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Exact Toric Intraocular Lens Calculations Using Currently Available Lens Constants

Exact Toric Intraocular Lens Calculations Using Currently Available Lens Constants The article by Goggin et al1 does an excellent job explaining that the ratio of the IOL plane cylinder needed to neutralize the corneal plane cylinder in toric IOLs cannot be a constant but must vary according to the effective lens position (ELP) and meridional powers of the toric IOL. Failure to compensate for these variables when selecting a toric IOL is a significant source of error, especially in unusual eyes. However, there are 2 differences in their calculations from those using standard IOL formulas (Holladay 1, SRK/T, Haigis, Hoffer Q, and Holladay 2) that make the results unique to their methods and do not apply to other IOL formulas.2 The first difference is related to the ELP. The authors used the distance from the posterior corneal vertex to the anterior vertex of the IOL (internal ACD + central corneal thickness). The calculation for converting the measured distance to the anterior vertex of the IOL to the equivalent thin lens plane was reported in 1998.3 All currently available lens constants (A-constant, ELP, Surgeon Factor) assume an infinitely thin IOL. For the equiconvex Alcon SN60T3-9 IOL used in the study, the equivalent thin lens plane is actually posterior to the back vertex of the IOL by approximately 0.60 mm. With a nominal thickness of approximately 0.65 mm for a 20-D power, the additional distance beyond the anterior vertex of the IOL would be 1.25 mm (0.60 + 0.65) more than the value used by the authors. An average value of 3.92 mm for the postoperative ELP found by the authors vs the manufacturer's average ELP of 5.20 mm (difference of 1.28 mm) agrees very closely with the 1.25-mm thin lens calculation. Using the shorter distance results in much lower IOL power and toricity than would be obtained using the higher value. The second difference relates to the index of refraction of 1.336, cited by the authors for aqueous and corneal tissue using Duke-Elder and Abrams4 as a reference. The index of refraction for corneal tissue is 1.376. The 1.336 used by the authors as the net index of refraction is far too high. Commonly used values range from 1.3215 to 1.3333 and, as reported in 2009, a value of 1.3283 is optimal.5 Using the higher value for the net index results in a higher corneal power that in turn results in lower IOL power and toricity than would normally be obtained with standard IOL calculations. As can be seen in Table 1 in their article,1 the constant ratio used by Alcon is 1.46 (obtained by dividing the IOL plane cylinder by the corneal plane cylinder). The authors would have found their average ratio to be 1.14 (1.46 × 1.58/2.02 = manufacturer's ratio × manufacturer's predicted mean cylinder/authors' predicted mean cylinder). This lower value of 1.14 will work in the authors' formula but will not work in the current standard IOL formulas mentioned here. This is why the authors could not use their formula for the actual spheroequivalent IOL calculation, as it would yield much lower powers than standard IOL calculations, resulting in significant hyperopic surprises. We recently published an article with a table that gives the ratios for IOL cylinder to corneal cylinder for various ELPs and spheroequivalent powers of an IOL.6 For an IOL with a spheroequivalent power of 34 D and an ELP of 4.0 mm, a low ratio of 1.20 is obtained (very near the authors' ratio of 1.14 with an ELP of 3.92 mm). For a spheroequivalent power of 10 D and an ELP of 6.5 mm, a high ratio of 1.75 is obtained. For a 22-D IOL and an ELP of 5.50 mm, a ratio of 1.45 is obtained, which is very close to the manufacturer's ratio of 1.46. The company could not have been as far from the mean constant value as suggested (1.14 vs 1.46, respectively) or they would not have been able to receive approval by the US Food and Drug Administration. However, it must be emphasized that the more unusual the actual patient values are, the larger the error made by using a constant ratio is. The only exact commercial calculators available at this time are the Abbott Medical Optics Express Calculator and the Holladay IOL Consultant Program7 for which I wrote the algorithms a few years ago. It is also possible to solve for the toricity and exact axis of the IOL from the postoperative refraction and postoperative keratometry so that one can determine the exact amount of rotation necessary to minimize the residual astigmatism if the IOL is misaligned. This solution is somewhat more complicated because it involves another intermediate cross-cylinder calculation when the IOL axis is not aligned with the steepest meridian of the cornea. I thank the authors for making this extremely important clinical observation and hope that these comments explaining the difference between their results and those using standard IOL formulas are helpful. It does not minimize the importance of their valuable contribution. Back to top Article Information Correspondence: Dr Holladay, PO Box 717, Bellaire, TX 77402-0717 (holladay@docholladay.com). Financial Disclosure: Dr Holladay is the author of the Holladay IOL Consultant Program and a consultant to Abbott Medical Optics. References 1. Goggin M, Moore S, Esterman A. Toric intraocular lens outcome using the manufacturer's prediction of corneal plane equivalent intraocular lens cylinder power. Arch Ophthalmol. 2011;129(8):1004-100821825184PubMedGoogle ScholarCrossref 2. Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg. 1997;23(9):1356-13709423908PubMedGoogle Scholar 3. Holladay JT, Maverick KJ. Relationship of the actual thick intraocular lens optic to the thin lens equivalent. Am J Ophthalmol. 1998;126(3):339-3479744366PubMedGoogle ScholarCrossref 4. Duke-Elder S, Abrams D. Optics. In: Duke-Elder S, ed. System of Ophthalmology: Ophthalmic Optics and Refraction. Vol 5. London, England: Henry Kimpton; 1970:77 5. Holladay JT, Hill WE, Steinmueller A. Corneal power measurements using scheimpflug imaging in eyes with prior corneal refractive surgery. J Refract Surg. 2009;25(10):862-86819835326PubMedGoogle ScholarCrossref 6. Holladay JT. Improving toric IOL outcomes. Ocular Surgery News. http://www.osnsupersite.com/view.aspx?rid=83309. Published May 25 and June 10, 2011. Accessed September 28, 2011 7. Holladay JT. Holladay IOL Consultant and Surgical Outcomes Assessment. http://www.hicsoap.com. Accessed September 28, 2011 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Ophthalmology American Medical Association

