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Instrument-induced measurement errors during strabismus surgery
Instrument-Induced Measurement Errors During Strabismus Surgery Robert A. Clark, MD, and Arthur L. Rosenbaum, MD Purpose: The purpose of this study was to determine the clinical setting where errors in measurements of muscle position during strabismus surgery made by the Scott curved ruler or by calipers become important and to characterize the magnitude of those errors. Methods: Geometric analysis was used to determine the measurement error between true arc lengths of 3.0 to 20.0 mm versus Scott curved ruler measurements and caliper measurements for axial lengths ranging from 18 to 30 mm. Results: For measurements less than 9.0 mm, neither the Scott curved ruler nor calipers had any clinically important measurement error for any axial length. For axial lengths substantially smaller than 21 mm or larger than 24 mm, the Scott curved ruler, although more accurate than calipers, caused clinically important measurement errors with arc length measurements as small as 12 mm in very small eyes and 14 mm in large eyes. For axial lengths of 30 mm or more, both calipers and the Scott curved ruler had similar accuracy for measuring long arc lengths. Conclusions: Both the Scott curved ruler and calipers are accurate in measuring arc lengths 9.0 mm or less. For longer arc length measurements, accuracy becomes dependent on axial length. The Scott curved ruler, although substantially more accurate than calipers for most common axial lengths, can introduce clinically important measurement errors when measuring arc lengths as small as 12 mm. Axial length should be considered when measuring muscle position during strabismus surgery. (J AAPOS 1999;3:18-25)
ccurate measurement of arc length position for scleral suture location is important in achieving accurate motor alignment from strabismus surgery. Studies suggest that an acceptable error rate in arc length measurement is between 0.35 mm to 0.5 mm per muscle, or between 0.70 mm1 and 1.0 mm2 combined for a 2-muscle surgery. In addition, it is well known that calipers, which measure chord length rather than arc length, cause unacceptably high measurement errors when used to measure large arc lengths.3 Current clinical practice has settled on measuring arc lengths less than 10 mm with calipers and arc lengths greater than 10 mm with the Scott curved ruler4 (Hansen Ophthalmic Development Laboratory, Iowa City, Iowa). The Scott curved ruler, however, can only measure the true arc length on a spherical globe with a radius of curvature exactly the same as the radius of curvature of the Scott curved ruler.3 For globe diameters less than 22 mm, the Scott curved ruler will underestimate the true arc length, resulting in a larger arc length than planned (Figure 1).
A
From the Department of Ophthalmology, University of California, Los Angeles. Supported by the Heed Ophthalmic Foundation, the American Ophthalmological SocietyKnapp Fund, the Bank of America-Giannini Foundation, and the Kimmel Research Grant. Submitted March 5, 1998. Revision accepted August 17, 1998. Reprint requests: Arthur L. Rosenbaum, MD, Jules Stein Eye Institute, 100 Stein Plaza, UCLA, Los Angeles, CA 90095-7002. Copyright © 1999 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/99 $8.00 + 0 75/1/95124
18
February 1999
For globe diameters greater than 22 mm, the Scott curved ruler will overestimate the true arc length, resulting in a smaller arc length than planned (Figure 1). We undertook the following geometric analysis to measure the magnitude of the errors produced by arc length measurements using either the Scott curved ruler or calipers for different arc lengths and axial length.
METHODS For the geometric analysis, the eye was modeled as 2 overlapping spheres, with the larger sphere representing the radius of curvature of the sclera and the smaller sphere representing the radius of curvature of the cornea.5 For strabismus surgery, the radius of curvature of the sclera determines the arc length for all measurements, and thus becomes the globe diameter necessary for comparison with the curvature of the Scott curved ruler. Figure 2 demonstrates the geometric analysis that is required to estimate scleral diameter from axial length. Axial length measurements are from the apex of the cornea to the anterior surface of the retina. The difference between axial length and scleral diameter is the difference between the small distance anteriorly (labeled “a” in Figure 2), where the cornea extends beyond the continuation of the scleral diameter, and the thickness of the posterior sclera, approximately 1 mm.6 The equation for axial lengths was solved for scleral diameters between 18 and 30 mm, corneal diameters between 10 and 13 mm, and corneal curvature between 8.65 mm (keratometry, 39 diopters) and 7.03 mm (keratometry, 48 diopters). Journal of AAPOS
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FIG 1. Arc of 11 mm radius (22 mm diameter), corresponding to radius of Scott curved ruler, superimposed on a small globe and a large globe. Scott curved ruler underestimates arc length in a small globe and overestimates arc length in a large globe.
FIG 2. The eye can be represented as 2 overlapping spheres. Large sphere represents scleral diameter. Small sphere represents corneal diameter. Axial length is measured from anterior surface of cornea to anterior surface of retina, corresponding to line segments (a + b + d + e + R). Scleral diameter is equal to axial length minus anterior extension of corneal radius a, plus posterior scleral thickness T, approximated as 1 mm.6 Solving for a yields an equation based on radius of curvature of cornea, radius of curvature of sclera, and corneal diameter. Scleral diameter can then be estimated from axial length as the difference (a – T) for various combinations of radii and corneal curvature.
Figure 3 demonstrates the geometric analysis that is required to determine arc length given chord length and the scleral radius of curvature.3 The equation for arc length was solved for scleral diameters between 18 and 30 mm for chord (caliper) lengths between 3 and 20 mm. For each chord length, the difference between the arc length of the Scott curved ruler (22 mm diameter globe) and the true arc length for each globe diameter was taken as the measurement error of the Scott curved ruler.
