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Criteria for assessing autorefractor accuracy and accommodation
LETTERS
facilitation of nucleus removal from the capsular bag without excessive zonular stress. Hydrodissection is rarely seen as a procedure that is highly efficacious in removing cortex and cells to combat PCO. For example, in Gimbel’s review of hydrodissection and hydrodelineation in 1994, PCO was scarcely mentioned.2 It is often forgotten that retained cortex, the material within the postoperative peripheral Soemmering’s ring, is composed of not only acellular, amorphous, proteinaceous lens fibers and strands but also clusters of residual equatorial lens epithelial cells. The latter are the actual precursors of clinical PCO. Thorough removal of these is critical in controlling PCO, and the hydrodissection maneuver is the most useful tool for this. The method described as cortical cleaving hydrodissection by Fine in 1992 as well as in his letter is precisely what is needed to achieve this long-term goal. Realizing now that this component of the cataract operation has quietly emerged as one of the numerous stellar achievements and improvements in cataract surgery provided by many surgeons over the years, a brief look back at its evolution is fitting. Gimbel has done this, providing an excellent clinical review.2 He outlines how various agents such as viscoelastic agents, Ringer’s solution, and balanced salt solution have been tried throughout the years. The article by Faust that we cited3 includes the first use of the term hydrodissection in the refereed literature. Faust’s sketches of the procedure were among the first to illustrate the general principles of this technique. We conducted the first systematic laboratory studies on the various hydrodissection/delineation techniques in 1989 (D.J. Apple, MD, R. Casanova, MD, J. Davison, MD, “Technique of PC IOL Implantation Using a Small Smooth Circular Continuous Tear Capsulotomy (Capsulorhexis); a Demonstration Using the Posterior Video Technique on Human Cadaver Eyes,” video presented at the annual meeting of the American Academy of Ophthalmology, New Orleans, Louisiana, USA, October 1989). Assia and coauthors4 continued this research into the pathophysiology of the various types of intralenticular injection. Fine’s procedure, which is highlighted by the fact that he tents up the anterior capsule during injection, reduces or eliminates the need for cortical aspiration in many cases. It represents the culmination and near perfection of this technique, which now serves us so well. The significance of our recent article is that it has, for the first time, called attention to the direct relationship between hydrodissection and PCO. The hydrodissection procedure itself, although never an attention getter in comparison to, for example, intraocular lenses and other biodevices and instruments, has been a close partner on our road to success with the cataract operation.—David J. Apple, MD, Qun Peng, MD References 1. Fine IH. Cortical cleaving hydrodissection. J Cataract Refract Surg 1992; 18:508 –512 2. Gimbel HV. Hydrodissection and hydrodelineation. Int Ophthalmol Clin 1994; 34:73–90 944
3. Faust DJ. Hydrodissection of soft nuclei. Am Intra-Ocular Implant Soc J 1984; 10:75–77 4. Assia EI, Blumenthal M, Apple DJ. Hydrodissection and visco extraction of the nucleus in planned extracapsular cataract extraction. Eur J Implant Refract Surg 1992; 4:3– 8
