Current Eye Research, Early Online, 1–6, 2014 ! Informa Healthcare USA, Inc. ISSN: 0271-3683 print / 1460-2202 online DOI: 10.3109/02713683.2014.959708
RESEARCH REPORT
Impact of Posterior Corneal Surface on Toric Intraocular Lens (IOL) Calculation Paul-Rolf Preussner1, Peter Hoffmann2 and Jochen Wahl1
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1
University Eye Hospital, Mainz, Germany, and 2Private Eye Clinic, Castrop-Rauxel, Germany
ABSTRACT Purpose: To quantify the impact of posterior cornea on toric IOL calculation accuracy using Placido-topography of anterior corneal surface and Scheimpflug measurements of corneal thickness. Materials and Methods: Three-hundred seventy-nine non-selected eyes undergoing cataract surgery with non-toric intraocular lens (IOL) implantation were measured with TMS-5 (Tomey, Japan), IOLMaster (Zeiss, Germany) and Lenstar (Haag-Streit, Switzerland). Anterior, posterior and total measured corneal astigmatisms were compared with astigmatisms from postoperative refraction by calculating vector differences. Results: The average absolute vector difference between anterior astigmatism and total astigmatism combining the measurements of anterior and posterior cornea was only 0.3 ± 0.2 D, with a median of only 0.27 D, but a maximum of 1.5 D. Measurements of anterior cornea alone show a systematic difference from refractive cylinder of 0.3–6 D at 90, 0.38 D at 89 and 0.28 D at 91 (IOLMaster, Lenstar and anterior TMS5), whereas the total TMS5 cylinder differs on average by only 0.14D at 81 from the refractive cylinder. With-the-rule (WTR) corneal astigmatism is slightly reduced and against-the-rule (ATR) astigmatism slightly increased on average when posterior corneal surface is taken into account additionally. This could also be confirmed by the calculation of an average pachymetry of all eyes in which the thinnest central part shows an ellipsoidal shape with horizontally long axis. Conclusion: Measurements of posterior cornea have on average only a small but significant impact on the outcome of toric IOL calculation, however, they are nevertheless recommended to detect outliers in which corneal irregularities (e.g. beginning keratokonus) may be overlooked. Keywords: Astigmatism, keratoconus, posterior corneal surface, toric IOL calculation, vector differences
INTRODUCTION
The influence of posterior corneal surface has already been investigated by many authors.2–19 However, the description of the optical characteristics in these papers is not uniform causing the results to be hardly comparable. The use of ‘‘K-values’’ for example has hidden implicit model assumptions about the ratio of anterior to posterior surface vertex radii,20 and also the definition of the astigmatism of an irregular surface is not really obvious and selfexplaining. Also in our approach we need some assumptions and commitments. They are made in such a way that the results are directly comparable with the results
In a recent paper,1 it was found that the accuracy of toric IOL calculation in 78 eyes could be improved when using anterior and posterior corneal surface compared to the data of anterior surface alone. The difference was not very high but nevertheless ‘‘statistically significant’’. In the present paper, we investigate the theoretical win in calculation accuracy in a much larger collective of 395 eyes. In order to exclude the impact of toric IOL misalignment this investigation in performed in eyes implanted with rotationally symmetric (non-toric) IOLs.
Received 11 April 2014; revised 23 July 2014; accepted 24 August 2014; published online 26 September 2014 Correspondence: Paul-Rolf Preussner, University Eye Hospital, Langenbeckstr. 1, Mainz D-55101, Germany. E-mail: [email protected]
1
2
P.-R. Preussner et al.
of raytracing for IOL power calculations.21–23 Such assumptions and commitments are needed because astigmatism is initially not defined in the environment of a raytracing calculation, see next section.
