75 +0.75 × 165 correcting the eye to 20/20. Topography showed a significant reduction in astigmatism.

Patient 3
A 29-year-old woman had LASIK in each eye. Her preoperative manifest refraction in the right eye was −4.00 sphere, correcting to 20/20. The referring surgeon reported that a free cap occurred during the procedure the right eye and that he had replaced the cap without being able to identify the orientation marks. One month after surgery, the UCVA was 20/60 and manifest refraction was −1.25 +2.00 × 065, giving 20/30 acuity. Topography showed regular astigmatism consistent with refraction (Figure 5, A ). Using the same algorithm, 45 degrees were subtracted from the observed steep axis of 65 degrees, giving 20 degrees. Multiplying by 2 gave 40 degrees, the angle of counterclockwise cap rotation. The cap was lifted, rotated 40 degrees clockwise, and replaced. Four weeks later, UCVA was 20/40 and the patient reported visual distortion in the right eye. The manifest refraction was −0.75 +2.25 × 117, giving 20/30 acuity (ie, the astigmatism had significantly changed axis but not magnitude). Topography again showed bow-tie astigmatism consistent with refraction (Figure 5, B ).

Figure 5.: A: Patient 3. Preoperatively, this eye's refraction was −4.0 sphere, correcting to 20/20. During LASIK, a free cap occurred. The surgeon performed the planned laser ablation and replaced the free cap without being able to identify the orientation marks. One month later, UCVA was 20/60, and refraction was −1.25 +2.00 × 65, giving 20/30 acuity. Topography showed astigmatism consistent with the refraction. B: Patient 3. It was calculated that the cap had been rotated 40 degrees counterclockwise. The cap was lifted, rotated 40 degrees clockwise, and replaced. Four weeks after the procedure, the patient reported visual distortion and UCVA of 20/40. Refraction was −0.75 +2.25 × 117, giving 20/30 vision. Topography showed steepening consistent with the measured astigmatism. C: Patient 3. It was hypothesized that this eye's original microkeratome cut was not exactly aligned with the horizontal axis, and this led to a miscalculation of the angle of cap rotation. The ratio of the magnitude of induced astigmatism before the rotation procedure was compared to the magnitude after the rotation. This ratio was used to solve for the angle of the microkeratome cut. This calculation led to the belief that the first rotation had moved the cap too far clockwise by 21 degrees. The cap was lifted a second time, rotated 20 degrees counterclockwise, and replaced. One month later, the eye's refraction was plano sphere and UCVA was 20/20. Topography showed a significant reduction in astigmatism.

This finding led to the hypothesis that during LASIK, the direction of the microkeratome pass might not have been exactly horizontal (ie, assumption 3 in Patients and Methods had not been valid). As before, the observed astigmatism had been caused by crossing of 1 convex cylinder (the cap) and 1 concave cylinder (the stromal bed), but in this case the stromal bed had been “misaligned” because the microkeratome axis was not at 0 degrees. The bisector between the cap and bed was indeed 45 degrees from the observed astigmatism, but the angle being bisected was not what had been expected. As a result, in the “corrective” procedure, rather than realigning the 2 cylinders, the rotated cap was moved so that the angle between the cap and stromal bed was now bisected by the 0 degrees axis.

In this situation, it is valuable to examine the magnitude of astigmatism induced by the rotated cap. In general, if 2 equal but opposite power cylinders are perfectly aligned, their net optical power will be zero. As the angle between the 2 cylinders increases from 0 degrees, so will the magnitude of induced astigmatism.

By using vector addition of astigmatism,^{4} it is possible to calculate the magnitude of this induced astigmatism. Here, the power of the rotated cap can be represented as a vector with length c and direction θ_{rot} degrees, the angle of counterclockwise rotation of the cap from the 0 degrees (horizontal) axis. The stromal bed's cylinder power can be represented by a vector in the 0 degrees direction with length −c , which is equivalent to a vector of length c at 180 degrees. In vector addition of astigmatism, each vector's angle is doubled and then the vectors are added geometrically. Finally, the angle of the sum vector is halved. The reader can verify that the magnitude of the sum vector produced in this manner can be calculated as follows:

The value of M reaches a maximum when the angle of separation is 90 degrees, which occurred in patient 2, whose induced astigmatism was 6.50 D before the corrective procedure.

In patient 3, it had not been not known that the microkeratome head was slightly rotated from the 0- to 180-degree axis. Using the assumptions and steps outlined in Surgical Technique, it was determined the angle of presumed cap position θ_{presumed} . After rotating the cap clockwise by θ_{presumed} , new induced cylinder, was created that can be calculated as

If the assumptions had been correct and the original microkeratome cut were at 0 degrees, θ_{rot} = θ_{presumed} and M′ = 0. Astigmatism would have been eliminated with the first rotation procedure, as was the case in patients 1 and 2. In patient 3, θ_{rot} and θ_{presumed} were apparently different angles, however. In this case, the ratio of astigmatism magnitudes can be simplified as

In this equation, M′, M, and θ_{presumed} are known (measured or calculated) quantities, so it is possible to solve for θ_{rot} .

Using the spreadsheet software Excel (Microsoft Corp.) “solver” function and using astigmatism values described for patient 3, θ_{rot} = 19 degrees was calculated. This suggested that the original angle of cap rotation was only 19 degrees, not 40 degrees as had been calculated. The cap had been 21 degrees clockwise too far.

