- Email: [email protected]
Postoperative astigmatism and rotational stability after artisan toric phakic intraocular lens implantation1
Postoperative astigmatism and rotational stability after Artisan toric phakic intraocular lens implantation Mana Tehrani, MD, H. Burkhard Dick, MD, Oliver Schwenn, MD, Eric Blom, MD, Alexander H. Schmidt, PhD, Hans-Reinhard Koch, MD Purpose: To evaluate deviations in the axis (intended versus achieved) and postoperative astigmatism after implantation of an Artisan toric phakic intraocular lens (IOL). Setting: University Eye Hospital, Mainz, Germany. Methods: This prospective study comprised 29 eyes with high ametropia and astigmatism. All eyes had uneventful implantation of a toric phakic IOL through a superior scleral tunnel incision at 12 o’clock. After a minimum of 6 months, the uncorrected visual acuity (UCVA), best correct visual acuity, refraction, and astigmatism were analyzed in all eyes. A multivariate analysis of postoperative astigmatism was performed. Results: After a follow-up of at least 6 months, 95% of eyes were within ⫾1.00 diopter (D) of emmetropia and 85% of eyes has a UCVA of 20/30 or better. The difference between the mean intended cylinder axis and achieved cylinder axis was 3.9 degrees (median 3 degrees; range to 13 degrees). The difference between the mean intended axis and the achieved axis between miosis and mydriasis was 1.8 degrees (median 1.5 degrees; range 0 to 5 degrees). The mean postoperative astigmatism after 6 months was 0.56 D with an axis of 31 degrees. Doubled-angle scatterplot analysis showed a tendency toward more flattening in the vertical meridian. Conclusions: During the 6-month follow-up, no significant rotation was observed after implantation of Artisan toric phakic IOLs to correct high ametropia. A sutureless sclerocorneal superior approach for phakic IOL insertion resulted in moderate to low astigmatism. Induced astigmatism should be taken into consideration during preoperative planning. J Cataract Refract Surg 2003; 29:1761–1766 © 2003 ASCRS and ESCRS
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onservative options such as spectacles and contact lenses can be considered the safest methods of correcting ametropia with astigmatism. Unfortunately, some patients cannot tolerate contact lenses, and spectacles can cause minimization and visual field limitations. Corneal reshaping procedures such as relaxing incisions, laser in situ keratomileusis, and photorefracAccepted for publication November 26, 2002. Reprint requests to Mana Tehrani, MD, Johannes Gutenberg-University, Department of Ophthalmology, Langenbeckstrasse 1, 55131 Mainz, Germany. E-mail: [email protected]. © 2003 ASCRS and ESCRS Published by Elsevier Inc.
tive keratectomy are currently popular. However, keratorefractive techniques can be associated with corneal weakening and thus an increased risk of corneal ectasia, decreased visual quality, and unpredictability, especially in eyes with a high refractive error.1 A recent alternative is the phakic intraocular lens (IOL), which provides intraocular correction of ametropia with astigmatism. Toric iris-claw lenses (Artisan, Ophtec) are available to correct corneal and lenticular astigmatism. The single-piece compression-molded Artisan is made of poly(methyl methacrylate) with 2(2⬘Hydroxy-3⬘-t-butyl-5⬘-methylphenyl)-5-chlorobenzo0886-3350/03/$–see front matter doi:10.1016/S0886-3350(03)00014-2
ASTIGMATISM AND STABILITY OF TORIC PHAKIC IOL
triazole (Tinuvin威 326). It has a 5.0 or 6.0 mm optic diameter, an overall length of 8.5 mm, and a maximum total width of 1.04 mm. In 1986, Worst and Fercher modified the existing iris-claw lens, producing a negative biconcave lens with a convex– concave optic, the Worst myopia claw lens. Since then, this IOL has been successfully implanted; its name changed to Artisan in 1998.1 Recently, the lens became available through AMO under the name Verisyse. The Artisan IOL is manufactured with a spherical anterior surface and a toric posterior surface. Two opposed haptics enable fixation on the iris (Figure 1). The IOL is available for myopia with refractive powers from –3.00 to –23.50 diopters (D) and for hyperopia from ⫹2.00 to ⫹12.00 D with an astigmatic correction to 7.00 D. The toric model can correct the total refractive error, both spherical and cylindrical.1,2 Rotational stability of the Artisan IOL and control of postoperative astigmatism are important to achieve the desired refractive outcome, especially in cases of astigmatic correction. This study sought to determine the difference between the achieved axis and intended axis after implantation of the Artisan toric IOL and to analyze postoperative astigmatism.