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
MATERIALS AND METHODS Three-hundred ninety-five eyes without prior ocular surgery or known pathology beside cataract or glaucoma were investigated consecutively with the Tomey TMS-5 prior to cataract surgery. The data were retrospectively analyzed and used for a representative sample of ‘‘normal’’, i.e. unselected eyes. In addition, corneal radii and axial lengths were measured with the Lenstar (Haag-Streit, Switzerland) and the IOLMaster (Zeiss, Germany). All eyes underwent subjective refraction 2 months after surgery. Magnitude and axis of the astigmatism was determined by the cross-cylinder method. The TMS-5 performes Placido topography of the anterior corneal surface and spatially resolved pachymetry by rotating Scheimpflug images, both aligned to the same center. This center is defined by the 1st Purkinje reflex of the cornea when the patient fixates the target of the machine. Local corneal radii and thicknesses as functions of the distance from the center in 360 semi-meridians (i.e. in polar coordinates) were exported from the TMS-5 into OKULIX raytracing software for subsequent evaluation. The steepest and flattest vertex radii being perpendicular to each other, their meridional angles and the asphericity of the anterior corneal surface were extracted for the 6mm optical zone by a 4-dimensional fit procedure which has already been described earlier.24 From the known anterior surface and the known local thickness, local posterior curvature radii were calculated by classical analytical geometry. For the posterior cornea then the same procedure as for the anterior one was applied to extract steepest and flattest vertex radii, their angles, and the posterior asphericity. Refractive power of a spherical surface is defined in Gaussian optics by (n2 - n1)/R with n1, n2: refractive indices of two adjacent media separated by a spherical surface with radius R. With this definition, the astigmatism of anterior and posterior corneal curvature could be calculated by the difference of the powers for the two different vertex radii mentioned above of either corneal surface. The astigmatisms of anterior and posterior cornea cannot simply be combined by vector addition because they occur at different locations. Instead, for each meridian, the resulting power of a thick lens in Gaussian optics is calculated from the local vertex radii of anterior and posterior surface which follow
the known cos2-distribution of astigmatic radii for either surface. The resulting thick-lens combined powers again have a cos2-distribution for which the meridional angle of maximum difference and the corresponding absolute value of this difference can be determined. This is what is called ‘‘total corneal astigmatism’’ Ac with its axis ac in this context. Without the measured information of the posterior cornea, i.e. only with the data of the anterior cornea, an ‘‘anterior astigmatism representative for the whole cornea’’ Aa with axis aa can be constructed as an alternative to the abovementioned Ac. It assumes a constant ratio of posterior to anterior vertex radii for all meridians. For this ratio we use a value of 0.83 corresponding to a fictitious ‘‘corneal refractive index’’20 of 1.327, in accordance with the meanwhile widely accepted eye model of Liou and Brennan.25 This procedure to calculate Aa is applied to the anterior surface measured by the TMS5 and to determine the keratometric astigmatism measured by the IOLMaster and the Lenstar.
RESULTS The mean absolute total astigmatism according to the TMS5-measurements was 0.88 D, the median 0.75 D. The Difference between the anterior (Aa) and the total (Ac) corneal astigmatism of the 395 eyes as defined in the previous section is shown in Figure 1. The arithmetic mean of 0.3 D and the standard deviation of 0.2 D should be looked at with care because of the high skewness of the distribution. The best measure of ‘‘average’’ is the median of 0.27 D. But note that the maximum difference is 1.5 D. The whole collective can be divided into 225 eyes of with-the-rule astigmatism (WTR, cylinder axis between 135 and 45 ) and 170 eyes of against the-rule astigmatism (ATR, cylinder axis between 45 and 135 ). Aa is used here for this division into WTR and ATR eyes. As can be seen in Figures 2 and 3, Ac compared to Aa of the WTR eyes is reduced on average, but increased in the ATR fraction. The average anterior corneal topography of all right and all left eyes is shown in Figure 4, together with the average pachymetries and the extracted anterior and posterior vertex radii and asphericities. The differences between the subjective astigmatisms and the astigmatisms measured by the IOLMaster and by the Lenstar are shown in Figure 5. The differences between the subjective astigmatisms and Aa and Ac are shown in Figure 6.