RESULTS For axial lengths less than 25 mm, the scleral diameter can be approximated as equaling the axial length. For axial
lengths greater than 25 mm, the scleral diameter can be approximated as the axial length minus 0.5 mm. Those estimates of scleral diameter were accurate with an error less than 0.5 mm for all but the largest (13 mm) corneas combined with the steepest curvature (keratometry, 48 diopters). The close relationship of axial length to scleral diameter occurs because, in most normal eyes, the protrusion of the cornea beyond the scleral diameter is only slightly greater than the 1 mm thickness of the posterior sclera. The relationships between chord length and arc length are summarized in Table 1. For all scleral diameters, chord length measurements 9.0 mm or less did not result in more
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FIG 3. Geometry solving for arc length given chord length, assuming scleral diameter is spherical.3 The larger the arc length, the greater the difference between arc length and chord length.
than 0.5 mm error from the true arc length. Chord lengths became more accurate for larger measurements in very long eyes, approximating the accuracy of the Scott curved ruler for scleral diameters 30 mm or greater. For scleral diameters between 18 and 29 mm, the Scott curved ruler was more accurate than the caliper for large chord measurements. The Scott curved ruler was accurate for scleral diameters between 21 and 24 mm for the full range of arc length measurements (3 to 20 mm). For scleral diameters 20 mm and less, however, the Scott curved ruler underestimated the arc length measurement by more than 0.5 mm for large arc lengths. For example, an arc length measurement by Scott curved ruler of 16.5 mm actually measured nearly 17 mm on a 20 mm globe and nearly 18 mm on an 18 mm globe. For scleral diameters 25 mm or greater, the Scott curved ruler underestimated the arc length measurements by more than 0.5 mm for large arc lengths. For example, an arc length measurement by Scott curved ruler of 16.5 mm actually measured 16 mm on a 26 mm globe and 15.7 mm on a 30 mm globe.
DISCUSSION Many potential sources of error have been identified in the evaluation and subsequent surgical management of strabis-
mus. In the clinical evaluation of the patient, the correct use of ophthalmic prisms7 and understanding the effects of myopic and hyperopic spectacle correction8 can help reduce the errors in preoperative measurement to the desired goal of less than 2 prism diopters error.1 In surgical technique, recognizing the effects of traction on the insertion site and advancement (resection) effect of suture placement through the muscle belly can help reduce errors in muscle position.4 Keech et al9 has shown that substantial measurement errors can occur if measurements are referenced to the muscle insertion after the muscle tendon has been disinserted. Errors occur because the muscle stump displaces anteriorly between 0.10 to 2.2 mm after the tendon is disinserted.9 Arc length recessions measured after muscle disinsertion are effectively reduced by the amount of anterior displacement of the muscle insertion, introducing up to 2 mm of measurement error into final muscle position. Surgical tables derived from measurements referenced to the postinsertional stump probably already incorporate a systematic increase in the amount of recession performed to account for this effect. These tables, however, do not benefit those patients who differ substantially from the average anterior displacement of the muscle stump. This
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TABLE 1. Caliper (chord length) versus arc length as a function of scieral diameter
True arc length as a function of caliper (chord) measurement and scleral diameter. Arc lengths of 22 mm scleral diameter, corresponding to radius of curvature of Scott curved ruler, are listed in italics. Area of table above first line represents region in which both calipers and Scott curved ruler are accurate within 0.5 mm of true arc length. Area of table between upper and lower lines, in bold, represents region in which calipers are not accurate but Scott curved ruler is still accurate within 0.5 mm. Bottom, shaded area represents area of table in which neither calipers nor Scott curved ruler are accurate within 0.5 mm.
measurement error can be minimized by referencing all measurements to the corneoscleral limbus.9 For example, when performing a medial rectus recession, the distance between the medial rectus insertion and the limbus is first measured. Then, the muscle tendon is disinserted, and subsequent measurements are taken from the limbus by adding the desired amount of recession to the distance between the original muscle insertion and the limbus.9
Using this method, modest recessions can require large arc length measurements, and clinically important measurement errors can be introduced by failing to account for the limitations of the measurement instruments. It has been well recognized that calipers are inadequate for arc length measurements greater than 10 mm, but it has not been previously recognized that the Scott curved ruler is only accurate for globes with axial lengths around 22 mm.
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22 Clark and Rosenbaum TABLE 2. Ages and refractive errors predictive of small eyes (axial length ≤20.50 mm) Age (yr)
Spherical equivalent
0.5 1.5 2.0 3.0 4.0 5.0 6.0 6.5 7.5 8.5 9.5
>Plano >+1 >+2 >+3 >+4 >+5 >+6 >+7 >+8 >+9 >+10
Predicted ages and spherical refractive equivalents associated with axial lengths less than 20.5 mm. The equation used for axial length estimates is: axial length = 20.354 + 0.026 × age (mo) – 0.276 × refractive error (diopters).11 From table, most normal eyes <1 year of age will be substantially smaller than curvature of Scott curved ruler. Then, between ages of 2 to 6 years, any refractive error greater than age (in yr) is predictive of a small eye.
