1. science
2. medicine
3. surgery

CLINICAL SCIENCES
Postoperative Astigmatism in the Second Eye
Undergoing Cataract Surgery
Christopher T. Leffler, MD, MPH; Martin Wilkes, MD; Juliana Reeves, MD; Muneera A. Mahmood, MD, FRCOphth
Objective: To predict postoperative refractive astig-
matism in the second eye undergoing cataract surgery
using standard biometry and information obtained
from the first eye.
Methods: We conducted a retrospective study of 160
patients undergoing bilateral sequential phacoemulsification with capsular bag implantation of a hydrophobic
acrylic lens at a Veterans Affairs medical center. Keratometric and refractive astigmatism were described by Jackson cross cylinder with-the-rule (J0) and oblique (JX) components. Preoperative predictors of postoperative
refractive astigmatism in the second eye were determined by multivariable regression.
Results: The postoperative refractive astigmatism in
the first eye predicted 40% of the variation in the second eye (r2 = 0.40; P ⬍ .001). The multivariable model
to predict postoperative with-the-rule astigmatism was
A
Author Affiliations:
Ophthalmology Section, Hunter
Holmes McGuire Veterans
Affairs Medical Center, and
Department of Ophthalmology,
Virginia Commonwealth
University School of Medicine,
Richmond, Virginia.
J0PostopEye2 = (0.376 ⫻ J0PostopEye1) ⫹ (0.327 ⫻ J0KeratomEye2) ⫹
(0.097 ⫻ J0PreopEye2) − 0.099 (P ⬍ .001 for first 2 terms;
r2 = 0.56). The multivariable model for oblique astigmatism was J X P o s t o p E y e 2 = (0.350 ⫻ J X K e r a t o m E y e 2 ) ⫹
(0.231 ⫻ J X K e r a t o m E y e 1 ) ⫹ (0.064 ⫻ J X P r e o p E y e 2 ) − 0.07
(P ⱕ .01 for first 2 terms; r2 =0.20).
Conclusions: Refractive with-the-rule astigmatism observed postoperatively in the first eye is a strong independent predictor of postoperative with-the-rule astigmatism in the second eye. Keratometric oblique
astigmatism in the first eye is a weak but statistically significant independent predictor of postoperative oblique
astigmatism in the second eye. Both findings are consistent with mirror symmetry of the corneas about the midsagittal plane and may improve the prediction (and hence
control) of postoperative astigmatism in the second eye.
Arch Ophthalmol. 2011;129(3):295-300
CCURATE PREDICTION OF
astigmatism after cataract
surgery is becoming increasingly significant owing to the availability and
increased use of treatments such as astigmatic keratotomy (including limbal relaxing incisions), toric intraocular lenses,
and laser-assisted in situ keratomileusis.1
Each method requires accurate prediction of postoperative astigmatism. The traditional thinking is that keratometry alone
determines the postoperative astigmatism because any difference between preoperative keratometric and refractive astigmatism reflects lenticular astigmatism,
which is eliminated by lensectomy.2 However, standard keratometry reflects only the
anterior paracentral corneal curvature and
neglects more peripheral corneal curvature and the entire posterior cornea.3 Indeed, a recent study showed that preoperative refraction, which is influenced by
these aspects of corneal curvature, is an
independent predictor of postoperative refractive astigmatism.4
Another source of information about
postprocedure refraction relies on interocular symmetry. Several reports have
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295
investigated whether postoperative refraction in the first eye can help to predict
spherical refraction in the second eye undergoing laser-assisted in situ keratomileusis5 or cataract surgery.6,7 Corneal curvature,8-14 refractive astigmatism,11,15-17 and
pupil center 18 demonstrate mirror interocular symmetry about the midsagittal plane. The purpose of this study was
to determine which variables available preoperatively for the second eye, such as
keratometry and postoperative refraction
in the first eye, were independently predictive of postoperative astigmatism in the
second eye.