DISCUSSION The vector differences between the anterior astigmatism Aa with axis aa and the total astigmatism Ac with Current Eye Research
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Posterior cornea
3
FIGURE 1. Difference between anterior and total astigmatism. A: histogram distribution of the absolute value Ac - Aa The arithmetic mean is 0.30 D, standard deviation 0.20 D, median 0.27 D, maximum 1.5 D. vector difference between Ac and Aa (TMS5-measurements). The absolute differences between Ac and Aa are statistically significantly different from zero (p51.0 10 4 in the Wilcoxon test for paired samples).
FIGURE 2. Two-hundred twenty-five eyes showing with-the-rule astigmatism (WTR). A: distribution of total corneal astigmatism Ac. B: distribution of anterior corneal astigmatism Aa. In these eyes the total astigmatism is decreased on average when the posterior surface is taken into account.
FIGURE 3. One-hundred seventy eyes showing against-the-rule astigmatism (ATR). A: distribution of total corneal astigmatism Ac. B: distribution of anterior corneal astigmatism Aa. In these eyes the total astigmatism is increased on average when the posterior surface is taken into .account.
axis ac directly contribute to the total astigmatic error when toric IOLs are implanted, assuming that only Ac describes the astigmatism correctly, but Aa is used for IOL calculation. On average, with a median of only !
2014 Informa Healthcare USA, Inc.
0.27 D, the difference between Ac and Aa is in the order of the recognition threshold and therefore clinically not very relevant, even if it was found that it was already ’’statistically significant’’ in a previous
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
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P.-R. Preussner et al.
FIGURE 4. Average tomographies. A: average anterior topography (local corneal radii) of 199 right eyes, including best-fit corneal vertex radii, axes and asphericities of anterior and posterior surface B: average pachymetry of 199 right eyes C: average anterior topography of 196 left eyes D: average pachymetry of 196 left eyes.
FIGURE 5. Difference between keratometry and refraction. The vector differences between the astigmatism Aa and the astigmatism of the subjective refraction is shown for the Lenstar (left) and the IOLMaster (right).
FIGURE 6. Difference between tomography and refraction. The vector differences between the total astigmatisms Ac and the astigmatisms of the subjective refraction are shown on the left, the vector differences between the anterior astigmatisms Aa and the astigmatisms of the subjective refraction are shown on the right.
Current Eye Research
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
Posterior cornea investigation1 in which 78 eyes were implanted with toric IOLs. Astigmatic vector errors are on average very similar in both papers. The differences between Aa and Ac are not fully randomly distributed as suggested when only looking to Figure 1. In cases of WTR astigmatism, Ac is decreased by the contribution of the posterior surface, in cases of ATR increased on average, Figures 2 and 3, which confirms the findings of other groups.2 This means that the central thinnest part of the cornea cannot be rotationally symmetric but should have an ellipsoidal shape with horizontal long axis on average, as confirmed in Figure 4. Clinically, this implies that the cylinder power of toric IOLs has a trend to be overestimated in WTR eyes and underestimated in ATR eyes when the calculation is only based on measurements of the anterior cornea, and that the cylinder axis is systematically rotated, particularly in case of an oblique axis. In addition to the found differences between Aa and Ac also measuring errors may play a role.26 They could not be investigated in this paper because no other measurements for comparisons where available. Measurement errors of the astigmatism of the cornea generally should be looked at as errors of fitting the theoretically ideal construct of the astigmatism to an irregular surface rather than as technical measurement errors of a measuring device. Also, the softness of the cornea including tear film is highly important. An additional hidden error when investigating corneal and refractive astigmatisms can occur from little IOL decentration or tilt. Even if these errors theoretically cause a coma rather than astigmatism, they can be partly corrected by cylindrical glasses. The centroid shift of 0.14 D for the difference between Ac and the refractive astigmatism may be caused by such IOL misalignments (Figure6, left subimage). Note that the contribution of the posterior corneal surface to the total astigmatism is nearly independent on the amount of the anterior astigmatism, as can be found by a comparison of the results of the present investigation with our earlier results1 which had significantly higher astigmatisms on average. The reason of (possibly overlooked) posterior astigmatism can best be understood by the non-rotationally symmetric corneal thickness as shown in Figure 4. The toric IOL axis error (in degrees) caused by an omission of the pachymetric measurement increases with decreasing anterior astigmatism. In the present investigation with 395 eyes we found a difference between Ac and Aa of 41 D in 0.75% of the cases (Figure 1). To detect this relatively small and statistically unimportant number a large collective of eyes was necessary. If implanted with toric IOLs calculated only from Aa, these cases would be candidates for ‘‘unhappy patients’’. For that reason, a corneal tomography including posterior surface is generally recommended, even if the big majority of !
