- Email: [email protected]
Reanalysis of refractive growth in pediatric pseudophakia and aphakia
Reanalysis of refractive growth in pediatric pseudophakia and aphakia Susan Whitmer, MD,a Aurora Xu,a,b and Scott McClatchey, MDa,c,d BACKGROUND
The current model of refractive growth in children (RRG2) is calculated as the slope of aphakic refraction at the spectacle plane versus the logarithm of adjusted age. However, this model fails in infants because of the optical effect of vertex distance of a spectacle lens on the effective power at the cornea. In this study, we developed a new model of refractive growth (RRG3) that eliminates the optical effect of vertex distance on the RRG2 model.
METHODS
We calculated RRG3 values for pseudophakic and aphakic eyes previously analyzed for RRG2. Inclusion criteria were age #10 years at the time of cataract surgery and follow-up time between measured refractions of at least 3.6 years and at least the age at first refraction plus 0.6 years. For both pseudophakic and aphakic eyes, we compared RRG3 values in children who had cataract surgery before age 6 months with those in children aged 6 months or older.
RESULTS
A total of 78 pseudophakic and 70 aphakic eyes met the inclusion criteria. Ages at surgery ranged from 0.25 to 9 years, with a 9.5-year mean follow-up time. The mean RRG3 value was not significantly different between the surgical age groups for both pseudophakic eyes (P 5 0.053) and aphakic eyes (P 5 0.59).
CONCLUSIONS
The RRG3 values were not significantly different between the surgical age groups for both pseudophakic and aphakic eyes. Consequently, RRG3 is theoretically applicable even in the small eyes of infants having surgery before 6 months of age. ( J AAPOS 2013;17: 153-157)
T
he growth of a child’s pseudophakic or aphakic eye results in a myopic shift.1-3 The logarithmic model of the rate of refractive growth (RRG) is based on a large, long-term observational case series of aphakic refractions in children.2,4,5 Authors of the RRG study found that the mean aphakic refraction follows a simple logarithmic decline from infancy through 20
Author affiliations: aOphthalmology Department, Naval Medical Center San Diego, San Diego, California; bByram Hills High School, Armonk, New York; cUniformed Services University of Health Sciences, Bethesda, Maryland; dLoma Linda University Medical Center, Loma Linda, California Study conducted at the Naval Medical Center San Diego, San Diego, California. Financial disclosures: patent application 13/430,145 (S.M.); patent application 13/430,145 (SW). The views expressed in this article are those of the authors and do not necessarily reflect the official policy or position of the Department of the Navy, Department of Defense, or the United States Government. Presented in part at the Symposium on Cataract, IOL and Refractive Surgery, The American Society of Cataract and Refractive Surgery, San Diego, California, March 25-29, 2011; and at the International Congenital Cataract Symposium, New York, New York, March 11, 2011. A patent application has been filed related to the study material as well. Submitted April 2, 2012. Revision accepted November 22, 2012. Published online March 25, 2013. Correspondence: LT Susan Whitmer, MC, USN, Bob Wilson Medical Center, Ophthalmology Suite 202, 34520 Bob Wilson Drive, San Diego, CA 92134 (email: susan. [email protected]). Copyright Ó 2013 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/$36.00 http://dx.doi.org/10.1016/j.jaapos.2012.11.013
Journal of AAPOS
years of age, with a high correlation (P \ 0.01, R2 5 0.97).5 Because of the asymptotic nature of the logarithmic curve, the model is known to be flawed for the youngest ages. In the original model, the value of RRG is defined as the slope of the line of the aphakic refraction at the spectacle plane versus the logarithm of the age. In 2010, a new model (RRG2) was developed that “adjusted” the ages by the addition of 0.6 years at each measured refraction to account for the growth of the eye in utero.6 A recalculation of the rate of refractive growth using RRG2 shows that part of the reason for the observed lower RRG values in the eyes of children undergoing surgery before 6 months of age is that the values for these eyes are skewed by the asymptotic nature of the RRG model. RRG2 bases its calculations on refractions at the spectacle plane. For the youngest children with high hyperopic aphakic refractive errors, the assumed vertex distance of 12 mm is much larger in proportion to the focal length of the spectacle lens than it is in an adult eye, which results in an artificially large difference between the aphakic refraction measured at the natural lens plane (the plane of the crystalline lens) and the aphakic refraction measured at the spectacle plane. Thus, RRG2 is confounded by the optical effect of vertex distance. This flaw reduces the calculated value of RRG2 in the smallest eyes, falsely indicating that these eyes are growing more slowly than larger eyes. To eliminate the effect of vertex distance from the model, we elected to mathematically shift the position of measured
153
154
Whitmer, Xu, and McClatchey
refraction for the study eyes by developing a new model of refractive growth. The new model, RRG3, is based on the aphakic refraction calculated at the natural lens plane instead of at the spectacle plane. This model was designed to eliminate the optical flaw and could theoretically provide a better prediction of future postoperative refractions, even in the youngest infants. The primary purpose of this retrospective observational case series study was to develop and test this model. We hypothesized that the observed difference in the RRG2 values between children who had cataract surgery with IOL implantation before 6 months of age versus those at age 6 months or older was caused by the optical effect of vertex distance on the RRG2 formula (e-Supplement 1, available at jaapos.org). Because RRG3 is based on calculations at the natural lens plane, an IOL formula that can be used for these calculations is necessary. We developed a novel IOL formula (W) that assumes proportional growth of all components of the eye (e-Supplement 2, available at jaapos.org). Because the formula assumes proportional growth, it might be theoretically valid for even the smallest eyes of premature infants, whereas current IOL formulas are designed for use in adults and are known to be less accurate when applied to children.2,7,8 The primary outcome measures were the mean values of the rate of refractive growth for pseudophakic and aphakic eyes, calculated with the revised model (RRG3). We also evaluated whether any of the following factors affect RRG3: age at surgery, postoperative best-corrected visual acuity (BCVA), sex, uni- versus bilaterality of the surgery, presence of glaucoma, presence of IOL, and calculated initial adjusted aphakic refraction.