Patients and Methods Artisan phakic toric IOLs were implanted in 29 eyes between January 2000 and August 2001 at the University Eye Hospital, Mainz, Germany. Among the exclusion criteria were an endothelial cell count less than 1500 cells/mm2; anisometropia; anterior segment, iris, uveal, or macular pathol-
ogy; glaucoma; and pupil abnormality. Preoperative and 1 week and 1, 3, and 6 months postoperative examinations were performed to determine the uncorrected visual acuity, best corrected visual acuity, keratometry and/or computerized corneal topography, mesopic pupil diameter, slitlamp findings, endothelial cell count (specular microscopy), and anterior chamber depth.1 The mean age in the myopic group (n ⫽ 20) was 35 years (range 23 to 47 years) and the male-to-female ratio, 9 to 11. The mean refraction (spherical equivalent [SE]) was –9.0 D ⫾ 5.0 (SD) (range –21.0 to –2.5 D). The mean preoperative cylinder was 3.9 ⫾ 1.4 D (range 1.8 to 7.0 D) and the mean preoperative astigmatism, 1.5 D at an axis of 86 degrees. The mean age in the hyperopic group (n ⫽ 9) was 40 years (range 32 to 49 years) and the male-to-female ratio, 6 to 3. The mean preoperative refraction (SE) was 3.8 ⫾ 1.5 D (range 1.4 to 6.1 D). The mean preoperative cylinder was 3.5 ⫾ 0.8 D (range 2.0 to 4.3D) and the mean preoperative astigmatism, 2.9 D at an axis of 89 degrees. The IOL calculations were based on the van der Heijde formula2 using the mean corneal curvature (K), the adjusted anterior chamber depth (ACD – 0.8 mm [distance between IOL and crystalline lens]), and the SE at a vertex distance of 12.0 mm. The IOL was available with cylindrical correction in 0.5 D steps. There are 2 toric phakic IOL models depending on the axis of astigmatism. In eyes with a preoperative cylinder axis between 0 and 45 degrees or between 135 and 180 degrees, an IOL with a torus at 0 degree is recommended (model A). In eyes with a preoperative cylinder axis between 45 and 135 degrees, a torus at 90 degrees is recommended (model B). Both models can be fixated in the required position.1,2 Preoperative preparation was the same as in conventional cataract surgery except miotic drops (pilocarpine 1% to 2%) were used instead of mydriatics. A superior sclerocorneal 2-step self-sealing 5.1 to 5.3 mm incision and 2 paracenteses were created. After viscoelastic material was inserted through the paracenteses, an iris-claw lens with a 5.0 mm optic diameter was enclosed in the iris. The precise cylindrical axial orientation was ensured using marks on the limbus or iris structures such as crypts or vessels.1 Slitlamp evaluation with an integrated axis scheme was done to determine the postoperative IOL torus axis. After medical mydriasis, changes in the torus axis between miosis and mydriasis were photodocumented. Individual postoperative astigmatism was transformed into Cartesian coordinates; thus, the angle describing the cylindrical axis was doubled as follows3: x ⫽ cylinder * cos (2 * axis)
Figure 1. (Tehrani) Clinical photograph of an eye after implantation of an Artisan toric phakic IOL (model A) for hyperopia. The cylinder axis is equal to the axis running through the IOL’s claws.
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y ⫽ cylinder * sin (2 * axis) The graphic of the points (x, y) is the doubled-angle plot.
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The mean astigmatisms (centroids) were obtained by calculating the arithmetic mean of the corresponding Cartesian coordinates4 x ⫽ 1/n * (x 1 ⫹ x 2 ⫹. . .⫹x n) y ⫽ 1/n * (y 1 ⫹ y 2 ⫹. . .⫹y n) Finally, the arithmetic mean was transformed back to cylinder-axis form using the following equation: Cylinder ⫽ 冑共x 2 ⫹ y 2兲 Axis ⫽ 1/2 * arctan 共y/x兲, if x ⬎ 0, y ⱖ 0
Figure 2. (Tehrani) Postoperative deviation from the intended torus position.
⫽ 1/2 * arctan 共y/x兲 ⫹ 180°, if x ⬎ 0, y ⬍ 0 ⫽ 1/2 * arctan (y/x) ⫹ 90°, if x ⬍ 0 ⫽ 45°, if x ⫽ 0, y ⬎ 0 ⫽ 135°, if x ⫽ 0, y ⬍ 0 ⫽ undefined, if x ⫽ 0, y ⫽ 0 To describe sample variability, a 95% confidence ellipse indicates the area of the Cartesian plane in which the true centroid (ie, the centroid of the population) is located with 95% probability. The construction of confidence ellipses has been described.5 The generalized sample variance6 was used as a quantitative measure for the sizes of the confidence areas. Analysis of the standard deviations of the cylinder and axis of the sample centroid was performed as follows: The centroid was calculated as shown above. A line g was defined through the origin of the Cartesian plane and the centroid. The points representing the individual astigmatism on the patient sample were projected onto line g. The distances between the projections on g and the centroid were used to calculate the cylinder standard deviation by applying the common formula for standard deviations. To assess the axial standard deviation, the differences between axes of individual astigmatism and the centroid axis were determined. The differences were defined as ⱕ90 degrees. Then, the axial stan-
dard deviation was calculated by applying the common standard deviation formula to these differences. The t2 test for 1 sample7 was used to ascertain whether the sample centroid was significantly different from the origin. All statistical analyses were performed using the ASTICALC software package for analysis of astigmatic data for Windows and Macintosh, which is under development at Dardenne Clinic, Bonn-Bad Godesberg, Germany.