2014 Informa Healthcare USA, Inc.
5
patients has only little accuracy win from this approach.
DECLARATION OF INTEREST Paul-Rolf Preussner is author of the commercially available software package OKULIX mentioned in the text. The other authors do not have commercial interest in any product or company or competing product or company mentioned in the text. This paper has not been supported by 3rd parties.
REFERENCES 1. Hoffmann PC, Wahl J, Hu¨tz WW, Preussner PR. A raytracing approach to calculate toric intraocular lenses. J Refract Surg 2013;29:402–408. 2. Koch DD, Ali SF, Weikert MP, Shirayama M, Jenkins R, Wang L. Contribution of posterior corneal astigmatism to total corneal astigmatism. J Cataract Refract Surg 2012;38: 2080–2087. 3. Aramberri J, Araiz L, Garcia A, Illaramendi I, Olmos J, Oyanarte I, et al. Dual versus single Scheimpflug for anterior segment analysis: precision and agreement. J Cataract Refract Surg 2012;36:1934–1949. 4. Cheng LS, Tsai CY, Tsai RJF, Liou SW, Ho JD. Estimation accuracy of surgically induced astigmatism on the cornea when neglecting the posterior corneal surface measurement. Acta Ophthalmologica 2011;89:417–422. 5. Dubbelman M, Weeber HA, van der Heijde RG, Vo¨lker-Dieben HJ. Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography. Acta Ophtalmol Scand 2002;80:379–383. 6. Dubbelman M, Sicam VA, van der Heijde RG. The contribution of the posterior corneal surface to the coma aberration of the human cornea. J Vis 2007;7:10–8. 7. Ho JD, Liou SW, Tsai RJF, Tsai CY. Effects of aging on anterior and posterior corneal astigmatism. Cornea 2010; 29:632–637. 8. HO JD, Tsai CY, Liou SW. Accuracy of corneal astigmatism estimation by neglecting the corneal surface measurement. Am J Opthalmol 2009;147:788–795. 9. Karimian F, Feizi S, Doozandeh A, Faramarzi A, Yaseri M. Comparison of corneal tomography using Galilei, Orbscan II and Placido-disk-based topographer systems. J Refract Surg 2011;27:502–508. 10. Koch DD. Astigmatism analysis: the spectrum of approaches. J Cataract Refract Surg 2006;32:1977–1978. 11. Mas D, Espinosa J, Domenech B, Perez J, Kasprzak H, Illueca C. Correlation between the dioptric power, astigmatism and surface shape of 11 the anterior and posterior corneal surfaces. Ophthalmic Physiol Opt 2009; 29:219–226. 12. Pinero DP, Alio´ JL, Aleso´n A, Vergara EM, Miranda M. Corneal volume, pachymetry, and correlation of anterior and posterior corneal shape in subclinical and different stages of clinical keratoconus. J Cataract Refract Surg 2010; 36:814–825. 13. Pin˜ero DP, Saenz Gonza´lez C, Alio´ JL. Intraobserver and interobserver repeatability of curvature and aberrometric measurements of the posterior corneal surface in normal eyes using Scheimpflug photography. J Cataract Refract Surg 2009;35:113–120.