METHODS
The study was performed after approval by the
institutional review board. Surgical procedures for cataract performed at a Veterans Affairs medical center during a 65-month period from January 1, 2004, to May 31, 2009,
were reviewed. Inclusion criteria consisted of
bilateral sequential cataract surgery, implantation of a hydrophobic acrylic lens (Acrysof
SA60AT lens; Alcon Laboratories, Fort Worth,
Texas) in the bag, documentation of keratometry axis and preoperative refraction for both
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eyes, and use of the same biometry method (IOL Master system [version 5; Carl Zeiss Meditec, Inc, Dublin, California] or
immersion ultrasonography) in both eyes. Exclusion criteria
consisted of ophthalmic surgery before cataract surgery, complications during the surgery preventing placement of an intraocular lens in the capsular bag, postoperative macular edema,
and postoperative best-corrected visual acuity of less than 20/60
in either eye.
Before 2007, biometry was performed using a keratometer
(Bausch & Lomb, Rochester, New York). Beginning in 2007,
new patients underwent measurements performed with the IOL
Master system if clarity of the optical media permitted.
All patients underwent phacoemulsification with placement
of the acrylic lens in the bag. Multiple residents performed most
of the surgical procedures. Selection of a 2.8-mm superior scleral
tunnel or a 2.8-mm temporal clear corneal incision was based on
the preference of the resident and the supervising attending physician and could differ for first and second eyes. Postoperative refraction was recorded 6 to 8 weeks after the operation.
For clear corneal incisions, a triplanar 2.8-mm self-sealing
corneal tunnel was prepared with the keratome centered just
off the horizontal meridian (eg, at the 8:30 clock position for a
right-handed surgeon and a right eye). Stromal hydration was
used at the end of the case.
For scleral tunnel incisions, light wet-field coagulation was
applied, and then a straight incision 2.8 mm wide and approximately 0.5 mm deep was made with the crescent blade, approximately 1.0 mm behind the limbus, centered just off the vertical
meridian (eg, at the 11:30 clock position for a right-handed surgeon). A triplanar, self-sealing corneoscleral tunnel 2.8 mm wide
was prepared and the anterior chamber was entered. A suture was
placed in scleral tunnel incisions if the surgeons believed the wound
was at risk of leaking postoperatively.
ASTIGMATISM NOTATION
All preoperative, postoperative, and expected refractions were
converted to the power vector components described by Thibos et al.19,20 In this system, refractions are considered to be the
sum of the following 3 components: the spherical equivalent,
a Jackson cross cylinder oriented at 180° ( J0), and a Jackson
cross cylinder oriented at 45° ( J45). The corneas display mirror symmetry; thus, an axis of 45° in the right eye has the same
anatomic orientation with respect to the eyelids and other facial structures as an orientation of 135° in the left eye.17,21 Therefore, oblique astigmatism, JX, was defined as JX =J45 for the right
eye and JX =−J45 for the left eye. In this article, J0 is referred to
as quantifying with-the-rule astigmatism (although if J0 is negative, the patient has against-the-rule astigmatism). If the astigmatic portion of a refraction includes a cylinder of power C with
axis ␪1, the cross cylinders are calculated with the following
equations19,20:
J0 =−(C/2)cos(2␪1)
and
J45 =−(C/2)sin(2␪1).
For instance, if a refraction is ⫹5.00 ⫹ 3.00 ⫻ 100, then
C=⫹3.00, ␪1 =100, J0 =1.41 diopters (D), and J45 =0.51 D.
Once the postoperative spherical equivalent (M), J0, and J45
are predicted, they are converted to a refraction in positive cylinder notation (S, ⫹C⫻B°) using the following equations19,20:
C=2冑( J02 ⫹J452),
S=M−C/2,
and
B=0.5tan−1( J45/J0)⫹90°.
STATISTICAL EVALUATION
Predictors of the postoperative astigmatic components ( J0 and
JX) in the second eye were determined by means of univariate
and multivariable linear regression analysis. Independent variables analyzed included age, preoperative refractive and keratometric astigmatism in both eyes, and mean preoperative keratometry readings. Nonsignificant variables were removed by
stepwise backward regression analysis. We used commercially available software (Statistica, version 7; StatSoft, Inc, Tulsa,
Oklahoma) to generate the regression coefficients (m values),
coefficient of determination (r2 values), and statistical significance (P values). To express the model fit in the familiar unit
of diopters, the square root of the mean squared (RMS) error
was calculated. The squared error for each patient was
C2 =4[( J0Observed −J0Expected)2 ⫹( J45Observed −J45Expected)2]. The RMS error is appropriate for assessing standard least squares regression, which minimizes the squared error.