Subjects and Methods This retrospective study (CIP# NMCSD.2010.0135 “A reanalysis of refractive growth in pediatric aphakia and pseudophakia”) was approved by the Institutional Review Board at Naval Medical Center San Diego, San Diego, California. We used data collected in previous studies of pseudophakic and aphakic children.9 The inclusion criteria were as follows: age #10 years at the time of cataract surgery; time span between first and last refraction .3.6 years; and time span between first and last refraction .0.6 1 age (in years) at first refraction (eg, minimum follow-up time for a child aged 10 years at first refraction would be 10.6 years). For the primary outcome measure, to calculate the mean RRG3 value, we extracted the following data: side (right or left eye), age at surgery, age at initial refraction after surgery, initial refraction, age at final refraction after surgery, and final refraction. For pseudophakic eyes, we also extracted the IOL power and A-constant. All refractions were measured or calculated to be at the spectacle plane; all contact lens refractions were converted to the refraction at the spectacle plane, assuming a vertex distance of 12 mm. For each measured refraction, we calculated the adjusted aphakic refraction, defined as the power of an IOL with an A-constant of 118.4 that would be required to make the eye emmetropic.
Volume 17 Number 2 / April 2013 For pseudophakic patients, we calculated an axial length that would (with proportional values for cornea parameters) result in the observed pseudophakic refraction. These calculated “axial lengths” were determined from the IOL power, A-constant, and the known postoperative refractions at the spectacle plane by iteration via use of the W formula: the axial length was first estimated, and then iteratively changed (using Microsoft Excel Visual Basic for Applications code) until the calculated spectacle plane refraction (using W) matched the known refraction within 0.001 D. Although we iteratively changed only the axial length, the proportional assumptions in the W formula resulted in the other parameters (anterior and posterior cornea curvature, cornea thickness, and anterior chamber depth) changing in proportion to axial length. We then used the resulting axial length and the other proportional parameters to calculate an IOL power for emmetropia, using the W formula. Although the precise axial lengths and cornea power calculated in this way may be somewhat incorrect (in inverse relationship), this has been shown elsewhere to make little difference in the resulting IOL power for a given pseudophakic refraction.1 From the adjusted aphakic refraction, we calculated the RRG3 values as the difference in the adjusted aphakic refractions divided by the difference in the logarithms of the adjusted ages: RRG35
AdjAR2 log AdjAge2
AdjAR1 log AdjAge1
where RRG3 is the rate of refractive growth, AdjAR the adjusted aphakic refraction, and AdjAge the patient’s age at the measured refraction plus 0.6 years to account for the time the eye is growing before birth. Initial and final measurements are indicated by subscripts 1 and 2, respectively. We performed unpaired two-tailed t tests assuming unequal variances to compare the mean values of RRG, RRG2, and RRG3 for the following groups: (1) pseudophakic patients \6 months of age at surgery versus pseudophakic patients $6 months of age at surgery, and (2) aphakic patients\6 months of age at surgery versus aphakic patients $6 months of age at surgery. We then performed unpaired two-tailed t tests assuming unequal variances for all pseudophakic patients versus all aphakic patients.10 For all t tests, a P value \0.05 was considered statistically significant. For secondary outcome analysis, to evaluate additional factors that may affect RRG3, we extracted (when available) the following data: age at surgery, BCVA, sex, unilaterality versus bilaterality of the surgery, presence of glaucoma, presence of IOL, and calculated initial adjusted aphakic refraction. For bilateral cases, only data from the right eye were used. Backward stepwise multiple regression analysis was used to analyze if the following secondary factors had a significant influence on RRG310: age at surgery, BCVA, sex, unilaterality versus bilaterality of the surgery, presence of glaucoma, presence of IOL, and calculated initial adjusted aphakic refraction.
Results A total of 78 pseudophakic and 70 aphakic eyes met the inclusion criteria. The age at surgery ranged from 0.25 to 9 years, with a mean follow-up time of 9.5 years.
Journal of AAPOS
Volume 17 Number 2 / April 2013
Whitmer, Xu, and McClatchey
155
Table 1. Characteristics of study eyes
Pseudophakic eyes Aphakic eyes
Age at surgery, years
Age at surgery \6 months
Mean time between measured refractions, years
Mean logMAR BCVA, Snellen notation
0.25-6.1 0.25-9.0
24% 31%
7.9 11.3
20/58 20/74
BCVA, best-corrected visual acuity at the spectacle plane. Table 2. Comparison of RRG3 in pseudophakic and aphakic eyes, using the t test Pseudophakic eyes Pseudophakic eyes
Age at surgery, months
Number of eyes
\6 $6 \6 $6
19 59 22 48
Mean RRG3, Da 11 4 14 7 15 9 17 10
Mean RRG3 at all ages, Da
P 5 0.053
13 6
P 5 0.59
16 10
P 5 0.01
D, diopters; RRG3, rate of refractive growth, new model. a Reported values for the rate of refractive growth are mean SD.
Characteristics of the eyes studied are shown in Table 1. The demographics of the pseudophakic and aphakic eyes were similar. The mean RRG3 value did not differ significantly for pseudophakic patients who had surgery before 6 months of age versus those who underwent surgery at 6 months of age or older ( 11 4 D vs 14 7 D, P 5 0.053; Table 2). The mean RRG3 value was also not significantly different for aphakic patients in these age groups ( 15 9 D vs 17 10 D, P 5 0.59; Table 2). Because the mean values for RRG3 in these groups (\6 months at surgery vs $ 6 months for both pseudophakic and aphakic patients) did not differ significantly, we grouped all ages together for further analysis. The mean RRG3 value for pseudophakic eyes of all ages was 13 6 D; for aphakic eyes of all ages, 16 10 D (P 5 0.01; Figure 1, Table 2). For eyes with surgery at \6 months of age versus those with surgery at an older age, the relative difference of calculated rate of refractive growth was less for the RRG3 model (P 5 0.053 for pseudophakic eyes, P 5 0.59 for aphakic eyes) than for the RRG model (P \ 0.01 for pseudophakic eyes, P 5 0.065 for aphakic eyes) or for the RRG2 model (P 5 0.016 for pseudophakic eyes, P 5 0.47 for aphakic eyes; see Tables 3 and 4). Thus, the mean values of RRG and RRG2 were significantly different between eyes with surgery before 6 months of age and eyes with surgery at older ages. For the RRG3 model, this age difference does not reach statistical significance. We used backward stepwise multiple regression to test whether any observed factor (presence of glaucoma, LogMAR BCVA, unilaterality versus bilaterality, age at surgery, presence of an IOL, and calculated initial adjusted aphakic refraction) affected the value of RRG3. This regression analysis provided an overall model with a P value of 0.001 and R2 of 0.11. LogMAR BCVA (P 5 0.13), presence of an IOL (P 5 0.01), and calculated initial adjusted aphakic refraction (P 5 0.03) contributed to the model. Because initial adjusted aphakic refraction should be closely correlated with age at surgery, we tested the model including age at surgery instead of the initial adjusted aphakic
Journal of AAPOS
refraction and found that age at surgery was not a significant factor (P 5 0.45). The R2 value (0.11) indicates that only 11% of the total variance in the observed value of RRG3 can be accounted for by a model incorporating logMAR BCVA, presence of an IOL, and calculated initial adjusted aphakic refraction. The other factors did not contribute significantly.