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14. Prisant O, Huang-Xuan T, Proano C, Hernandez E, Awad S, Azar DT. Vector summation of anterior and posterior corneal topographical astig-matism. J Cataract Refract Surg 2002;28:1636–1643. 15. Qian YS, Huang J, Liu R, Chu RY, Xu Y, Zhou XT, et al. Influence of internal optical astigmatism on the correction of myopic astigmatism by Lasik. J Refract Surg 2011;27: 863–868. ¨O ¨ , Cetinkor V, O ¨ zkan M, Kanpolat A. 16. Uc¸akhan O Evaluation of Scheimpflug imaging parameters in subclinical keratoconus, keratoconusand normal eyes. J Cataract Refract Surg 2011;37:1116–1124. 17. Wang L, Mahmoud AM, Anderson BL, Koch DD, Roberts CJ. Total corneal power estimation: ray tracing method versus Gaussian optics formula. Invest Ophtalmol Vis Sci 2011;52:1716–1722. 18. Wang L, Shirayama M, Koch DD. Repeatability of corneal power and wavefront aberration measurements with a dual Scheimpflug Placido corneal topographer. J Cataract Refract Surg 2010;36:425–430. 19. Zhang L, Wang Y. The shape of posterior corneal surface in normal, post-Lasik and post-epi-Lasik eyes. Invest Ophthalmol Vis Sci 2010;51:3468–3475.
20. Olsen T. On the calculation of power from curvature of the cornea. Br J Ophthalmol 1986;70:152–154. 21. Preussner PR, Wahl J, Lahdo H, Findl O, Dick B. Raytracing for in-traocular lens calculation. J Cat Refract Surg 2000;28:1412–1419. 22. Preußner PR. Consistent IOL calculation in normal and odd eyes with the raytracing program OKULIX. In: Garg A, Hoyos JE, Dementiev D, editors. Mastering the techniques of IOL power calculations. New Delhi: Jaypee Brothers Medical Publishers ltd.; 2005. pp 285–291. 23. Preußner PR, Olsen T, Hoffmann P, Findl O. IOL calculation accuracy limits in normal eyes. J Cataract Refract Surg 2008;34:802–808. 24. Preußner PR, Wahl J, Weitzel. Topography based IOL power selection. J Cataract Refract Surg 2005;31: 525–533. 25. Liou HL, Brennan NA. Anatomically accurate, finite model eye for optical modeling. J Opt Soc Am 1997;14: 1684–1695. 26. Szalai E, Berta A, Hassan Z, Modis L. Reliability and repeatability of swept-source Fourier-domain optical coherence tomography and Scheimpflug imaging in keratoconus. J Cataract Refract Surg 2012;38:485–494.