Keratometric astigmatism will have a greater effect in the
spectacle plane for myopic eyes, and a lesser effect in the spectacle plane for hyperopic eyes.3,22 However, after cataract surgery, patients are close to emmetropia; therefore, keratometric astigmatism is almost unchanged when translated to the
spectacle plane for typical data sets.4 A related question is
whether astigmatism in the preoperative refraction, which deviates more from emmetropia, can be moved to the corneal plane.
The present study addressed this question using standard formulas for vertexing spherocylinders to the corneal plane.3
For analysis of with-the-rule astigmatism, incision location was coded as 1 for superior, −1 for temporal, or 0 for not
applicable. For analysis of oblique astigmatism, the incision location quadrant was estimated on the basis of surgeon handedness (eg, a right-handed surgeon performing a superior scleral
tunnel incision on a right eye would be expected to produce
an incision centered in the superotemporal quadrant) and was
coded as 1 for the superonasal or inferotemporal quadrants, −1
for the superotemporal quadrant, and 0 for not applicable.
RESULTS
The second eyes of 160 patients who underwent bilateral sequential phacoemulsification were included in the
study. Of these patients, 156 (97.5%) were male, and 40
(25.0%) were black. The mean (SD) age was 71.3 (9.9)
years. Manual keratometry was used for both eyes in 102
patients (63.8%), and the IOL Master system was used
in both eyes in the remainder. The following linear regression showed that the preoperative refractive cylinder power could be moved to the corneal plane without
substantial modification: C (in the corneal plane)
=0.001⫹ 0.981C (in the spectacle plane; r2 =0.987).
Preoperative and postoperative refraction reflected a
small amount of against-the-rule astigmatism on average (J0 ⬍ 0; Table 1). For each measure, there was interpatient variability (SD of J0, 0.40-0.49). There was less
oblique astigmatism in the keratometry and refraction,
as indicated by the smaller mean and SD values for JX
(Table 1). Most patients (95.0%) had an absolute difference of preoperative keratometric astigmatism magnitude of 1.13 D or less and of mean keratometry of 0.85
D or less.
The univariate predictors of postoperative with-therule astigmatism ( J0) in the second eye included age,
preoperative refractive and keratometric astigmatism
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Table 1. Refractive and Keratometric Data for the Second Eye Undergoing Surgery
Mean (SD), D
Preoperative keratometry
Preoperative refraction
Postoperative refraction
SE
J0
JX
43.50 (1.30)
−0.70 (2.43)
−0.25 (0.71)
−0.03 (0.53)
−0.25 (0.49)
−0.21 (0.40)
−0.02 (0.22)
−0.001 (0.33)
−0.07 (0.23)
Abbreviations: D, diopter; J0, with-the-rule astigmatism; JX, oblique astigmatism; SE, spherical equivalent.
Table 2. Predictors of Postoperative Refractive J0 in the Second Eye
Multivariable Analysis a
Univariate Analysis
Age
First eye
Preoperative refraction, J0
Preoperative keratometry, J0
Postoperative refraction, J0
Second eye
Unsutured incision location b
Sutured incision location b
Preoperative refraction, J0
Preoperative keratometry, J0
Multivariable model intercept
m Value
Intercept
r 2 Value
P Value
m Value
P Value
−0.011
0.54
0.07
⬍.001
...
...
0.401
0.477
0.705
−0.10
−0.20
−0.06
0.21
0.30
0.40
⬍.001
⬍.001
⬍.001
...
...
0.376
...
...
⬍.001
−0.065
0.011
0.370
0.518
...
−0.21
−0.22
−0.12
−0.20
...
0.02
⬍0.001
0.21
0.47
...
.08
.87
⬍.001
⬍.001
...
...
...
0.097
0.327
−0.099
...
...