Discussion The ability to predict the rate of refractive growth of a child’s eye would simplify the decision of which IOL power to insert when performing cataract surgery. For example, a surgeon, knowing that during the next 10 years a child would become 7 D more myopic, could aim for present emmetropia or choose an optimal IOL power for some point in the future. The rate of refractive growth in the RRG2 model can be thought of as the amount of aphakic myopic shift (in diopters) of the spectacle power for emmetropia when the ratio of adjusted ages is 10-fold; in the RRG3 model, as the amount of myopic shift (in diopters) of the IOL power for emmetropia with 10-fold ratio of adjusted ages. We found that the RRG3 values were not significantly different in infants \6 months of age versus $6 months of age at the time of surgery for either pseudophakic or aphakic eyes. This finding is consistent with our hypothesis that the optical effect of the vertex distance was a reason for the previously observed age-related difference in mean values for RRG and for RRG2. However, the mean RRG3 values for both pseudophakic and aphakic eyes are more negative than their corresponding RRG and RRG2 values as a result of the difference in how the aphakic refraction is calculated—at the spectacle plane in RRG and RRG2 versus at the natural lens plane in RRG3. Although the difference in the observed RRG3 value (P 5 0.053) between pseudophakic eyes that had surgery at different ages did not meet our criterion for statistical significance (P \ 0.05), this P value suggests that there is a difference in the rate of refractive growth of pseudophakic eyes at different ages.
156
Whitmer, Xu, and McClatchey
Volume 17 Number 2 / April 2013 Table 4. Comparison of mean RRG, RRG2, and RRG3 values in aphakic eyes Mean rate of refractive growth, Da Model RRG RRG2 RRG3
Age \6 monthsb 4.9 3 6.6 4 15 9
Age $6 monthsb
P value
6.5 4 7.3 5 17 10
0.065 0.47 0.59
D, diopters; RRG, rate of refractive growth. Reported values for rate of refractive growth are mean SD. b Age at surgery. a
FIG 1. RRG3 versus percent of eyes. Distribution of the rate of refractive growth (RRG3) values for individual eyes. Table 3. Comparison of mean RRG, RRG2, and RRG3 values in pseudophakic eyes Mean rate of refractive growth, Da Model RRG RRG2 RRG3
Age \6 monthsb 3.3 1 4.9 2 11 4
Age $6 monthsb 5.5 3 6.6 3 14 7
P value \0.01 0.016 0.053
D, diopters; RRG, rate of refractive growth. Reported values for rate of refractive growth are mean standard deviation. b Age at surgery. a
Because this was a retrospective study, some of the data were sparse and not uniformly gathered, and the eyes were not randomized. These shortcomings can produce bias in the results; the large numbers of eyes and long periods between measured refractions relative to the age at surgery may reduce the effect of these sources of error. In particular, the long follow-up time was included to allow sufficient growth of the eye between refraction measurements to reduce the effect of measurement error. The entry criteria for this study were stricter than those used in the original RRG9 and RRG211 studies: length of time between measured refraction data had to be at least 3.6 years and at least as long as the child’s age at surgery plus 0.6 years, and only data from the right eye were used in bilateral cases. Thus, the data in this study were a subset of the data used in the previous studies, and the results may not be directly comparable. The backward stepwise multiple regression was used to evaluate whether and by how much any of the secondary factors affect RRG3, not whether RRG3 is a valid model. Because the R2 value was 0.11 for the overall model, the secondary factors have very little effect on RRG3: only logMAR BCVA, presence of an IOL, and calculated initial adjusted aphakic refraction had any significant influence. We found that logMAR BCVA was negatively correlated with RRG3: as vision became worse, RRG3 became more negative. In rabbits, Verolino and colleagues12 found that
visual deprivation, induced by suturing the eyelids closed, led to an increase in axial elongation. If the retinal image quality was poor, the eye lost an important regulator of emmetropization.3,13-15 Even after the sutures were removed, the amblyopic eyes in this rabbit study continued to have greater axial elongation than did the normal rabbit eyes. Because ocular growth in these experiments was affected by the quality of the retinal image, one might expect RRG3 to be affected by visual acuity in humans as well; however, because BCVA is the long-term result of both good image quality on the retina and proper management of amblyopia, BCVA is not a direct substitute for the effect of image quality. In addition, because unilateral cataract patients have a much greater rate of amblyopia than those with bilateral cataracts, this apparent correlation between BCVA and RRG3 may be further confounded by laterality of the cataract. We found no correlation between any of the following factors and RRG3: age at surgery, sex, presence of glaucoma, and unilaterality versus bilaterality of the surgery. Finding RRG3 to be independent of age at surgery is especially helpful because this one model can be used for all ages instead of needing to use separate models for patients of different ages. Better understanding of the factors influencing pediatric eye growth will assist in IOL power calculation and the prediction of refractive changes after IOL implantation.7 We found that the mean RRG3 value was significantly less negative in pseudophakic eyes than in aphakic eyes. In previous studies in children, investigators found that pseudophakic eyes had less axial elongation than aphakic eyes.8,9 Previous studies in monkeys found that both aphakic eyes16,17 and pseudophakic eyes17 had less axial elongation than their fellow unoperated eyes. However, measurements in children of axial length have shown no significant difference over time between pseudophakic eyes and their fellow unoperated eyes,3 which suggests that most pseudophakic eyes grow normally and are consequently expected to have a large myopic shift.7 Further inspection of the plot of RRG3 versus percent of eyes showed that the mode value of RRG3 was more negative in pseudophakic eyes than in aphakic eyes ( 13 D vs 10 D; Figure 1). It may be that the mean RRG3 value for aphakic eyes was skewed by outliers with extremely negative values. Thus this result should be interpreted with caution.17