Current Eye Research
RESEARCH REPORT
Impact of Posterior Corneal Surface on Toric Intraocular Lens (IOL) Calculation Paul-Rolf Preussner1, Peter Hoffmann2 and Jochen Wahl1
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
1
University Eye Hospital, Mainz, Germany, and 2Private Eye Clinic, Castrop-Rauxel, Germany
ABSTRACT Purpose: To quantify the impact of posterior cornea on toric IOL calculation accuracy using Placido-topography of anterior corneal surface and Scheimpflug measurements of corneal thickness. Materials and Methods: Three-hundred seventy-nine non-selected eyes undergoing cataract surgery with non-toric intraocular lens (IOL) implantation were measured with TMS-5 (Tomey, Japan), IOLMaster (Zeiss, Germany) and Lenstar (Haag-Streit, Switzerland). Anterior, posterior and total measured corneal astigmatisms were compared with astigmatisms from postoperative refraction by calculating vector differences. Results: The average absolute vector difference between anterior astigmatism and total astigmatism combining the measurements of anterior and posterior cornea was only 0.3 ± 0.2 D, with a median of only 0.27 D, but a maximum of 1.5 D. Measurements of anterior cornea alone show a systematic difference from refractive cylinder of 0.3–6 D at 90, 0.38 D at 89 and 0.28 D at 91 (IOLMaster, Lenstar and anterior TMS5), whereas the total TMS5 cylinder differs on average by only 0.14D at 81 from the refractive cylinder. With-the-rule (WTR) corneal astigmatism is slightly reduced and against-the-rule (ATR) astigmatism slightly increased on average when posterior corneal surface is taken into account additionally. This could also be confirmed by the calculation of an average pachymetry of all eyes in which the thinnest central part shows an ellipsoidal shape with horizontally long axis. Conclusion: Measurements of posterior cornea have on average only a small but significant impact on the outcome of toric IOL calculation, however, they are nevertheless recommended to detect outliers in which corneal irregularities (e.g. beginning keratokonus) may be overlooked. Keywords: Astigmatism, keratoconus, posterior corneal surface, toric IOL calculation, vector differences
INTRODUCTION
The influence of posterior corneal surface has already been investigated by many authors.2–19 However, the description of the optical characteristics in these papers is not uniform causing the results to be hardly comparable. The use of ‘‘K-values’’ for example has hidden implicit model assumptions about the ratio of anterior to posterior surface vertex radii,20 and also the definition of the astigmatism of an irregular surface is not really obvious and selfexplaining. Also in our approach we need some assumptions and commitments. They are made in such a way that the results are directly comparable with the results
In a recent paper,1 it was found that the accuracy of toric IOL calculation in 78 eyes could be improved when using anterior and posterior corneal surface compared to the data of anterior surface alone. The difference was not very high but nevertheless ‘‘statistically significant’’. In the present paper, we investigate the theoretical win in calculation accuracy in a much larger collective of 395 eyes. In order to exclude the impact of toric IOL misalignment this investigation in performed in eyes implanted with rotationally symmetric (non-toric) IOLs.
Received 11 April 2014; revised 23 July 2014; accepted 24 August 2014; published online 26 September 2014 Correspondence: Paul-Rolf Preussner, University Eye Hospital, Langenbeckstr. 1, Mainz D-55101, Germany. E-mail: [email protected]
1
2
P.-R. Preussner et al.
of raytracing for IOL power calculations.21–23 Such assumptions and commitments are needed because astigmatism is initially not defined in the environment of a raytracing calculation, see next section.
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
MATERIALS AND METHODS Three-hundred ninety-five eyes without prior ocular surgery or known pathology beside cataract or glaucoma were investigated consecutively with the Tomey TMS-5 prior to cataract surgery. The data were retrospectively analyzed and used for a representative sample of ‘‘normal’’, i.e. unselected eyes. In addition, corneal radii and axial lengths were measured with the Lenstar (Haag-Streit, Switzerland) and the IOLMaster (Zeiss, Germany). All eyes underwent subjective refraction 2 months after surgery. Magnitude and axis of the astigmatism was determined by the cross-cylinder method. The TMS-5 performes Placido topography of the anterior corneal surface and spatially resolved pachymetry by rotating Scheimpflug images, both aligned to the same center. This center is defined by the 1st Purkinje reflex of the cornea when the patient fixates the target of the machine. Local corneal radii and thicknesses as functions of the distance from the center in 360 semi-meridians (i.e. in polar coordinates) were exported from the TMS-5 into OKULIX raytracing software for subsequent evaluation. The steepest and flattest vertex radii being