Results Within a minimum of 6 months, the mean deviation between the achieved axis and the intended axis was 3.9 degrees (median 3.0 degrees; range 0 to 13 degrees) (Figure 2). The mean difference in axis position between miosis and mydriasis was 1.8 degrees (median 1.5 degrees; range 0 to 5 degrees). Photographic analysis revealed no significant toric phakic IOL rotation (⬎2 degrees) and a stable IOL position over the 6-month follow-up. The mean astigmatism was 1.92 ⫾ 2.91 D at an axis of 88 ⫾ 37 degrees preoperatively and 0.56 ⫾ 0.75 D at an axis 31 ⫾ 28 degrees at 6 months. Table 1 shows the results of the preoperative and postoperative evaluations.
Table 1. Preoperative and postoperative data. Eyes (n)
Cylinder (D)
Axis (Degrees)
GSV
P Value
29
1.92 ⫾ 2.91
88 ⫾ 37
31.06
.0046
1 week
29
0.24 ⫾ 0.67
51 ⫾ 34
0.09
.1298
1 month
27
0.40 ⫾ 0.78
33 ⫾ 26
0.12
.0443
Follow-up Preoperative Postoperative
3 months
25
0.41 ⫾ 0.56
31 ⫾ 24
0.03
.0024
6 months
20
0.56 ⫾ 0.75
31 ⫾ 28
0.10
.0096
GSV ⫽ generalized sample variance
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Table 1 also shows the preoperative and postoperative generalized sample variance (GSV), a measure of the size of the confidence ellipses. The preoperative GSV (31.06) varied significantly more than the postoperative values (range 0.03 to 0.12). The error probability ␣ (P value), in which the hypothesis that the centroid of the sample equals zero can be rejected, is also shown. All P values after the first postoperative week were smaller than 0.05 as a result of the significant difference of the centroid from zero at level 0.05. Figure 3 graphs the centroids with the corresponding 95% confidence ellipses in a doubled-angle plot. Only the confidence ellipse in the first postoperative week contains the origin of the plane because the corresponding centroid is not significantly different from 0 (at level 0.05).
Discussion Successful correction of preoperative corneal and lenticular astigmatism depends on rotational stability and centration of the IOL. Rotation of a toric IOL is associated with an exponential decrease in astigmatic correction.8 For example, an IOL rotation of 15 degrees can decrease the cylindrical correction by approximately 50%. This study was designed to analyze the deviation between the intended axis and achieved axis postopera-
Figure 3. Centroids and corresponding 95% confidence ellipses (doubled-angle plot) (red ⫽ preoperative; green ⫽ 1 week postoperative; yellow ⫽ 1 month postoperative; blue ⫽ 3 months postoperative; purple ⫽ 6 months postoperative).
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tively and to calculate the postoperative astigmatism after implantation of an Artisan toric phakic IOL. To our knowledge, no published study has addressed these issues. We found a mean deviation between the intended axis and achieved axis of 3.9 degrees (median 3.0 degrees; range 0 to 13 degrees) over a 6-month follow-up. Because of the iris fixation of the IOL, we examined the difference in axis position between miosis and mydriasis and found a small mean deviation of 1.8 degrees. Design-dependent rotational stability is a potential weakness of toric IOLs, especially single-piece, platehaptic, posterior chamber models.9 –11 Rotational stability of aphakic IOLs has been studied by several authors. Patel and coauthors12 compared rotational stability between plate-haptic and loop-haptic lenses. Plate-haptic toric IOLs had a higher rate of rotation (24% over 30 degrees) than loop-haptic lenses (9% over 30 degrees) (P ⫽ .36). Ruhswurm et al.9 report rotation of up to 25.0 degrees in 18.9% of cases after implantation of single-piece, posterior chamber silicone lenses with plate haptics. The development of foldable, toric, posterior chamber IOLs with C-loop and Z-loop haptics seems to have achieved a higher degree of stability than plate-haptic lenses. Gerten and coauthors8 describe rotation of more than 10 degrees in 26% of 26 eyes after implantation of a foldable, 3-piece, posterior chamber toric IOL. All rotation was observed within the first 3 weeks after surgery. Leyland coauthors13 found rotation of more than 30 degrees in 9% of 22 eyes after implantation of a foldable, 3-piece, posterior chamber toric IOL. With toric posterior chamber IOLs, the relationship between the IOL and capsular bag and postoperative capsular bag shrinkage is primary and remains an unpredictable factor influencing rotational stability. Design modifications to increase rotational stability are expected. In general, enclavating the haptic ends of the IOL in the iris provides a higher degree of stability with less or no rotation over time. The literature describes several methods of calculating surgically induced astigmatism (SIA).14,15 Some are inconsistent or inaccurate. Naeser16 reviewed and evaluated these methods. There are 3 main problems in calculating SIA. First, regular astigmatism is characterized by 2 quantities: cylinder and axis. These quantities are nonorthogonal.4 In addition, the axis of astigmatism