Journal of AAPOS
Volume 17 Number 2 / April 2013 An accurate IOL formula is necessary for surgeons to predict the growth of a child’s eye and choose the optimal IOL power. We designed the W formula, assuming proportional growth of the components of the eye, to allow IOL power calculation in the smallest eyes. Current IOL formulas are designed for use in adults.2,7,8 Several studies have been conducted to test their validity when applied to children. The mean absolute error in many of these studies ranged from 1.06 D to 1.4 D,11,18-21 which was greater than the mean absolute error of 0.5 D to 0.7 D found in adults.22,23 In more recent studies, authors have found mean absolute prediction errors of 0.76 to 1.18 when they applied the adult IOL formulas to pediatric patients,24,25 still with only 43% of eyes with less than 0.5 D of error.24 The theoretic formulas have been found to be more accurate than the regression formulas when applied to adults22,24 and to perform better, although not clinically significantly, when applied to children.19 Although we chose to shift the plane of refractive correction to the natural crystalline lens plane in the RRG3 model to eliminate the optical effect of vertex distance, we recognize that calculating the rate of refractive growth using a contact lens refraction at the corneal plane would give an equally valid result.26 RRG3 should be further tested with data from a large, randomized prospective study to further assess its validity. The possibility of a difference in the RRG3 value between pseudophakic eyes that had surgery at younger versus older ages can be studied in future observations of RRG3 in infant and older pseudophakic eyes. It could be particularly useful to evaluate the model’s performance in children \3 months of age at the time of surgery since all children included in this study were 3 months of age or older at the time of surgery.
Acknowledgments Special thanks to Dr. Robert Riffenburgh for his help with the statistical analysis. References 1. McClatchey SK, Parks MM. Theoretic refractive changes after lens implantation in childhood. Ophthalmology 1997;104:1744-51. 2. Astle WF, Ingram AD, Isaza GM, Echeverri P. Paediatric pseudophakia: Analysis of intraocular lens power and myopic shift. Clin Exp Ophthalmol 2007;35:244-51. 3. Kora Y, Shimizu K, Inatomi M, Fukado Y, Ozawa T. Eye growth after cataract extraction and intraocular lens implantation in children. Ophthalmic Surg 1993;24:467-75.
Journal of AAPOS
Whitmer, Xu, and McClatchey
157
4. McClatchey SK. Refractive changes after lens implantation in childhood: Author’s reply. Ophthalmology 1998;105:1572-4. 5. McClatchey SK, Parks MM. Myopic shift after cataract removal in childhood. J Pediatr Ophthalmol Strabismus 1997;34:88-95. 6. McClatchey SK, Hofmeister EM. The optics of aphakic and pseudophakic eyes in childhood. Surv Ophthalmol 2010;55:174-82. 7. Eibschitz-Tsimhoni M, Archer SM, Del Monte MA. Intraocular lens power calculation in children. Surv Ophthalmol 2007;52:474-82. 8. Krishnamurthy R, Vander Veen DK. Infantile cataracts. Int Ophthalmol Clin 2008;48:175-92. 9. McClatchey SK, Dahan E, Maselli E, et al. A comparison of the rate of refractive growth in pediatric aphakic and pseudophakic eyes. Ophthalmology 2000;107:118-22. 10. Kramer MS. Clinical epidemiology and biostatistics. Berlin: Springer-Verlag; 1988. 11. McClatchey SK. Choosing IOL power in pediatric cataract surgery. Int Ophthalmol Clin 2010;50:115-23. 12. Verolino M, Nastri G, Sellitti L, Costagliola C. Axial length increase in lid-sutured rabbits. Surv Ophthalmol 1999;44:S103-8. 13. McClatchey SK. Intraocular lens calculator for childhood cataract. J Cataract Refract Surg 1998;24:1125-9. 14. Rabin J, Van Sluyters RC, Malach R. Emmetropization: A visiondependent phenomenon. Invest Ophthalmol Vis Sci 1981;20:561-4. 15. von Noorden GK, Lewis RA. Ocular axial length in unilateral congenital cataracts and blepharoptosis. Invest Ophthalmol Vis Sci 1987;28:750-52. 16. Lambert SR. The effect of age on the retardation of axial elongation following a lensectomy in infant monkeys. Arch Ophthalmol 1998; 116:781-4. 17. Lambert SR, Fernandes A, Drews-Botsch C, Tigges M. Pseudophakia retards axial elongation in neonatal monkey eyes. Invest Ophthalmol Vis Sci 1996;37:451-8. 18. Andreo LK, Wilson ME, Saunders RA. Predictive value of regression and theoretical IOL formulas in pediatric intraocular lens implantation. J Pediatr Ophthalmol Strabismus 1997;34:240-43. 19. Mezer E, Rootman DS, Abdolell M, Levin AV. Early postoperative refractive outcomes of pediatric intraocular lens implantation. J Cataract Refract Surg 2004;30:603-10. 20. Moore DB, Ben Zion I, Neely DE, et al. Accuracy of biometry in pediatric cataract extraction with primary intraocular lens implantation. J Cataract Refract Surg 2008;34:1940-47. 21. Tromans C, Haigh PM, Biswas S, Lloyd IC. Accuracy of intraocular lens power calculation in paediatric cataract surgery. Br J Ophthalmol 2001;85:939-41. 22. Hoffer KJ. The Hoffer Q formula: A comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:700-12. 23. Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz RS. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17-24. 24. Nihalani BR, VanderVeen DK. Comparison of intraocular lens power calculation formulae in pediatric eyes. Ophthalmology 2010;117: 1493-9. 25. Trivedi RH, Wilson ME, Reardon W. Accuracy of the Holladay 2 intraocular lens formula for pediatric eyes in the absence of preoperative refraction. J Cataract Refract Surg 2011;37:1239-43. 26. Superstein R, Archer SM, Del Monte MA. Minimal myopic shift in pseudophakic versus aphakic pediatric cataract patients. J AAPOS 2002;6:271-6.