perpendicular to each other, their meridional angles and the asphericity of the anterior corneal surface were extracted for the 6mm optical zone by a 4-dimensional fit procedure which has already been described earlier.24 From the known anterior surface and the known local thickness, local posterior curvature radii were calculated by classical analytical geometry. For the posterior cornea then the same procedure as for the anterior one was applied to extract steepest and flattest vertex radii, their angles, and the posterior asphericity. Refractive power of a spherical surface is defined in Gaussian optics by (n2 - n1)/R with n1, n2: refractive indices of two adjacent media separated by a spherical surface with radius R. With this definition, the astigmatism of anterior and posterior corneal curvature could be calculated by the difference of the powers for the two different vertex radii mentioned above of either corneal surface. The astigmatisms of anterior and posterior cornea cannot simply be combined by vector addition because they occur at different locations. Instead, for each meridian, the resulting power of a thick lens in Gaussian optics is calculated from the local vertex radii of anterior and posterior surface which follow
the known cos2-distribution of astigmatic radii for either surface. The resulting thick-lens combined powers again have a cos2-distribution for which the meridional angle of maximum difference and the corresponding absolute value of this difference can be determined. This is what is called ‘‘total corneal astigmatism’’ Ac with its axis ac in this context. Without the measured information of the posterior cornea, i.e. only with the data of the anterior cornea, an ‘‘anterior astigmatism representative for the whole cornea’’ Aa with axis aa can be constructed as an alternative to the abovementioned Ac. It assumes a constant ratio of posterior to anterior vertex radii for all meridians. For this ratio we use a value of 0.83 corresponding to a fictitious ‘‘corneal refractive index’’20 of 1.327, in accordance with the meanwhile widely accepted eye model of Liou and Brennan.25 This procedure to calculate Aa is applied to the anterior surface measured by the TMS5 and to determine the keratometric astigmatism measured by the IOLMaster and the Lenstar.
RESULTS The mean absolute total astigmatism according to the TMS5-measurements was 0.88 D, the median 0.75 D. The Difference between the anterior (Aa) and the total (Ac) corneal astigmatism of the 395 eyes as defined in the previous section is shown in Figure 1. The arithmetic mean of 0.3 D and the standard deviation of 0.2 D should be looked at with care because of the high skewness of the distribution. The best measure of ‘‘average’’ is the median of 0.27 D. But note that the maximum difference is 1.5 D. The whole collective can be divided into 225 eyes of with-the-rule astigmatism (WTR, cylinder axis between 135 and 45 ) and 170 eyes of against the-rule astigmatism (ATR, cylinder axis between 45 and 135 ). Aa is used here for this division into WTR and ATR eyes. As can be seen in Figures 2 and 3, Ac compared to Aa of the WTR eyes is reduced on average, but increased in the ATR fraction. The average anterior corneal topography of all right and all left eyes is shown in Figure 4, together with the average pachymetries and the extracted anterior and posterior vertex radii and asphericities. The differences between the subjective astigmatisms and the astigmatisms measured by the IOLMaster and by the Lenstar are shown in Figure 5. The differences between the subjective astigmatisms and Aa and Ac are shown in Figure 6.
DISCUSSION The vector differences between the anterior astigmatism Aa with axis aa and the total astigmatism Ac with Current Eye Research
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
Posterior cornea
3
FIGURE 1. Difference between anterior and total astigmatism. A: histogram distribution of the absolute value Ac - Aa The arithmetic mean is 0.30 D, standard deviation 0.20 D, median 0.27 D, maximum 1.5 D. vector difference between Ac and Aa (TMS5-measurements). The absolute differences between Ac and Aa are statistically significantly different from zero (p51.0 10 4 in the Wilcoxon test for paired samples).
FIGURE 2. Two-hundred twenty-five eyes showing with-the-rule astigmatism (WTR). A: distribution of total corneal astigmatism Ac. B: distribution of anterior corneal astigmatism Aa. In these eyes the total astigmatism is decreased on average when the posterior surface is taken into account.
FIGURE 3. One-hundred seventy eyes showing against-the-rule astigmatism (ATR). A: distribution of total corneal astigmatism Ac. B: distribution of anterior corneal astigmatism Aa. In these eyes the total astigmatism is increased on average when the posterior surface is taken into .account.
axis ac directly contribute to the total astigmatic error when toric IOLs are implanted, assuming that only Ac describes the astigmatism correctly, but Aa is used for IOL calculation. On average, with a median of only !