For very small and very large eyes, the Scott ruler does not substantially extend the effective range of accurate clinical measurement of arc length much beyond that achieved with calipers (Table 1). Several large studies have shown that axial lengths for patients with strabismus vary from less than 18 mm to more than 25 mm.5,10 In addition, it has also been shown that very small eyes (axial lengths less than 20.25 mm) have a larger dose/response effect with surgery for esotropia than larger eyes.11 Because of the enhanced response to surgery, accurate measurement of muscle position is even more critical in these small eyes than in eyes with normal axial lengths. An equation to estimate axial length from age (in months) and refractive error (in spherical equivalents) previously has been shown to be accurate in predicting the location of the equator in globes for patients less than 10 years of age and with refractive errors less than 5.0 diopters of myopia.12 Use of the same equation before operation may identify patients with axial lengths sufficiently different from 22 mm to justify special attention to instrument-induced measurement errors. Using an estimated axial length of less than 20.5 mm as important, Table 2 gives a list of ages and refractive errors that are predictive of small eyes. From Table 2, it is clear that the majority of children younger than 1 year of age will have axial lengths less than 20.5 mm and thus will have clinically important measurement errors with the Scott curved ruler. This finding is particularly important because several large multicenter trials are currently being proposed for treating infantile strabismus that rely on the Scott curved ruler to minimize measurement error. The variability in surgical response to bilateral lateral rectus recession may partly be explained by instrument error as well. Most recessions involving the lateral rectus are larger than recessions involving the medial rectus13
and may exceed 10 mm when measured from the previous insertion site or 17 mm when measured from the limbus. In addition, exotropia is found more commonly in myopic eyes,14 which tend to have a longer axial length and also may have a more elliptical, flatter scleral curvature than predicted for a simple spherical model of the eye.15 In addition, stretching the sclera by traction on the globe can flatten the radius of curvature substantially from its normal shape, decreasing the accuracy of the Scott curved ruler and increasing the accuracy of calipers. Assuming a perfectly spherical shape, the Scott ruler substantially overestimated the actual arc length for long arc length measurements in axial lengths longer than 24 mm, resulting in less arc length recession than the amount measured. Six possible approaches could be taken to minimize instrument-induced measurement error. The first approach is to take several measurement steps with the calipers when making a large measurement. For example, in a 19 mm globe, three 5.0 mm measurements generate only 0.18 mm of measurement error versus a single 15 mm Scott curved ruler measurement error of approximately 0.60 mm. A potential problem with this approach is ensuring accuracy for successive radial measurements. The measurement errors induced by multiple sequential measurements may exceed the theoretical increased accuracy over a single measurement with the Scott curved ruler. A second approach is to use Table 3 to set the calipers to accurately measure true arc length for each globe diameter. For example, when measuring a 15.0 mm arc length on a 19 mm globe, the calipers should be set for 13.5 mm instead of 15.0 mm. A potential problem with this approach is difficulty in accurately setting the standard calipers accurately within 0.1 mm. For larger measurements in small eyes, an error in caliper settings of 0.2 mm would cause an error in arc length measurement of 0.5 mm. Another potential problem is positioning the calipers in tight orbital spaces for large arc measurements. A third approach is to artificially compress the globe with the Scott curved ruler so that the curvature of the globe lies flush with and approximates the curvature of the Scott curved ruler. In our experience, this approach works well and is perhaps used inadvertently much of the time by surgeons when using the Scott curved ruler. For infants, however, a substantial amount of force is necessary to adequately deform the 18 mm globe into a 22 mm radius of curvature, raising the risk of a corneal abrasion or other unintentional globe injury. A fourth approach is to measure the correct distance with a piece of suture against a flat ruler, then lay the suture along the globe as a measuring device.16 In our experience, this technique is cumbersome compared with using either calipers or the Scott curved ruler. The standard sutures used in strabismus surgery have a substantial amount of material memory that resists alignment against the curvature of the globe. In addition, preparing the suture with a knot, measuring the length precisely, and placing it in position adds several additional steps to the
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TABLE 3. Caliper settings to give true arc lengths as a function of scieral diameter
Caliper settings required to give true arc length as a function of scleral diameter. Area of table in bold beneath line represents area of table in which standard measurements with calipers will cause measurement errors greater than 0.5 mm.
strabismus surgery compared with using instruments to make a mark on the sclera. A fifth approach would involve using a small curved ruler (radius of curvature corresponding to a 19 mm globe) for small eyes and a large curved ruler (radius of curvature corresponding to a 26 mm globe) for large eyes. The small curved ruler would extend the range of accurate measurements to more than 18 mm of arc length for eyes with axial lengths between 18 and 20 mm. The large curved ruler would extend the range of accurate measurements to more than 19 mm of arc length for eyes with axial lengths between 25 and 30 mm. A combination of the current 22 mm curved Scott ruler, a 19 mm curved ruler, and a 26 mm curved ruler would cover the entire useful clinical range of axial length measurements for eyes with axial lengths between 18 to 30 mm.