Criteria for Assessing Autorefractor Accuracy and Accommodation esemann and Dick1 use 4 quantities to assess the performance of a handheld autorefractor. However, 2 (difference of cylindrical power and weighted axes difference) violate the condition of invariance2 under spherocylindrical transposition and, hence, are not satisfactory for use in such studies. Analysis of power requires the use of quantities that satisfy basic requirements of invariance and closure.3 Quantities should not be defined more or less arbitrarily for use in a particular context but should be based on a solid foundation and be standard for use in all contexts.3 Furthermore, powers should be treated as integral wholes and not in terms of separate quantities. A methodology that satisfies all these requirements is available.3– 6 Table 1 will be used for illustrative purposes. It lists 7 pairs of powers, (a) to (g), expressed in conventional form and corresponding properties calculated from them; DSE is the difference of spherical equivalents; DC is the difference of cylindrical powers; DA is the weighted axes difference; and DCC is the difference in cylindrical correction. The symbols and terminology are those of Wesemann and Dick.1 They give explicit formulas for the 4 quantities. Table 1 also lists differences in nearest equivalent sphere (⌬Fnes), ortho-astigmatism (⌬For), and oblique astigmatism (⌬Fob). Nearest equivalent sphere, ortho-astigmatism, and oblique astigmatism are defined elsewhere.3 The DSE and ⌬Fnes are equivalent. The powers 3 ⫺1 ⫻ 100 and 2 1 ⫻ 10 are identical; one is merely the spherocylindrical transposition of the other. Thus, the pair of powers (b) in Table 1 is identical to the pair (a). Meaningful quantities calculated for the pairs must be the same. This is the principle of invariance under spherocylindrical transposition.2 With the exception of DC and DA, they are the same for all the quantities in Table 1. This is sufficient to demonstrate that the quantities DC and DA used by
W
J CATARACT REFRACT SURG—VOL 26, JULY 2000
LETTERS
Table 1. Pairs of powers expressed in conventional form and corresponding differences calculated for them. The units are diopters throughout except for the angles of the axes in the conventional expressions for powers. Pair
FS1
FC1 ⴛ ␣1
FS2
FC2 ⴛ ␣2
DSE
DCC
⌬Fnes
⌬For
⌬Fob
(a)
2
1 ⫻ 40
2
1 ⫻ 10
0
0
1
0
0.383
⫺0.321
(b)
2
1 ⫻ 40
3
⫺1 ⫻ 100
0
2
1
0
0.383
⫺0.321
(c)
2
0 ⫻ 40
2
1 ⫻ 10
⫺0.5
⫺1
(d)
2
0 ⫻ 10
2
1 ⫻ 10
⫺0.5
⫺1
1
1
⫺0.5
0.470
0.171
0
1
⫺0.5
0.470
0.171
(e)
2
1 ⫻ 20
2
1 ⫻ 170
0
0
⫺1
1
0
0.087
⫺0.492
(f)
2
1 ⫻ 10
2
0 ⫻ 40
0.5
1
0
1
0.5
⫺0.470
⫺0.171
(g)
2
1 ⫻ 40
3
⫺1 ⫻ 130
0
2
2
0
0
Wesemann and Dick1 violate invariance and, hence, are not meaningful quantities. A formal test2 confirms this conclusion. A satisfactory methodology should work for all powers. In particular, it should work for special cases such as pure spheres. Of course, the powers 2 0 ⫻ 40 and 2 0 ⫻ 10 are the power usually written as 2 DS. Thus, physically, the pairs (c) and (d) in Table 1 are identical, and they should exhibit identical differences. As Table 1 shows, their DAs are not the same; all the other differences are. The axes in pair (a) differ by 30 degrees as they do in pair (e). In fact, pair (a) is pair (e) rotated by 20 degrees. One would expect identical weighted axes differences. However, Table 1 shows they are not the same. Interchanging the 2 powers in pair (c) results in pair (f). Differences in the 2 cases should have identical magnitudes. They do in Table 1 except for DA. The powers in (g) are identical. All meaningful differences should be zero. However, Table 1 shows DC and DA are not zero. By contrast ⌬Fnes, ⌬For, and ⌬Fob satisfy invariance, do not suffer from the difficulties described here for DC and DA, and are satisfactory vehicles for quantitative analyses. W.F. HARRIS, PHD, FAAO R.D. VAN GOOL, DPHIL Johannesburg, South Africa References 1. Wesemann W, Dick B. Accuracy and accommodation capability of a handheld autorefractor. J Cataract Refract Surg 2000; 26: 62–70 2. Harris WF. Invariance of ophthalmic properties under spherocylindrical transposition. Optom Vis Sci 1997; 74:459 – 462 3. Harris WF. Astigmatism. Ophthalmic Physiol Opt 2000; 20: 11–30
DC
DA 1 ⫺1.732
0
0
4. Harris WF. Dioptric power: its nature and its representation in three- and four-dimensional space. Optom Vis Sci 1997; 74: 349 –366 5. Harris WF. A unified paraxial approach to astigmatic optics. Optom Vis Sci 1999; 76:480 – 499 6. Harris WF. Representation of dioptric power in Euclidean 3-space. Ophthalmic Physiol Opt 1991; 11:130 –136