.053
⬍.001
⬍.001
Abbreviations: ellipses, not applicable; J0, with-the-rule astigmatism; m, linear regression coefficient.
a Multivariable model r 2 =0.56.
b Coded as 1 for superior, −1 for temporal, and 0 for not applicable.
(J0) in both eyes, and postoperative refractive astigmatism ( J0) in the first eye (all P ⬍ .001; Table 2). The
best predictors were the preoperative keratometric
astigmatism in the second eye (r2 =0.47) and the postoperative refractive astigmatism in the first eye
(r2 = 0.40; Table 2 and Figure). The following multivariable model predicted postoperative with-the-rule
astigmatism in the second eye:
J0PostopEye2 = (0.376 ⫻ J0PostopEye1 ) ⫹ (0.327 ⫻ J0KeratomEye2 )
⫹(0.097⫻J0PreopEye2)−0.099,
where P ⬍ .001 for the first 2 terms, and the model
r2 =0.56 (Table 2).
The univariate predictors of postoperative oblique
astigmatism (JX) in the second eye included the preoperative keratometric astigmatism ( JX) in both eyes (both
P⬍.001) and the preoperative refractive astigmatism (JX)
in the second eye (P = .007; Table 3). The best predictors were the preoperative keratometric astigmatism in
the second eye (r2 = 0.16) and in the first eye (r2 =0.07;
Table 3). We used the following multivariable model for
postoperative oblique astigmatism in the second eye:
JXPostopEye2 = (0.350 ⫻ JXKeratomEye2) ⫹ (0.231 ⫻ JXKeratomEye1)
⫹(0.064⫻JXPreopEye2) − 0.07,
where Pⱕ.01 for the first 2 terms, and the model r2 =0.20
(Table 3). When analyses were conducted with J45 instead of JX, refractive and keratometric J45 values in the
first eye were negatively associated with postoperative refractive J45 in the second eye, consistent with mirror symmetry of the corneas.17
The RMS error for keratometry alone was 0.72 D. The
RMS error for the multivariable models incorporating contralateral eye information in Table 2 and Table 3 was 0.67
D, a reduction of 6.8%.
PREDICTIVE VALUE OF INCISION LOCATION
In all, 106 patients (66.2%) had superior scleral tunnel
incisions. Of these, 43 (40.6%) had a suture and 68
(64.2%) had the same approach in the first eye. Of the
54 patients with a clear corneal incision, 29 (53.7%) had
the same approach in the first eye. Unsutured incisions
were associated with a small amount of flattening in the
axis of the incision, although the changes were not statistically significant (P ⱖ .08; r2 ⱕ 0.02; Table 1 and
Table 2). Sutured incisions had on average no effect on
the corneal curvature and no ability to predict refraction (r2 ⬍0.001), although the standard errors for the regression coefficients were 50% to 75% greater than those
for the unsutured incisions. This result was consistent
with more variability in the effect of sutured incisions.
Multivariable models incorporating incision location confirmed the value of the contralateral eye information. For
instance, a conventional model incorporating preoperative keratometry for the second eye and sutured and unsutured incision location had an r2 value of 0.47 for prediction of postoperative J0 in the second eye, and only
the keratometric term was significant (P⬍ .001). Addition of information from the first eye (postoperative refractive astigmatism [J0; P ⬍ .001] and incision location) to the model improved the r2 value to 0.57. For
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P⬍ .01 for the first 2 terms, P =.58 for the J0PreopEye2 term,
and the model r2 =0.62. In these patients, the multivariable model for postoperative oblique astigmatism in the
second eye was J XPostopEye2 = (0.449 ⫻ J XKeratomEye2 ) ⫹
(0.231 ⫻ JXKeratomEye1) ⫹ (0.033 ⫻ JXPreopEye2) − 0.09, where
Pⱕ.001 for JXKeratomEye2, P=.05 for JXKeratomEye1, P=.72 for
JXPreopEye2, and the model r2 =0.36. Compared with ipsilateral preoperative keratometry alone, with an RMS error of 0.77 D, the multivariable models improved the RMS
error to 0.67 D.