The current model of refractive growth in children (RRG2) is calculated as the slope of aphakic refraction at the spectacle plane versus the logarithm of adjusted age. However, this model fails in infants because of the optical effect of vertex distance of a spectacle lens on the effective power at the cornea. In this study, we developed a new model of refractive growth (RRG3) that eliminates the optical effect of vertex distance on the RRG2 model.
METHODS
We calculated RRG3 values for pseudophakic and aphakic eyes previously analyzed for RRG2. Inclusion criteria were age #10 years at the time of cataract surgery and follow-up time between measured refractions of at least 3.6 years and at least the age at first refraction plus 0.6 years. For both pseudophakic and aphakic eyes, we compared RRG3 values in children who had cataract surgery before age 6 months with those in children aged 6 months or older.
RESULTS
A total of 78 pseudophakic and 70 aphakic eyes met the inclusion criteria. Ages at surgery ranged from 0.25 to 9 years, with a 9.5-year mean follow-up time. The mean RRG3 value was not significantly different between the surgical age groups for both pseudophakic eyes (P 5 0.053) and aphakic eyes (P 5 0.59).
CONCLUSIONS
The RRG3 values were not significantly different between the surgical age groups for both pseudophakic and aphakic eyes. Consequently, RRG3 is theoretically applicable even in the small eyes of infants having surgery before 6 months of age. ( J AAPOS 2013;17: 153-157)
T
he growth of a child’s pseudophakic or aphakic eye results in a myopic shift.1-3 The logarithmic model of the rate of refractive growth (RRG) is based on a large, long-term observational case series of aphakic refractions in children.2,4,5 Authors of the RRG study found that the mean aphakic refraction follows a simple logarithmic decline from infancy through 20
Author affiliations: aOphthalmology Department, Naval Medical Center San Diego, San Diego, California; bByram Hills High School, Armonk, New York; cUniformed Services University of Health Sciences, Bethesda, Maryland; dLoma Linda University Medical Center, Loma Linda, California Study conducted at the Naval Medical Center San Diego, San Diego, California. Financial disclosures: patent application 13/430,145 (S.M.); patent application 13/430,145 (SW). The views expressed in this article are those of the authors and do not necessarily reflect the official policy or position of the Department of the Navy, Department of Defense, or the United States Government. Presented in part at the Symposium on Cataract, IOL and Refractive Surgery, The American Society of Cataract and Refractive Surgery, San Diego, California, March 25-29, 2011; and at the International Congenital Cataract Symposium, New York, New York, March 11, 2011. A patent application has been filed related to the study material as well. Submitted April 2, 2012. Revision accepted November 22, 2012. Published online March 25, 2013. Correspondence: LT Susan Whitmer, MC, USN, Bob Wilson Medical Center, Ophthalmology Suite 202, 34520 Bob Wilson Drive, San Diego, CA 92134 (email: susan. [email protected]). Copyright Ó 2013 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/$36.00 http://dx.doi.org/10.1016/j.jaapos.2012.11.013
Journal of AAPOS
years of age, with a high correlation (P \ 0.01, R2 5 0.97).5 Because of the asymptotic nature of the logarithmic curve, the model is known to be flawed for the youngest ages. In the original model, the value of RRG is defined as the slope of the line of the aphakic refraction at the spectacle plane versus the logarithm of the age. In 2010, a new model (RRG2) was developed that “adjusted” the ages by the addition of 0.6 years at each measured refraction to account for the growth of the eye in utero.6 A recalculation of the rate of refractive growth using RRG2 shows that part of the reason for the observed lower RRG values in the eyes of children undergoing surgery before 6 months of age is that the values for these eyes are skewed by the asymptotic nature of the RRG model. RRG2 bases its calculations on refractions at the spectacle plane. For the youngest children with high hyperopic aphakic refractive errors, the assumed vertex distance of 12 mm is much larger in proportion to the focal length of the spectacle lens than it is in an adult eye, which results in an artificially large difference between the aphakic refraction measured at the natural lens plane (the plane of the crystalline lens) and the aphakic refraction measured at the spectacle plane. Thus, RRG2 is confounded by the optical effect of vertex distance. This flaw reduces the calculated value of RRG2 in the smallest eyes, falsely indicating that these eyes are growing more slowly than larger eyes. To eliminate the effect of vertex distance from the model, we elected to mathematically shift the position of measured
153
154
Whitmer, Xu, and McClatchey
refraction for the study eyes by developing a new model of refractive growth. The new model, RRG3, is based on the aphakic refraction calculated at the natural lens plane instead of at the spectacle plane. This model was designed to eliminate the optical flaw and could theoretically provide a better prediction of future postoperative refractions, even in the youngest infants. The primary purpose of this retrospective observational case series study was to develop and test this model. We hypothesized that the observed difference in the RRG2 values between children who had cataract surgery with IOL implantation before 6 months of age versus those at age 6 months or older was caused by the optical effect of vertex distance on the RRG2 formula (e-Supplement 1, available at jaapos.org). Because RRG3 is based on calculations at the natural lens plane, an IOL formula that can be used for these calculations is necessary. We developed a novel IOL formula (W) that assumes proportional growth of all components of the eye (e-Supplement 2, available at jaapos.org). Because the formula assumes proportional growth, it might be theoretically valid for even the smallest eyes of premature infants, whereas current IOL formulas are designed for use in adults and are known to be less accurate when applied to children.2,7,8 The primary outcome measures were the mean values of the rate of refractive growth for pseudophakic and aphakic eyes, calculated with the revised model (RRG3). We also evaluated whether any of the following factors affect RRG3: age at surgery, postoperative best-corrected visual acuity (BCVA), sex, uni- versus bilaterality of the surgery, presence of glaucoma, presence of IOL, and calculated initial adjusted aphakic refraction.