We have used a prototype small curved ruler to perform surgical measurements on young children (Figures 4 and 5). For these children, no preoperative axial length measurement or estimation was performed. Instead, surgery was performed in the standard fashion, and measurements were attempted using the Scott curved ruler. In cases in which the Scott curved ruler obviously did not approximate the curvature of the operated eye, the small curved ruler was then used to match the curvature of the small globe. Our uncontrolled comparisons of the measurements made showed that the Scott curved ruler measured more than 0.5 mm more than the small curved ruler in these children for measurements as small as 7 or 8 mm. This error is more than would be predicted from the geometric analysis, probably because of the difficulty in
24 Clark and Rosenbaum
FIG 4. Photograph shows calipers (A), Scott curved ruler (B), and prototype small curved ruler (C). Inset illustrates different radius of curvature for standard Scott curved ruler (11.0 mm) versus prototype small curved ruler (9.5 mm). White arrow is directed toward the point on the end of prototype small curved ruler used to mark sclera.
obtaining an accurate mark when the Scott curved ruler does not smoothly oppose the globe. A sixth approach would involve constructing a curved ruler of flexible material, such as Mylar or even soft metal, that could deform to the shape of the globe regardless of the globe’s radius of curvature. Such a material would have to be carefully chosen, however, because many deformable materials can stretch over time, introducing yet another potential cause of instrument-induced measurement error. There is one important concern in changing the way strabismus surgeons measure arc lengths. Most current surgical tables, including individualized surgical tables, are based on performing strabismus surgery in the same, standardized fashion. A bias may already exist within the surgical tables for performing larger arc length recessions than the millimeter amounts measured with calipers to achieve the desired surgical outcome. This effect may be particularly prominent in esotropia because those surgical tables are derived from surgeries performed in younger children. Changing surgical technique to improve the accuracy of the surgical measurements may have the undesired secondary effect of causing undercorrections in some of these patients. Surgical dosing may need to be changed to account for this effect. Regardless, knowing the precise arc lengths of surgery actually performed is important to minimizing the variability in surgical results caused by different globe sizes. In summary, both the Scott curved ruler and calipers are accurate for measuring arc lengths 9.0 mm or less. For
Journal of AAPOS Volume 3 Number 1 February 1999
FIG 5. Photographs of intraoperative measurement made during surgery to recess left medial rectus muscle 5.0 mm in a 6-month-old boy with esotropia. Before disinsertion, distance from corneoscleral limbus to a muscle hook pulled taut behind medial rectus insertion was measured as 5.5 mm. After disinsertion, asterisk shows re-mark 5.5 mm posterior to corneoscleral limbus, almost 2 mm behind residual stump of postinsertional stump. Anterior migration of postinsertional stump would have caused a substantial overestimation of actual amount of recession performed if recession was referenced to postinsertional stump. Instead, the desired 5.0 mm recession was added to original measured distance between medial rectus insertion and corneoscleral limbus—5.5 mm—for a total measurement of 10.5 mm posterior to corneoscleral limbus. Points A, B, and C represent marks made by calipers, Scott curved ruler, and prototype small curved ruler, respectively, measuring 10.5 mm from corneoscleral limbus. Although no axial length measurements were obtained, during surgery the prototype small curved ruler clearly approximated globe curvature better than Scott curved ruler.
longer arc length measurements, accuracy becomes dependent on axial length. The Scott curved ruler, although substantially more accurate than calipers for most common axial lengths, can introduce clinically important measurement errors when measuring arc lengths as small as 12 mm in small eyes and as small as 14 mm in large eyes. The Scott curved ruler underestimates the arc length in small eyes, resulting in a larger true arc length than measured, and overestimates the arc length in large eyes, resulting in a smaller true arc length than measured. Using pressure to deform the globe to the curvature of the Scott curved ruler will extend its accurate range of measurements, but other techniques should be used to determine the arc length measurements in globes that cannot be flattened against the curved ruler. References 1. Mims JL, Treff G, Wood RC. Variability of strabismus surgery for acquired esotropia. Arch Ophthalmol 1986;104:1780-2. 2. Repka MX, Connett JE, Baker JD, Rosenbaum AL. Surgery in the prism adaptation study: accuracy and dose response. J Pediatr Ophthalmol Strabismus 1992;29:150-6. 3. Scott WE, Martin-Casals A, Braverman DE. Curved ruler for mea-
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4.
5.
6.
7. 8.
9.
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surement along the surface of the globe. Arch Ophthalmol 1978;96:1084. Kushner BJ, Preslan MW, Vrabec M. Artifacts of measuring during strabismus surgery. J Pediatr Ophthalmol Strabismus 1987;24:15964. Kushner BJ, Lucchese NJ, Morton GV. Variation in axial length and anatomical landmarks in strabismic patients. Ophthalmology 1991;98:400-6. Denny M, editor. The eye. In: Section 2: Fundamentals and principles of ophthalmology. San Francisco: American Academy of Ophthalmology, 1994. p. 44. Thompson JT, Guyton DL. Ophthalmic prisms: measurement errors and how to minimize them. Ophthalmology 1983;90:204-10. Scattergood KD, Brown MH, Guyton DL. Artifacts introduced by spectacle lenses in the measurement of strabismic deviations. Am J Ophthalmol 1983;96:439-48. Keech RV, Scott WE, Baker JD. The medial rectus muscle insertion site in infantile esotropia. Am J Ophthalmol 1990;109:79-84.