Postoperative Refractive J0 in Eye 2, D
1.5
1.0
0.5
0.0
– 0.5
– 1.0
y = 0.705 × – 0.06
r ² = 0.40
– 1.5
– 2.0
– 1.5
– 1.0
– 0.5
0
0.5
COMMENT
1.0
Postoperative Refractive J0 in Eye 1, D
Figure. Association of postoperative refractive with-the-rule astigmatism
( J0) in the first and second eyes. D indicates diopters.
oblique astigmatism, the corresponding conventional
model had an r2 value of 0.17, with only the keratometric term significant (P ⬍.001). Addition of keratometry
in the first eye (P = .03) and incision location improved
the r2 value to 0.21. The RMS error of the conventional
model was 0.75 D, and the addition of the information
from the first eye improved the RMS error to 0.70 D, a
reduction of 7.1%.
The right eye was the second eye to have surgery in
39.4% of the cases. Laterality of surgery in the second
eye was not predictive of postoperative refractive astigmatism ( J0, P = .83; r2 = 0.0003; m = 0.01 D) ( JX, P = .09;
r2 =0.02; m=−0.06 D). Among the surgical procedures in
the second eye, 64.4% were performed by a righthanded surgeon. Right-handedness was a weak predictor of postoperative refractive astigmatism in univariate
analyses ( J0, P = .05; r2 = 0.02; b = 0.13 D) ( JX, P = .03;
r2 = 0.03; b = −0.08 D) but, after controlling for ipsilateral keratometry, this relationship was not significant
(P=.17 for J0; P = .07 for JX).
SUBGROUP ANALYSIS
Similar findings were seen in subgroup analysis. In the
102 patients undergoing manual keratometry for both
eyes, the multivariable model to predict postoperative
with-the-rule astigmatism in the second eye was J0PostopEye2 =
(0.254 ⫻ J0PostopEye1) ⫹ (0.367 ⫻ J0KeratomEye2) ⫹
(0.123⫻J0PreopEye2) − 0.126, where P⬍ .01 for the first 2
terms, P=.06 for the J0PreopEye2 term, and the model r2 =0.55.
For these patients, the multivariable model for postoperative oblique astigmatism in the second eye was
JXPostopEye2 = (0.225 ⫻ JXKeratomEye2) ⫹ (0.204 ⫻ JXKeratomEye1) ⫹
(0.074⫻JXPreopEye2) − 0.05, where the P values for terms
1 to 3 were .06, .19, and .28, respectively, and the model
r2 = 0.08. Compared with ipsilateral preoperative keratometry alone, with an RMS error of 0.68 D, the multivariable models improved the RMS error to 0.65 D.
In the 58 patients for whom the IOL Master system
was used for both eyes, the multivariable model to predict postoperative with-the-rule astigmatism in the second eye was J 0 P o s t o p E y e 2 = (0.606 ⫻ J 0 P o s t o p E y e 1 ) ⫹
(0.251⫻ J0KeratomEye2) ⫹(0.043⫻J0PreopEye2) − 0.047, where
This study demonstrated that the postoperative refractive with-the-rule astigmatism in the second eye having
cataract surgery is predicted by that in the first eye,
independent of preoperative keratometry. Moreover,
the preoperative keratometric oblique astigmatism in
the first eye independently predicts postoperative
refractive oblique astigmatism in the second eye,
although this association is weaker. The astigmatic predictions represent incremental improvements over ipsilateral keratometry alone. For instance, the absolute
increase in the explained variation in with-the-rule
astigmatism was 9% (with the r2 value improving from
0.47 to 0.56).
Both findings depend on interocular symmetry, which
also underlies other algorithms for using the postoperative refraction in the first eye to improve refractive predictions in the second eye.5-7 Although there has been
some debate about whether corneal shape and refraction exhibit predominantly direct or mirror symmetry,23 our results add to the body of literature demonstrating mirror symmetry of the corneas about the
midsagittal plane.8-17,21 Indeed, mirror symmetry is expected in bilateral organs16 and is observed, at least grossly,
in other features of eye anatomy, such as extraocular
muscles and retinal organization.24 For the corneas, this
symmetry may result from genetic factors or from corresponding symmetry of facial structure or eyelid orientation, extraocular muscle tension, or other developmental factors.21,25
Because 95% of the patients had an interocular difference in keratometry readings of less than 0.85 D mean
and less than 1.13 D astigmatism magnitude, the method
should not be applied for patients with a greater degree
of interocular asymmetry until additional data are
available.