Subjects and Methods This retrospective study (CIP# NMCSD.2010.0135 “A reanalysis of refractive growth in pediatric aphakia and pseudophakia”) was approved by the Institutional Review Board at Naval Medical Center San Diego, San Diego, California. We used data collected in previous studies of pseudophakic and aphakic children.9 The inclusion criteria were as follows: age #10 years at the time of cataract surgery; time span between first and last refraction .3.6 years; and time span between first and last refraction .0.6 1 age (in years) at first refraction (eg, minimum follow-up time for a child aged 10 years at first refraction would be 10.6 years). For the primary outcome measure, to calculate the mean RRG3 value, we extracted the following data: side (right or left eye), age at surgery, age at initial refraction after surgery, initial refraction, age at final refraction after surgery, and final refraction. For pseudophakic eyes, we also extracted the IOL power and A-constant. All refractions were measured or calculated to be at the spectacle plane; all contact lens refractions were converted to the refraction at the spectacle plane, assuming a vertex distance of 12 mm. For each measured refraction, we calculated the adjusted aphakic refraction, defined as the power of an IOL with an A-constant of 118.4 that would be required to make the eye emmetropic.
Volume 17 Number 2 / April 2013 For pseudophakic patients, we calculated an axial length that would (with proportional values for cornea parameters) result in the observed pseudophakic refraction. These calculated “axial lengths” were determined from the IOL power, A-constant, and the known postoperative refractions at the spectacle plane by iteration via use of the W formula: the axial length was first estimated, and then iteratively changed (using Microsoft Excel Visual Basic for Applications code) until the calculated spectacle plane refraction (using W) matched the known refraction within 0.001 D. Although we iteratively changed only the axial length, the proportional assumptions in the W formula resulted in the other parameters (anterior and posterior cornea curvature, cornea thickness, and anterior chamber depth) changing in proportion to axial length. We then used the resulting axial length and the other proportional parameters to calculate an IOL power for emmetropia, using the W formula. Although the precise axial lengths and cornea power calculated in this way may be somewhat incorrect (in inverse relationship), this has been shown elsewhere to make little difference in the resulting IOL power for a given pseudophakic refraction.1 From the adjusted aphakic refraction, we calculated the RRG3 values as the difference in the adjusted aphakic refractions divided by the difference in the logarithms of the adjusted ages: RRG35
AdjAR2 log AdjAge2
AdjAR1 log AdjAge1
where RRG3 is the rate of refractive growth, AdjAR the adjusted aphakic refraction, and AdjAge the patient’s age at the measured refraction plus 0.6 years to account for the time the eye is growing before birth. Initial and final measurements are indicated by subscripts 1 and 2, respectively. We performed unpaired two-tailed t tests assuming unequal variances to compare the mean values of RRG, RRG2, and RRG3 for the following groups: (1) pseudophakic patients \6 months of age at surgery versus pseudophakic patients $6 months of age at surgery, and (2) aphakic patients\6 months of age at surgery versus aphakic patients $6 months of age at surgery. We then performed unpaired two-tailed t tests assuming unequal variances for all pseudophakic patients versus all aphakic patients.10 For all t tests, a P value \0.05 was considered statistically significant. For secondary outcome analysis, to evaluate additional factors that may affect RRG3, we extracted (when available) the following data: age at surgery, BCVA, sex, unilaterality versus bilaterality of the surgery, presence of glaucoma, presence of IOL, and calculated initial adjusted aphakic refraction. For bilateral cases, only data from the right eye were used. Backward stepwise multiple regression analysis was used to analyze if the following secondary factors had a significant influence on RRG310: age at surgery, BCVA, sex, unilaterality versus bilaterality of the surgery, presence of glaucoma, presence of IOL, and calculated initial adjusted aphakic refraction.
Results A total of 78 pseudophakic and 70 aphakic eyes met the inclusion criteria. The age at surgery ranged from 0.25 to 9 years, with a mean follow-up time of 9.5 years.
Journal of AAPOS
Volume 17 Number 2 / April 2013
Whitmer, Xu, and McClatchey
155
Table 1. Characteristics of study eyes
Pseudophakic eyes Aphakic eyes
Age at surgery, years
Age at surgery \6 months
Mean time between measured refractions, years
Mean logMAR BCVA, Snellen notation
0.25-6.1 0.25-9.0
24% 31%
7.9 11.3
20/58 20/74
BCVA, best-corrected visual acuity at the spectacle plane. Table 2. Comparison of RRG3 in pseudophakic and aphakic eyes, using the t test Pseudophakic eyes Pseudophakic eyes
Age at surgery, months
Number of eyes
\6 $6 \6 $6
19 59 22 48
Mean RRG3, Da 11 4 14 7 15 9 17 10
Mean RRG3 at all ages, Da
P 5 0.053
13 6
P 5 0.59
16 10
P 5 0.01
D, diopters; RRG3, rate of refractive growth, new model. a Reported values for the rate of refractive growth are mean SD.
Characteristics of the eyes studied are shown in Table 1. The demographics of the pseudophakic and aphakic eyes were similar. The mean RRG3 value did not differ significantly for pseudophakic patients who had surgery before 6 months of age versus those who underwent surgery at 6 months of age or older ( 11 4 D vs 14 7 D, P 5 0.053; Table 2). The mean RRG3 value was also not significantly different for aphakic patients in these age groups ( 15 9 D vs 17 10 D, P 5 0.59; Table 2). Because the mean values for RRG3 in these groups (\6 months at surgery vs $ 6 months for both pseudophakic and aphakic patients) did not differ significantly, we grouped all ages together for further analysis. The mean RRG3 value for pseudophakic eyes of all ages was 13 6 D; for aphakic eyes of all ages, 16 10 D (P 5 0.01; Figure 1, Table 2). For eyes with surgery at \6 months of age versus those with surgery at an older age, the relative difference of calculated rate of refractive growth was less for the RRG3 model (P 5 0.053 for pseudophakic eyes, P 5 0.59 for aphakic eyes) than for the RRG model (P \ 0.01 for pseudophakic eyes, P 5 0.065 for aphakic eyes) or for the RRG2 model (P 5 0.016 for pseudophakic eyes, P 5 0.47 for aphakic eyes; see Tables 3 and 4). Thus, the mean values of RRG and RRG2 were significantly different between eyes with surgery before 6 months of age and eyes with surgery at older ages. For the RRG3 model, this age difference does not reach statistical significance. We used backward stepwise multiple regression to test whether any observed factor (presence of glaucoma, LogMAR BCVA, unilaterality versus bilaterality, age at surgery, presence of an IOL, and calculated initial adjusted aphakic refraction) affected the value of RRG3. This regression analysis provided an overall model with a P value of 0.001 and R2 of 0.11. LogMAR BCVA (P 5 0.13), presence of an IOL (P 5 0.01), and calculated initial adjusted aphakic refraction (P 5 0.03) contributed to the model. Because initial adjusted aphakic refraction should be closely correlated with age at surgery, we tested the model including age at surgery instead of the initial adjusted aphakic
Journal of AAPOS
refraction and found that age at surgery was not a significant factor (P 5 0.45). The R2 value (0.11) indicates that only 11% of the total variance in the observed value of RRG3 can be accounted for by a model incorporating logMAR BCVA, presence of an IOL, and calculated initial adjusted aphakic refraction. The other factors did not contribute significantly.