O
10. Gillies WE, McIndoe A. Measurement of strabismus eyes with a scan ultrasonography. Aust J Ophthal 1981;9:231-2. 11. Kushner BJ, Lucchese NJ, Morton GV. The influence of axial length on the response to strabismus surgery. Arch Ophthalmol 1989;107: 1616-8. 12. Kushner BJ, Qui CO, Lucchese NJ, Fisher MR. Axial length estimation in strabismic patients. J Pediatr Ophthalmol Strabismus 1996;33:257-61. 13. Denny M, editor. Surgery of the extraocular muscles. In Section 6: Pediatric ophthalmology and strabismus. San Francisco: American Academy of Ophthalmology 1994:348-9. 14. von Noorden GK. Etiology of heterophoria and heterotropia. In: Binocular vision and ocular motility. 5th ed. St Louis: Mosby; 1996. p. 137. 15. Meyer-Schwickerath G, Gerke E. Biometric studies of the eyeball and retinal detachment. Br J Ophthalmol 1984;68:29-31. 16. Kushner BJ. A measuring suture for large strabismus measurements. Ophthalmic Surg 1981;12:650-1.
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ccurate measurement of arc length position for scleral suture location is important in achieving accurate motor alignment from strabismus surgery. Studies suggest that an acceptable error rate in arc length measurement is between 0.35 mm to 0.5 mm per muscle, or between 0.70 mm1 and 1.0 mm2 combined for a 2-muscle surgery. In addition, it is well known that calipers, which measure chord length rather than arc length, cause unacceptably high measurement errors when used to measure large arc lengths.3 Current clinical practice has settled on measuring arc lengths less than 10 mm with calipers and arc lengths greater than 10 mm with the Scott curved ruler4 (Hansen Ophthalmic Development Laboratory, Iowa City, Iowa). The Scott curved ruler, however, can only measure the true arc length on a spherical globe with a radius of curvature exactly the same as the radius of curvature of the Scott curved ruler.3 For globe diameters less than 22 mm, the Scott curved ruler will underestimate the true arc length, resulting in a larger arc length than planned (Figure 1).
A
From the Department of Ophthalmology, University of California, Los Angeles. Supported by the Heed Ophthalmic Foundation, the American Ophthalmological SocietyKnapp Fund, the Bank of America-Giannini Foundation, and the Kimmel Research Grant. Submitted March 5, 1998. Revision accepted August 17, 1998. Reprint requests: Arthur L. Rosenbaum, MD, Jules Stein Eye Institute, 100 Stein Plaza, UCLA, Los Angeles, CA 90095-7002. Copyright © 1999 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/99 $8.00 + 0 75/1/95124
18
February 1999
For globe diameters greater than 22 mm, the Scott curved ruler will overestimate the true arc length, resulting in a smaller arc length than planned (Figure 1). We undertook the following geometric analysis to measure the magnitude of the errors produced by arc length measurements using either the Scott curved ruler or calipers for different arc lengths and axial length.
METHODS For the geometric analysis, the eye was modeled as 2 overlapping spheres, with the larger sphere representing the radius of curvature of the sclera and the smaller sphere representing the radius of curvature of the cornea.5 For strabismus surgery, the radius of curvature of the sclera determines the arc length for all measurements, and thus becomes the globe diameter necessary for comparison with the curvature of the Scott curved ruler. Figure 2 demonstrates the geometric analysis that is required to estimate scleral diameter from axial length. Axial length measurements are from the apex of the cornea to the anterior surface of the retina. The difference between axial length and scleral diameter is the difference between the small distance anteriorly (labeled “a” in Figure 2), where the cornea extends beyond the continuation of the scleral diameter, and the thickness of the posterior sclera, approximately 1 mm.6 The equation for axial lengths was solved for scleral diameters between 18 and 30 mm, corneal diameters between 10 and 13 mm, and corneal curvature between 8.65 mm (keratometry, 39 diopters) and 7.03 mm (keratometry, 48 diopters). Journal of AAPOS
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FIG 1. Arc of 11 mm radius (22 mm diameter), corresponding to radius of Scott curved ruler, superimposed on a small globe and a large globe. Scott curved ruler underestimates arc length in a small globe and overestimates arc length in a large globe.
FIG 2. The eye can be represented as 2 overlapping spheres. Large sphere represents scleral diameter. Small sphere represents corneal diameter. Axial length is measured from anterior surface of cornea to anterior surface of retina, corresponding to line segments (a + b + d + e + R). Scleral diameter is equal to axial length minus anterior extension of corneal radius a, plus posterior scleral thickness T, approximated as 1 mm.6 Solving for a yields an equation based on radius of curvature of cornea, radius of curvature of sclera, and corneal diameter. Scleral diameter can then be estimated from axial length as the difference (a – T) for various combinations of radii and corneal curvature.
Figure 3 demonstrates the geometric analysis that is required to determine arc length given chord length and the scleral radius of curvature.3 The equation for arc length was solved for scleral diameters between 18 and 30 mm for chord (caliper) lengths between 3 and 20 mm. For each chord length, the difference between the arc length of the Scott curved ruler (22 mm diameter globe) and the true arc length for each globe diameter was taken as the measurement error of the Scott curved ruler.
