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Double-K method to calculate IOL power after refractive surgery
LETTERS
contact inhibition of cell movement? I think, perhaps, that Dr. Nishi refers to inhibition of cell migration at a sharp optic edge as ‘‘contact inhibition’’ because he believes cell contact with a sharp capsule bend ceases migration. Even if this is true, although it is unlikely, the phenomenon cannot be called contact inhibition because of the reasons mentioned above. Even when a sharp capsule bend blocks cell migration, other term should be to explain the mechanism. I cannot understand the point Dr. Nishi is making with respect to Figure 2, B. Where is the sharp capsule bend? When cells migrate, they extend lamellipodia toward the migrating direction and make new adhesive contacts; they then break the adhesive contacts, locating at the area opposite the migrating direction. They move their body to the migrating direction according to contraction of their body. They do not have to bend their body rectangularly while climbing the rectangular wall from the bottom of the well. They simply extend the leading edge on the rectangular wall and make adhesive contact. Bhermi and coauthors2 clearly demonstrated that, under adequate conditions, LECs can migrate over a sharp rectangular edge of a well and can climb the rectangular wall from the bottom. Next, I would like to answer Dr. Nishi’s other questions. Although we might not be able to measure real contact pressure between the optic edge and the capsule, we can speculate the pressure theoretically or calculate it mathematically. As mentioned above, Boyce and coauthors1 mathematically calculated the contact pressure between the optic and posterior capsule and concluded that IOLs with a square-edged optic exert higher pressure on the posterior capsule than IOLs with a round-edged optic. In an earlier study,3 Dr. Fujiwara and I made a straight groove on a plastic sheet using a knife and then bent the sheet at the reverse side of the groove, easily making a sharp bend. Although we did not demonstrate the sharp capsule bend in our paper, Bhermi and coauthors2 clearly showed the sharp bend at the well corner and demonstrated that LECs can migrate over a sharp rectangular edge of collagencoated poly(methyl methacrylate) well. We also demonstrated that cells migrate over the sharp bend of the posterior capsule. I do not understand what the ‘‘thickness of each IOL’’ means. Is that the thickness of the optic at the center or the thickness of the ridge and edge? Finally, Dr. Nishi’s comments and questions include many misunderstandings and seem to be incorrect based on scientific theories and findings in cell biology and physics. I believe the conclusion in our study is adequate.dToshiyuki Nagamoto, MD, PhD
254
References 1. Boyce JF, Bhermi GS, Spalton DJ. El-Osta AR. Mathematical modeling of the forces between an intraocular lens and the capsule. J Cataract Refract Surg 2002; 28:1853– 1859 2. Bhermi GS, Spalton DJ, El-Osta AA, Marshall J. Failure of a discontinuous bend to prevent lens epithelial cell migration in vitro. J Cataract Refract Surg 2002; 28: 1256–1261 3. Nagamoto T, Fujiwara T. Inhibition of lens epithelial cell migration at the intraocular lens optic edge; role of capsule bending and contact pressure. J Cataract Refract Surg 2003; 29:1605–1612
Double-K method to calculate IOL power after refractive surgery
W