Discussion The ability to predict the rate of refractive growth of a child’s eye would simplify the decision of which IOL power to insert when performing cataract surgery. For example, a surgeon, knowing that during the next 10 years a child would become 7 D more myopic, could aim for present emmetropia or choose an optimal IOL power for some point in the future. The rate of refractive growth in the RRG2 model can be thought of as the amount of aphakic myopic shift (in diopters) of the spectacle power for emmetropia when the ratio of adjusted ages is 10-fold; in the RRG3 model, as the amount of myopic shift (in diopters) of the IOL power for emmetropia with 10-fold ratio of adjusted ages. We found that the RRG3 values were not significantly different in infants \6 months of age versus $6 months of age at the time of surgery for either pseudophakic or aphakic eyes. This finding is consistent with our hypothesis that the optical effect of the vertex distance was a reason for the previously observed age-related difference in mean values for RRG and for RRG2. However, the mean RRG3 values for both pseudophakic and aphakic eyes are more negative than their corresponding RRG and RRG2 values as a result of the difference in how the aphakic refraction is calculated—at the spectacle plane in RRG and RRG2 versus at the natural lens plane in RRG3. Although the difference in the observed RRG3 value (P 5 0.053) between pseudophakic eyes that had surgery at different ages did not meet our criterion for statistical significance (P \ 0.05), this P value suggests that there is a difference in the rate of refractive growth of pseudophakic eyes at different ages.
156
Whitmer, Xu, and McClatchey
Volume 17 Number 2 / April 2013 Table 4. Comparison of mean RRG, RRG2, and RRG3 values in aphakic eyes Mean rate of refractive growth, Da Model RRG RRG2 RRG3
Age \6 monthsb 4.9 3 6.6 4 15 9
Age $6 monthsb
P value
6.5 4 7.3 5 17 10
0.065 0.47 0.59
D, diopters; RRG, rate of refractive growth. Reported values for rate of refractive growth are mean SD. b Age at surgery. a
FIG 1. RRG3 versus percent of eyes. Distribution of the rate of refractive growth (RRG3) values for individual eyes. Table 3. Comparison of mean RRG, RRG2, and RRG3 values in pseudophakic eyes Mean rate of refractive growth, Da Model RRG RRG2 RRG3
Age \6 monthsb 3.3 1 4.9 2 11 4
Age $6 monthsb 5.5 3 6.6 3 14 7
P value \0.01 0.016 0.053
D, diopters; RRG, rate of refractive growth. Reported values for rate of refractive growth are mean standard deviation. b Age at surgery. a
Because this was a retrospective study, some of the data were sparse and not uniformly gathered, and the eyes were not randomized. These shortcomings can produce bias in the results; the large numbers of eyes and long periods between measured refractions relative to the age at surgery may reduce the effect of these sources of error. In particular, the long follow-up time was included to allow sufficient growth of the eye between refraction measurements to reduce the effect of measurement error. The entry criteria for this study were stricter than those used in the original RRG9 and RRG211 studies: length of time between measured refraction data had to be at least 3.6 years and at least as long as the child’s age at surgery plus 0.6 years, and only data from the right eye were used in bilateral cases. Thus, the data in this study were a subset of the data used in the previous studies, and the results may not be directly comparable. The backward stepwise multiple regression was used to evaluate whether and by how much any of the secondary factors affect RRG3, not whether RRG3 is a valid model. Because the R2 value was 0.11 for the overall model, the secondary factors have very little effect on RRG3: only logMAR BCVA, presence of an IOL, and calculated initial adjusted aphakic refraction had any significant influence. We found that logMAR BCVA was negatively correlated with RRG3: as vision became worse, RRG3 became more negative. In rabbits, Verolino and colleagues12 found that
visual deprivation, induced by suturing the eyelids closed, led to an increase in axial elongation. If the retinal image quality was poor, the eye lost an important regulator of emmetropization.3,13-15 Even after the sutures were removed, the amblyopic eyes in this rabbit study continued to have greater axial elongation than did the normal rabbit eyes. Because ocular growth in these experiments was affected by the quality of the retinal image, one might expect RRG3 to be affected by visual acuity in humans as well; however, because BCVA is the long-term result of both good image quality on the retina and proper management of amblyopia, BCVA is not a direct substitute for the effect of image quality. In addition, because unilateral cataract patients have a much greater rate of amblyopia than those with bilateral cataracts, this apparent correlation between BCVA and RRG3 may be further confounded by laterality of the cataract. We found no correlation between any of the following factors and RRG3: age at surgery, sex, presence of glaucoma, and unilaterality versus bilaterality of the surgery. Finding RRG3 to be independent of age at surgery is especially helpful because this one model can be used for all ages instead of needing to use separate models for patients of different ages. Better understanding of the factors influencing pediatric eye growth will assist in IOL power calculation and the prediction of refractive changes after IOL implantation.7 We found that the mean RRG3 value was significantly less negative in pseudophakic eyes than in aphakic eyes. In previous studies in children, investigators found that pseudophakic eyes had less axial elongation than aphakic eyes.8,9 Previous studies in monkeys found that both aphakic eyes16,17 and pseudophakic eyes17 had less axial elongation than their fellow unoperated eyes. However, measurements in children of axial length have shown no significant difference over time between pseudophakic eyes and their fellow unoperated eyes,3 which suggests that most pseudophakic eyes grow normally and are consequently expected to have a large myopic shift.7 Further inspection of the plot of RRG3 versus percent of eyes showed that the mode value of RRG3 was more negative in pseudophakic eyes than in aphakic eyes ( 13 D vs 10 D; Figure 1). It may be that the mean RRG3 value for aphakic eyes was skewed by outliers with extremely negative values. Thus this result should be interpreted with caution.17
Journal of AAPOS
Volume 17 Number 2 / April 2013 An accurate IOL formula is necessary for surgeons to predict the growth of a child’s eye and choose the optimal IOL power. We designed the W formula, assuming proportional growth of the components of the eye, to allow IOL power calculation in the smallest eyes. Current IOL formulas are designed for use in adults.2,7,8 Several studies have been conducted to test their validity when applied to children. The mean absolute error in many of these studies ranged from 1.06 D to 1.4 D,11,18-21 which was greater than the mean absolute error of 0.5 D to 0.7 D found in adults.22,23 In more recent studies, authors have found mean absolute prediction errors of 0.76 to 1.18 when they applied the adult IOL formulas to pediatric patients,24,25 still with only 43% of eyes with less than 0.5 D of error.24 The theoretic formulas have been found to be more accurate than the regression formulas when applied to adults22,24 and to perform better, although not clinically significantly, when applied to children.19 Although we chose to shift the plane of refractive correction to the natural crystalline lens plane in the RRG3 model to eliminate the optical effect of vertex distance, we recognize that calculating the rate of refractive growth using a contact lens refraction at the corneal plane would give an equally valid result.26 RRG3 should be further tested with data from a large, randomized prospective study to further assess its validity. The possibility of a difference in the RRG3 value between pseudophakic eyes that had surgery at younger versus older ages can be studied in future observations of RRG3 in infant and older pseudophakic eyes. It could be particularly useful to evaluate the model’s performance in children \3 months of age at the time of surgery since all children included in this study were 3 months of age or older at the time of surgery.