Exact Toric Intraocular Lens Calculations Using Currently Available Lens Constants

Archives of Ophthalmology , Volume 130 (7) – Jul 1, 2012

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Publisher
American Medical Association
Copyright
Copyright © 2012 American Medical Association. All Rights Reserved.
ISSN
0003-9950
eISSN
1538-3687
DOI
10.1001/archophthalmol.2011.1917
Publisher site
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Abstract

The article by Goggin et al1 does an excellent job explaining that the ratio of the IOL plane cylinder needed to neutralize the corneal plane cylinder in toric IOLs cannot be a constant but must vary according to the effective lens position (ELP) and meridional powers of the toric IOL. Failure to compensate for these variables when selecting a toric IOL is a significant source of error, especially in unusual eyes. However, there are 2 differences in their calculations from those using standard IOL formulas (Holladay 1, SRK/T, Haigis, Hoffer Q, and Holladay 2) that make the results unique to their methods and do not apply to other IOL formulas.2 The first difference is related to the ELP. The authors used the distance from the posterior corneal vertex to the anterior vertex of the IOL (internal ACD + central corneal thickness). The calculation for converting the measured distance to the anterior vertex of the IOL to the equivalent thin lens plane was reported in 1998.3 All currently available lens constants (A-constant, ELP, Surgeon Factor) assume an infinitely thin IOL. For the equiconvex Alcon SN60T3-9 IOL used in the study, the equivalent thin lens plane is actually posterior to the back vertex of the IOL by approximately 0.60 mm. With a nominal thickness of approximately 0.65 mm for a 20-D power, the additional distance beyond the anterior vertex of the IOL would be 1.25 mm (0.60 + 0.65) more than the value used by the authors. An average value of 3.92 mm for the postoperative ELP found by the authors vs the manufacturer's average ELP of 5.20 mm (difference of 1.28 mm) agrees very closely with the 1.25-mm thin lens calculation. Using the shorter distance results in much lower IOL power and toricity than would be obtained using the higher value. The second difference relates to the index of refraction of 1.336, cited by the authors for aqueous and corneal tissue using Duke-Elder and Abrams4 as a reference. The index of refraction for corneal tissue is 1.376. The 1.336 used by the authors as the net index of refraction is far too high. Commonly used values range from 1.3215 to 1.3333 and, as reported in 2009, a value of 1.3283 is optimal.5 Using the higher value for the net index results in a higher corneal power that in turn results in lower IOL power and toricity than would normally be obtained with standard IOL calculations. As can be seen in Table 1 in their article,1 the constant ratio used by Alcon is 1.46 (obtained by dividing the IOL plane cylinder by the corneal plane cylinder). The authors would have found their average ratio to be 1.14 (1.46 × 1.58/2.02 = manufacturer's ratio × manufacturer's predicted mean cylinder/authors' predicted mean cylinder). This lower value of 1.14 will work in the authors' formula but will not work in the current standard IOL formulas mentioned here. This is why the authors could not use their formula for the actual spheroequivalent IOL calculation, as it would yield much lower powers than standard