RESULTS For axial lengths less than 25 mm, the scleral diameter can be approximated as equaling the axial length. For axial
lengths greater than 25 mm, the scleral diameter can be approximated as the axial length minus 0.5 mm. Those estimates of scleral diameter were accurate with an error less than 0.5 mm for all but the largest (13 mm) corneas combined with the steepest curvature (keratometry, 48 diopters). The close relationship of axial length to scleral diameter occurs because, in most normal eyes, the protrusion of the cornea beyond the scleral diameter is only slightly greater than the 1 mm thickness of the posterior sclera. The relationships between chord length and arc length are summarized in Table 1. For all scleral diameters, chord length measurements 9.0 mm or less did not result in more
20 Clark and Rosenbaum
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FIG 3. Geometry solving for arc length given chord length, assuming scleral diameter is spherical.3 The larger the arc length, the greater the difference between arc length and chord length.
than 0.5 mm error from the true arc length. Chord lengths became more accurate for larger measurements in very long eyes, approximating the accuracy of the Scott curved ruler for scleral diameters 30 mm or greater. For scleral diameters between 18 and 29 mm, the Scott curved ruler was more accurate than the caliper for large chord measurements. The Scott curved ruler was accurate for scleral diameters between 21 and 24 mm for the full range of arc length measurements (3 to 20 mm). For scleral diameters 20 mm and less, however, the Scott curved ruler underestimated the arc length measurement by more than 0.5 mm for large arc lengths. For example, an arc length measurement by Scott curved ruler of 16.5 mm actually measured nearly 17 mm on a 20 mm globe and nearly 18 mm on an 18 mm globe. For scleral diameters 25 mm or greater, the Scott curved ruler underestimated the arc length measurements by more than 0.5 mm for large arc lengths. For example, an arc length measurement by Scott curved ruler of 16.5 mm actually measured 16 mm on a 26 mm globe and 15.7 mm on a 30 mm globe.
DISCUSSION Many potential sources of error have been identified in the evaluation and subsequent surgical management of strabis-
mus. In the clinical evaluation of the patient, the correct use of ophthalmic prisms7 and understanding the effects of myopic and hyperopic spectacle correction8 can help reduce the errors in preoperative measurement to the desired goal of less than 2 prism diopters error.1 In surgical technique, recognizing the effects of traction on the insertion site and advancement (resection) effect of suture placement through the muscle belly can help reduce errors in muscle position.4 Keech et al9 has shown that substantial measurement errors can occur if measurements are referenced to the muscle insertion after the muscle tendon has been disinserted. Errors occur because the muscle stump displaces anteriorly between 0.10 to 2.2 mm after the tendon is disinserted.9 Arc length recessions measured after muscle disinsertion are effectively reduced by the amount of anterior displacement of the muscle insertion, introducing up to 2 mm of measurement error into final muscle position. Surgical tables derived from measurements referenced to the postinsertional stump probably already incorporate a systematic increase in the amount of recession performed to account for this effect. These tables, however, do not benefit those patients who differ substantially from the average anterior displacement of the muscle stump. This
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TABLE 1. Caliper (chord length) versus arc length as a function of scieral diameter
True arc length as a function of caliper (chord) measurement and scleral diameter. Arc lengths of 22 mm scleral diameter, corresponding to radius of curvature of Scott curved ruler, are listed in italics. Area of table above first line represents region in which both calipers and Scott curved ruler are accurate within 0.5 mm of true arc length. Area of table between upper and lower lines, in bold, represents region in which calipers are not accurate but Scott curved ruler is still accurate within 0.5 mm. Bottom, shaded area represents area of table in which neither calipers nor Scott curved ruler are accurate within 0.5 mm.
measurement error can be minimized by referencing all measurements to the corneoscleral limbus.9 For example, when performing a medial rectus recession, the distance between the medial rectus insertion and the limbus is first measured. Then, the muscle tendon is disinserted, and subsequent measurements are taken from the limbus by adding the desired amount of recession to the distance between the original muscle insertion and the limbus.9
Using this method, modest recessions can require large arc length measurements, and clinically important measurement errors can be introduced by failing to account for the limitations of the measurement instruments. It has been well recognized that calipers are inadequate for arc length measurements greater than 10 mm, but it has not been previously recognized that the Scott curved ruler is only accurate for globes with axial lengths around 22 mm.
Journal of AAPOS Volume 3 Number 1 February 1999
22 Clark and Rosenbaum TABLE 2. Ages and refractive errors predictive of small eyes (axial length ≤20.50 mm) Age (yr)
Spherical equivalent
0.5 1.5 2.0 3.0 4.0 5.0 6.0 6.5 7.5 8.5 9.5
>Plano >+1 >+2 >+3 >+4 >+5 >+6 >+7 >+8 >+9 >+10
Predicted ages and spherical refractive equivalents associated with axial lengths less than 20.5 mm. The equation used for axial length estimates is: axial length = 20.354 + 0.026 × age (mo) – 0.276 × refractive error (diopters).11 From table, most normal eyes <1 year of age will be substantially smaller than curvature of Scott curved ruler. Then, between ages of 2 to 6 years, any refractive error greater than age (in yr) is predictive of a small eye.