Reply: Harris and Van Gool point out that 2 of our quality criteria are not invariant under spherocylindrical transposition. They propose that we should use criteria developed by Harris instead. We understand their argument; however, we believe that our quality criteria are better suited for our intended purpose. The reader should consider the following points: 1. Harris and Van Gool construct their examples by applying our formulas in an incorrect manner. (1) Difference of cylinder power (DC): In our paper, we stated that only minuscylinder values were used in our measurements. If only minuscylinder values are used, our formula for DC delivers correct and reliable results. We think the reader understands that it is not particularly meaningful to subtract apples from oranges or, in our case, plus-cylinder from minus-cylinder values as Harris and Van Gool did in their table. (2) Axis difference (DA): Harris and Van Gool point out that our formula for the DA does not work properly, when the cylinder power is zero. From our point of view, this argument is invalid since the terms “axis” and “axis difference” have no ophthalmic meaning when the cylinder power is zero and the refraction data are purely spherical. Therefore, we calculated axis differences in our paper for only those eyes in which cylinder powers greater than 0 diopter were found with both measurement techniques. In addition, we transformed all axis differences into the range (90 degrees, 90 degrees). Furthermore, the reader should consider that Harris and Van Gool cannot offer an alternate formula for the “axis error” because the term “axis” is an unimportant variable in their framework. 2. Harris and Van Gool’s approach is not optimum for a journal that is not primarily read by physicists and optical engineers. Harris and Van Gool propose an alternate methodology and cite 4 of Harris’ papers. In these papers, he pro-
J CATARACT REFRACT SURG—VOL 26, JULY 2000
945
facilitation of nucleus removal from the capsular bag without excessive zonular stress. Hydrodissection is rarely seen as a procedure that is highly efficacious in removing cortex and cells to combat PCO. For example, in Gimbel’s review of hydrodissection and hydrodelineation in 1994, PCO was scarcely mentioned.2 It is often forgotten that retained cortex, the material within the postoperative peripheral Soemmering’s ring, is composed of not only acellular, amorphous, proteinaceous lens fibers and strands but also clusters of residual equatorial lens epithelial cells. The latter are the actual precursors of clinical PCO. Thorough removal of these is critical in controlling PCO, and the hydrodissection maneuver is the most useful tool for this. The method described as cortical cleaving hydrodissection by Fine in 1992 as well as in his letter is precisely what is needed to achieve this long-term goal. Realizing now that this component of the cataract operation has quietly emerged as one of the numerous stellar achievements and improvements in cataract surgery provided by many surgeons over the years, a brief look back at its evolution is fitting. Gimbel has done this, providing an excellent clinical review.2 He outlines how various agents such as viscoelastic agents, Ringer’s solution, and balanced salt solution have been tried throughout the years. The article by Faust that we cited3 includes the first use of the term hydrodissection in the refereed literature. Faust’s sketches of the procedure were among the first to illustrate the general principles of this technique. We conducted the first systematic laboratory studies on the various hydrodissection/delineation techniques in 1989 (D.J. Apple, MD, R. Casanova, MD, J. Davison, MD, “Technique of PC IOL Implantation Using a Small Smooth Circular Continuous Tear Capsulotomy (Capsulorhexis); a Demonstration Using the Posterior Video Technique on Human