A second procedure was performed, lifting the flap and rotating it counterclockwise by 20 degrees to reverse the “overrotation” of the first attempt. One month after this procedure, UCVA was 20/20 and the eye's refraction was plano sphere. Topography showed a reduction in corneal astigmatism (Figure 5, C ) to 1.4 D, which is consistent with superimposing the desired 2.0 D cylindrical correction upon the preoperative corneal astigmatism of 3.2 D. The 1.4 D of corneal astigmatism that remained after this final procedure was negated by preexisting lenticular astigmatism.

DISCUSSION
As these 3 cases demonstrate, inadvertent rotation of a free cap during LASIK can induce astigmatism and loss of BCVA because of irregularity of the cap's thickness. Basic optical principles can be applied to determine the angle of cap rotation. Lifting and rotating the cap to an astigmatically neutral position can reduce the induced astigmatism and achieve improved BCVA and UCVA.

Each patient had mixed astigmatism after surgery resulting from misalignment of a plus cylinder in the cap and a minus cylinder in the bed. Because the cap behaved as a cross-cylinder with the stromal bed, there was no significant observed shift in spherical refraction.

Several considerations should be made in applying these techniques to future patients. First, in our initial treatment of all 3 cases, we initially assumed that the horizontal movement of the microkeratome occurred at an axis of exactly 0 degrees. In patient 3, this proved to be an erroneous assumption. However, the actual angle of misalignment could be deduced by applying simplified formulas of vector change in astigmatism, and the error was corrected. Second, not all microkeratomes are designed for a nasal hinge. It would be necessary to adjust calculations for patients treated with a superior or other hinge location. Finally, it is essential to rule out other causes of postoperative astigmatism after LASIK such as faulty preoperative measurements, incorrect laser programming, or other LASIK flap abnormalities such as epithelial ingrowth, striae, or corneal ectasia.

In all 3 patients, the misaligned cap behaved optically like a plus cylinder. Theoretically, it is possible that a free cap could act as a concave cylinder. This would occur if the microkeratome cut began its pass deeply in the stromal tissue, then became shallow and finally deep again. This is similar to, but less dramatic than, what occurs with a buttonhole flap.

Rubin's principal^{3} implies that the axis of observed astigmatism (in plus cylinder format) is always at least 45 degrees from the power of the minus cylinder in the stromal bed. If the minus cylinder is indeed in the bed of the microkeratome cut along the 0- to 180-degree meridian, the refractive astigmatism will have its axis between 45 degrees and 135 degrees. Conversely, if somehow the microkeratome cut produced a stromal bed with a plus-cylinder power, the refractive astigmatism would have its axis between 0 degrees and 45 degrees or 135 degrees and 180 degrees. Because this principal is true for any angle of cap rotation, the axis of astigmatism determines whether the rotated cap is convex or concave. Therefore, assuming a microkeratome cut passing from 0 to 180 degrees, induced astigmatism at 45 to 135 degrees implies a plus-cylinder rotated cap and 0 to 45 degrees or 135 to 180 degrees implies a minus-cylinder rotated cap.

In the case of a misaligned minus-cylinder free cap, treatment would follow the same optical principles described above. However, in step 1 of the algorithm described in Surgical Technique, one would add, not subtract, 45 degrees to the axis of observed astigmatism to find the bisector angle.

Assumption 3 states that any angle of cap misalignment can be corrected with a clockwise rotation less than 180 degrees. It is plausible, though, that a surgeon could leave a cap misaligned by rotating it, say, 30 degrees clockwise. In such a case, our method would correct the misalignment by rotating the cap a further 150 degrees clockwise, leaving it misaligned by 180 degrees. If the cap were a symmetrical cylinder like an optical trial lens, this would neutralize the cross-cylinder, leaving no astigmatism. If the cap were asymmetric, however, it is reasonable to assume that coma or other nonspherocylindrical aberration might develop, resulting in a loss of BCVA. This situation did not arise in any of the patients presented here. If, however, an eye's astigmatism is corrected by the method described in this article but there remains a loss of BCVA, it may be possible to correct this distortion in a second procedure by rotating the cap another 180 degrees clockwise. Before invoking this explanation for the eye's residual loss of BCVA, it would be necessary to rule out other causes such as cap striae or ocular surface disease.

Rotation of a misaligned cap as described here carries the risk for loss of the free cap tissue. With careful handling, placement of a contact lens, and patching the eye postoperatively, this did not occur in our series.

The method described here has several advantages over other techniques of astigmatism correction. All patients presented with regular appearing bow-tie astigmatism topographically. However, each patient lost at least 1 line of BCVA. This implies that some degree of irregular astigmatism was present. After cap rotation reversal, both regular and irregular astigmatism components were corrected. A laser ablation or incisional procedure could not correct the irregular component of the patients' astigmatism as completely and would not result in improved BCVA.

Laser in situ keartomileusis surgeons may place fiduciary ink marks on the cornea, as was done in these cases, to aid in flap alignment. Inevitably, though, the ink washes off in some cases, and the method presented here may be useful. Cap rotation reversal involves minimal tissue manipulation, giving less surgical risk than a LASIK enhancement procedure, which requires laser ablation. Cap rotation reversal corrects the source of the problem rather than masking the result. It takes advantage of the full LASIK flap diameter for its optical zone. Finally, it is completely reversible; if the desired effect is not achieved, the surgeon can again lift the cap and undo the cap rotation procedure.