For very small and very large eyes, the Scott ruler does not substantially extend the effective range of accurate clinical measurement of arc length much beyond that achieved with calipers (Table 1). Several large studies have shown that axial lengths for patients with strabismus vary from less than 18 mm to more than 25 mm.5,10 In addition, it has also been shown that very small eyes (axial lengths less than 20.25 mm) have a larger dose/response effect with surgery for esotropia than larger eyes.11 Because of the enhanced response to surgery, accurate measurement of muscle position is even more critical in these small eyes than in eyes with normal axial lengths. An equation to estimate axial length from age (in months) and refractive error (in spherical equivalents) previously has been shown to be accurate in predicting the location of the equator in globes for patients less than 10 years of age and with refractive errors less than 5.0 diopters of myopia.12 Use of the same equation before operation may identify patients with axial lengths sufficiently different from 22 mm to justify special attention to instrument-induced measurement errors. Using an estimated axial length of less than 20.5 mm as important, Table 2 gives a list of ages and refractive errors that are predictive of small eyes. From Table 2, it is clear that the majority of children younger than 1 year of age will have axial lengths less than 20.5 mm and thus will have clinically important measurement errors with the Scott curved ruler. This finding is particularly important because several large multicenter trials are currently being proposed for treating infantile strabismus that rely on the Scott curved ruler to minimize measurement error. The variability in surgical response to bilateral lateral rectus recession may partly be explained by instrument error as well. Most recessions involving the lateral rectus are larger than recessions involving the medial rectus13
and may exceed 10 mm when measured from the previous insertion site or 17 mm when measured from the limbus. In addition, exotropia is found more commonly in myopic eyes,14 which tend to have a longer axial length and also may have a more elliptical, flatter scleral curvature than predicted for a simple spherical model of the eye.15 In addition, stretching the sclera by traction on the globe can flatten the radius of curvature substantially from its normal shape, decreasing the accuracy of the Scott curved ruler and increasing the accuracy of calipers. Assuming a perfectly spherical shape, the Scott ruler substantially overestimated the actual arc length for long arc length measurements in axial lengths longer than 24 mm, resulting in less arc length recession than the amount measured. Six possible approaches could be taken to minimize instrument-induced measurement error. The first approach is to take several measurement steps with the calipers when making a large measurement. For example, in a 19 mm globe, three 5.0 mm measurements generate only 0.18 mm of measurement error versus a single 15 mm Scott curved ruler measurement error of approximately 0.60 mm. A potential problem with this approach is ensuring accuracy for successive radial measurements. The measurement errors induced by multiple sequential measurements may exceed the theoretical increased accuracy over a single measurement with the Scott curved ruler. A second approach is to use Table 3 to set the calipers to accurately measure true arc length for each globe diameter. For example, when measuring a 15.0 mm arc length on a 19 mm globe, the calipers should be set for 13.5 mm instead of 15.0 mm. A potential problem with this approach is difficulty in accurately setting the standard calipers accurately within 0.1 mm. For larger measurements in small eyes, an error in caliper settings of 0.2 mm would cause an error in arc length measurement of 0.5 mm. Another potential problem is positioning the calipers in tight orbital spaces for large arc measurements. A third approach is to artificially compress the globe with the Scott curved ruler so that the curvature of the globe lies flush with and approximates the curvature of the Scott curved ruler. In our experience, this approach works well and is perhaps used inadvertently much of the time by surgeons when using the Scott curved ruler. For infants, however, a substantial amount of force is necessary to adequately deform the 18 mm globe into a 22 mm radius of curvature, raising the risk of a corneal abrasion or other unintentional globe injury. A fourth approach is to measure the correct distance with a piece of suture against a flat ruler, then lay the suture along the globe as a measuring device.16 In our experience, this technique is cumbersome compared with using either calipers or the Scott curved ruler. The standard sutures used in strabismus surgery have a substantial amount of material memory that resists alignment against the curvature of the globe. In addition, preparing the suture with a knot, measuring the length precisely, and placing it in position adds several additional steps to the
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TABLE 3. Caliper settings to give true arc lengths as a function of scieral diameter
Caliper settings required to give true arc length as a function of scleral diameter. Area of table in bold beneath line represents area of table in which standard measurements with calipers will cause measurement errors greater than 0.5 mm.
strabismus surgery compared with using instruments to make a mark on the sclera. A fifth approach would involve using a small curved ruler (radius of curvature corresponding to a 19 mm globe) for small eyes and a large curved ruler (radius of curvature corresponding to a 26 mm globe) for large eyes. The small curved ruler would extend the range of accurate measurements to more than 18 mm of arc length for eyes with axial lengths between 18 and 20 mm. The large curved ruler would extend the range of accurate measurements to more than 19 mm of arc length for eyes with axial lengths between 25 and 30 mm. A combination of the current 22 mm curved Scott ruler, a 19 mm curved ruler, and a 26 mm curved ruler would cover the entire useful clinical range of axial length measurements for eyes with axial lengths between 18 to 30 mm.
We have used a prototype small curved ruler to perform surgical measurements on young children (Figures 4 and 5). For these children, no preoperative axial length measurement or estimation was performed. Instead, surgery was performed in the standard fashion, and measurements were attempted using the Scott curved ruler. In cases in which the Scott curved ruler obviously did not approximate the curvature of the operated eye, the small curved ruler was then used to match the curvature of the small globe. Our uncontrolled comparisons of the measurements made showed that the Scott curved ruler measured more than 0.5 mm more than the small curved ruler in these children for measurements as small as 7 or 8 mm. This error is more than would be predicted from the geometric analysis, probably because of the difficulty in
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FIG 4. Photograph shows calipers (A), Scott curved ruler (B), and prototype small curved ruler (C). Inset illustrates different radius of curvature for standard Scott curved ruler (11.0 mm) versus prototype small curved ruler (9.5 mm). White arrow is directed toward the point on the end of prototype small curved ruler used to mark sclera.