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has a periodicity of 180 degrees rather than the 360 degrees of a common angle. Bivariate statistical methods must also be used, which requires the transformation from polar values to Cartesian coordinates that must contain a doubling of the angles. The transformation we used is mathematically identical to the polar-value method.17 The coordinates x and y are, apart from signs, the polar values KP 90 and KP 135. Describing sample variability in terms of bivariate statistics (eg, by using confidence ellipses or GSV) is difficult because these quantities are hard to interpret in terms of ophthalmology. Therefore, we used the centroid as basis for standard deviations of the cylinder and axis to simplify the description of sample variability for an ophthalmologist. Our analysis showed postoperative astigmatism of 0.56 D at 31 degrees 6 months after surgery, which is comparable to findings in other studies. Huang and Tseng18 report postoperative astigmatism of 0.61 D after surgery using sutureless 5.0 to 5.2 mm superior scleral incisions. Lyhne and Corydon19 report a median postoperative astigmatism of – 0.44 to – 0.64 D after a 5.2 mm superior scleral incision. A noticeable increase in cylinder power and a change in axis caused by incisioninduced corneal changes might be observed in the postoperative progression. In all cases, we used the Artisan IOL with a 5.0 mm optic. In 1997, a new spherical model with a 6.0 mm optic became available to minimize photic phenomena in patients with larger pupils. A 6.3 mm incision is required to implant the larger Artisan lens, which might induce more corneal changes. A new foldable Artisan IOL is under development. This IOL can be implanted through a smaller incision.
Conclusion Implantation of an Artisan toric phakic IOL is a new option for correcting high ametropia and astigmatism in a single procedure. An advantage of this method is satisfactory IOL rotational stability. Moreover, toric phakic IOL implantation through a sclerocorneal incision results in moderate to low postoperative astigmatism. The determination of postoperative astigmatism is important regardless of the type of incision. It is man-
datory to consider postoperative astigmatism in preoperative planning to achieve the desired postoperative refraction, especially when implanting toric IOLs.
References 1. Dick HB, Alio´ J, Bianchetti M, et al. Toric phakic intraocular lens: European multicenter study. Ophthalmology 2003; 110:150 –162 2. Budo C, Hessloehl JC, Izak M, et al. Multicenter study of the Artisan phakic intraocular lens. J Cataract Refract Surg 2000; 26:1163–1171 3. Jaffe NS, Clayman HM. The pathophysiology of corneal astigmatism after cataract extraction. Trans Am Acad Ophthalmol Otolaryngol 1975; 79:OP615–OP630 4. Holladay JT, Moran JR, Kezirian GM. Analysis of aggregate surgically induced refractive change, prediction error, and intraocular astigmatism. J Cataract Refract Surg 2001; 27:61–79 5. Naeser K, Hjortdal J. Multivariate analysis of refractive data; mathematics and statistics of spherocylinders. J Cataract Refract Surg 2001; 27:129 –142 6. Rencher AC. Methods of Multivariate Analysis. New York, NY, Wiley, 1995 7. Hotelling H. The generalisation of student’s ratio. Ann Math Stat 1931; 2:360 –378 8. Gerten G, Michels A, Olmes A. Torische Intraokularlinsen; Klinische Ergebnisse und Rotationsstabilita¨t. Ophthalmologe 2001; 98:715–720 9. Ruhswurm I, Scholz U, Zehetmayer M, et al. Astigmatism correction with a foldable toric intraocular lens in cataract patients. J Cataract Refract Surg 2000; 26:1022–1027 10. Shimizu K, Misawa A, Suzuki Y. Toric intraocular lenses: correcting astigmatism while controlling axis shift. J Cataract Refract Surg 1994; 20:523–526 11. Sun X-Y, Vicary D, Montgomery P, Griffiths M. Toric intraocular lenses for correcting astigmatism in 130 eyes. Ophthalmology 2000; 107:1776 –1781; discussion by RM Kershner, 1781–1782 12. Patel CK, Ormonde S, Rosen P, Bron AJ. Postoperative intraocular lens rotation; a randomized comparison of plate and loop haptic implants. Ophthalmology 1999; 106:2190 –2195; discussion by DJ Apple, 2196 13. Leyland M, Zinicola E, Bloom P, Lee N. Prospective evaluation of a plate haptic toric intraocular lens. Eye 2001; 15:202–205 14. Koch DD. How should we analyze astigmatic data? [editorial] J Cataract Refract Surg 2001; 27:1–3 15. Koch DD. Measuring patient outcomes after refractive surgery [editorial]. J Cataract Refract Surg 2001; 27:645– 646
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16. Naeser K. Popperian falsification of methods of assessing surgically induced astigmatism. J Cataract Refract Surg 2001; 27:25–30 17. Naeser K, Behrens JK, Naeser EV. Quantitative assessment of corneal astigmatic surgery: expanding the polar values concept. J Cataract Refract Surg 1994; 20:162– 168 18. Huang F-C, Tseng S-H. Comparison of surgically induced astigmatism after sutureless temporal clear corneal and scleral frown incisions. J Cataract Refract Surg 1998; 24:477–481 19. Lyhne N, Corydon L. Astigmatism after phacoemulsification with adjusted and unadjusted sutured versus
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sutureless 5.2 mm superior scleral incisions. J Cataract Refract Surg 1996; 22:1206 –1210 From the Department of Ophthalmology, Johannes Gutenberg-University, Mainz (Tehrani, Dick, Schwenn), and Dardenne Clinic, BonnBad Godesberg (Schmidt, Koch), Germany, and John A. Moran Eye Center, University of Utah Health Sciences Center, Salt Lake City, Utah, USA (Blom). Presented in part at the German Society of Ophthalmology Symposium on Cataract and Refractive Surgery, Berlin, Germany, September 2001. Prof. Koch and Dr. Schmidt are establishing the ASTICALC computer program, in which they will have a future financial interest. None of the other authors has a proprietary or financial interest in any material or method mentioned.