The very small impact of incision location on refractive astigmatism may be surprising but is consistent with
a previous study by our group.4 Unsutured incisions typically produce flattening in the axis of the incision,26,27 although the effect is less prominent with smaller incisions.28,29 In a randomized trial comparing a 3.0-mm
unsutured superior scleral tunnel incision vs a 3.0-mm
unsutured temporal clear corneal incision in patients with
at least 0.5 D of against-the-rule astigmatism, the difference between groups in keratometric against-the-rule
astigmatism at 1 month was 0.18 D, but there was no
group difference in uncorrected visual acuity.30 Refractive astigmatism, which was assessed in the present study
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Table 3. Predictors of Postoperative Refractive JX in the Second Eye
Multivariable Analysis a
Univariate Analysis
First eye
Preoperative refraction, JX
Preoperative keratometry, JX
Postoperative refraction, JX
Second eye
Unsutured incision location b
Sutured incision location b
Preoperative refraction, JX
Preoperative keratometry, JX
Multivariable model intercept
m Value
Intercept
r 2 Value
P Value
m Value
P Value
0.010
0.326
0.105
−0.07
−0.07
−0.07
⬍0.01
0.07
0.01
.86
⬍.001
.17
...
0.231
...
...
.01
...
0.028
0.001
0.154
0.422
...
−0.08
−0.08
−0.07
−0.06
...
0.01
⬍0.001
0.05
0.16
...
.22
.99
.007
⬍.001
...
...
...
0.064
0.350
−0.070
...
...
.23
⬍.001
⬍.001
Abbreviations: ellipses, not applicable; JX, oblique astigmatism; m, linear regression coefficient.
a Multivariable model r 2 =0.20.
b Coded as 1 for superonasal or inferotemporal, −1 for superotemporal, and 0 for not applicable.
and is most important clinically, may not always match
keratometric changes because of an opposing effect of the
posterior or peripheral cornea. Small effects might be more
difficult to define with statistical certainty when there is
inconsistency due to the involvement of multiple resident surgeons. In the present study, the incisions that
were sutured owing to concern about postoperative leaking probably might have produced a greater than average degree of flattening if left unsutured. Sutured incisions had a net null effect on astigmatism, although there
was variability, because the incision might produce flattening or steepening depending on suture tightness.31,32
The degree of astigmatism induced by the incision will
likely assume an even smaller role as practices transition to incisions close to 2 mm.33,34 Ideally, surgeons
should estimate the surgically induced astigmatism within
their own practice.
If confirmed, the regression equations could be used
to predict refraction after cataract surgery in the second
eye. The findings may be specific to our particular practice, consisting mostly of male patients and multiple
surgeons in a teaching environment. In addition, the
findings are based on retrospective calculations. The
next step in evaluating the clinical value of this strategy
would be a prospective randomized trial of adjusting
astigmatism control in the second eye on the basis of
refractive results in the first eye vs standard care. The
uncorrected near and far visual acuity would be an
important end point. In studies of toric intraocular
lenses, the benefit might be reduced by the fact that
lenses are available in discrete increments. Based on the
present study, when astigmatism control is contemplated along with cataract surgery, consideration should
be given to delaying surgery in the second eye until an
accurate postoperative refraction can be obtained in the
first eye. An unexpected refractive astigmatic outcome
in the first eye should prompt a close evaluation of possible causes, including the influence of posterior or
peripheral corneal curvature, which might also be
manifested in the results in the second eye.
Submitted for Publication: March 15, 2010; final revision received July 13, 2010; accepted July 13, 2010.
Correspondence: Muneera A. Mahmood, MD, FRCOphth,
Eye Clinic, Room 112, Hunter Holmes McGuire Veterans
Affairs Medical Center, 1201 Broad Rock Blvd, Richmond, VA 23249 ([email protected]).
Financial Disclosure: None reported.
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