obtaining an accurate mark when the Scott curved ruler does not smoothly oppose the globe. A sixth approach would involve constructing a curved ruler of flexible material, such as Mylar or even soft metal, that could deform to the shape of the globe regardless of the globe’s radius of curvature. Such a material would have to be carefully chosen, however, because many deformable materials can stretch over time, introducing yet another potential cause of instrument-induced measurement error. There is one important concern in changing the way strabismus surgeons measure arc lengths. Most current surgical tables, including individualized surgical tables, are based on performing strabismus surgery in the same, standardized fashion. A bias may already exist within the surgical tables for performing larger arc length recessions than the millimeter amounts measured with calipers to achieve the desired surgical outcome. This effect may be particularly prominent in esotropia because those surgical tables are derived from surgeries performed in younger children. Changing surgical technique to improve the accuracy of the surgical measurements may have the undesired secondary effect of causing undercorrections in some of these patients. Surgical dosing may need to be changed to account for this effect. Regardless, knowing the precise arc lengths of surgery actually performed is important to minimizing the variability in surgical results caused by different globe sizes. In summary, both the Scott curved ruler and calipers are accurate for measuring arc lengths 9.0 mm or less. For
Journal of AAPOS Volume 3 Number 1 February 1999
FIG 5. Photographs of intraoperative measurement made during surgery to recess left medial rectus muscle 5.0 mm in a 6-month-old boy with esotropia. Before disinsertion, distance from corneoscleral limbus to a muscle hook pulled taut behind medial rectus insertion was measured as 5.5 mm. After disinsertion, asterisk shows re-mark 5.5 mm posterior to corneoscleral limbus, almost 2 mm behind residual stump of postinsertional stump. Anterior migration of postinsertional stump would have caused a substantial overestimation of actual amount of recession performed if recession was referenced to postinsertional stump. Instead, the desired 5.0 mm recession was added to original measured distance between medial rectus insertion and corneoscleral limbus—5.5 mm—for a total measurement of 10.5 mm posterior to corneoscleral limbus. Points A, B, and C represent marks made by calipers, Scott curved ruler, and prototype small curved ruler, respectively, measuring 10.5 mm from corneoscleral limbus. Although no axial length measurements were obtained, during surgery the prototype small curved ruler clearly approximated globe curvature better than Scott curved ruler.
longer arc length measurements, accuracy becomes dependent on axial length. The Scott curved ruler, although substantially more accurate than calipers for most common axial lengths, can introduce clinically important measurement errors when measuring arc lengths as small as 12 mm in small eyes and as small as 14 mm in large eyes. The Scott curved ruler underestimates the arc length in small eyes, resulting in a larger true arc length than measured, and overestimates the arc length in large eyes, resulting in a smaller true arc length than measured. Using pressure to deform the globe to the curvature of the Scott curved ruler will extend its accurate range of measurements, but other techniques should be used to determine the arc length measurements in globes that cannot be flattened against the curved ruler. References 1. Mims JL, Treff G, Wood RC. Variability of strabismus surgery for acquired esotropia. Arch Ophthalmol 1986;104:1780-2. 2. Repka MX, Connett JE, Baker JD, Rosenbaum AL. Surgery in the prism adaptation study: accuracy and dose response. J Pediatr Ophthalmol Strabismus 1992;29:150-6. 3. Scott WE, Martin-Casals A, Braverman DE. Curved ruler for mea-
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5.
6.
7. 8.
9.
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surement along the surface of the globe. Arch Ophthalmol 1978;96:1084. Kushner BJ, Preslan MW, Vrabec M. Artifacts of measuring during strabismus surgery. J Pediatr Ophthalmol Strabismus 1987;24:15964. Kushner BJ, Lucchese NJ, Morton GV. Variation in axial length and anatomical landmarks in strabismic patients. Ophthalmology 1991;98:400-6. Denny M, editor. The eye. In: Section 2: Fundamentals and principles of ophthalmology. San Francisco: American Academy of Ophthalmology, 1994. p. 44. Thompson JT, Guyton DL. Ophthalmic prisms: measurement errors and how to minimize them. Ophthalmology 1983;90:204-10. Scattergood KD, Brown MH, Guyton DL. Artifacts introduced by spectacle lenses in the measurement of strabismic deviations. Am J Ophthalmol 1983;96:439-48. Keech RV, Scott WE, Baker JD. The medial rectus muscle insertion site in infantile esotropia. Am J Ophthalmol 1990;109:79-84.
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10. Gillies WE, McIndoe A. Measurement of strabismus eyes with a scan ultrasonography. Aust J Ophthal 1981;9:231-2. 11. Kushner BJ, Lucchese NJ, Morton GV. The influence of axial length on the response to strabismus surgery. Arch Ophthalmol 1989;107: 1616-8. 12. Kushner BJ, Qui CO, Lucchese NJ, Fisher MR. Axial length estimation in strabismic patients. J Pediatr Ophthalmol Strabismus 1996;33:257-61. 13. Denny M, editor. Surgery of the extraocular muscles. In Section 6: Pediatric ophthalmology and strabismus. San Francisco: American Academy of Ophthalmology 1994:348-9. 14. von Noorden GK. Etiology of heterophoria and heterotropia. In: Binocular vision and ocular motility. 5th ed. St Louis: Mosby; 1996. p. 137. 15. Meyer-Schwickerath G, Gerke E. Biometric studies of the eyeball and retinal detachment. Br J Ophthalmol 1984;68:29-31. 16. Kushner BJ. A measuring suture for large strabismus measurements. Ophthalmic Surg 1981;12:650-1.
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