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onservative options such as spectacles and contact lenses can be considered the safest methods of correcting ametropia with astigmatism. Unfortunately, some patients cannot tolerate contact lenses, and spectacles can cause minimization and visual field limitations. Corneal reshaping procedures such as relaxing incisions, laser in situ keratomileusis, and photorefracAccepted for publication November 26, 2002. Reprint requests to Mana Tehrani, MD, Johannes Gutenberg-University, Department of Ophthalmology, Langenbeckstrasse 1, 55131 Mainz, Germany. E-mail: [email protected]. © 2003 ASCRS and ESCRS Published by Elsevier Inc.
tive keratectomy are currently popular. However, keratorefractive techniques can be associated with corneal weakening and thus an increased risk of corneal ectasia, decreased visual quality, and unpredictability, especially in eyes with a high refractive error.1 A recent alternative is the phakic intraocular lens (IOL), which provides intraocular correction of ametropia with astigmatism. Toric iris-claw lenses (Artisan, Ophtec) are available to correct corneal and lenticular astigmatism. The single-piece compression-molded Artisan is made of poly(methyl methacrylate) with 2(2⬘Hydroxy-3⬘-t-butyl-5⬘-methylphenyl)-5-chlorobenzo0886-3350/03/$–see front matter doi:10.1016/S0886-3350(03)00014-2
ASTIGMATISM AND STABILITY OF TORIC PHAKIC IOL
triazole (Tinuvin威 326). It has a 5.0 or 6.0 mm optic diameter, an overall length of 8.5 mm, and a maximum total width of 1.04 mm. In 1986, Worst and Fercher modified the existing iris-claw lens, producing a negative biconcave lens with a convex– concave optic, the Worst myopia claw lens. Since then, this IOL has been successfully implanted; its name changed to Artisan in 1998.1 Recently, the lens became available through AMO under the name Verisyse. The Artisan IOL is manufactured with a spherical anterior surface and a toric posterior surface. Two opposed haptics enable fixation on the iris (Figure 1). The IOL is available for myopia with refractive powers from –3.00 to –23.50 diopters (D) and for hyperopia from ⫹2.00 to ⫹12.00 D with an astigmatic correction to 7.00 D. The toric model can correct the total refractive error, both spherical and cylindrical.1,2 Rotational stability of the Artisan IOL and control of postoperative astigmatism are important to achieve the desired refractive outcome, especially in cases of astigmatic correction. This study sought to determine the difference between the achieved axis and intended axis after implantation of the Artisan toric IOL and to analyze postoperative astigmatism.