Cadaver Eyes,” video presented at the annual meeting of the American Academy of Ophthalmology, New Orleans, Louisiana, USA, October 1989). Assia and coauthors4 continued this research into the pathophysiology of the various types of intralenticular injection. Fine’s procedure, which is highlighted by the fact that he tents up the anterior capsule during injection, reduces or eliminates the need for cortical aspiration in many cases. It represents the culmination and near perfection of this technique, which now serves us so well. The significance of our recent article is that it has, for the first time, called attention to the direct relationship between hydrodissection and PCO. The hydrodissection procedure itself, although never an attention getter in comparison to, for example, intraocular lenses and other biodevices and instruments, has been a close partner on our road to success with the cataract operation.—David J. Apple, MD, Qun Peng, MD References 1. Fine IH. Cortical cleaving hydrodissection. J Cataract Refract Surg 1992; 18:508 –512 2. Gimbel HV. Hydrodissection and hydrodelineation. Int Ophthalmol Clin 1994; 34:73–90 944
3. Faust DJ. Hydrodissection of soft nuclei. Am Intra-Ocular Implant Soc J 1984; 10:75–77 4. Assia EI, Blumenthal M, Apple DJ. Hydrodissection and visco extraction of the nucleus in planned extracapsular cataract extraction. Eur J Implant Refract Surg 1992; 4:3– 8
Criteria for Assessing Autorefractor Accuracy and Accommodation esemann and Dick1 use 4 quantities to assess the performance of a handheld autorefractor. However, 2 (difference of cylindrical power and weighted axes difference) violate the condition of invariance2 under spherocylindrical transposition and, hence, are not satisfactory for use in such studies. Analysis of power requires the use of quantities that satisfy basic requirements of invariance and closure.3 Quantities should not be defined more or less arbitrarily for use in a particular context but should be based on a solid foundation and be standard for use in all contexts.3 Furthermore, powers should be treated as integral wholes and not in terms of separate quantities. A methodology that satisfies all these requirements is available.3– 6 Table 1 will be used for illustrative purposes. It lists 7 pairs of powers, (a) to (g), expressed in conventional form and corresponding properties calculated from them; DSE is the difference of spherical equivalents; DC is the difference of cylindrical powers; DA is the weighted axes difference; and DCC is the difference in cylindrical correction. The symbols and terminology are those of Wesemann and Dick.1 They give explicit formulas for the 4 quantities. Table 1 also lists differences in nearest equivalent sphere (⌬Fnes), ortho-astigmatism (⌬For), and oblique astigmatism (⌬Fob). Nearest equivalent sphere, ortho-astigmatism, and oblique astigmatism are defined elsewhere.3 The DSE and ⌬Fnes are equivalent. The powers 3 ⫺1 ⫻ 100 and 2 1 ⫻ 10 are identical; one is merely the spherocylindrical transposition of the other. Thus, the pair of powers (b) in Table 1 is identical to the pair (a). Meaningful quantities calculated for the pairs must be the same. This is the principle of invariance under spherocylindrical transposition.2 With the exception of DC and DA, they are the same for all the quantities in Table 1. This is sufficient to demonstrate that the quantities DC and DA used by
W
J CATARACT REFRACT SURG—VOL 26, JULY 2000
LETTERS
Table 1. Pairs of powers expressed in conventional form and corresponding differences calculated for them. The units are diopters throughout except for the angles of the axes in the conventional expressions for powers. Pair
FS1
FC1 ⴛ ␣1
FS2
FC2 ⴛ ␣2
DSE
DCC
⌬Fnes
⌬For
⌬Fob
(a)
2
1 ⫻ 40
2
1 ⫻ 10
0
0
1
0
0.383
⫺0.321
(b)
2
1 ⫻ 40
3
⫺1 ⫻ 100
0
2
1
0
0.383
⫺0.321
(c)
2
0 ⫻ 40
2
1 ⫻ 10
⫺0.5
⫺1
(d)
2
0 ⫻ 10
2
1 ⫻ 10
⫺0.5
⫺1
1
1
⫺0.5
0.470
0.171
0
1
⫺0.5
0.470
0.171
(e)
2
1 ⫻ 20
2
1 ⫻ 170
0
0
⫺1
1
0
0.087
⫺0.492
(f)