e read with interest the article by Dr. Aramberri.1 We would like to congratulate his great effort in trying to solve one of the main problems we will face in a near future: calculating intraocular lens (IOL) power in eyes that have had refractive surgery. We tried to use the formula reported in Appendix. This was difficult until we figured out there were errors. We would like to point these out so others will not have the same problems. 1. In equation 4, rpre2 and Cw2/4 should be changed to rpre2 and Cw2/4 so that H ¼ rpre Sqrt rpre 2 Cw2=4Þ
will be changed to H ¼ rpre Sqrt rpre 2 Cw2=4Þ
Moreover, if [rpre2 (Cw2/4)] is ! 0, the value obtained should be 0. 2. In equation 10, n should be changed in na so that IOLemme ¼ ½1000 na n rpost nc ml LOPT = ½ðLOPT ACDest Þ na rpost nc ml ACDest
will be changed to IOLemme ¼ ½1000 na ðna r post nc ml LOPTÞ= ½ðLOPT ACDest Þ na rpost nc ml ACDest
J CATARACT REFRACT SURG—VOL 31, FEBRUARY 2005
LETTERS
3. In equation 5 is the variable ACDconst, which the author says equals the ‘‘IOL constant (can be computed from A-constant).’’ We suggest specifying that ACDconst Z 0.62467 A 68.74709, where A Z SRK constant. Although these may seem to be insignificant changes, they will make a difference to those trying to use these formulas. This will prevent this interesting study from being marred by printing mistakes. NICOLA ROSA, LUIGI CAPASSO, MICHELE LANZA, Naples,
MD MD MD Italy
Reference
Equation 1: Preoperative corneal radius of curvature: rpre ¼ 337:5=Kpre Equation 2: Corrected axial length (LCOR): If L!Z24:2; LCOR ¼ L If L > 24:2; LCOR ¼ 3:446 þ 1:716 L 0:0237 L2 Equation 3: Computed corneal width (Cw): Cw ¼ 5:41 þ 0:58412 LCOR þ 0:098 Kpre Equation 4: Corneal height (H): H ¼ rpre Sqrt ABS rpre 2 Cw2=4 Equation 5: Offset value:
1. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double-K method. J Cataract Refract Surg 2003; 29:2063–2068
Offset ¼ ACDconst 3:336 Equation 6: Estimated postop ELP (ACD): ACDest ¼ H þ Offset
Reply: Dr Rosa and coauthors are correct highlighting errors in the formula Appendix: 1. In equation 4, rpre2 must be changed to rpre 2 and Cw2/4 must be changed to Cw2/4. It is true that when ðrpre2 ðCw2=4ÞÞ!0; the formula fails to predict any effective lens position (ELP) and IOL power as Sqrt (n) Z e. This happens for certain values of K and axial length (AL); ie, K Z 45 and AL O 33.12. This error can be also found in the original formula I copied from IOL power calculation.1 Although I have not found the solution to this error, it is obvious from the predicted IOL powers that available software applies the solution Dr. h Rosaiand coauthors propose; that is, when rpre 2 Cw2=4 ! 0; the result will be 0. In my experience, however, this algorithm leads to an overestimation of ELP and thus to underestimation of IOL power, resulting in postoperative hyperopia. I would propose a more accurate solution, which I have been using for several years: to make this result absolute and h thenisquare root it. So, H ¼ rpre Sqrt rpre 2 Cw2=4 must be changed to H ¼ rpre io n h 2 : Sqrt ABS rpre 2 Cw =4 2. I agree that in equation 10, n must be changed to na. 3. It is useful to add the conversion formula from A-constant to ACD constant (ACDconst). With these changes, the corrected version of the formula appendix would be:
Equation 7: Constants: V ¼ 12; na ¼ 1:336; nc ¼ 1:333; nc ml ¼ 0:333 Equation 8: Retinal thickness (RETHICK) and optical axial length (LOPT): RETHICK ¼ 0:65696 0:02029 L LOPT ¼ L þ RETHICK Equation 9: Postoperative corneal radius of curvature (rpost): rpost ¼ 337:5=Kpost Equation 10: Emmetropia IOL power (IOLemme): IOLemme ¼ ½1000 na ðna rpost nc ml LOPTÞ= ½ðLOPT ACDest Þ ðna rpost nc ml ACDest Þ Equation 11: Conversion from IOL A-constant to IOL ACD constant: ACDconst ¼ 0:62467 A-constant 68:747 Variables L Z axial length; Kpre Z pre refractive surgery K-value; Kpost Z post refractive surgery K-value; ACDconst Z IOL