2014 Informa Healthcare USA, Inc.
0.27 D, the difference between Ac and Aa is in the order of the recognition threshold and therefore clinically not very relevant, even if it was found that it was already ’’statistically significant’’ in a previous
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
4
P.-R. Preussner et al.
FIGURE 4. Average tomographies. A: average anterior topography (local corneal radii) of 199 right eyes, including best-fit corneal vertex radii, axes and asphericities of anterior and posterior surface B: average pachymetry of 199 right eyes C: average anterior topography of 196 left eyes D: average pachymetry of 196 left eyes.
FIGURE 5. Difference between keratometry and refraction. The vector differences between the astigmatism Aa and the astigmatism of the subjective refraction is shown for the Lenstar (left) and the IOLMaster (right).
FIGURE 6. Difference between tomography and refraction. The vector differences between the total astigmatisms Ac and the astigmatisms of the subjective refraction are shown on the left, the vector differences between the anterior astigmatisms Aa and the astigmatisms of the subjective refraction are shown on the right.
Current Eye Research
Curr Eye Res Downloaded from informahealthcare.com by University of Montreal on 12/03/14 For personal use only.
Posterior cornea investigation1 in which 78 eyes were implanted with toric IOLs. Astigmatic vector errors are on average very similar in both papers. The differences between Aa and Ac are not fully randomly distributed as suggested when only looking to Figure 1. In cases of WTR astigmatism, Ac is decreased by the contribution of the posterior surface, in cases of ATR increased on average, Figures 2 and 3, which confirms the findings of other groups.2 This means that the central thinnest part of the cornea cannot be rotationally symmetric but should have an ellipsoidal shape with horizontal long axis on average, as confirmed in Figure 4. Clinically, this implies that the cylinder power of toric IOLs has a trend to be overestimated in WTR eyes and underestimated in ATR eyes when the calculation is only based on measurements of the anterior cornea, and that the cylinder axis is systematically rotated, particularly in case of an oblique axis. In addition to the found differences between Aa and Ac also measuring errors may play a role.26 They could not be investigated in this paper because no other measurements for comparisons where available. Measurement errors of the astigmatism of the cornea generally should be looked at as errors of fitting the theoretically ideal construct of the astigmatism to an irregular surface rather than as technical measurement errors of a measuring device. Also, the softness of the cornea including tear film is highly important. An additional hidden error when investigating corneal and refractive astigmatisms can occur from little IOL decentration or tilt. Even if these errors theoretically cause a coma rather than astigmatism, they can be partly corrected by cylindrical glasses. The centroid shift of 0.14 D for the difference between Ac and the refractive astigmatism may be caused by such IOL misalignments (Figure6, left subimage). Note that the contribution of the posterior corneal surface to the total astigmatism is nearly independent on the amount of the anterior astigmatism, as can be found by a comparison of the results of the present investigation with our earlier results1 which had significantly higher astigmatisms on average. The reason of (possibly overlooked) posterior astigmatism can best be understood by the non-rotationally symmetric corneal thickness as shown in Figure 4. The toric IOL axis error (in degrees) caused by an omission of the pachymetric measurement increases with decreasing anterior astigmatism. In the present investigation with 395 eyes we found a difference between Ac and Aa of 41 D in 0.75% of the cases (Figure 1). To detect this relatively small and statistically unimportant number a large collective of eyes was necessary. If implanted with toric IOLs calculated only from Aa, these cases would be candidates for ‘‘unhappy patients’’. For that reason, a corneal tomography including posterior surface is generally recommended, even if the big majority of !
2014 Informa Healthcare USA, Inc.
5
patients has only little accuracy win from this approach.
DECLARATION OF INTEREST Paul-Rolf Preussner is author of the commercially available software package OKULIX mentioned in the text. The other authors do not have commercial interest in any product or company or competing product or company mentioned in the text. This paper has not been supported by 3rd parties.
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