Patients and Methods Artisan phakic toric IOLs were implanted in 29 eyes between January 2000 and August 2001 at the University Eye Hospital, Mainz, Germany. Among the exclusion criteria were an endothelial cell count less than 1500 cells/mm2; anisometropia; anterior segment, iris, uveal, or macular pathol-
ogy; glaucoma; and pupil abnormality. Preoperative and 1 week and 1, 3, and 6 months postoperative examinations were performed to determine the uncorrected visual acuity, best corrected visual acuity, keratometry and/or computerized corneal topography, mesopic pupil diameter, slitlamp findings, endothelial cell count (specular microscopy), and anterior chamber depth.1 The mean age in the myopic group (n ⫽ 20) was 35 years (range 23 to 47 years) and the male-to-female ratio, 9 to 11. The mean refraction (spherical equivalent [SE]) was –9.0 D ⫾ 5.0 (SD) (range –21.0 to –2.5 D). The mean preoperative cylinder was 3.9 ⫾ 1.4 D (range 1.8 to 7.0 D) and the mean preoperative astigmatism, 1.5 D at an axis of 86 degrees. The mean age in the hyperopic group (n ⫽ 9) was 40 years (range 32 to 49 years) and the male-to-female ratio, 6 to 3. The mean preoperative refraction (SE) was 3.8 ⫾ 1.5 D (range 1.4 to 6.1 D). The mean preoperative cylinder was 3.5 ⫾ 0.8 D (range 2.0 to 4.3D) and the mean preoperative astigmatism, 2.9 D at an axis of 89 degrees. The IOL calculations were based on the van der Heijde formula2 using the mean corneal curvature (K), the adjusted anterior chamber depth (ACD – 0.8 mm [distance between IOL and crystalline lens]), and the SE at a vertex distance of 12.0 mm. The IOL was available with cylindrical correction in 0.5 D steps. There are 2 toric phakic IOL models depending on the axis of astigmatism. In eyes with a preoperative cylinder axis between 0 and 45 degrees or between 135 and 180 degrees, an IOL with a torus at 0 degree is recommended (model A). In eyes with a preoperative cylinder axis between 45 and 135 degrees, a torus at 90 degrees is recommended (model B). Both models can be fixated in the required position.1,2 Preoperative preparation was the same as in conventional cataract surgery except miotic drops (pilocarpine 1% to 2%) were used instead of mydriatics. A superior sclerocorneal 2-step self-sealing 5.1 to 5.3 mm incision and 2 paracenteses were created. After viscoelastic material was inserted through the paracenteses, an iris-claw lens with a 5.0 mm optic diameter was enclosed in the iris. The precise cylindrical axial orientation was ensured using marks on the limbus or iris structures such as crypts or vessels.1 Slitlamp evaluation with an integrated axis scheme was done to determine the postoperative IOL torus axis. After medical mydriasis, changes in the torus axis between miosis and mydriasis were photodocumented. Individual postoperative astigmatism was transformed into Cartesian coordinates; thus, the angle describing the cylindrical axis was doubled as follows3: x ⫽ cylinder * cos (2 * axis)
Figure 1. (Tehrani) Clinical photograph of an eye after implantation of an Artisan toric phakic IOL (model A) for hyperopia. The cylinder axis is equal to the axis running through the IOL’s claws.
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y ⫽ cylinder * sin (2 * axis) The graphic of the points (x, y) is the doubled-angle plot.
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The mean astigmatisms (centroids) were obtained by calculating the arithmetic mean of the corresponding Cartesian coordinates4 x ⫽ 1/n * (x 1 ⫹ x 2 ⫹. . .⫹x n) y ⫽ 1/n * (y 1 ⫹ y 2 ⫹. . .⫹y n) Finally, the arithmetic mean was transformed back to cylinder-axis form using the following equation: Cylinder ⫽ 冑共x 2 ⫹ y 2兲 Axis ⫽ 1/2 * arctan 共y/x兲, if x ⬎ 0, y ⱖ 0
Figure 2. (Tehrani) Postoperative deviation from the intended torus position.
⫽ 1/2 * arctan 共y/x兲 ⫹ 180°, if x ⬎ 0, y ⬍ 0 ⫽ 1/2 * arctan (y/x) ⫹ 90°, if x ⬍ 0 ⫽ 45°, if x ⫽ 0, y ⬎ 0 ⫽ 135°, if x ⫽ 0, y ⬍ 0 ⫽ undefined, if x ⫽ 0, y ⫽ 0 To describe sample variability, a 95% confidence ellipse indicates the area of the Cartesian plane in which the true centroid (ie, the centroid of the population) is located with 95% probability. The construction of confidence ellipses has been described.5 The generalized sample variance6 was used as a quantitative measure for the sizes of the confidence areas. Analysis of the standard deviations of the cylinder and axis of the sample centroid was performed as follows: The centroid was calculated as shown above. A line g was defined through the origin of the Cartesian plane and the centroid. The points representing the individual astigmatism on the patient sample were projected onto line g. The distances between the projections on g and the centroid were used to calculate the cylinder standard deviation by applying the common formula for standard deviations. To assess the axial standard deviation, the differences between axes of individual astigmatism and the centroid axis were determined. The differences were defined as ⱕ90 degrees. Then, the axial stan-
dard deviation was calculated by applying the common standard deviation formula to these differences. The t2 test for 1 sample7 was used to ascertain whether the sample centroid was significantly different from the origin. All statistical analyses were performed using the ASTICALC software package for analysis of astigmatic data for Windows and Macintosh, which is under development at Dardenne Clinic, Bonn-Bad Godesberg, Germany.
Results Within a minimum of 6 months, the mean deviation between the achieved axis and the intended axis was 3.9 degrees (median 3.0 degrees; range 0 to 13 degrees) (Figure 2). The mean difference in axis position between miosis and mydriasis was 1.8 degrees (median 1.5 degrees; range 0 to 5 degrees). Photographic analysis revealed no significant toric phakic IOL rotation (⬎2 degrees) and a stable IOL position over the 6-month follow-up. The mean astigmatism was 1.92 ⫾ 2.91 D at an axis of 88 ⫾ 37 degrees preoperatively and 0.56 ⫾ 0.75 D at an axis 31 ⫾ 28 degrees at 6 months. Table 1 shows the results of the preoperative and postoperative evaluations.