J CATARACT REFRACT SURG—VOL 31, FEBRUARY 2005
255
contact inhibition of cell movement? I think, perhaps, that Dr. Nishi refers to inhibition of cell migration at a sharp optic edge as ‘‘contact inhibition’’ because he believes cell contact with a sharp capsule bend ceases migration. Even if this is true, although it is unlikely, the phenomenon cannot be called contact inhibition because of the reasons mentioned above. Even when a sharp capsule bend blocks cell migration, other term should be to explain the mechanism. I cannot understand the point Dr. Nishi is making with respect to Figure 2, B. Where is the sharp capsule bend? When cells migrate, they extend lamellipodia toward the migrating direction and make new adhesive contacts; they then break the adhesive contacts, locating at the area opposite the migrating direction. They move their body to the migrating direction according to contraction of their body. They do not have to bend their body rectangularly while climbing the rectangular wall from the bottom of the well. They simply extend the leading edge on the rectangular wall and make adhesive contact. Bhermi and coauthors2 clearly demonstrated that, under adequate conditions, LECs can migrate over a sharp rectangular edge of a well and can climb the rectangular wall from the bottom. Next, I would like to answer Dr. Nishi’s other questions. Although we might not be able to measure real contact pressure between the optic edge and the capsule, we can speculate the pressure theoretically or calculate it mathematically. As mentioned above, Boyce and coauthors1 mathematically calculated the contact pressure between the optic and posterior capsule and concluded that IOLs with a square-edged optic exert higher pressure on the posterior capsule than IOLs with a round-edged optic. In an earlier study,3 Dr. Fujiwara and I made a straight groove on a plastic sheet using a knife and then bent the sheet at the reverse side of the groove, easily making a sharp bend. Although we did not demonstrate the sharp capsule bend in our paper, Bhermi and coauthors2 clearly showed the sharp bend at the well corner and demonstrated that LECs can migrate over a sharp rectangular edge of collagencoated poly(methyl methacrylate) well. We also demonstrated that cells migrate over the sharp bend of the posterior capsule. I do not understand what the ‘‘thickness of each IOL’’ means. Is that the thickness of the optic at the center or the thickness of the ridge and edge? Finally, Dr. Nishi’s comments and questions include many misunderstandings and seem to be incorrect based on scientific theories and findings in cell biology and physics. I believe the conclusion in our study is adequate.dToshiyuki Nagamoto, MD, PhD
254
References 1. Boyce JF, Bhermi GS, Spalton DJ. El-Osta AR. Mathematical modeling of the forces between an intraocular lens and the capsule. J Cataract Refract Surg 2002; 28:1853– 1859 2. Bhermi GS, Spalton DJ, El-Osta AA, Marshall J. Failure of a discontinuous bend to prevent lens epithelial cell migration in vitro. J Cataract Refract Surg 2002; 28: 1256–1261 3. Nagamoto T, Fujiwara T. Inhibition of lens epithelial cell migration at the intraocular lens optic edge; role of capsule bending and contact pressure. J Cataract Refract Surg 2003; 29:1605–1612
Double-K method to calculate IOL power after refractive surgery
W
e read with interest the article by Dr. Aramberri.1 We would like to congratulate his great effort in trying to solve one of the main problems we will face in a near future: calculating intraocular lens (IOL) power in eyes that have had refractive surgery. We tried to use the formula reported in Appendix. This was difficult until we figured out there were errors. We would like to point these out so others will not have the same problems. 1. In equation 4, rpre2 and Cw2/4 should be changed to rpre2 and Cw2/4 so that H ¼ rpre Sqrt rpre 2 Cw2=4Þ