IOL calculations, resulting in significant hyperopic surprises. We recently published an article with a table that gives the ratios for IOL cylinder to corneal cylinder for various ELPs and spheroequivalent powers of an IOL.6 For an IOL with a spheroequivalent power of 34 D and an ELP of 4.0 mm, a low ratio of 1.20 is obtained (very near the authors' ratio of 1.14 with an ELP of 3.92 mm). For a spheroequivalent power of 10 D and an ELP of 6.5 mm, a high ratio of 1.75 is obtained. For a 22-D IOL and an ELP of 5.50 mm, a ratio of 1.45 is obtained, which is very close to the manufacturer's ratio of 1.46. The company could not have been as far from the mean constant value as suggested (1.14 vs 1.46, respectively) or they would not have been able to receive approval by the US Food and Drug Administration. However, it must be emphasized that the more unusual the actual patient values are, the larger the error made by using a constant ratio is. The only exact commercial calculators available at this time are the Abbott Medical Optics Express Calculator and the Holladay IOL Consultant Program7 for which I wrote the algorithms a few years ago. It is also possible to solve for the toricity and exact axis of the IOL from the postoperative refraction and postoperative keratometry so that one can determine the exact amount of rotation necessary to minimize the residual astigmatism if the IOL is misaligned. This solution is somewhat more complicated because it involves another intermediate cross-cylinder calculation when the IOL axis is not aligned with the steepest meridian of the cornea. I thank the authors for making this extremely important clinical observation and hope that these comments explaining the difference between their results and those using standard IOL formulas are helpful. It does not minimize the importance of their valuable contribution. Back to top Article Information Correspondence: Dr Holladay, PO Box 717, Bellaire, TX 77402-0717 (holladay@docholladay.com). Financial Disclosure: Dr Holladay is the author of the Holladay IOL Consultant Program and a consultant to Abbott Medical Optics. References 1. Goggin M, Moore S, Esterman A. Toric intraocular lens outcome using the manufacturer's prediction of corneal plane equivalent intraocular lens cylinder power. Arch Ophthalmol. 2011;129(8):1004-100821825184PubMedGoogle ScholarCrossref 2. Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg. 1997;23(9):1356-13709423908PubMedGoogle Scholar 3. Holladay JT, Maverick KJ. Relationship of the actual thick intraocular lens optic to the thin lens equivalent. Am J Ophthalmol. 1998;126(3):339-3479744366PubMedGoogle ScholarCrossref 4. Duke-Elder S, Abrams D. Optics. In: Duke-Elder S, ed. System of Ophthalmology: Ophthalmic Optics and Refraction. Vol 5. London, England: Henry Kimpton; 1970:77 5. Holladay JT, Hill WE, Steinmueller A. Corneal power measurements using scheimpflug imaging in eyes with prior corneal refractive surgery. J Refract Surg. 2009;25(10):862-86819835326PubMedGoogle ScholarCrossref 6. Holladay JT. Improving toric IOL outcomes. Ocular Surgery News. http://www.osnsupersite.com/view.aspx?rid=83309. Published May 25 and June 10, 2011. Accessed September 28, 2011 7. Holladay JT. Holladay IOL Consultant and Surgical Outcomes Assessment. http://www.hicsoap.com. Accessed September 28, 2011

Journal

Archives of OphthalmologyAmerican Medical Association

Published: Jul 1, 2012

References