2
1 ⫻ 10
2
0 ⫻ 40
0.5
1
0
1
0.5
⫺0.470
⫺0.171
(g)
2
1 ⫻ 40
3
⫺1 ⫻ 130
0
2
2
0
0
Wesemann and Dick1 violate invariance and, hence, are not meaningful quantities. A formal test2 confirms this conclusion. A satisfactory methodology should work for all powers. In particular, it should work for special cases such as pure spheres. Of course, the powers 2 0 ⫻ 40 and 2 0 ⫻ 10 are the power usually written as 2 DS. Thus, physically, the pairs (c) and (d) in Table 1 are identical, and they should exhibit identical differences. As Table 1 shows, their DAs are not the same; all the other differences are. The axes in pair (a) differ by 30 degrees as they do in pair (e). In fact, pair (a) is pair (e) rotated by 20 degrees. One would expect identical weighted axes differences. However, Table 1 shows they are not the same. Interchanging the 2 powers in pair (c) results in pair (f). Differences in the 2 cases should have identical magnitudes. They do in Table 1 except for DA. The powers in (g) are identical. All meaningful differences should be zero. However, Table 1 shows DC and DA are not zero. By contrast ⌬Fnes, ⌬For, and ⌬Fob satisfy invariance, do not suffer from the difficulties described here for DC and DA, and are satisfactory vehicles for quantitative analyses. W.F. HARRIS, PHD, FAAO R.D. VAN GOOL, DPHIL Johannesburg, South Africa References 1. Wesemann W, Dick B. Accuracy and accommodation capability of a handheld autorefractor. J Cataract Refract Surg 2000; 26: 62–70 2. Harris WF. Invariance of ophthalmic properties under spherocylindrical transposition. Optom Vis Sci 1997; 74:459 – 462 3. Harris WF. Astigmatism. Ophthalmic Physiol Opt 2000; 20: 11–30
DC
DA 1 ⫺1.732
0
0
4. Harris WF. Dioptric power: its nature and its representation in three- and four-dimensional space. Optom Vis Sci 1997; 74: 349 –366 5. Harris WF. A unified paraxial approach to astigmatic optics. Optom Vis Sci 1999; 76:480 – 499 6. Harris WF. Representation of dioptric power in Euclidean 3-space. Ophthalmic Physiol Opt 1991; 11:130 –136
Reply: Harris and Van Gool point out that 2 of our quality criteria are not invariant under spherocylindrical transposition. They propose that we should use criteria developed by Harris instead. We understand their argument; however, we believe that our quality criteria are better suited for our intended purpose. The reader should consider the following points: 1. Harris and Van Gool construct their examples by applying our formulas in an incorrect manner. (1) Difference of cylinder power (DC): In our paper, we stated that only minuscylinder values were used in our measurements. If only minuscylinder values are used, our formula for DC delivers correct and reliable results. We think the reader understands that it is not particularly meaningful to subtract apples from oranges or, in our case, plus-cylinder from minus-cylinder values as Harris and Van Gool did in their table. (2) Axis difference (DA): Harris and Van Gool point out that our formula for the DA does not work properly, when the cylinder power is zero. From our point of view, this argument is invalid since the terms “axis” and “axis difference” have no ophthalmic meaning when the cylinder power is zero and the refraction data are purely spherical. Therefore, we calculated axis differences in our paper for only those eyes in which cylinder powers greater than 0 diopter were found with both measurement techniques. In addition, we transformed all axis differences into the range (90 degrees, 90 degrees). Furthermore, the reader should consider that Harris and Van Gool cannot offer an alternate formula for the “axis error” because the term “axis” is an unimportant variable in their framework. 2. Harris and Van Gool’s approach is not optimum for a journal that is not primarily read by physicists and optical engineers. Harris and Van Gool propose an alternate methodology and cite 4 of Harris’ papers. In these papers, he pro-
J CATARACT REFRACT SURG—VOL 26, JULY 2000
945