will be changed to H ¼ rpre Sqrt rpre 2 Cw2=4Þ
Moreover, if [rpre2 (Cw2/4)] is ! 0, the value obtained should be 0. 2. In equation 10, n should be changed in na so that IOLemme ¼ ½1000 na n rpost nc ml LOPT = ½ðLOPT ACDest Þ na rpost nc ml ACDest
will be changed to IOLemme ¼ ½1000 na ðna r post nc ml LOPTÞ= ½ðLOPT ACDest Þ na rpost nc ml ACDest
J CATARACT REFRACT SURG—VOL 31, FEBRUARY 2005
LETTERS
3. In equation 5 is the variable ACDconst, which the author says equals the ‘‘IOL constant (can be computed from A-constant).’’ We suggest specifying that ACDconst Z 0.62467 A 68.74709, where A Z SRK constant. Although these may seem to be insignificant changes, they will make a difference to those trying to use these formulas. This will prevent this interesting study from being marred by printing mistakes. NICOLA ROSA, LUIGI CAPASSO, MICHELE LANZA, Naples,
MD MD MD Italy
Reference
Equation 1: Preoperative corneal radius of curvature: rpre ¼ 337:5=Kpre Equation 2: Corrected axial length (LCOR): If L!Z24:2; LCOR ¼ L If L > 24:2; LCOR ¼ 3:446 þ 1:716 L 0:0237 L2 Equation 3: Computed corneal width (Cw): Cw ¼ 5:41 þ 0:58412 LCOR þ 0:098 Kpre Equation 4: Corneal height (H): H ¼ rpre Sqrt ABS rpre 2 Cw2=4 Equation 5: Offset value:
1. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double-K method. J Cataract Refract Surg 2003; 29:2063–2068
Offset ¼ ACDconst 3:336 Equation 6: Estimated postop ELP (ACD): ACDest ¼ H þ Offset
Reply: Dr Rosa and coauthors are correct highlighting errors in the formula Appendix: 1. In equation 4, rpre2 must be changed to rpre 2 and Cw2/4 must be changed to Cw2/4. It is true that when ðrpre2 ðCw2=4ÞÞ!0; the formula fails to predict any effective lens position (ELP) and IOL power as Sqrt (n) Z e. This happens for certain values of K and axial length (AL); ie, K Z 45 and AL O 33.12. This error can be also found in the original formula I copied from IOL power calculation.1 Although I have not found the solution to this error, it is obvious from the predicted IOL powers that available software applies the solution Dr. h Rosaiand coauthors propose; that is, when rpre 2 Cw2=4 ! 0; the result will be 0. In my experience, however, this algorithm leads to an overestimation of ELP and thus to underestimation of IOL power, resulting in postoperative hyperopia. I would propose a more accurate solution, which I have been using for several years: to make this result absolute and h thenisquare root it. So, H ¼ rpre Sqrt rpre 2 Cw2=4 must be changed to H ¼ rpre io n h 2 : Sqrt ABS rpre 2 Cw =4 2. I agree that in equation 10, n must be changed to na. 3. It is useful to add the conversion formula from A-constant to ACD constant (ACDconst). With these changes, the corrected version of the formula appendix would be:
Equation 7: Constants: V ¼ 12; na ¼ 1:336; nc ¼ 1:333; nc ml ¼ 0:333 Equation 8: Retinal thickness (RETHICK) and optical axial length (LOPT): RETHICK ¼ 0:65696 0:02029 L LOPT ¼ L þ RETHICK Equation 9: Postoperative corneal radius of curvature (rpost): rpost ¼ 337:5=Kpost Equation 10: Emmetropia IOL power (IOLemme): IOLemme ¼ ½1000 na ðna rpost nc ml LOPTÞ= ½ðLOPT ACDest Þ ðna rpost nc ml ACDest Þ Equation 11: Conversion from IOL A-constant to IOL ACD constant: ACDconst ¼ 0:62467 A-constant 68:747 Variables L Z axial length; Kpre Z pre refractive surgery K-value; Kpost Z post refractive surgery K-value; ACDconst Z IOL
J CATARACT REFRACT SURG—VOL 31, FEBRUARY 2005
255