Acknowledgments Special thanks to Dr. Robert Riffenburgh for his help with the statistical analysis. References 1. McClatchey SK, Parks MM. Theoretic refractive changes after lens implantation in childhood. Ophthalmology 1997;104:1744-51. 2. Astle WF, Ingram AD, Isaza GM, Echeverri P. Paediatric pseudophakia: Analysis of intraocular lens power and myopic shift. Clin Exp Ophthalmol 2007;35:244-51. 3. Kora Y, Shimizu K, Inatomi M, Fukado Y, Ozawa T. Eye growth after cataract extraction and intraocular lens implantation in children. Ophthalmic Surg 1993;24:467-75.
Journal of AAPOS
Whitmer, Xu, and McClatchey
157
4. McClatchey SK. Refractive changes after lens implantation in childhood: Author’s reply. Ophthalmology 1998;105:1572-4. 5. McClatchey SK, Parks MM. Myopic shift after cataract removal in childhood. J Pediatr Ophthalmol Strabismus 1997;34:88-95. 6. McClatchey SK, Hofmeister EM. The optics of aphakic and pseudophakic eyes in childhood. Surv Ophthalmol 2010;55:174-82. 7. Eibschitz-Tsimhoni M, Archer SM, Del Monte MA. Intraocular lens power calculation in children. Surv Ophthalmol 2007;52:474-82. 8. Krishnamurthy R, Vander Veen DK. Infantile cataracts. Int Ophthalmol Clin 2008;48:175-92. 9. McClatchey SK, Dahan E, Maselli E, et al. A comparison of the rate of refractive growth in pediatric aphakic and pseudophakic eyes. Ophthalmology 2000;107:118-22. 10. Kramer MS. Clinical epidemiology and biostatistics. Berlin: Springer-Verlag; 1988. 11. McClatchey SK. Choosing IOL power in pediatric cataract surgery. Int Ophthalmol Clin 2010;50:115-23. 12. Verolino M, Nastri G, Sellitti L, Costagliola C. Axial length increase in lid-sutured rabbits. Surv Ophthalmol 1999;44:S103-8. 13. McClatchey SK. Intraocular lens calculator for childhood cataract. J Cataract Refract Surg 1998;24:1125-9. 14. Rabin J, Van Sluyters RC, Malach R. Emmetropization: A visiondependent phenomenon. Invest Ophthalmol Vis Sci 1981;20:561-4. 15. von Noorden GK, Lewis RA. Ocular axial length in unilateral congenital cataracts and blepharoptosis. Invest Ophthalmol Vis Sci 1987;28:750-52. 16. Lambert SR. The effect of age on the retardation of axial elongation following a lensectomy in infant monkeys. Arch Ophthalmol 1998; 116:781-4. 17. Lambert SR, Fernandes A, Drews-Botsch C, Tigges M. Pseudophakia retards axial elongation in neonatal monkey eyes. Invest Ophthalmol Vis Sci 1996;37:451-8. 18. Andreo LK, Wilson ME, Saunders RA. Predictive value of regression and theoretical IOL formulas in pediatric intraocular lens implantation. J Pediatr Ophthalmol Strabismus 1997;34:240-43. 19. Mezer E, Rootman DS, Abdolell M, Levin AV. Early postoperative refractive outcomes of pediatric intraocular lens implantation. J Cataract Refract Surg 2004;30:603-10. 20. Moore DB, Ben Zion I, Neely DE, et al. Accuracy of biometry in pediatric cataract extraction with primary intraocular lens implantation. J Cataract Refract Surg 2008;34:1940-47. 21. Tromans C, Haigh PM, Biswas S, Lloyd IC. Accuracy of intraocular lens power calculation in paediatric cataract surgery. Br J Ophthalmol 2001;85:939-41. 22. Hoffer KJ. The Hoffer Q formula: A comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:700-12. 23. Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz RS. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17-24. 24. Nihalani BR, VanderVeen DK. Comparison of intraocular lens power calculation formulae in pediatric eyes. Ophthalmology 2010;117: 1493-9. 25. Trivedi RH, Wilson ME, Reardon W. Accuracy of the Holladay 2 intraocular lens formula for pediatric eyes in the absence of preoperative refraction. J Cataract Refract Surg 2011;37:1239-43. 26. Superstein R, Archer SM, Del Monte MA. Minimal myopic shift in pseudophakic versus aphakic pediatric cataract patients. J AAPOS 2002;6:271-6.