Table 1. Preoperative and postoperative data. Eyes (n)
Cylinder (D)
Axis (Degrees)
GSV
P Value
29
1.92 ⫾ 2.91
88 ⫾ 37
31.06
.0046
1 week
29
0.24 ⫾ 0.67
51 ⫾ 34
0.09
.1298
1 month
27
0.40 ⫾ 0.78
33 ⫾ 26
0.12
.0443
Follow-up Preoperative Postoperative
3 months
25
0.41 ⫾ 0.56
31 ⫾ 24
0.03
.0024
6 months
20
0.56 ⫾ 0.75
31 ⫾ 28
0.10
.0096
GSV ⫽ generalized sample variance
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Table 1 also shows the preoperative and postoperative generalized sample variance (GSV), a measure of the size of the confidence ellipses. The preoperative GSV (31.06) varied significantly more than the postoperative values (range 0.03 to 0.12). The error probability ␣ (P value), in which the hypothesis that the centroid of the sample equals zero can be rejected, is also shown. All P values after the first postoperative week were smaller than 0.05 as a result of the significant difference of the centroid from zero at level 0.05. Figure 3 graphs the centroids with the corresponding 95% confidence ellipses in a doubled-angle plot. Only the confidence ellipse in the first postoperative week contains the origin of the plane because the corresponding centroid is not significantly different from 0 (at level 0.05).
Discussion Successful correction of preoperative corneal and lenticular astigmatism depends on rotational stability and centration of the IOL. Rotation of a toric IOL is associated with an exponential decrease in astigmatic correction.8 For example, an IOL rotation of 15 degrees can decrease the cylindrical correction by approximately 50%. This study was designed to analyze the deviation between the intended axis and achieved axis postopera-
Figure 3. Centroids and corresponding 95% confidence ellipses (doubled-angle plot) (red ⫽ preoperative; green ⫽ 1 week postoperative; yellow ⫽ 1 month postoperative; blue ⫽ 3 months postoperative; purple ⫽ 6 months postoperative).
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tively and to calculate the postoperative astigmatism after implantation of an Artisan toric phakic IOL. To our knowledge, no published study has addressed these issues. We found a mean deviation between the intended axis and achieved axis of 3.9 degrees (median 3.0 degrees; range 0 to 13 degrees) over a 6-month follow-up. Because of the iris fixation of the IOL, we examined the difference in axis position between miosis and mydriasis and found a small mean deviation of 1.8 degrees. Design-dependent rotational stability is a potential weakness of toric IOLs, especially single-piece, platehaptic, posterior chamber models.9 –11 Rotational stability of aphakic IOLs has been studied by several authors. Patel and coauthors12 compared rotational stability between plate-haptic and loop-haptic lenses. Plate-haptic toric IOLs had a higher rate of rotation (24% over 30 degrees) than loop-haptic lenses (9% over 30 degrees) (P ⫽ .36). Ruhswurm et al.9 report rotation of up to 25.0 degrees in 18.9% of cases after implantation of single-piece, posterior chamber silicone lenses with plate haptics. The development of foldable, toric, posterior chamber IOLs with C-loop and Z-loop haptics seems to have achieved a higher degree of stability than plate-haptic lenses. Gerten and coauthors8 describe rotation of more than 10 degrees in 26% of 26 eyes after implantation of a foldable, 3-piece, posterior chamber toric IOL. All rotation was observed within the first 3 weeks after surgery. Leyland coauthors13 found rotation of more than 30 degrees in 9% of 22 eyes after implantation of a foldable, 3-piece, posterior chamber toric IOL. With toric posterior chamber IOLs, the relationship between the IOL and capsular bag and postoperative capsular bag shrinkage is primary and remains an unpredictable factor influencing rotational stability. Design modifications to increase rotational stability are expected. In general, enclavating the haptic ends of the IOL in the iris provides a higher degree of stability with less or no rotation over time. The literature describes several methods of calculating surgically induced astigmatism (SIA).14,15 Some are inconsistent or inaccurate. Naeser16 reviewed and evaluated these methods. There are 3 main problems in calculating SIA. First, regular astigmatism is characterized by 2 quantities: cylinder and axis. These quantities are nonorthogonal.4 In addition, the axis of astigmatism
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has a periodicity of 180 degrees rather than the 360 degrees of a common angle. Bivariate statistical methods must also be used, which requires the transformation from polar values to Cartesian coordinates that must contain a doubling of the angles. The transformation we used is mathematically identical to the polar-value method.17 The coordinates x and y are, apart from signs, the polar values KP 90 and KP 135. Describing sample variability in terms of bivariate statistics (eg, by using confidence ellipses or GSV) is difficult because these quantities are hard to interpret in terms of ophthalmology. Therefore, we used the centroid as basis for standard deviations of the cylinder and axis to simplify the description of sample variability for an ophthalmologist. Our analysis showed postoperative astigmatism of 0.56 D at 31 degrees 6 months after surgery, which is comparable to findings in other studies. Huang and Tseng18 report postoperative astigmatism of 0.61 D after surgery using sutureless 5.0 to 5.2 mm superior scleral incisions. Lyhne and Corydon19 report a median postoperative astigmatism of – 0.44 to – 0.64 D after a 5.2 mm superior scleral incision. A noticeable increase in cylinder power and a change in axis caused by incisioninduced corneal changes might be observed in the postoperative progression. In all cases, we used the Artisan IOL with a 5.0 mm optic. In 1997, a new spherical model with a 6.0 mm optic became available to minimize photic phenomena in patients with larger pupils. A 6.3 mm incision is required to implant the larger Artisan lens, which might induce more corneal changes. A new foldable Artisan IOL is under development. This IOL can be implanted through a smaller incision.
Conclusion Implantation of an Artisan toric phakic IOL is a new option for correcting high ametropia and astigmatism in a single procedure. An advantage of this method is satisfactory IOL rotational stability. Moreover, toric phakic IOL implantation through a sclerocorneal incision results in moderate to low postoperative astigmatism. The determination of postoperative astigmatism is important regardless of the type of incision. It is man-
datory to consider postoperative astigmatism in preoperative planning to achieve the desired postoperative refraction, especially when implanting toric IOLs.
References 1. Dick HB, Alio´ J, Bianchetti M, et al. Toric phakic intraocular lens: European multicenter study. Ophthalmology 2003; 110:150 –162 2. Budo C, Hessloehl JC, Izak M, et al. Multicenter study of the Artisan phakic intraocular lens. J Cataract Refract Surg 2000; 26:1163–1171 3. Jaffe NS, Clayman HM. The pathophysiology of corneal astigmatism after cataract extraction. Trans Am Acad Ophthalmol Otolaryngol 1975; 79:OP615–OP630 4. Holladay JT, Moran JR, Kezirian GM. Analysis of aggregate surgically induced refractive change, prediction error, and intraocular astigmatism. J Cataract Refract Surg 2001; 27:61–79 5. Naeser K, Hjortdal J. Multivariate analysis of refractive data; mathematics and statistics of spherocylinders. J Cataract Refract Surg 2001; 27:129 –142 6. Rencher AC. Methods of Multivariate Analysis. New York, NY, Wiley, 1995 7. Hotelling H. The generalisation of student’s ratio. Ann Math Stat 1931; 2:360 –378 8. Gerten G, Michels A, Olmes A. Torische Intraokularlinsen; Klinische Ergebnisse und Rotationsstabilita¨t. Ophthalmologe 2001; 98:715–720 9. Ruhswurm I, Scholz U, Zehetmayer M, et al. Astigmatism correction with a foldable toric intraocular lens in cataract patients. J Cataract Refract Surg 2000; 26:1022–1027 10. Shimizu K, Misawa A, Suzuki Y. Toric intraocular lenses: correcting astigmatism while controlling axis shift. J Cataract Refract Surg 1994; 20:523–526 11. Sun X-Y, Vicary D, Montgomery P, Griffiths M. Toric intraocular lenses for correcting astigmatism in 130 eyes. Ophthalmology 2000; 107:1776 –1781; discussion by RM Kershner, 1781–1782 12. Patel CK, Ormonde S, Rosen P, Bron AJ. Postoperative intraocular lens rotation; a randomized comparison of plate and loop haptic implants. Ophthalmology 1999; 106:2190 –2195; discussion by DJ Apple, 2196 13. Leyland M, Zinicola E, Bloom P, Lee N. Prospective evaluation of a plate haptic toric intraocular lens. Eye 2001; 15:202–205 14. Koch DD. How should we analyze astigmatic data? [editorial] J Cataract Refract Surg 2001; 27:1–3 15. Koch DD. Measuring patient outcomes after refractive surgery [editorial]. J Cataract Refract Surg 2001; 27:645– 646
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16. Naeser K. Popperian falsification of methods of assessing surgically induced astigmatism. J Cataract Refract Surg 2001; 27:25–30 17. Naeser K, Behrens JK, Naeser EV. Quantitative assessment of corneal astigmatic surgery: expanding the polar values concept. J Cataract Refract Surg 1994; 20:162– 168 18. Huang F-C, Tseng S-H. Comparison of surgically induced astigmatism after sutureless temporal clear corneal and scleral frown incisions. J Cataract Refract Surg 1998; 24:477–481 19. Lyhne N, Corydon L. Astigmatism after phacoemulsification with adjusted and unadjusted sutured versus
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sutureless 5.2 mm superior scleral incisions. J Cataract Refract Surg 1996; 22:1206 –1210 From the Department of Ophthalmology, Johannes Gutenberg-University, Mainz (Tehrani, Dick, Schwenn), and Dardenne Clinic, BonnBad Godesberg (Schmidt, Koch), Germany, and John A. Moran Eye Center, University of Utah Health Sciences Center, Salt Lake City, Utah, USA (Blom). Presented in part at the German Society of Ophthalmology Symposium on Cataract and Refractive Surgery, Berlin, Germany, September 2001. Prof. Koch and Dr. Schmidt are establishing the ASTICALC computer program, in which they will have a future financial interest. None of the other authors has a proprietary or financial interest in any material or method mentioned.
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